143462729 52642 093 Chap 14 3 Classification by Screens and Cyclones[1]

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1481

CHAPTER 14.3

Casscat b Scrs ad Ccs

Brian Flintoff and Ronald Kuehl II

inTRoDCTion

The classication of particles based on size is an importantstep in almost all mineral processing ow sheets. Althoughthe technical focus in plant design, control, and optimizationis most often on comminution (e.g., size control and mineralliberation) and/or separation equipment (e.g., recovery/yieldand grade), classication plays a critical role in optimizing

process efciency. This chapter focuses on two major classesof classication unit operations: screens and hydrocyclones.

SCReenSMatthews (1985) said, “Screening is dened precisely as amechanical process that accomplishes a separation of parti-cles on the basis of size and their acceptance or rejection bya screening surface. Particles are presented to the apertures in

a screening surface and are rejected if larger than the open-ing or accepted and passed through if smaller.” The screening

process has been a part of mineral processing ow sheets for along time, and like many other unit operations, screening hasseen some interesting mechanical and process developmentsover the past few years.

Looking across all of the process industries, there aremany different kinds of screens and applications. However,the authors have restricted the discussion to the most commonapplications in the mining industry. Figure 14.3-1 is a genericgraphical representation of the major applications of screen-ing in mining: scalping, size control, and sorting.

Table 14.3-1 provides more amplication on the type of screen one might nd in given applications.

Screen types can generally be categorized as follows:

• Fixed types: grizzlies, rifes, sieve bends, and so forth• Moving (linear) types: vibrating, reciprocating, and

resonance• Moving (rotating) types: cylindrical trommels

Figures 14.3-2 through 14.3-6 are photographs of a griz-zly screen, vibrating screen, trommel screen, Stack Sizer, andsieve bend. In general, these are the workhorses of the miningindustry, with the vibrating screen standing out as the most

widely employed screening unit operation. It is for this reason

that most of the chapter is devoted to the vibrating screen.

brat Scr BascsThe vibrating screen is ubiquitous in mineral processing

plants. One would imagine that with this breadth and historyof application and its apparent simplicity, there would be fewremaining unknowns in the screening process. However, thedesign and operation of screening systems remains a blendof art and science—a statement used by many other authors(e.g., Mathews 1985). It is interesting to note that the screen-ing process is enjoying something of a renaissance today, asnew simulation tools offer a closer examination of the phys-ics of the process, providing quantitative insights into mecha-nisms and their relation to design variables. In addition, new

instrumentation offers real-time modulation and measurementof mechanical and process condition. The following sectiondeals with vibrating screen basics and introduces some of thelatest tools and techniques in the design, analysis, control, andoptimization of vibrating screens.

Principles of Operation The vibrating screen is used here as a proxy for all other screens, as the basic operating principles are similar or thesame. In the screening process, a feed material comprised of

particles of varying sizes is presented to the screen media (col-lectively, the screen deck) in such a way that those particlesner than the screen aperture fall through to the undersizestream, and those that are larger than the screen aperture con-

tinue moving along the screen surface to eventually report tothe oversize stream.

Screening can be carried out with wet or dry feeds,although coarser particle separation (greater than a 5-mmaperture) is usually performed dry (at the surface moistureof the feed). Wet screening usually involves either sticky/clayey feeds or ner particle sizes where the solid materialhas been slurried to facilitate transportation and processing. Indry applications, some combination of vibration and gravityare responsible for particle transportation. In wet applications,

Brian Flintoff, Senior VP Tech. Dev., Equipment & Systems Business Line, Metso Mining & Construction Technology, Kelowna, British Columbia, CanadaRonald Kuehl II, General Manager, Vibrating Equipment & Systems Business Line, Metso Mining & Construction Technology, Columbia, South Carolina, USA



1482 SMe M er hadb

Tab 14.3-1 Tps f scr prats

oprat ad Dscrpt Tp f Scr Cmm empd

Scap: Scalping is strictly the removal of a small amount of oversize from

a feed consisting predominantly of nes. Scalping typically consists of theremoval of oversize from a feed with a maximum of 5% oversize and aminimum of 50% half size. Coarse scalping is typically smaller than 150 mm(6 in.) and larger than 50 mm (2 in.).

Coarse (grizzly), ne (same as ne separation), and ultrane (same as ultraneseparation).Example : Grizzlies are usually used to scalp oversize material from primarycrusher feed or are used to scalp nes from the feed to crushers or grinding rolls.

Curs sparat: Consists of making a size separation smaller than50 mm (2 in.) and larger than 5 mm

Vibrating screens (banana, incline, and horizontal) and trommel screens.Examples: The removal of pebbles from a semiautogenous grinding dischargestream, sizing material for the next crushing stage, and sizing material forleach pile or product pile.

sparat: Consists of making a size separation smaller than 5 mmand larger than 0.3 mm (48 mesh)

Vibrating screens (banana, incline, and horizontal), which are typically setup with a high speed and a low amplitude or stroke; sifter screens; staticsieves; and centrifugal screens.Examples: Sorting coal into ±28 mesh fractions for washing, and iron oreprocessing

traf sparat: Consists of making a size separation smaller than0.3 mm (48 mesh)

High-speed, low-amplitude vibrating screens; sifter screens; static sieves;centrifugal screens.

Example: Size control on grinding circuit product

Dwatr: Consists of the removal of free water from a solid-watermixture and generally limited to 4 mesh and above

Decline vibrating, horizontal vibrating, inclined vibrating (about 10°), andcentrifugal screens.Example: Wet quarrying operations

Tras rmva: Consists of the removal of extraneous foreign matter.This is essentially a form of scalping operation, and the type of screendepends on the size range of the processed material.

Vibrating screens (horizontal or inclined), sifter screens, static sieves, andcentrifugal screens.Example : The removal of extraneous organic and other matter from the leachfeed in a gold plant

otr appcats: Other applications include desliming (the removal of extremely fine particles from wet material by passing it over a screeningsurface), conveying (in some instances, the transport of a material maybe as important as the screen operation), dense media recovery, acombination washing and dewatering operation, and concentration.

Vibrating screens (banana, incline, or horizontal), oscillating screens, andcentrifugal screens.Example : Dense medium recovery in a coal washing plant, a wobbler feederfor conveying, and classifying sticky materials to a crusher

Source: Adapted from Mathews 1985.

Scalping

Sorting

e.g., Crushing

Size Control

e.g., Crushing, Autogenous/Semiautogenous Grinding

e.g., Fine/MidsizeCoal Circuits,Sand/Slime Flotation

Product 1

Product 2

e.g., AggregatesProduct 3 e.g., Carbon Removal,

Heavy MediumRecovery, Dewatering

ur 14.3-1 examps f t appcat casss fr scr m



Casscat b Scrs ad Ccs 1483

(A) (B)

ur 14.3-2 (A) Statc rzz (scap vrsz frm a prmar jaw crusr fd) ad (B) vbrat rzz scr

(A) (B)

ur 14.3-3 brat scr wt a dust cct sstm

(A) (B)

ur 14.3-4 (A) Trmm scr ad (B) m dscar trmm scr



1484 SMe M er hadb

some form of vibrator mechanisms dictates the movementof material. However, hydrodynamic (drag) forces are intro-duced. In wet applications, deck water sprays or ood boxesare sometimes used to aid in classication. Spray selection ischosen based on two criteria: it must be decided whether thegoal is to ush material through the deck or to wash off thenes. A general guideline is that water added to the feed ismore effective than water sprayed on the deck in improvingthe classication.

Figure 14.3-7 is a schematic representation of the resultsof an experiment with a small horizontal vibrating screen hav-ing a screen aperture of 10 mm. (This particular screen andtest [from Hilden 2007] is referenced throughout the text.) Theshaded bars depict the relative mass ows, and the annota-

tions show the mass mean size for each stream. As the feedis introduced onto the deck, it forms a bed that is usually sev-eral times the screen aperture in thickness. The bed moves

under the inuence of gravitation and vibrational motion, and

in the process, the particles stratify as the ner materials movequickly through the interstices of the larger particles and ndtheir way to and then through the screen apertures. In thisinitial zone on the screen, rapid segregation means there isalways sufcient ne material in the layer next to the screendeck that the ow through the screen apertures is more or lessconstant. This is said to be typical of crowded or saturationscreening. However, as the nes are depleted, the bed heightis reduced, and at some point the particles begin to act moreor less as individual entities. This is the zone of separated or statistical screening, that is, each time the particle approachesthe deck it has a chance (or a statistical trial) to pass throughthe aperture. (This notion of repetitive trials underpins manysemi-empirical screen models.)

Figure 14.3-7 shows that the greatest ow of material tothe undersize stream occurs closest to the feed end, which istypical of crowded screening. Segregation ensures that these

particles presented to the apertures are small enough that the probability of passage to the undersize stream is ~1.0. Themass ow to the undersize stream decreases along the lengthof the deck, which is typical of the transition to separatedscreening, more typical of the coarser particles (the so-called“nearsize,” as it is near to the size of the aperture) that remainin the bed. For these particles, the probability of passage onany one trial is signicantly less than 1.0. The increase in themass mean size along the deck also reects the fact that theremaining material on the deck becomes coarser as it movesfrom the feed end to the discharge. This helps to explain whyscreen length governs efciency. On the other hand, screenwidth is related to the amount of material that can be fed tothe screen and be effectively separated, and therefore this isthe major factor governing capacity.

On this latter point, a guideline for good dry-screen oper-ation is for the bed depth at the discharge point to be three tofour screen apertures in thickness. A guideline for wet screen-ing is to design for a bed depth of four to six times the opening.With anything larger, the efciency of removal of the particlesclose to the aperture size is reduced, as segregation is moredifcult. This suggests that multiple screen decks probablyshould be considered, using a larger aperture size on the topdeck to scalp out much of the larger oversize and reduce the

loading on the lower deck for the nal classication. Anythingless and these particles will probably bounce excessively,reducing the number of trials and the screen efciency. (It is

3.3 3.9 5.0 5.6 6.2 6.9 mmd =

d = 10 mm

d = 5.8 mm

Oversize

Feed

Undersize

Source: Hilden 2007.

ur 14.3-7 T ratv mass fws ad ma partcszs fr a rzta vbrat scr

Courtesy of Multotec Process Equipment

ur 14.3-6 Sv bd

Courtesy of Derrick Corporation.ur 14.3-5 Drrc Stac Szr




also sometimes useful to install weirs on the deck’s surface tohold back the ow as an aid to sustaining an active bed.)

Screen design and operation is about matching the screencharacteristics to the (range of) feed conditions. Table 14.3-2

provides a summary of the important variables for each.When focusing on design variables, screen area is impor-

tant because capacity is proportional to width (W ) and ef-ciency is proportional to length ( L). It is common for L ≈ 2to 3 W . Because of the mechanical ttings on and around thescreen decks, the effective area is often approximated as 90%to 95% of the actual area ( LW ). Screens are standard products,

so the manufacturers dictate the actual sizes. It is thereforecommon to require more than one screen, operating in paral-lel, to effectively separate a feed.

Open area (OA) is expressed as the ratio of the total areaof the apertures over the total active area of the screen deck.Figure 14.3-8 illustrates this for the screen in Figure 14.3-7with a square aperture of 10 mm in a wire mesh screen witha wire diameter of 2 mm. From the explanations of screening

mechanism, it is clear that the greater the OA, the greater thecapacity of the screen. In practice, OA is limited by the needfor sufcient mechanical strength and wear resistance of thedeck and is a function of the media materials of construction,for example, wire mesh versus perforated plate.

This is a good point to introduce some common, andoccasionally confusing, jargon associated with phenomenathat act to reduce the OA and, hence, the capacity. The rstis pegging (also called blinding or plugging), which occurswhen a nearsize particle becomes rmly lodged in an aper-ture effectively eliminating it from the screening process. Thesecond is blinding (also called bridging), which is the phe-nomena whereby smaller particles aggregate in such a waythat they combine to block up the aperture, having the sameoverall effect as pegging, as shown in Figure 14.3-9. Blindingis more of a problem with moist or sticky materials and smallaperture sizes.

The aperture size is, by convention, the minimum lin-ear measurement in an opening; for example, the diameter for a round hole and the width (where width ≤ length) for aslot or a square. (Because screen performance assessmentsstart with sieving samples of process streams and becausethe sieve has square apertures, the best correlations occur with square apertures in the screen media.) What is perhapsmore important is the so-called throughfall size, hT , whichaccounts for the change in effective opening as the screenis inclined. This is illustrated in Figure 14.3-10, where the

angle of inclination is exaggerated to show the difference between the aperture size, h, and the throughfall size for awire mesh screen surface. (There is a similar effect for rect-angular slots.)

Although square apertures may be the most common,there is a multitude of aperture shapes. Some of the morecommon shapes are illustrated in Figure 14.3-11. Square or round shapes generally allow for better control of the separa-tion size, although circular apertures are most often used incoarse-screening applications. Longitudinal slotted aperturesallow slabby particles into the undersize stream. This increasescapacity and reduces pegging and blinding. Transverse slotsare mainly used in dewatering applications. (For steel or poly-meric screen media, it is possible to design tapers and other

forms of relief into the apertures to minimize pegging—seethe insert in Figure 14.3-11 for an example.) Finally, thescreen deck or panel is designed to withstand the load andmaximize wear life. Therefore, in the case of a large spread infeed particle sizes and/or some large particles in the feed, it iscommon to use multiple screen decks to satisfy both mechani-cal and process requirements.

Inclining a screen deck increases the slope and causesthe feed material to move more quickly on the deck, reduc-ing the residence time and increasing capacity and sometimesefciency. Vibration motion on a horizontal screen deck usu-ally means that material velocities of 10 to 16 m/min (33 to52 fpm), with an inclination in the neighborhood of 20°, willincrease this into the range of 20 to 28 m/min (66 to 92 fpm).

Generally, inclinations range from horizontal to as high as30°, although ~20° is the usual limit. This led to the evolutionof the multislope screen (also commonly known as a banana

Tab 14.3-2 Ds ad prat varabs fr vbratscrs

Ds arabs oprat arabs

Screen area and open area

Aperture size and shape

Slope of screen deck

Speed

Magnitude of stroke

Type of motion

Feed arrangement

Particle size, shape, and distribution

Solids feed rate, distribution, andbed depth

Feed moisture content

Source: Bothwell and Mular 2002.

10 mm

2 mm

OA = = 69.4%102

122

ur 14.3-8 Cmput p ara

ur 14.3-9 Bd a scr dc



1486 SMe M er hadb

screen). The banana screen (Figure 14.3-12) has a relativelyhigh slope in the initial screening zone, which takes advantageof the fast kinetics of ne particle removal. The slope thendecreases, which slows particle movement and offers an addi-tional G-force to accelerate removal of the larger ne material.In the nal section, the slope is relatively at, yielding mini-mal velocity and maximum residence time, for ner nearsize

particle removal to the undersize stream.Vibrating screen deck motion is circular, elliptical, or

straight line, with the vibrating mechanism rotating in thedirection of ow or counter to the ow. Strokes are usually inthe range of 3 to 20 mm (0.118 to 0.787 in.) and speed rangesfrom 650 to 950 rpm. A key parameter here is the G-force (G),which is computed by Equation 14.3-1.

1,789,129G

N S 2= (14.3-1)

whereG = the G-force (also known as the throw number)N = speed (rpm)S = stroke (mm)

Typical G-forces are in the 3.5-to-5.0 range, tending to

higher values with heavy loads, sticky materials, or where pegging and blinding are issues. The G-force is usuallyhigher in a horizontal screen, as it must provide the means

for both stratication and material movement. (For example,with the horizontal test screen in Figure 14.3-7, the speedwas 981 rpm and the stroke 5 mm [0.197 in.], giving a G of 2.69.) Table 14.3-3 amplies on the conditions prevalent over a broad range of G-forces.

Figure 14.3-13 is a simplied graphic of particle motionwith different trajectories, and Figure 14.3-14 shows howdeck motion can be induced using weights on the shaft. Of

Slope, degrees

Velocity, m/s

35

2.00

30

1.66

25

1.23

20

0.84

15

0.58

10

0.46

5

0.40

0

0.30

(A)0.4 m/s

Incline Screen Multislope Screen

1.3 m/s

0.9 m/s

0.5 m/s

ur 14.3-12 Baaa scr dc

(B)

Tab 14.3-3 g-frc mpcats cd vbrat scrsg-rc Cmmt

<1.5 Practically no movement on the deck, so it is of no use.

1.5–2.5 The stratication is limited and the relative velocity between theparticle and the deck is low. These parameters are suitable for softscreening and where size degradation is problematic and there isa low tolerance to impact.

3.0–3.5 The particle is presented to the screen deck at its maximumrelative velocity and offers the best screening condition forinclined screens. The stratication is adequate.

4.0–5.0 The stratication is good, but the relative velocity between thedeck and particle is low, offering poor screening efciency.Bearing life is shortened.

5–6 The stratication is good, but the particle projection is in excess

of the pitch (particles are in ight too long) and screeningopportunities are lost. The relative velocity between the screenand particle is low, combining to give poor parameters forefcient inclined screening. The high acceleration forces canact negatively on the screen structure, and bearing life is furthershortened.

Source: Moon 2003.

a

hT

h

d

hT = (h + d )cos(α) – d

ur 14.3-10 T rat btw t trufa sz (h T )ad t aprtur sz (h )

Uniform

Slotted

Insert

ur 14.3-11 Cmm scr aprtur saps




course, there are other methods to induce motion and other,more complex orbits.

The stroke angle, measured relative to the length of thedeck and in the direction of ow, can affect efciency andcapacity. Very low (~0°) or high (~180°) angles do little other than accelerate wear. For other angles, there is a component

of vertical movement (aiding stratication) and a horizontalcomponent aiding (<90°) or retarding (>90°) material ow.(For the screen in Figure 14.3-7, the stroke angle was 50°.)

The designer for the screening application chooses theorbit motion (circular, elliptical, or linear) based on a compro-mise between material movement (capacity), which empha-sizes linear motion, and efciency, which emphasizes circular motion. The ellipse is an optimized solution. All give goodstratication with the correct stroke angle. For horizontaland banana screens, linear motion is the defacto standard asmaterial movement is critical. For inclined screens, circular or elliptical orbits are more common.

Finally, there is the matter of feeding the screen. Here,there are the following three general rules:

1. It is important that the feed be uniformly distributed

across the width of the screen for the unit to achieve ratedcapacity.

2. It is important that feed rate be modulated where possible(e.g., using belt feeders) to ensure that the screen worksefciently in the face of changing feed conditions.

3. Where possible, it is good to introduce the feed havinga motion opposite to the eventual material ow, whichhelps in distribution and avoids ooding in the initialzone of the screen deck.

Table 14.3-4 provides a review of the major design vari-ables of a vibrating screen and indicates usual design rangeswhere appropriate. This “one-variable-at-a-time” approachdoes not always take into account the myriad interactions

among these variables.

Screen Selection Many opinions and methods of screen selection suggest fertileground for development and renement. Three general selec-tion method classes follow:

• Class 1: Empirical methods based on correlations derivedfrom extensive databases of industrial experimental results

• Class 2: Lab screening tests with empirical model-basedscale-up procedures

• Class 3: Fundamental model-based methods (these arerelatively new and are described later in more detail)

Class 2 methods have been used sparingly in the past,

but recent work (Hilden 2007) suggests there is good scopefor improvement and further suggests there is room to com-

bine Class 2 and Class 3 methods very effectively. Despite the

Tab 14.3-4 Prcss matrx fr a vbrat scr*

Ds arabScr

Capact Scr

effcc drszMa Sz

P/Bd

Screen area + 0 0 0

Open area + + or 00 0

Aperture size + + + –

Aperture shape(increasingnonuniformity)

+ + or 0 + –

Deck inclination + – or 0 – – or 0

Speed + + 0 –

Stroke angle – + 0 – or 0

Stroke + + 0 –

Orbit (from lineartoward circular)

– + 0 +

*All other factors being equal, an increase in the design parameter will causean increase (+), a decrease (–), or no change (0) in the performance metric.

I n c l i n e d

Horizontal

CircularMotion

EllipticalMotion

Horizontal

Straight-LineMotion

Straight-LineThrow

I n c l i n e d

ur 14.3-13 Partc mt as a fuct f t dc rbt

Linear

Twin Contra-Rotating Shafts

Center of Gravity

Center of Gravity

Circular

Single Rotating Shaft

ur 14.3-14 s wts t duc spcfc rbts



1488 SMe M er hadb

potential of using Class 2 and Class 3 methods, most indus-trial vibrating screens are still selected using Class 1 methods.Because in most cases these screens operate more or less asdesigned, it is understandable why these methods have sur-vived with a few improvements for 70 years.

Class 1 selection methods employ empirical correlationsto deduce screen area. The design process can begin once theapplication (e.g., a pebble screen on a semiautogenous grind-ing [SAG] mill discharge), the design feed rate of solids, andthe typical feed particle size distribution are given. Early deci-

sions on the number of decks, inclination, motion, lo-head or hi-head screens, and so forth, come from the design basis docu-ments and past practices in similar applications. Once these

parameters are set, the correlations can be used to computescreen area requirements, and the deck with the largest areadetermines the screen size. The task is then to match one of the standard products to the design. This often is an iterativedesign process.

Two usual approaches can be used to solve the Class 1design problem—one based on the total solids feed rate to thescreen and the other based on the solids feed rate of undersizematerial to the screen. Not surprisingly, this is also an area of debate, as the scientic community tends to prefer the latter method, yet the former is very commonly used. The former method will be described in an abbreviated way simply for illustrative purposes. To provide a real example, the data for the screen shown in Figure 14.3-7 is used.

The fundamental equation for determining the screen arearequired is given in the Equation 14.3-2 (Allis Chalmers, n.d.)

AC M K Q Q Q Q Q Q

T

1 2 3 4 5 6

= (14.3-2)

whereA = required screen areaT = mass ow of feed to screenC = basic capacity factor M = oversize factor (percent larger than aperture size

in feed)K = undersize factor (percent smaller that ½ aperture

size in feed)Q1 = bulk density factor (usually ~60% of rock density)Q2 = aperture shape factor Q3 = particle shape factor Q4 = OA correction factor Q5 = wet or dry screening factor

Q6 = surface moisture factor

Figures 14.3-15 through 14.3-17 provide the basis for estimating the factors C, M, and K, respectively. Table 14.3-5

provides the means for estimating the Q factors. (OA andaperture shape come from Figure 14.3-8.) Table 14.3-6 pres-ents the summary data for the calculations, showing both theinput data required and the empirical corrections, as deducedfrom the previously mentioned graphs and tables (whichare adapted from Allis Chalmers, n.d.). The required areaallows for a 6% loss due to mechanical ttings and so forth.Following the rough rule that L = 3W , this screen would havethe approximate dimensions of 0.34 # 1.03 m (1.12 # 3.38 ft).In fact, the screen in Figure 14.3-7 is 0.34 # 1.67 m (1.03 #

5.48 ft). The width is the same, but the test screen has extralength, so a higher classication efciency might be expected.This topic is discussed in the following subsection.

Performance Assessment Mechanical and process performance can be distinguished,

but this subsection only focuses on the latter.A single parameter can be calculated in several ways

that will quantify screen performance. Among these, the mostcommon are E u, which is dened as the efciency of removalof undersize material from the oversize stream, and Ru, whichis dened as the efciency of undersize removal from thefeed stream. Referring to Figure 14.3-18, Equations 14.3-3and 14.3-4 are used to compute numerical values:

E O

F f o

11u

uu= =

−−

t

t

^^

hh (14.3-3)

10

100

300

C F

a c t o r ,

d r y t / h / m 2

Aperture Size, mm

1 10 100 1,000

Source: Allis Chalmers, n.d.

ur 14.3-15 Basc capact factr (C) as a fuct faprtur sz

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

M C

o r r e c t i o n F a c t o r

% Oversize in Screen Feed

0 20 40 60 80 100


ur 14.3-16 Crrct factr (M) as a fuct f prct vrsz

0.8

0.4

1.2

1.6

2.0

K

C o r r e c t i o n

F a c t o r

% Passing Half Size of Aperture

0 20 40 60 80 100


ur 14.3-17 Crrct factr (k) as a fuct f prct af sz




R Ff

U

f o

f o

1u

u u u

u u= =

−

−

t t t

t t

^

^

h

h(14.3-4)

where

F = feed rateO = oversize mass ow rateU = undersize mass ow rate

f ut = cumulative mass fraction in the feed passing the

aperture size o

ut

= cumulative mass fraction in the oversize stream

To utilize these performance measures, one is requiredto perform a sampling experiment around the screen whileit is running at steady-state conditions. This raises topics

beyond the scope of this chapter (e.g., experimental design,sampling theory, sample preparation and analysis, and datamassage). Fortunately, for the screen shown in Figure 14.3-7,the balanced data are already available and are summarized in

Table 14.3-7.Using these results, E u = 77.9% and Ru = 93.5%. The

data suggest that there is a considerable amount of ner (less

than the aperture size of 10 mm [0.4 in.]) nearsize material inthe oversize stream. In terms of assessing performance, themanufacturers have a curve that relates E u to the rated capac-ity of the screen. This is shown in Figure 14.3-19, and the

rated capacity is the ratio of the actual tonnage (or area) tothe calculated tonnage (or area) from Equation 14.3-2. Therespective area gures for the example are 0.35 and 0.57 m 2,

Tab 14.3-5 Q crrct factrs

Bu Dst actr au

Bulk density, dry t/m3 Q1

0.4 0.25

0.8 0.51.6 1

2.08 1.3

Apr tur Sap actr

Opening shape Q2

Square 1

Rounded 0.8

Slotted

2:1 Slot 1.15

3:1 Slot 1.2

4:1 Slot 1.25

Partc Sap actr

Particle shape Q3

Cubical 1

Slabby 0.9

op Ara actr

Open area Q4

Calculation Q4 = percent open area ÷ 50%

Wt r Dr Scr actr

Opening Q5

Dry 1

Wet

0.8 to 3.2 mm 1.25

4.8 to 6.4 mm 1.4

8 to 12.7 mm 1.2

14.3 to 25.4 mm 1.1

Surfac Mstur actr

Surface moisture Q6

≤3% 1

3% to 6% 0.85

6% to 9% 0.7

Wet screen 1

Tab 14.3-6 Scr sz xamp

Paramtr au

Feed rate, dry t/h 15.7

Aperture (square), mm 10

Rock density, dry t/m2 2.7

Application Dry

C Factor, dry t/h/m2 40.12

M Factor 0.972

K Factor 0.88

Q Factors

Q1 1.00

Q2 1.00

Q3 1.00

Q4 1.39

Q5 1.00

Q6 1.00

Adjusted unit capacity, dry m/t/h/m2 47.64

Area required, m2 0.34

Sz, mm d Dstrbut, %

13.2 5.6

9.5 16.6

8 11.4

6.7 11.1

4.75 24.1

3.35 10.7

2.8 6.5

Pan 14.0

Percent +10 mm 18.7

Percent –5 mm 34.0

Source: Data from Hilden 2007.

F , f i , f u

O , o i , o u

U , ui , uu

Symbology

Feed rate, dry t/hMass fraction retainedin i th size classCumulative mass fractionpassing aperture size in feed

F =f i =

f u =

Mass Balance

F = O + U

Ff i = Oo i + Uui

Ff u = Oo u + Uuu

ˆ

ˆ ˆˆ

ˆ

ˆ

ˆ

ur 14.3-18 Scr prfrmac paramtrs



1490 SMe M er hadb

which give a rated capacity of 59.9%. This point is plotted onthe curve for reference.

This comparison indicates that the test screen inFigure 14.3-7 is not performing as well as would be expectedat the given operating conditions, and further analysis of thesituation would be required to validate the result and improve

performance.Another very common measure of efciency is to use

the data in Table 14.3-7 to compute an experimental parti-tion curve, which can then be modeled with any number of simple functional forms. The model parameters are efciencymeasures. Again, looking to the example in Figure 14.3-7, the

experimental partition factors for the various size fractions arecomputed from Equation 14.3-5 and are dened as the massfraction of material in a certain size fraction in the feed thatreports to the oversize stream:

p Ff

Ooi

i

i= (14.3-5)

wherepi = observed partition factor for size class if i = mass fraction retained in the ith class of the feedoi = mass fraction retained in the ith class of the

oversize stream

A very common model and one that will be further dis-cussed later is the so-called Rosin–Rammler curve, and

the estimated partition factors are computed according toEquation 14.3-6:

1 p e .d d 0 69350

– i

i= −

γ

c m (14.3-6)

wherepi = calculated partition factor for size class id i = the characteristic size for size class i

d 50 = cut size—particles of this size have an equalchance (50/50) of going to the undersize or oversize

g = sharpness of separation (larger values mean better separation)

The parameters (d 50 and g) are obtained by minimizinga least-squares objective function using nonlinear regression

(e.g., Solver in Microsoft Excel). That is, the parameters areselected in such a way that the sum of the squares of the dif-ferences in the observed and calculated partition factors isminimized. Figure 14.3-20 presents the results for the screenin Figure 14.3-7.

One would normally expect the cut size to be close to thethroughfall aperture size, and it is clear that the value is a littlelow here (in part because of the way the characteristic sizewas dened for this study). The sharpness of separation for screens cutting in the aperture size range is usually around 6,so a value of close to 13 suggests that efciency is high. Takentogether, the implication is that the screen is not processingthe ner nearsize material very well, which would require fur-ther investigation.

Interestingly, the data acquired for the screen inFigure 14.3-7 permit the calculation of the cumulative parti-tion curve as a function of the position along the length of thedeck. The experimental results are shown in Figure 14.3-21.Given the explanation related to crowded and separatedscreening given previously, it is no surprise to see that thene material moves quickly through the screen—collectively,

particles do not have to progress far down the deck before allof the very ne material has passed through the apertures (andthe corresponding pi = 0). For the ne, nearsize material, it isclear that the process is a lot slower.

The periodic measurement of screen efciency is asimportant to the maintenance of process performance as the

periodic measurement of, for instance, bearing condition is tothe maintenance of mechanical performance. Unfortunately,it is often the case that the process aspects of screens are

Tab 14.3-7 Sampd data summar fr t rzta scr ur 14.3-7

Sz, mm d, % ovrsz, % drsz, %

13.2 5.6 20.8 0.0

9.5 16.6 61.8 0.08 11.4 13.9 10.5

6.7 11.1 3.5 13.9

4.75 24.1 0.0 33.0

3.35 10.7 0.0 14.6

2.8 6.5 0.0 8.9

Pan 14.0 0.0 19.1

Mass fraction 1.00 0.27 0.73

Percent –10 mm 81.3 22.1 100.0

Mass ow, dry t/h 15.7 4.2 11.5


60

20

100

140

180

220

% o

f R a t e d S c r e e n C a p a c i t y

Screening Efficiency—E , %

20 40 60 80 100

u

ExperimentalValue

95%Maximum

ur 14.3-19 Prct f ratd capact vrsus E u

0.50

0.25

0.00

0.75

1.00

P a r t i t i o n

F a c t o r

Passing Size, mm

0 3 6 9 12 15

d 50 = 8.3 mmγ = 12.9

ModelExperimental Data


ur 14.3-20 exprmta ad mdd partt fuctdata




ignored. However, they are robust devices, and they oftenhave a direct impact on the performance of comminution andseparation equipment, for which a systems thinking approachmust be applied.

Recent Developments This subsection provides a brief introduction into some of thedevelopments emerging in the vibrating screen market.

Real-time condition monitoring. Using vibration,thermographic, and occasionally other specialty sensors toautomate the more usual manual inspections of predictivemaintenance is becoming increasingly commonplace. Whereit is done, this is still usually reserved for the typical appli-cations of monitoring bearing health. Manufacturers such as

Metso (Screen Security Package) have taken this a step fur-ther by using additional accelerometers to compute screenorbits, which can then be compared to expected values fromrun-in tests and/or to nite element modeling to analyze themechanical and process health of the screen. Figure 14.3-22is an example of normal orbits and the kinds of trends thatdevelop when there is a problem, such as with the supportingsprings. Loose media on the screen deck and other kinds of serious problems have their own orbit “signature.”

In the case of the normal orbits (Figure 14.3-22A), both arelinear and superimposed, showing the same stroke and angle.In the case of the abnormal conditions (Figure 14.3-22B), theorbits are now elliptical and the strokes are different.

The frequency spectrum of the accelerometers also

provides useful information on the mechanical state of thedeck, loading, and other interesting performance parameters,Moreover, when these signals are combined with others (e.g.,

from load cells and vision systems) in a kind of sensor fusionapproach, the analytical detail and reliability can be dramati-cally increased.

Real-time deck motion modulation. As seen in the pro-cess matrix of Table 14.3-4, deck motion (stroke, angle, andorbit) all affect performance, and in light of the fact that screenfeeds often change (mass ow and particle size distribution),there is a school of thought that says the ability to modulatethese parameters on line would support real-time screen per-

formance management. A number of manufacturers are imple-menting this kind of solution on selected screen models.

Instrumentation. One of the exciting areas of potentialfor performance monitoring is “machine vision,” primarilyas applied to measuring feed or product size. Typically, dryscreening is very dusty and requires hoods covering the entirescreening surface for effective dust control. Therefore, appli-cations on the deck itself (oversize velocity, load, etc.) arechallenging. However, in the case where the product streamsare discharged onto belts, the standard technology, such asMetso’s VisioRock, can be applied. For example, in the pro-duction of iron ore, lump size control is very important, andthe early warning of a problem is essential if, for example, thescreen media is broken, thereby producing off-spec material

in the undersize stream. One operator is now using machinevision to detect and react to these types of quality-assuranceevents, and Figure 14.3-23 shows the VisioRock installation

0.50

0.25

0.00

0.75

1.00

P a r t i t i o n

F a c t o r

Passing Size, mm

0 3 6 9 12 15

LengthIncreasing

ApertureSize


ur 14.3-21 Partt factrs as fuct f pst dc

5

4

3

21

0

–1

–2

–3

–4

–5

–6–6 – 5 –4 – 3 –2 – 1 0 1 2 3 4 5 6

G

G

5

4

3

21

0

–1

–2

–3

–4

–5

–6–6 – 5 –4 – 3 –2 – 1 0 1 2 3 4 5 6

G

G

(A) (B)

ur 14.3-22 d d rbts (A) rma ad(B) abrma prat

ur 14.3-23 sRc staat ad tpca utput dspa



1492 SMe M er hadb

as well as the output from data processing. In this case, imagesare analyzed at a rate of approximately 10 per second, which ismore than sufcient to monitor everything that passes.

Acoustics also offer interesting potential for analyzingscreen performance, but it is very early for research in this

area.Population balance simulation methods. Population

balance methods (PBMs) are not new, having been in use for at least two decades, but as the design and operations needsturn increasingly toward simulation to accelerate the activities,higher and higher delity is required. These are an elementof the Class 2 methods previously mentioned in the “ScreenSelection” subsection. Although the industry is moving in thisdirection, older approaches are still in use in most of the simu-lation packages. One of these is the model by Karra (1979),which is based on a Class 1 selection method, although in thiscase it is based on the method of sizing relating to the massow rate of undersize in the feed stream.

Using the model in Equation 14.3-6, Karra developed acorrelation based on the empirical screen sizing factors usedin the screen selection approach. The factors have been modi-ed over time, and their estimation is described elsewhere(e.g., King 2001), but the equation for computing d 50 is

d

ABCDEF

G h50

.T

H

c T

0 148u

= `e j o(14.3-7)

whered 50 = cut sizeGc = nearsize correction factor hT = throughfall aperture (King 2001)T u = tons of undersize in the feed (dry t/h)

H = effective screen area (m2)A = basic capacity factor B = oversize factor C = ne size factor D = deck location factor E = wet screen factor F = bulk density factor

Because a number of the properties for the screen inFigure 14.3-7 have been given, Table 14.3-8 is a shortenedsummary of the Karra calculation of d 50. The agreement withthe experimental value in Figure 14.3-20 is good.

Karra assumes g is a constant at 5.9, and in the authors’experience, numbers in the region are pretty typical for coarsescreening. This number does not agree very well with thevalue in Figure 14.3-20, which highlights that Karra’s simpletwo-parameter model approach probably requires additional

parameters. Nevertheless, using the model of Equat ion 14.3-7 and

the feed data in Table 14.3-7, Karra’s model can be used to predict the expected size distributions for the undersize andoversize products, and these are shown in Figure 14.3-24along with the actual experimental results. The predictionsare satisfactory, but the importance of g is clear. The calcu-lated fractional mass splits of 0.26 and 0.74 compare wellwith the product mass ows reported in Table 14.3-7.

Discrete element simulation methods. In the pursuit

of higher-delity simulation of screen performance, the ulti-mate tool is probably discrete element modeling (DEM).Very briey, this approach is based on fundamental models

drawn from physics (e.g., Newton’s laws of motion.) Usinga mathematical description of the body and motion of thescreen; some typical physical properties; and the feed sizedistribution, ow rate, and particle shapes, the DEM simula-tion can be run from only rst principles (e.g., no correlationsand no parameters drawn for experimental data). Althoughthis sounds simple in concept, solving the problem is oner-ous, as there are millions of particles, each requiring severaldifferential equations to describe translational and rotationalmotion in time and space. Because of the interactions of the

particles among themselves and with the screen itself, theintegration intervals are very short—on the order of one mil-lionth of a second. Simulating several seconds of real-timeoperation can take days, weeks, or months, depending on the

problem size, the computational capability, and the simula-tion code efciency. It is for this reason that the goal is tocombine DEM and PBMs, the former to work out the realmechanisms and the latter to abstract these and providespeedy calculations.

Because of the vast quantities (gigabytes or even tera- bytes) of numerical data generated in such simulations, it iscommon practice to use visualization techniques to “see theresults.” However, the numerical data must be used for anycalculations. Figure 14.3-25 presents a snapshot of visualiza-tion, and Figure 14.3-26 shows the predicted (lines) and mea-sured (bullets) particle size distributions from a simulation

of the banana screen pictured in Figure 14.3-12B. The agree-ment in Figure 14.3-26 is very good, which provides someinsight into the power this tool will bring to screen modeling.

Tab 14.3-8 Cmput karra’s d 50 fr t scr ur 14.3-7

Smb actr ts Rsut

T u Feed dry t/h 15.67

H Effective screen area m2

0.57hT Throughfall aperture mm 10

G c Nearsize correction factor — 0.82

A Basic capacity factor t/h/m2 17.85

B Oversize factor t/h/m2 1.38

C Fine size factor t/h/m2 1.12

D Deck location factor t/h/m2 1.00

E Wet screen factor t/h/m2 1.00

F Bulk density factor t/h/m2 1.01

d 50 Cut size mm 8.34

50

25

0

75

100

C u m u l a t i v e % P

a s s i n g

Passing Size, mm

0 3 6 9 12 15

UndersizeFeedOversizeModelPredictions

ur 14.3-24 karra’s md prdcts ad actuacumuatv sz dstrbut curvs fr t scr ur 14.3-7




Screen Media Because screen media is often the single largest operationalexpense for a vibrating screen, this chapter would be incom-

plete without a brief discussion on this topic. The governingobjective here is the absolute lowest total cost, which implies

that availability, cost, wear life, downtime, and so forth must be considered in making the nal media selection.

Three major materials of construction for screen mediaare steel (punched plate or wire mesh), rubber, and polyure-thane. The polymeric compounds of rubber and polyurethaneare usually more expensive, but they tend to exhibit superior wear performance in those applications that permit alterna-tives. Service life can be extended by factors of more than vewith polymerics.

Figures 14.3-27 through 14.3-29 show wire mesh, rubber,and polyurethane media, respectively. Media specialists often

break down the applications as scalping, standard production(size control and sorting), and washing (sorting).

Wire mesh can have standard weaves, as shown inFigure 14.3-27A, or slotted antiblinding or even customweaves, as shown in Figure 14.3-27B. The wires are normalhigh-carbon or stainless steels.

Typical applications for rubber screen decks (Figure 14.3-28) include high-impact scalping type duty or situations whereabrasion and/or blinding are a serious concern. The decks aremanufactured by punching or molding.

Polyurethane decks (Figure 14.3-29) are usually found instandard production applications and in washing or dewater-ing applications. They are manufactured by casting or injec-tion molding processes.

The polymeric materials lend themselves to modular installation or paneling. Table 14.3-9 weighs the pros and cons

of steel versus the polymerics.As a cautionary note, although there might be a tendencyto choose thicker panels to increase wear life, this will reducecapacity and accuracy and will induce higher levels of peggingand blinding. Media suppliers familiar with best practices can

be very helpful in these selections, and it is also recommendedthat the original equipment manufacturer (OEM) is consultedwhen changing the design of media.

Standard Screen Sizing and Relative Pricing Table 14.3-10 provides a glimpse of a typical vibrating screen

product line, and while the price data supplied here is some-what out of date, the relative pricing of the screen equipmentis more or less the same.

ScrIn general, wet ne particle classication is achieved bymechanical/hydraulic means (e.g., rake or spiral/screw

ur 14.3-25 DeM vsuazat f scr prat

1 10

Particle Size, mm

100 1,0000

20

40

60

80

100

% P

a s s i n g

1 10

Particle Size, mm

100 1,0000

20

40

60

80

100

% P

a s s i n g

SimulationMeasurement

SimulationMeasurement

(B)

(A)

ur 14.3-26 DeM prdcts f (A) vrsz ad (B)udrsz partc sz dstrbuts

(A) (B)

ur 14.3-27 Wr ms mda



1494 SMe M er hadb

classiers), hydrocyclones (discussed later in this chapter),and ne screens. Although the mechanical devices still havetheir place, ne screens, and especially hydrocyclones, domi-nate ne and ultrane classication. Fine screening is theterm generally reserved for ne and ultrane separations, asdened in Table 14.3-1. It is performed dry or wet, althoughin most mining or quarrying applications, this is a wet process.Consequently, the emphasis here is on wet ne screening.

The principles described previously for vibrating screensapply to most screening processes. One notable difference isthat ne screening generally involves much higher rotationalspeeds (e.g., ~3,600 rpm). Therefore, much smaller strokesare required. Another major difference for ne screening is

that the selection of the appropriate screen is as much an art(i.e., past practices in similar applications) as it is a science(i.e., laboratory testing of specic screens on the expectedfeed material and supplier databases). This complexity is duein large measure to the critically important aspect of uidmechanics, as drag forces tend to govern wet ne and ultra-ne separations. Sufce it to say, the expertise in ne-screendesign generally lies with the major supplier organizations,such as Derrick Corporation, Conn-Weld Industries, KrooshTechnologies, Pansep, Multotec Group, and Wedgewire.

The two most common wet ne screening devices arethe sieve bend (i.e., a stationary version of the banana screen,Figure 14.3-6) and the more conventional, high-frequency nescreen (i.e., having a more conventional geometry and repre-

sented herein by the Derrick product line, including the Stack Sizer [Figure 14.3-5], the multifeed screen, and the repulpscreen). Wet ne screening is essentially the only ow-sheet

option in a number of applications (see sorting class inFigure 14.3-1), for example, in coal preparation desliming andiron ore coarse silica removal. (A more complete review onthis topic is available in Valine and Wennen (2002).

Many other applications provide wet screening as analternative to hydrocyclones or other mechanical devices, as itoffers some signicant advantages in classication efciency

(as measured by g or E u). In some applications, both sieve bends and high-frequency screens are used in conjunctionwith hydrocyclones to exploit the physical and classication

ur 14.3-28 Rubbr scr dcs

ur 14.3-29 Purta pas

Tab 14.3-9 Advatas ad dsadvatas f st vrsuspmrc scr dcs

Wr Rubbr/Purta

Advantages• Price• Accuracy of cut• Open area is high (on installation)

Disadvantages• Shorter life• More downtime• Pegging problems• Blinding problems• Reduces open area (in operation)• Noise levels

Advantages• Longer life• Less downtime• Shock resistance• Accuracy• Reduced pegging• Reduced blinding• Open area (in operation)• Noise reduction

Disadvantages• Price

• Open area (on installation)(e.g., although these screenstend to have lower open areasout of the manufacturing pro-cess than wire mesh, they retainopen area much better)




attributes for each type of separator. In other instances, it may

also be possible to feed a wet screen by gravity, rather thanthe pumping systems more commonly associated with hydro-cyclone batteries. Nevertheless, in these kinds of trade-off studies, it generally comes down to the footprint advantagesof hydrocyclones versus the process efciency advantages of wet screening. For example, one study (Vince 2007) in coalindicated that purely from a capacity perspective, two to threeDerrick Stack Sizers were the equivalent of one 900-mm(35.4-in.) classifying hydrocyclone. Interestingly, that samestudy came to the conclusion that the Stack Sizer should beconsidered for coal-preparation applications with cut points inthe 100-to-350-µm range, while sieve bends could be consid-ered for cut sizes in the 250-to-350-µm range. Of even greater interest was the observation that “similar” equipment made

by different suppliers can have quite different performancecharacteristics— caveat emptor (buyer beware).

One area of growing interest for ne screening is closene-grinding (ball mill or even stirred-mill) circuits (e.g., seeWennen et al. 1997). The opportunities to exploit improvedefciency to reduce specic energy and media requirementsand to improve downstream metallurgical efciency (e.g., byminimizing the overgrinding of valuable minerals) are veryappealing, both technically and economically. In addition,while hydrocyclones separate based on particle mass (i.e., par-ticle size and density are rst-order effects), wet ne screensseparate predominantly on size (i.e., density is a higher order effect, mainly related to particle stratication). For example,in iron-ore grinding, the cut size on a screen is the same for the

iron minerals and silica, whereas in a hydrocyclone, the cutsize for the iron minerals is about one-third of that for silica,

which is to say that a lot of ne liberated iron mineral can besent back to the grinding mill by a hydrocyclone.

Consider the partition curves shown in Figure 14.3-30.(The parameter Rf is dened later in Figure 14.3-49 and inEquation 14.3-17, but it effectively represents the very nematerial hydraulically entrained in the oversize stream—the

bypass.) Although there are some “apples to oranges” compar-isons in terms of the cut sizes, these example are drawn fromthe same plant in similar applications (Aquino and Vizcarra2007); the real interest comes from the comparison of thesharpness of separation (g) and the efciency (here inverselyrelated to Rf ). The benets of wet screening are obvious,

which makes it a technical option to cut sizes ranging down to100 µm. For the hydrocyclone partition curve, the inections

Tab 14.3-10 Stadard scr sz ad ratv prc

Scr Sz, W × l, m

lar Mt, lw-had, hrzta,Mutfw Baaa Scrs* icd Crcuar Mt Rp- Scrs†

S Dc, $ Dub Dc, $ S Dc, $ Dub Dc, $

1.2 × 4.8 70,200 95,160 58,500 93,600

1.8 × 4.8 76,440 138,060 74,880 109,200

1.8 × 6.1 136,500 175,500 117,000 143,520

2.4 × 4.8 113,100 152,100 105,300 127,140

2.4 × 6.1 145,860 269,100 124,800 156,000

2.4 × 7.3 175,500 388,600 179,400 218,400

3.0 × 4.8 117,000 232,440 N/A‡ N/A

3.0 × 6.1 210,600 310,440 155,220 226,200

3.0 × 7.3 237,900 343,200 202,800 249,600

3.0 × 8.5 257,400 374,400 N/A N/A

3.6 × 6.1 252,720 368,940 N/A N/A

3.6 × 7.3 280,800 382,200 N/A N/A

3.6 × 8.5 308,880 444,600 N/A N/A

4.2 × 6.1 265,200 443,040 N/A N/A

4.2 × 7.3 304,200 530,400 N/A N/A

*Low-head and multiow pricing includes motor and modular polyurethane screen surfaces.†Ripl-Flo screens include motor or motors and woven wire screen surfaces.‡N/A = not available.

50

25

0

75

100

P a r t i t i o n

F a c t o r

Characteristic Size, µm

0 100 1,000

Stack SizerCyclone

d 50c = 141 µmγ = 1.3Rf = 0.3

d 50c = 477 µmγ = 5.6Rf = 0.03

ur 14.3-30 Partt curvs fr a 254-mm (10-.)drcc ad a Drrc Stac Szr



1496 SMe M er hadb

and rather poor sharpness of separation are a partial conse-quence of the existence of liberated heavy and light minerals

in the feed (i.e., the density effect).Finally, Figure 14.3-31 provides a glimpse of the abil-

ity of this ne screen to preserve efciency over a range of aperture sizes (i.e., the sharpness in separation is good and the

bypass is low).

CyCloneSCyclones (named for the spiraling motion within the body of the device) are one of a large number of classication devicesaimed at separating ne particles in a uid (water or air). For examples, see Kelly and Spottiswood (1982) or Svarovsky(2000). Cyclone classication is generally reserved for theseparation of particles on the basis of size. For this reason,other applications for cyclones, such as thickening and dense-

medium separation, are not considered here. Broadly speaking,cyclone classiers can either treat dry feeds (the air classier or air separator) or wet/slurry feeds (the hydrocyclone). Theemphasis here will be on wet applications.

Unlike the vibrating screen, which employs a physicalmeans (the screen media) to effect a separation, the cycloneclassier uses differential settling properties of particles of different mass. The cyclonic action within the body of thedevice develops G-forces signicantly greater than gravity,which accelerate the separation process. In general, cyclonesare robust, compact (small footprint), and relatively efcientsize-separation devices.

Figure 14.3-32 shows the most common applications of wet cyclones in mining. Air classiers are also commonlyused in these applications, for example, as a size-controldevice in dry grinding (most notably in refractory gold, coal-red power plant pulverizers, or cement clinker applications)and as sorters (usually in de-dusting applications).

Figure 14.3-33 shows the geometry of a standard hydro-cyclone, the shape of which clearly resembles the natural phe-nomenon that gives rise to the name. The separator comprisesa feed section, cylindro-conical section, discharge spigot, vor-tex nder, and overow. In some cases, usually with larger diameters, each of these is supplied as a separate entity,whereas in others they may be cast into a single unit (i.e., withsmaller diameters).

The capacity of a hydrocyclone is a function of its size

and, subject to operational constraints, the rate and solids con-centration at which the feed (slurry) material is supplied. Insome cases, hydrocyclones are gravity fed from surge tanks,

but the majority of applications use a feed sump and pumparrangement. Consequently, it is common to utilize a groupof hydrocyclones operating in parallel to achieve the required

process throughput capacity. As Figure 14.3-34 shows, thecompact design of the units permits the use of a radial header to distribute feed to a number of hydrocyclones. This is com-monly called a hydrocyclone cluster or battery, or a Cyclopac.Moreover, as Figure 14.3-34B highlights, the use of knife-gatevalves to open or close a hydrocyclone is very convenient,

both from an online process control point of view as wellas for maintenance purposes. On the latter point, and giventhe relative cost of a hydrocyclone, it is typical to remove a

Reversed Closed Circuit

Size Control

e.g., Single-Stage Autogenous/SemiautogenousBall Mill Circuits, Regrind Circuits

e.g., Sand-Slime Flotation, Tailings Dam Construction

Sorting

Standard Closed Circuit

ur 14.3-32 examps f t appcat casss frdrccs m

0.2

0.4

0.6

0.8

0

1.0

P a r t i t i o n

F a c t o r


0 100 1,000

Aperture 2 3 0 µ

m

3 0 0

µ m

5 0 0

µ

m

6 0 0

µ m

ur 14.3-31 Partt curvs fr a Drrc Stac Szr wtdffrt scr aprturs

Courtesy of Weir Minerals.

ur 14.3-33 hdrcc




hydrocyclone for maintenance and simply replace it with arefurbished spare.

There are a number of variants on the more typical hydro-cyclone geometry of Figure 14.3-33. Figure 14.3-35 shows thewater-only or automedium cyclone that is frequently used inwashing ne (–0.6 mm) coal. (The truncated lower cone sec-tion is employed to set up a secondary density separation in arotating particle bed.) The at-bottomed hydrocyclone occa-sionally used in mineral processing applications has a verysimilar kind of body geometry.

Air separators tend to be designed to treat the whole feedow, so they are larger units, as shown in Figure 14.3-36.These devices can be either static (such as the hydrocyclone)or dynamic (including moving blades, and so forth, to enhanceseparation).

Figure 14.3-36 illustrates a typical dry grinding circuitwith the air separator used for classication and a cycloneused for solids recovery. The cutaway view on the right illus-trates the internals and the drive for this dynamic air separator.

hdrcc Bascs

The hydrocyclone evolved into its current role in mineral pro-cessing in the period from approximately 1950 to 1970, bywhich time it had become a key element in the design of most

large-scale grinding circuits. The hydrocyclone offers highcapacities in small footprints and arguably enabled the ongo-ing development of very large grinding circuits. Althoughthey still have their place, mechanical classiers were effec-tively rendered obsolete in plant design by the hydrocyclone.Despite the numerous benets of hydrocyclones, there havealways been issues with efciency, as introduced earlier inthe discussion on ne screening. As today’s operators look for ways to address energy efciency and as competitive tech-nologies emerge, hydrocyclone manufacturers have redoubledtheir development efforts. As is the case for screens, they are

using the very latest simulation tools to help rene existingdesigns and develop new ones for specic applications, withgood success. The following subsections provide a refresher on hydrocyclone basics and introduce some of the latest toolsand techniques for the design, analysis, control, and optimiza-tion of hydrocyclones.

Principles of Operation Figure 14.3-37 provides a sketch of a typical hydrocy-clone showing the main design components. The principaldimensional variable is the diameter of the upper cylindri-cal section of the hydrocyclone body, Dc. The inlet ( Di) anddischarge ( Do and Du) dimensions usually lie within someratio of D

c, (e.g., 0.2 D

c≤ D

o≤ 0.45 D

c). Because the inlet

is usually more rectangular in nature, to facilitate a reduc-tion in turbulence on entry (involute designs—see Olsonand Turner 2002), Di is defined as the diameter of circlewith an area equivalent to the actual inlet area. In the past,smaller hydrocyclones have had lower cone angles (~10°),

but because of headroom considerations, larger hydrocy-clones tend to have larger cone angles (~20°). Some typicaldimensions for a hydrocyclone with Dc = 760 mm (30 in.)are shown in the figure.

The feed enters the hydrocyclone near the top of thecylindrical section, usually through some sort of invo-lute inlet design, which is intended to introduce the slurryinto the hydrocyclone with a minimum of turbulence, as

this can have a deleterious effect on efficiency and wear.Figure 14.3-34A clearly shows this involute design. Therotational motion set up in the body of the hydrocyclone

(A)

(A) Courtesy of Weir Minerals; (B) Courtesy of FLSmidth Krebs.

ur 14.3-34 hdrcc custrs: (A) sd vw ad(B) tp vw

(B) Courtesy of FLSmidth Krebs.

ur 14.3-35 Watr- cc



1498 SMe M er hadb

gives rise to the G-forces that accelerate the particle separa-tion process. All of the particles are subjected to the centrif-ugal forces directing them to the wall of the hydrocyclone,where this material moves downward in a helical fashionto be discharged through the apex, as underflow. However,as the particles migrate to the outer wall of the hydrocy-clone, they necessarily displace the fluid, which must moveinward. The fluid exerts drag forces on the particles andretards their outward motion and, in the case of the finer

part icles, actually causes them to move inward. This streammoves upward in a helical path to be discharged through thevortex finder, as overflow. When the hydrocyclone is oper-

ating normally, the centrifugal forces acting on the slurrycreate low pressure along the central axis, establishing theconditions necessary for development of the characteristicair core.

To look more closely at the separation process, consider Stokes’ law for laminar settling, given by Equation 14.3-8.(Whether it is Stokes’ law, Newton’s law, or somethingelse—as experimental data would seem to indicate—thetrends predicted by Stokes’ law are seen in practice.)

v gd

18t s l

2

=μ

ρ ρ−^ h(14.3-8)

wherev

t = terminal settling velocity

r s = solids specic gravity rl = carrier uid specic gravity g = gravitational or centrifugal force acting on the

particlesd = particle diameter µ = carrier uid viscosity

From the explanation given previously, anything that actsto increase the particle settling velocity increases the chancesof particle reporting to the underow stream. Clearly, thelarger the particle, the more likely it is to go to the underow.Similarly, higher G-forces (meaning higher feed ows or pres-sure drops) will also act to increase the probability that a par-

ticle will nd its way to the underow stream. Particles withhigher specic gravities will also have a higher probability of reaching the underow stream.

However, if the feed material contains a lot of very neclay material, thereby increasing the effective viscosity, the

particles will be less likely to reach the underow stream.Similarly, with high-density hydrocyclone feeds, there is asignicant concentration of ne particles in the carrier uid,which increases the uid specic gravity and makes it lesslikely for particles to reach the underow stream.

To further complicate things, the size of the vortex nder also has an inuence on the separation outcome. Smaller vor-tex nders will create a ner particle overow stream, andvice versa. Although to a lesser extent, the apex size will alsohave an impact, as a smaller apex tends to limit the underowcapacity, diverting some coarser particles toward the upper regions of the hydrocyclone, the nest of which will then beentrained in the overow stream.

Figure 14.3-38 (absent the air core) was developed byRenner and Cohen (1978) and shows roughly the main regionsinside a cyclone. Region A is relatively narrow area in thevicinity of the inlet that is characterized by a size distribu-tion similar to that of the feed. Most of the conical section is

Region D, which is characterized by a coarser size distribu-tion similar to the underow. Region B is the ner materialwith a size distribution very similar to the overow product.

Cyclone

Vent

Fan

Mill

Gyrotor

GyrotorCutaway

ur 14.3-36 A grtr ar sparatr a tpca dr rd crcut

α

Apex (or Spigot)Diameter (D u ) ≈ 0.15D c

Cylindrical SectionDiameter = D c

Height ≈ D c

Inlet Diameter (D i ) ≈ 0.25D c

Vortex FinderDiameter (D o ) ≈ 0.35D c

Conical SectionHeight ≈ 2D c

Angle (α) = 10°–20°

Example:ForThen

D c = 0.76 mD o ≈ 0.27 mD i ≈ 0.19 mD u ≈ 0.11 m

ur 14.3-37 Prcpa ds mts f a drcc




Region C is perhaps the most critical region, as it was foundto contain signicant quantities of nearsize particles, whichsuggests that they tend to accumulate here until physicalcapacity constraints force them to move to one product zoneor the other. Arguably, this is the region of active classica-

tion, and poor operation would be expected if it fails to form properly, possibly because of poor design or excessive feedsolids concentrations.

Rather than produce a process matrix for the hydrocyclone,the authors have chosen to illustrate these concepts with thePlitt model (see Flintoff et al. 1987) given in Equation 14.3-9.This is the correlation for the corrected cut size, d 50c. For example, increasing the hydrocyclone diameter, Dc, would beexpected to lead to a coarser cut size. Similarly, increasing thefeed ow, Q, would lead to a ner cut size.

μ50

.

d

D h Q

CD D D e

1 65

. . .

. . . . .

c

u s l

k c i o

V

0 71 0 28 0 48

0 46 0 6 1 21 0 5 0 063

=ρ ρ−; E

(14.3-9)

whered 50c = corrected cut size

C = a calibration constantDc = hydrocyclone diameter Di = inlet diameter Do = overow apex diameter V = volume percent concentration of solids in

hydrocyclone feedDu = underow apex diameter

h = free vortex heightQ = feed volumetric ow ratek = settling exponent (e.g., 0.5 in Equation 14.3-8)

A correlation exists for g as well, but it is much weaker, gener-ally indicating that g will improve at lower ows (longer resi-dence times) and lower feed solids volumetric concentrations,

both of which are intuitively acceptable.A couple of phenomena are worthy of some amplication.

The rst is the phenomenon known as roping (a name basedon the appearance of the underow stream in this regime).Roping occurs when the volumetric ow rate of the underowstream causes the air core to collapse. When this happens, theusual helical spray from the apex alters appearance, as shownin Figure 14.3-39. Consequently, roping will increase the owof coarser particles to the overow stream (i.e., a coarser cutsize). The impact on efciency (as measured by g in a partitioncurve) appears to depend on the hydrocyclone feed density— higher densities having a more deleterious effect. Roping doestend to maximize the underow density. Thus, it minimizesthe fraction of ne material that reports with the carrier liquidto this stream.

The other phenomenon is particle density. There aremany cases (coal, iron ore, massive sulde ores, and so forth)where liberated particles of widely different densities exist.Equation 14.3-8 indicates that, for a constant settling veloc-ity, the particle size is related to solids specic gravity as d a(r s – rl )

0.5. In practice, and because of other phenomena sucha secondary density separation occurring in the rotating bed,the exponent is usually much greater than 0.5, which meansthat density effects are exacerbated in the hydrocyclone. To

illustrate, consider Figure 14.3-40, which shows coal slurry being processed in a hydrocyclone. Sink and oat analysis

on the products allows the reconstruction of separate parti-tion curves for each specic gravity (SG) class, all of whichhave a reasonable shape. However, looking only at the over-all curve could suggest poor classication.

The last item of interest is hydrocyclone mounting. Withthe development of larger and larger hydrocyclones, mountingthem in a vertical orientation puts a signicant head on theunderow stream, which can inuence wear and separation.However, tilting these hydrocyclones (usually at ~45°) allowsoperation at lower pressures while still producing a goodunderow product, albeit at a coarser cut size. Maintenance-saving claims for wear in the lower region of the hydrocycloneare impressive (80%, e.g., Schmidt and Turner 1993), but it

can be more difcult to perform in-situ maintenance for thiskind of installation.

A A

BB

C C

DD

Source: Renner and Cohen 1978.ur 14.3-38 Rs a cc

90-mm DiameterSpigot Pattern

Spray Flow Pattern (Ideal)

30-mm DiameterSpigot Pattern

Characterized by • Feed Density Correct • Ideal Spigot Diameter

Rope Flow Pattern (Not Ideal)

Characterized by • Feed Density Too High • Spigot Diameter Too Small

Classification Size

Small Large

Courtesy of Weir Minerals

ur 14.3-39 Spra ad rp dscar



1500 SMe M er hadb

Hydrocyclone Selection The selection of hydrocyclones is normally a task best per-formed with a supplier, as these rms possess the knowledge,expertise, databases, and tools to ensure that the best resultsare achieved. In most cases, it is possible to avoid pilot testing.However, there are some instances where this is preferable and

even inevitable. One of the more challenging design problemsis the closed-circuit grinding application, illustrated on the leftin Figure 14.3-32. This is challenging because the hydrocy-clone feed characteristics depend very much on mill perfor-mance, which in turn depends on the hydrocyclone underowcharacteristics, which in turn depend on the feed. Experiencehas given most suppliers a very good understanding of this

problem; nevertheless, circuit simulation tools can be usefuladjuncts in developing a hydrocyclone design basis. (Publicdomain hydrocyclone models, e.g., Equation 14.3-9, includemost of the basic design parameters, yet these are seeminglynot commonly used in the design process, which underscoresthe experience factor necessary in this process.)

For the purposes of this chapter, the techniques of hydro-

cyclone design documented by FLSmidth Krebs are brieyreviewed (for more detail, see Arterburn 1982 and Olson andTurner 2002). The required information is summarized inFigure 14.3-41.

A set of standard tests under very specic design andoperating conditions was performed to develop a relationship

between what is called the base corrected cut size (d 50c-base) andthe principal dimensional variable, the hydrocyclone diameter,

Dc. The outcome of this work is captured in Figure 14.3-42, based on Equation 14.3-10, and is also given in the alternateform as Equation 14.3-11.

50 2.84d D .c base c

0 66- = (14.3-10)

0.206 50 D d .

c c base1 515

-= (14.3-11)

0

20

40

60

80

100

10 20 50 100 200 500 1,000 2,000

2.35

1.8

1.5

1.3

1 . 3

7 5

Overall Solids Classification


P a r t i t i o n F a c t o r , %

Parameter Is Mean SolidsSpecific Gravity

Rf = 12%

Source: Reprinted with permission of the Canadian Insti tute of Mining, Metallurgy and Petroleum. Originallypublished in the CIM Bulletin, Vol. 80, No. 905, p. 43.

ur 14.3-40 Partt curvs fr ca surr a drcc

Target Product

Expected FeedSolids = 812 t/hWater = 562 t/hSolids SG = 2.9

Slurry = 1,374 t/h% Solids = 59.1 w/o% Solids = 33.3 v/oSlurry SG = 1.63Slurry Flow = 842 m3/h

Assume ∆ P = 50 kPa

Underflow Assumptions

200% Circulating Load at 72% SolidsSolids = 541 t/hWater = 210 t/hSlurry = 396 m3/h

60% Passing 74 µm

Source: Arterburn 1982.

ur 14.3-41 hdrcc ds

10

100

d 5 0 c - b a s e , µ m

Cyclone Diameter, cm10 100


ur 14.3-42 r stadard drccs, d 50c-base vrsusdrcc damtr




Not unlike the screen design methodology introducedearlier, the hydrocyclone design approach illustrated hererelies on a number of empirical correction factors to scale the

performance of the standard hydrocyclone to the expectedindustrial operation. In this case, the key scaling parameter isthe d 50c, and the key design formula is given by

50 50d d CP CP CP

CD CD CD

1 2 3

1 2 3

…

…

c actual c base- -= ^ ^ ^ ^

^ ^ ^ ^

h h h h

h h h h(14.3-12)

whered 50c-actual = the expected corrected cut size in

industrial operationd 50c-base = the corrected cut size for the

standard hydrocycloneCP 1, CP 2, CP 3… = process related correction factors

(e.g., feed volume [~ viscosity]

correction factor)CD1, CD2, CD3… = design-based correction factors,

(e.g., vortex nder diameter)

In practice, Equation 14.3-12 is rearranged and used inthe form of Equation 14.3-13:

50d CP CP CP

CD CD CD

d

1 2 3

1 2 3

50

…

…

c base

c actual

-

-=

^ ^ ^ ^

^ ^ ^ ^

h h h h

h h h h

(14.3-13)

With this short introduction, the basic steps in hydrocy-clone design are as follows.

Step 1—Estimation of the d 50c-actual . Table 14.3-11

provides the relationship between the overow size speci-cation and d 50c-actual . For the overow specication inFigure 14.3-41, 60% corresponds to a factor of 2.08, whichwhen multiplied by the reference size of 74 mm gives the esti-mate for d 50c-actual of 154 mm.

Step 2—Calculation of the correction factors andestimation of d 50c-base. Three important published process-related correction factors are the solids feed volume concen-tration (CP 1), the operating pressure drop (CP 2), and thesolids specic gravity (CP 3).

CP 1 is the correction for the feed volumetric concen-tration, which is in effect a rst-order approximation toviscosity. Of course, viscosity also depends on water tem-

perature, clay concentrations, particle shape, and other fac-

tors—clays in ne tailings is what gave rise to the tailingscurve in Figure 14.3-43. In this gure, Olson and Turner

(2002) extended Arterburn’s method, which was based on thestandard curve in Equation 14.3-14.

1CP V

53

53 .1 43

=− −

8 B (14.3-14)

In this example the standard curve is assumed, and with V =33.3%, then CP 1 = 4.09.

CP 2 is the correction factor for the operating pressuredrop—usually the difference between the measured pressurein the radial header and atmosphere. Larger hydrocyclonestend to run at lower pressures, and vice versa. Figure 14.3-44and Equation 14.3-15 show this relationship.

2 3.27CP P .0 28= Δ − (14.3-15)

where ∆ P is the pressure drop in kPa.In this example, it was assumed that ∆ P = 50 kPa

(7.25 psig), which should give relatively good hydrocyclone performance while minimizing wear. From Equation 14.3-15,CP 2 = 1.09.

CP 3 is the correction factor for the solids specic gravityand is shown in Figure 14.3-45 and Equation 14.3-16. For asolids specic gravity of 2.9, the correction factor CP 3 = 0.93.

3

.

CP

1 65 .

s l

0 5

= ρ ρ−; E (14.3-16)

Tab 14.3-11 emprca crrat btw t rfrc szad d 50c-actual

Rqurd ovrfw Sz Dstrbut(Prct Pass) f Spcfd

Mcrmtr

Mutpr(T B sd t actr t

Spcfd Mcrmtr Sz)

98.8 0.54

95 0.73

90 0.91

80 1.25

70 1.67

60 2.08

50 2.78

0.1

3

1

∆ P

C o r r e c t i o n

F a c t o r

Pressure Drop, kPa

10 500100

Source: Arterburn 1982.ur 14.3-44 Prssur drp crrct factr

1

100

10

% S

o l i d s C o r r e c

t i o n F a c t o r

Feed Concentration, % by Volume

0 10 20 30 40 50 60 70

Tailings Standard

Closed-CircuitGrinding

Source: Olson and Turner 2002.

ur 14.3-43 Crrct factrs fr drcc fdsds vumtrc cctrat



1502 SMe M er hadb

CD1 is the correction factor for the vortex nder diam-eter. In this example the default design of Do = 0.3 Dc is used,

but Figure 14.3-46 and Equation 14.3-17 illustrate the natureof the correction.

1.

CD D

D

0 3

.

c

o0 6

= ; E (14.3-17)

Equation 14.3-11 then solves as

50. . .

µ37 µd

4 09 1 09 0 93 1

154 mmc base- = =

^ ^ ^ ^h h h h(14.3-18)

Step 3—Select size and number of hydrocyclones. From Equation 14.3-11 or Figure 14.3-42, the diameter of the hydrocyclone required to give this d 50c-base is 49.1 cm(19.3 in.). Hydrocyclones, like screens, come in certain stan-dard sizes, usually dened by Dc. As seen in Figure 14.3-47,the closest size to the “theoretical” value computed previouslyis a hydrocyclone with Dc = 51 cm (20.1 in.).

For a pressure drop of 50 kPa (7.25 psig), the capacity of a single 51-cm (20.1-in.) hydrocyclone will be approximately140 m3/h (616 gpm). From Figure 14.3-41, the total feed volu-metric ow is 842 m3/h (3,707 gpm), so approximately sixhydrocyclones will be required in operation. In practice, twoor three additional hydrocyclones would be added to accom-modate maintenance as well as peaks in the feed ow rate. It

is also not uncommon to provide an additional off-take valvein the radial header to be used for sample-collection purposes.

Step 4—Select apex size. The last step is to determinethe apex size, and that comes from Figure 14.3-48. For a totalunderow rate of 396 m3/h (1,744 gpm), the ow througheach apex would be ~66 m3/h (291 gpm), corresponding toan apex size of ~9.3 cm (3.66 in.). The manufacturer’s closestsize would be chosen, if possible tending to a smaller size inanticipation of wear.

Of course, after the hydrocyclones are installed and inoperation, the reality of the application is known, and the opti-mization process (process variables and design variables suchas Do and Du) can be modied as required.

Although the suppliers have undoubtedly added manyrenements to their proprietary methods for hydrocyclonedesign, such as screens, the published methods for design

have changed little since the 1980s. However, with the adventof some of the new, more efcient hydrocyclone technology

0.5

3.0

2.5

2.0

1.5

1.0

S p e c i f i c G r a v i t y C o

r r e c t i o n F a c t o r

Solids Specific Gravity

1 10


ur 14.3-45 Spcfc ravt crrct factr

0.75

1.35

1.25

1.15

1.05

0.95

0.85 D o

C o r r e c t i o n

F a c t o r

Ratio D o /D c

0.20 0.450.400.350.300.25

Source: Olson and Turner 2002.

ur 14.3-46 rtx fdr crrct factr

100

10

1

1,000

3,000

C y c l o n e C a p a c i t y , m 3 / h

Pressure Drop, kPa

50010010

76 cm

D c

66 cm

51 cm

38 cm

25 cm

15 cm

10 cm


ur 14.3-47 hdrcc capact crrat

1

20

10

A p e x S i z e , c m

Apex Capacity, m3/h

1 10 100 400


ur 14.3-48 Apx sz crrat




to be discussed later, these published methods will require anadaptation.

Performance Assessment Hydrocyclone efciencies are usually assessed through the

partition curve, and this implies a sampling experiment toacquire the necessary data. However, unlike screens, the factthat hydrocyclones are treating ne particles in slurries intro-duces another dimension to the simple modeling approachused for screening (Equation 14.3-6). The liquid phase report-ing with the underow stream carries with it ne particlesthat should have otherwise reported to the overow stream.A common conceptual model is illustrated in Figure 14.3-49.It is assumed that a fraction of the feed material is bypasseddirectly to the underow stream and the rest of the materialis then subjected to the classication process (characterized

by g and d 50c). (In this gure, upper case letters F and U aremass ows in the feed and underow, while f i, and ui are themass fractions retained in the ith size class. pc

i is the cor-rected partition factor for the ith size class, usually given byEquation 14.3-6. Modeling convention is to number the sizeclasses from 1 (coarsest size fraction) to N (the so-called panfraction) from the sieve analysis. For example, in Table 14.3-12, the particles greater than 6,730 µm will be size Class 1,those falling into the interval 6,730 # 4,760 µm, will be sizeClass 2, and so on.

Thus, the basic partition curve model for hydrocyclonesis given by

Rf 1 − p Rf e1 .i d

d 0 693

50c

i= + − −

γ

^ ch m8 B (14.3-19)

where Rf is the the bypass fraction.

Table 14.3-12 provides some experimental data for anoperating hydrocyclone. Figure 14.3-50 compares the experi-mental data with modeling results with Equation 14.3-19, andthe t is seen to be very good. (The inefcient hydrocyclonewas chosen for this illustration as the data are used to exploreother measures of efciency.)

The corrected partition curve (the term in the bracesin Equation 14.3-19) is shown as the dashed line inFigure 14.3-50. Removing the effect of Rf in this way permitsa more objective assessment of d 50c and g. The d 50 for theexperimental data in Figure 14.3-50 is about 106 µm, not veryclose to the d 50c value of 344 µm. Of course, this ner cutis because of the large number of ne particles carried to theunderow by the water—the Rf factor.

To amplify on Rf , the very ne particles (d i → 0 mm) areassumed to be more or less trapped in the water by virtue of the extraordinary drag forces. Hence, it is expected that the Rf deduced from the partition curve analysis will be equivalentto the water recovered from the feed to the underow stream.In a well-constructed and executed experiment, the Rf esti-mated from curve tting and the Rf (water) calculated fromthe water split should indicate good agreement, as evidencedin Figure 14.3-50.

For completeness, not all experimental partition curves behave like those for a homogenous ore (i.e., a low-gradeore with a gangue matrix of approximately constant specicgravity). For example, it is not uncommon to see the so called

“sh-hook” behavior at the ne end of a partition curve, wherethe pi values actually dip signicantly below the expected Rf (water) value, before coming back to this level at the

Classification

p c i

Underflow

Overflow

(1 – Rf )(Rf i )p c i

Uui = [Rf + (1 – Rf )p c i ]Ff i or p i = Uui /Ff i = Rf + (1 – Rf )p c i

(1 – Rf )(Ff i )

Ff i Feed

Rf (Ff i )BypassRf

ur 14.3-49 Ccptua md f drcc prat

Tab 14.3-12 exprmta data fr a fct drcc

Sz, µm Cc d Cc drfw exprmta

Partt

6,730 0.17 0.24 1.00

4,760 0.41 0.57 1.00

3,360 0.53 0.74 1.00

1,680 6.77 9.49 1.00

850 14.89 20.40 0.98

600 10.21 13.03 0.91

425 11.37 12.97 0.81

300 11.05 10.59 0.68

212 7.96 6.61 0.59

106 12.07 8.86 0.52

74 4.11 2.65 0.46

53 2.80 1.77 0.45

Pan 17.66 12.07 0.49

Total 100.0 100.0 —

Mass 1,237.3 880.9 —

Percent solids 65.1 73.6

Rf (water) 0.47 — —

0.0

1.0

0.8

0.6

0.4

0.2

P a r t i t i o n

F a c t o r


10 10,0001,000100

d 50c = 344γ = 1.76Rf = 0.46

Rf (water) = 0.47

ExperimentalModelCorrected Curve

ur 14.3-50 Partt curv fr a ffct drcc



1504 SMe M er hadb

ultrane sizes. While beyond the scope of this work, there areways to model this if necessary, but the physical explanationsare not so straightforward. Similarly, there can be inectionsat the coarser end of the curve, so called “humps” or even“dips,” and these are usually related to the separate classica-tion action of liberated heavy and light mineral particles. Inthis latter case, one must separate these fractions experimen-tally (or mathematically) and model the curves separately.

From an operational point of view, maximum efciencyis achieved when g is maximized (values of ~2.5 or larger are considered “good”) and Rf is minimized (values of 0.3 or less are considered “good”). In closed-circuit grinding, Rf is aclear indication of the amount of ne material needlessly sent

back to the mill. In practice, there is always a compromise between efciency and operational objectives. In general bothg and Rf will improve with a lowering of the solids volumetricconcentration in the feed. Rf can be also reduced using at-

bottom or inclined hydrocyclones, both of which maximizethe underow solids content.

A nal word of caution on partition curves is that thereare numerous simple two-parameter functional forms usedto characterize the corrected partition curve. They all have incommon the parameters d 50c and g. However, while the d 50cvalues will usually compare well, the same is not true for theg values. It is important that one be aware of the underlyingfunctional form in drawing any comparisons between plantresults and those quoted by others. To very quickly illustrate,another commonly used model is given in Equation 14.3-18.

exp exp

exp

p Rf Rf

d

d

d

d

1

502

501

c

i

c

i

i =

γ γ

γ

+ −

+ −

−

^c ^

ch

m h

m

;;

EE

(14.3-20)

When Equation 14.3-18 is t to the data in Figure 14.3-47,the parameter values are d 50c = 340 µm, Rf = 0.44, andg = 2.13. For a given data set, g values from the model inEquation 14.3-20 are always higher than those from the modelgiven by Equation 14.3-19.

A number of other efciency measures, such as imper-fection and probable error, are sometimes used with hydro-

cyclones. Many of these are based on the partition curve. Inaddition, some people use the efciencies dened earlier for screening (Equations 14.3-3 and 14.3-4). To illustrate, the

partition curve in Figure 14.3-50 is seen to be rather inef-cient, both in terms of g and especially in terms of Rf . (This isa high-density feed with older model hydrocyclones.) The cor-responding gures are E u = 62.2% (nes removal from over-size) and Ru = 41.2% (nes removal from feed to overow).

Not surprisingly, these poor performance gures, especially Ru, have been the main drivers to explore ne-screening solu-tions and more efcient hydrocyclone designs.

Recent Developments Design enhancement on existing hydrocyclones.

Recently, both FLSmidth Krebs (gMAX) and Weir Minerals(Cavex) have introduced new, more efcient hydrocyclonedesigns. In both cases it appears that design improvementswere made in the feed inlet to minimize turbulence when thenew feed enters the body of the hydrocyclone, which impactscapacity, wear, and efciency. Moreover, both OEMs madechanges to the hydrocyclone body design as well. FLSmidthKrebs (Krebs Engineers 2000) exploited the potential for ef-ciency improvements associated with increasing residence timein the critical conical section of the hydrocyclone, as shown inFigure 14.3-51. An extensive redesign campaign yielded opti-mal combinations of cylinder and cone length, as well as conedesign for each standard gMAX hydrocyclone diameter.

Mohanty et al. (2002) reported that a conventional hydrocy-clone separating a ne coal feed (~45 µm cut target) yielded anefciency of Ru = 37%, while the gMAX improved this to 68%.Adding the FLSmidth Krebs Cyclowash attachment (a means of injecting water into the lower cone section of a hydrocyclone toremove nes) gave a further increase to 70%. (Further technicaldetails may be found on the supplier’s Web site.)

New hydrocyclone systems. In addition to the work

underway to improve traditional hydrocyclone designs, newdesigns are also under study by equipment manufacturers andresearchers alike, although in general these are application-specic products. Two good examples of this are the three-

product hydrocyclone (University of Cape Town) and theReCyclone (Weir Minerals).

Briey, the three-product hydroyclone (e.g., Mainza etal. 2004) is intended for use in applications where there arecomponents of distinctly different densities. In conventionalhydrocyclones, the heavier minerals concentrate near thehydrocyclone wall, which creates a heavy medium that selec-tively sends the larger, lighter particles toward the inside of the hydrocyclone, where they can be sent to the overow. Inthe case of the platinum ores in South Africa, the lighter silica

gangue contains the platinum group metals, while the heavier chromite is barren. Larger silica particles that report to theoverow represent potential recovery losses in the otation

process. The three-product hydrocyclone uses concentric vor-tex nders to produce two overow products, and the inner vortex nder collects the ne particles, which are sent directlyto otation. The outer vortex nder collects a coarser mid-dlings overow, rich in coarse silica, which is then screenedto ensure that the coarser material gets to the mill for further grinding, while the ner heavy material joins the otationfeed. Development work continues with this system, whichwould appear to have other applications in the mineral pro-cessing industry.

The ReCyclone (D. Switzer, E. Castro, and J. Lopez,

personal communications) uses two-stage classication as ameans to reduce Rf and increase g. This concept has been stud-ied and promoted by many academics and a few operators. It

0.0

1.0

0.8

0.6

0.4

0.2

P a r t i t i o n

F a c

t o r


10 1,000100

= 10.5° ConeD c = 25 cmQ = 85 m3/hd 50c = 79 µmγ = 2.69

= 20° ConeD c = 25 cmQ = 73 m3/hd 50c = 115 µmγ = 2.34

Source: Krebs Engineers 2000.

ur 14.3-51 effct f c a drccprfrmac




does nd application in some coal and iron-ore ow sheets, but generally the extra footprint and the capital and operat-ing expenses associated with such an approach has diminishedinterest among plant designers. One area where this has beenextensively applied is in tailings dam construction, where itis critically important to move as much of the nes as pos-

sible from the sand product used to construct the dam. Inthese cases, two batteries of hydrocyclones (larger primariesfollowed by smaller secondaries) are common, to ensure thatsand percolation rates are sufciently high to avoid stability

problems in the dam. The ReCylone performs these steps ina single unit.

Figure 14.3-52 is an illustration of the ReCylone unit andFigure 14.3-53 presents partition curves for the primary andsecondary units and for the overall curve. Note the adjustmentsystem on the primary underow, which acts conceptually likea variable apex. The effects on Rf and, hence, ne particle con-tent in the underow are clear. All of the case studies reported

by D. Switzer, E. Castro, and J. Lopez (personal communica-tions) are on tailings. However, one can easily envisage other

applications.Instrumentation. Although little has been published

thus far, the major hydrocyclone suppliers and some third

parties are actively looking at technology value additions thatwould help to improve performance and minimize mainte-nance costs. For example, hydrocyclones are known to vibratewhen they transition from normal underow spray to a ropingregime, and vibration and/or acoustics (e.g., Wedeles 2007)could be applied to diagnose this event or other events such asapex plugging (e.g., tramp grinding balls in the hydrocyclonefeed). Another example is the elusive measurement of the rela-tive wear of hydrocyclone liners, an area also under study by

pump manufacturers. The interested reader should contact thesuppliers directly on this topic.

Computational uid dynamics (CFD). As was seenearlier in the discussion on screens, most major suppliers arerapidly embracing sophisticated simulation tools as a way tocreate and screen virtual machines for the purposes of designand optimization. Although this does not preclude the neces-sary step of eld testing prototypes, it does help in the selectionof the most appropriate candidate designs, reducing researchand development costs and technical risk, and shortening thetime to market.

CFD is the simulation technique of choice for uid sys-tems such as the hydrocyclone. However, at this stage it isimpossible to simulate real slurries, and the standard approachis to simulate the uid and then to use these results with some“tracer particles” (within CFD or in the DEM environment)

to gain insight on classication efciency. This one-way cou- pling (the uid inuences the particles, but the converse isnot true), albeit with dilute suspensions, provides quantitative

predictions based on rst principles.Sufce it to say, CFD played a major role in the devel-

opment of both the Cavex and gMAX hydrocyclone designsdescribed earlier. For the interested reader, the paper byDelgadillo and Rajamani (2007) provides a current vision of the

benets of CFD in advancing the hydrocyclone state of the art.

Media Briey, hydrocyclones are usually constructed of urethane or steel. Steel hydrocyclones are lined with wear-resistant mate-rials such as rubber, ceramics, or urethane, and they can some-

times employ special metallic-based compounds. Again, theOEM is in a very good position to provide expert applicationadvice on media choices.

Underflow

S e c o n d a r y O v e r f l o w

P r i m a r y

O v e r f l o w

Common

Overflow

Feed

Wash

Water

Courtesy of Weir Minerals.

ur 14.3-52 Scmatc ad staat f t RCc

0.0

1.0

0.8

0.6

0.4

0.2 P a r t i t i o n

F a c t o r


10 1,000100

Primary ConeSecondary ConeOverall

Courtesy of D. Switzer, E. Castro, and J. Lopez.

ur 14.3-53 Partt curvs fr a RCc



1506 SMe M er hadb

Standard Hydrocyclone Sizing and Relative Pricing Each hydrocyclone manufacturer has a specic standard prod-uct size range, as shown in Figure 14.3-47. Generalizing acrossseveral of these suppliers, the usual sizes are approximately 10,15, 25, 40, 50, 65, and 85 cm (3.9, 5.9, 9.8, 15.7, 19.7, 25.6, and33.5 in.).

From an investment point of view, the total installationcost depends on the number of hydrocyclones, the materi-als of construction and lining, the type of radial header, thelevel of automation (manual versus automatic valves), and soforth. Figure 14.3-54 simply indicates the approximate costof a single hydrocyclone and demonstrates the usual spreaddepending on whether lesser or more expensive materials areemployed.

ACknoWleDgMenTSAll gures and tables not specically referenced are includedcourtesy of Metso Mining. The authors extend their most sin-cere thanks to Derrick Corp., Weir Minerals, FLSmidth Krebs,and our many colleagues at Metso Mining who provided muchof the information contained herein, as well as some veryhelpful feedback.

ReeRenCeSAllis Chalmers. n.d. Theory and Practice of Screen Selection.

Allis Chalmers Technical Note.Aquino, B., and Vizcarra, J. 2007. Re-engineering the metal-

lurgical processes at Colquirjirca mine. Sociedad Mineral

El Brocal S.A.A., Mineria, Peru, October. pp. 30–38.Arterburn, R. 1982. The sizing and selection of hydrocyclones.

In Design and Installation of Comminution Circuits. Edited by A.L. Mular and G.J. Jergensen. Littleton, CO:SME. pp. 592–607.

Bothwell, M.A., and Mular, A.L. 2002. Coarse screening.In Proceedings of Mineral Processing Plant Design,

Practice and Control , Vol. 1. Littleton, CO: SME. pp. 894–916.

Delgadillo, J., and Rajamani, K. 2007. Exploration of hydro-cyclone designs using computational uid dynamics. Int.

J. Miner. Process. 84:252–261.

Flintoff, B., Plitt, L.R., and Turak, A. 1987. Cyclone modeling:A review of present technology. CIM Bull. (September):39–50.

Hilden, M.M. 2007. A Dimensional Analysis Approach tothe Scale-up and Modelling of Industrial Screens. Ph.D.

Thesis, University of Queensland, Australia.Karra, V.K. 1979. Development of a model for predicting

screening performance of a vibrating screen. CIM Bull .(April): 167–171.

Kelly, E.G., and Spottiswood, D.J. 1982. Introduction to Mineral Processing. New York: John Wiley and Sons. pp. 200–201.

King, R.P. 2001. Modeling and Simulation of Mineral Processing Systems. Boston: Butterworth-Heinemann. pp. 81–125.

Krebs Engineers. 2000. Krebs gMAX™ Cyclones—For Finer Separations with Larger Diameter Cyclones. www.krebs.com. Accessed September 2009.

Mainza, A., Powell, M., and Knopjes, B. 2004. A compari-son of different cyclones in addressing challenges inthe classication of the dual density UG2 platinumores. In Proceedings of the First International PlatinumConference “Platinum Adding Value.” Sun City, SouthAfrica: SAIMM. pp. 341–348.

Mathews, C.W. 1985. Screening. In Mineral Processing Handbook . Edited by N.L. Weiss. Littleton, CO: SME. pp. 3E1–3E13.

Mohanty, M., Palit, A., and Dube, B. 2002. A Comparativeevaluation of new ne particle separation technologies.

Miner. Eng. 15(10):727–736.Moon, D. 2003. Understanding screen dynamics for opti-

mum efciency. Presented at the 34th Conference of the

Institute of Quarrying Southern Africa, March.Olson, T., and Turner, P. 2002. Hydrocyclone selection for plant design. In Mineral Processing Plant Design, Practice and Control , Vol. 1. Edited by A.L. Mular, D.N.Halbe, and D.J. Barratt. pp. 880–893.

Renner, V., and Cohen, H. 1978. Measurement and the inter- pretation of size distributions within a cyclone. Trans. Inst. Chem. Eng. 87:C139–C145.

Schmidt, M., and Turner, P. 1993. Flat bottom or horizontalcyclones—Which is right for you? World Min. Equip. (September): 151–152.

Svarovsky, L. 2000. Solids–Liquid Separation, 4th ed. Boston:Butterworth-Heinemann. pp. 191–245.

Valine, S., and Wennen, J. 2002. Fine screening in mineral

processing operations. In Mineral Processing Plant Design and Control . Edited by A.L. Mular, D.N. Halbe,and D.J. Barratt. Littleton, CO: SME. pp. 917–928.

Vince, A. 2007. Improved Classication at 100–350 Microns.Australian Coal Association Research Program (ACARP).www.acarp.com.au/abstracts.aspx?repID=C15051.Accessed September 2009.

Wedeles, M. 2007. Smart cyclone: A tool for optimizingcyclone operation. Presented at SAG 2007, Vina del Mar,Chile (also available from FLSmidth Krebs).

Wennen, J., Nordstrom, W., and Murr, D. 1997. National SteelPellet Company’s secondary grinding circuit modica-tions. In Comminution Practices. Edited by S.K. Kawatra.Littleton, CO: SME.

100

100,000

10,000

1,000

A p p r o p r i a t e C o s t , $

Hydrocyclone Diameter, cm

1 10010

ur 14.3-54 Tpca drcc prc

143462729 52642 093 Chap 14 3 Classification by Screens and Cyclones[1]

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Transcript of 143462729 52642 093 Chap 14 3 Classification by Screens and Cyclones[1]