Feed Concentrate Tailing Middling Chapter 17. Metallurgical Process Assessment 17. INTRODUCTION The objective of all mineral processing operations is to concentrate the minerals of interest and reject the unwanted material associated with the ores. The process is often complex as seen in the previous chapters since minerals exist both physically and chemically combined with each other. Ideal clean separation of the mineral from the unwanted fraction, known as gangue or tailings, is therefore almost impossible. In the process of separation therefore a third fraction appears which is a mixture of the gangue constituents and the minerals of interest. This fraction is known as the middlings and is retreated to recover as much of the valuable mineral as possible to increase recovery but at the same time maintain a high product grade. On repeated treatment, some of the middlings finds their way to the concentrates and some report to the tailings. Thus both the concentrate and the tailings are diluted resulting in a loss of grade of the concentrate. To what extent this loss of grade can be accepted would depend on the economics of the process. The scheme of operation usually followed is represented by Fig. 17.1 where it can be seen that the middlings fraction could be repeatedly treated to recover some mineral of interest that is relatively less contaminated with the gangue minerals. Each stream has therefore to be assessed to determine the mass and the concentration of the mineral of interest. This chapter deals with the method of assessing the distribution of minerals in the concentrate, middlings and tailings streams and their recovery. 17.1. Analyses of Constituents The first step in analyzing the constituents of each stream is to obtain representative samples of the streams. The methods of sampling, the sample size and the errors involved Feed Fig. 17.1 Production of concentrate, middling and tailing streams.
Transcript
Feed
Concentrate
Tailing
Middling
Chapter 17. Metallurgical Process Assessment
17. INTRODUCTION
The objective of all mineral processing operations is to concentrate the minerals of interestand reject the unwanted material associated with the ores. The process is often complex asseen in the previous chapters since minerals exist both physically and chemically combinedwith each other. Ideal clean separation of the mineral from the unwanted fraction, known asgangue or tailings, is therefore almost impossible. In the process of separation therefore athird fraction appears which is a mixture of the gangue constituents and the minerals ofinterest. This fraction is known as the middlings and is retreated to recover as much of thevaluable mineral as possible to increase recovery but at the same time maintain a high productgrade.
On repeated treatment, some of the middlings finds their way to the concentrates and somereport to the tailings. Thus both the concentrate and the tailings are diluted resulting in a lossof grade of the concentrate. To what extent this loss of grade can be accepted would dependon the economics of the process. The scheme of operation usually followed is represented byFig. 17.1 where it can be seen that the middlings fraction could be repeatedly treated torecover some mineral of interest that is relatively less contaminated with the gangue minerals.
Each stream has therefore to be assessed to determine the mass and the concentration ofthe mineral of interest.
This chapter deals with the method of assessing the distribution of minerals in theconcentrate, middlings and tailings streams and their recovery.
17.1. Analyses of ConstituentsThe first step in analyzing the constituents of each stream is to obtain representative
samples of the streams. The methods of sampling, the sample size and the errors involved
Feed
Fig. 17.1 Production of concentrate, middling and tailing streams.
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have been discussed in Chapter 1. Correct representative sampling is a challenge. Inindustrial large scale continuous operations, where the streams are ever changing, sampling iseven more difficult. At best a large number of samples provide data for an average value.
Initial qualitative assessment of the raw material that forms the feed stream to a separatingprocess is done by identifying the minerals present under an optical microscope. To get abetter idea, X-Ray diffraction (XRD) and X-Ray Fluorescence (XRF) analysers are employed.These provide quantitative analysis of elements in the rock sample. The nature ofinterlocking of minerals in rocks and grains is normally assessed by examining polishedsections of the rock particles under an optical and/or electron microscopes which can beoperated at large magnifications (from 5,000 to more than 10,000 times magnification iscommon). For observing, the distribution of elements within a grain, polished sections areexamined by Scanning Electron Microscope. The Electron Probe Micro-analyser helps toquantify the distributions of different elements within a grain. Recently Scanning TunnellingMicroscopes have been tried to examine individual atoms on the surface while Time of Flight- Secondary Ion Mass Spectrometers (ToF-SIMS) can analyse surface atoms from eithermineral surfaces or adsorbed species. These instruments provide a means of understandingthe complexities of separation of minerals and also indicate the possibility of liberation orotherwise. These assessments are essentially in the dry state and on small samples.
For estimating quantitatively the presence of elements in continuous operating stream, wetanalytical chemical methods are most reliable. However, this is a slow process. To speed upthe determinations and to get an equally reliable result Atomic Adsorption Spectro-photometers or Inductively Coupled Plasma atomic emission spectrometers are used where asolution containing the metal ion of interested is aspirated in a flame (AAS) or a plasma (ICP)in which the metal ion is converted into a free atom vapour. A monochromatic light beam isdirected through the flame and the amount of radiation of a specific energy level is detected.This electron energy level is specific for an element which helps to identify it. A calibrationcurve with known amounts of the element and flame intensity helps in quantifying thepresence of each element.
In operating plants where analytical results are required with least delay, attempts havebeen made to analyse the composition in situ while the process is in progress. Both dry andwet methods have been attempted with varying degrees of success. For example, in the ironore industry, the iron (Fe) content of the ore is examined as it travels on the conveyor belt.The Fe- content is determined by using a neutron-capture, y-ray transmission and pairproduction technique. In this method, the ore is irradiated by Ra 26 y-radical placed at thebottom of a conveyor belt. This produces electron-positron pairs. The intensity of the pairproduction is related to the iron content. Tests by Aylmer, Holmes and Rutherford [1] indicatereliable results are possible with iron ore streams.
In wet streams, as in grinding circuits, continuous quantitative analysis of more than oneelement in a stream is obtained by the use of On-Stream or In-Stream analysers. Here a radio-active source is used to irradiate elements present in a stream (or slurry). Several elementscan be detected and quantified simultaneously. For details, any text book on instrumentalanalysis can be consulted.
In some operations the feed stream is from a single supply of ore from one mine whensampling and assaying is relatively easy, but in most cases ores from several sources form thefeed to a process. In such circumstances either each source is separately sampled and blendedat pre-arranged proportion (according to grade and availability) or a composite sample isanalysed.
It is a general experience that in industry a sampling error of ± 2% is acceptable.
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17.2. Definition of TermsWe need to be clear about the definition of terms used in assessing the different streams in
a process.
17.2.1. Mass or WeightThe weight of an object is the effect of gravity acting on the mass of the object and is equal tothe mass x gravitational acceleration = M g. Therefore the weight of an object will changedepending on the value of g which will change depending on the geological location of theobject. In outer space for example, objects are weightless. The object in outer space willhowever still have mass and though weightless, a heavy object will require a larger force tomove it than a lighter object. Back on earth, the object on a spring balance will record theweight of the object. A larger gravitational acceleration as experienced at sea level comparedto a mountain top for example, will extend the spring more recording a larger weight for thesame object mass. The same object on a knife edge or double pan balance will record themass of the object as the influence of gravity is negated by the equal force acting on thesecond pan of standard masses. On a single pan electronic balance, the object's mass is alsorecorded as the influence of gravity is compensated for electronically. Since mass is theabsolute measurement and weight is variable and mass is the usual quantity measured on mostbalances, unless using a spring balance, this text will refer to mass exclusively.
In a mineral processing operation, the throughputs and capacities of units are expressed astonnes/h or tonnes/day. These tonnages invariably refer to the dry tonnes passing through aprocess even if the process is treating a slurry of solid and water. This is principally due tothe fact that it is the solid that contains the valuable mineral and hence the mass of thiscomponent is of the most concern.
77.22 SlurryA slurry is a suspension of solids in a liquid. It is also referred to as pulp. In themetallurgical industry, the liquid is almost always water. The concentration of solids in aslurry, C, is expressed as:
C = Massof solids i n s l u n y ^ ( m )^ ( m )
Mass of solids in slurry + Mass of liquid
It can also be expressed on a volumetric basis (mass = volume x density) and is oftenreferred to as percent solids usually by mass by also by volume. Thus the % solids of theslurry can be written as:
C = %S = — xlOO (17.2)Ms +ML
Thus a 30% solids slurry by mass means 30 g (or kg or tonnes) of solids in 70 g (or kg ortonnes) of water.
The concentration may also be expressed as per cent solids in the slurry, that is, if %S isthe percent solids by mass in the slurry and PSL and ps the densities of the slurry and solids, itfollows that in a slurry:
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1. volume fraction of solids = SL (17.3)100 P s
( l00p,-%Sp s , )2. volume fraction of water = - — ^^- (17.4)
100 ps
That is, "SPsL + ( 1 0 ° P S - * S P » L ) = L Q
100 ps 100 ps
and
0/o _ 100 PS(PSL-PL)- -. r
PSL(PS-PL)100p,p, M,+M,and pSL = - t -^t — = _ s L n7_5)
pL%S + (l00-%S)ps VS+VL J
The mass of 1 litre of slurry = PSL x 10"3 kg for density in units of kg/m3. (17.6)
The percent solids in a slurry will most often be quoted as mass % rather than volume %since mass is the property of main concern. Percent solids in some plants is also referred to aspulp density, though in reality the two terms mean different things as shown in Eqs. (17.2)and (17.5). The reader should be careful to make the distinction.
The specific gravity of common solids, at different solid-water ratios are given inAppendix A-l and the pulp properties given in Appendix A-6.
17.2.3. GradeGrade refers to the concentration of a mineral in a stream and is expressed as a percentage. Itis determined by chemical assaying and may be expressed as:
_ , Mass of Mineral constituent in a stream , „„ , , _ ~Grade = xlOO (17.7)
(Mass of Mineral + Mass of gangue) in the stream
For a number of ores, such as base metal ores, grade is quoted in terms of the containedmetal rather than the mineral.
17.2.4. RecoveryRecovery describes the amount of mineral or metal of interest that is present in theconcentrate in relation to that present in the feed stream. This is usually expressed as apercentage and written as:
Mass of mineral or metal in the concentrate stream „„Recovery = xlOO (17.8)
Mass of mineral or metal in the feed stream
Thus if we take 100 kg of a feed stream containing 2.5% nickel and if 20% by mass of thefeed stream forms the concentrate, then the mass of concentrate is 20 kg. If the grade of
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nickel in the concentrate equals 10%, then 20 kg of concentrate will contain 0.1 x 20 = 2 kgnickel. Hence Ni recovered is 2/2.5 x 100 = 80% by mass.
17.2.5. DistributionThe concept of distribution can be seen from the following illustration. In the above exampleonly 80% of the mineral present has been accounted for in the concentrate, the rest of themineral must be in the tailings, neglecting the existence of a middling product. Since the massof the concentrate is 20 kg, then the mass of the tailings must be 80 kg. Let us assume thatchemical analysis indicated that the nickel in the tailings was 0.6%. The nickel distributionbetween the concentrate and tailing product streams is then calculated as illustrated in Table17.1.
Table 17.1Metallurgical statement of the distribution of nickel between the streams
Stream Mass of stream, kg Ni Assay, % Mass of Ni DistributionM A MxA MA/£(MA)
Thus 80% of nickel has been recovered into the concentrate and 19.2% lost in the tailings.Table 17.1 is almost an ideal case as such clear separation is never possible in mineral
processing operations. A fraction invariably appears as middling. The distribution in themiddlings fraction is determined in the same manner as described above. That is, theanalysis of metal in all the streams is ascertained and the distribution calculated. Provided theassays of the streams are accurate then the distribution or recovery in each of the streams willbalance or add up to 100%. In Table 17.1 the total distribution of nickel adds up to 99.2% asa result of sampling or assay errors.
17.3. Material BalanceMaterial balance estimations is one of the most useful and powerful methods of assessing unitand integrated operations. It is used to calculate recoveries and distributions of valuablecomponents at the end of the monthly accounting period or for estimating quantities instreams (mass or assay) that can't be easily measured. The results from a mass balance isstrongly influenced by the accuracy of stream sampling and assaying. Where difficulties arisein the balancing of a circuit the it is usually one or both of these factors that should be suspect.Streams that are difficult to sample (e.g. cyclone underflow) or difficult to assay (e.g. lowvalue streams such as tailing streams) need special attention. Mass balancing described herein only basic as the complexity in balancing increases with more complex circuits and recyclestreams and with less information from sampled streams. The modern spreadsheetprogrammes are idea for these calculations and specialised mass balancing programs such asJKMetAccount, JKSimMet, Limn and USBC are available for complex calculations.
The basic principle involved is the conservation of mass. For a process at equilibrium orsteady state, it can be expressed as:
mass input in all streams to a unit or circuit =mass output in all streams from a unit or circuit (17.9)
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However, in actual practice, during a continuous operation, a steady state is difficult tomaintain with feed variations and process hiccups. Therefore it will be more correct torewrite Eq. (17.9) as:
mass input in all streams to a unit or circuit = mass output in all streamsfrom a unit or circuit ± holdup within a process (17.10)
The units are in mass or mass rates, either of the total material or of the constituent ofinterest, that is:
mass input in all streams of component i = mass output in all streams ofcomponent! ± holdup of component! within a process (17.11)
Water can be one of the constituents used in a mass balance for a wet process. In a sizeseparation unit such as a screen or classifier the mass in specific size fractions can be used ascomponents in a mass balance.
For a material balance to provide meaningful data, several samples need to be taken andthe variance of errors to be established. Errors originate not only in the procedure ofsampling but also in the method of measuring. Napier-Munn et al [2] suggests that:
1. Error = 1% for > 9% (by mass) in a V2 size fraction.2. Error = [0.1+ actual %] x 10'1 for < 9% (by mass) in a V2 size fraction.
Where the mass balance of multi-component system is concerned, the error of eachcomponent is more difficult to establish. For an acceptable representative stream, the sum ofthe squares of errors in each size fraction should be minimum. This would give the best fit ofmass split.
Consider the two product process in Fig. 17.2 at steady state. In the metallurgicaloperation a feed, F, containing a size i is split into two products with the underflow (classifier)containing the mass fraction C and (1-C) going to the overflow. C is the mass split to theunderflow (underflow mass/feed mass) and (1-C) the mass split to the overflow (overflowmass/feed mass). Also let the mass fraction of size i in the feed, underflow and overflowstreams be m, (F> m; (uj and m* (o) respectively, then according to Napier-Munn et al. [2] themass-balance error (Ai) of each size fraction, (here size i), will be given by:
Feed Operation
Overflow
Underflowt
C,
Fig. 17.2. A two product separation process
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A, =m i C F ) -Cm i ( U ) - ( l -C)m i ( 0 ) (17.12)
The errors in each stream will not be the same but will have to be determined against thevariance of each size fraction. The best fit, C, to the underflow is:
Lti(O) ~ mi(U) ) (mi(F) ~ mi(O)
C = - -i ^ 2 (17.13)v(mi(O)-mi(U))
where cjj is the standard deviation for the particle size i over a number of samples from thefeed. Eq. (17.13) accounts for errors in each input stream, after which estimates of recoverycan be made reasonably accurately.
17.3.1. Two Product FormulaIn an operation where the interest is to recover a mineral in a single concentrate, the set up isusually called a two product system, producing one concentrate and one tailing stream. Tocalculate the recovery of the metal or mineral, the material balance method is applied. Theresulting formula is known as the Two Product Formula [3].
To derive the formula let us assume that in an operation, samples are taken simultaneouslyfrom feed, concentrate and tailing streams and that the weighted average corrected analysis ofeach stream is:
1, Feed stream
Feed mass = M^, andmineral assay in the feed =
2. Concentrate stream
Concentrate mass = M(Q, andmineral assay in the concentrate = A(Q
3. Tailings stream
Tailings mass = M(D, andmineral assay in the tails = A<T)
For a two product process, the material balance will be:
Input mass of feed = Output mass of concentrate + Output mass of tailings.
That is: M(F) = M(C) + M m (17.14)
Similarly for the component metal:
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(17.15)
From Eqs. (17,14) and (17.15), Mg) can be eliminated by multiplying Eq. (17.14) by ATand subtracting the result from Eq. (17.15), thus:
Eq. (17.17) can also be written in terms of tailing mass by eliminating the concentrate massfrom Eqs. (17.14) and (17.15).
By definition, Eq. (17.8), recovery R = (C) (C) x 100M(F)A(F)
—A \A.and from Eq. (17.17), R = j - ^ 0 2 L J 5 . x ioo (17.18)
Eq. (17.18) is applicable in any plant or laboratory situation where two products are involvedin an operation. This is illustrated by the Example 17.1
Example 17.1A gold ore containing 20 ppm gold was fed to a ball mill in a concentrator at the rate of 200t/h. The concentrate analyzed 400 ppm and the tailings 0.15 ppm Au. Calculate the recoveryand distribution of gold.
SolutionSteplThe given data indicates: A(F) = 20 ppm, A(Q = 400 ppm and Afr) = 0.15 ppm and M(F)200 t/h. The concentrate mass, M(Q is unknown but can be determined using Eq. (17.17),
Step 3The distribution of gold in the streams is best illustrated in the following table:
Stream
FeedConcentrateTailings
Mass.Mt/h200
99.94100.06
Gold assay,A,ppm
2040
0.02
M x A
40003997.6
2.00
Recovery orDistribution,%
10099.90.1
The units of assay can be any mass based concentration unit as long as the same unit is usedthroughout, e.g. ppm, g/t or mass%.
17.3.2. Three Product FormulaWhen a process produces three output streams such as an additional middling or secondconcentrate stream, then the mineral or metal distribution can be calculated using the sameprinciple as that of the two product formula. Such situations frequently occur in metallurgicalplants. The recovery formula is generally known as the Three product formula [3].
To illustrate the method, the presence of only two metals, (A and B) is considered here fora metallurgical circuit involving crushing, grinding, classification and flotation. In each unitprocess, the feed is considered as the concentrate from the previous process. Let us assumethat the masses and concentrations of the minerals (metals) in the three streams are as given inTable 17.2
Table 17.2Nomenclature for a three product process
Considering the overall material and metal balances of the system the following equationsapply:
= M(ci) + M(C2) + M(T) for the overall mass balance (17.19)M{F)AA(F) = M(cDAA(ci)+M{C2)AA(C2) + MmAA(T) for component A (17.20)M(F)AB(F) = M(CI)AB(CI)+M(C2) AB(C2) + M(T} AB(T) for component B (17.21)
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As before eliminating T from the Eqs. (17.20) and (17.21) the value of M(ci> will be given by:
M(c2) _ v^A(F) ^A(T) j(AB(Ci) AB ( T ) j (A^pj AB(T)J^AA(C1) AA(T)J
A A ( T ) J^AB(C1:) A B ( T ) jM(;
The recovery of metal A in concentrate 1 will be = A(C1) (C1) x 100 (17.24)AA(F)M(F)
and the recovery of metal B in concentrate 2 will be - B(C2) (C2) x 100 (17.25)A M
The application of the method is best understood by Example 17.2
Example 17.2A copper-zinc ore was fed to an integrated mineral processing system at the rate of 250 t/h.The final products were a copper concentrate and a zinc concentrate and tailing. Analysis ofeach stream were:
Stream
FeedCopper concentrateZinc concentrateTailings
%Cu25.078.22.10.7
Assay%Zn3.16.355.40.8
Determine the mass flows in the two concentrate streams and the recovery of metal in eachproduct stream.
SolutionSteplTo determine the masses of copper and zinc concentrate streams, Eqs. (17.22) and (17.23) canbe directly applied. Thus:
nrn (25-0.7)(55.4-0.8)-(3.1-0.8)(2.1-0.7)Mass of copper concentrate = 250 x
Mass of zinc concentrate = (25.0-0.7X6.3-0.8)-(3.1-0.8X78.2-0.7) _ 2 f i 1
(2.1 - 0.7X6.3 - 0.8) - (55.4 - 0.8X78.2 - 0.7)
Step 2
Recovery of copper = 7 8 - 2 x 7 8 - 4 x l 0 0 = 9 8 Oo/0
25.0x250
2 64 x55 4and Recovery of zinc = — —xlOO = 18.9%
250x3.1
A spreadsheet such as MS Excel can be used to calculate the distributions in each streamsand Solver can be used to estimate the concentrate masses without using the three productformulae above. A simple spreadsheet to do this is shown below.
12345B7e910111213141516171B19
A B C D
Stream
Feed0 nnZn Con
Tail
Mass
250.07S 3
* 2Br m-<n
/Fitted using Solver
E
Cu Assay
25.078.22.10.7
F
Zn Assay
3.16.3
55.40.8
2.76=-06| 7.63E-12-B.7E-06
T
7 64E-11B.4E-11
G
MxA fCu)
6250.0
G12G.15.5
11B.3
H
MxA (Zn)
775.0433.5146.2135.2
square ofdifference
4
I
RecoveryCu
100.09B.00.11.9
J
RecoveryZn
100.0 k
G3.71B.917.4
K
Vz\\\Sum of recoveriee
Sum of square of difference
difference in total recovery and 100%
Cells D6, D7 are the unknown concentrate massesCell D8 is the feed minus the concentrate masses
Recoveries in cells 16:J8 are calculated in the same manner as in Table 17.1. The sum ofthe recoveries in the concentrates and tailing should add up to 100% as in cells 15, J5. If thesystem is not balanced, the sum of the recoveries will be different from 100% and thedifference is calculated in cell El4 for copper and cell El5 for zinc. These differences aresquared in cells F14:F15 to remove negative numbers and the sum of the squares in cell F16is minimised using Solver and cells D6 and D7 as variables. The Solver solution is shown inthe above spreadsheet and the recoveries or distribution of copper and zinc calculated in cellsI6:J8.
Example 17.3A lead-zinc ore was treated at the rate of 100 t/h to an integrated system to produceconcentrates of lead and zinc minerals. A closed circuit was chosen so that the middlingproduced was re-treated. The average lead and zinc concentrations in each stream were:
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Stream
FeedPb. ConcentratePb tail ( head of zinc )Zn concentrateTails
Assay,Pb. Stream,%
1.882.00.5
29.50.3
AssayZn stream,%
23.52.0
24.077.11.2
Determine the mass flowrates of the product stream and the distribution of lead and zinc.
Solution
SteplUsing the two product formula:
Mass of Pb Concentrate = 100 x(1.8-0.5)
(82.0-0.5)= 1.60 t/h, using the lead assays
and(23.5-24.0)
= 100 x -̂ 7—:—: ^ = 2.27 t/h, using the zinc assays
Mass of Zn concentrate =
(2.0-24.0)
x (24.0-1.2)(100-1.6) x-; —:(- = 29.55 t/h, using the zinc assaysV ; (77.1-1.2) B J
or(0.5-0.3)
(100 -1.6) x 7 f = 25.56 t/h, using the lead assays(1.0-0.3)
A judgement will need to be made as to the reliability of the analytical techniques and/orthe sampling procedures before deciding on the accuracy of the calculated values.
Step 2The distribution of the metals is calculated in a similar manner to Table 17.1 and Example17.2. The results is shown in the following table. The calculated feed or head assay is a goodmeans of checking the balance if a measured head assay is available.
Stream
FeedPbConZnCon
Tail
Masst/h
100.01.60
29.5668.8
**** Calculated head
Pb Assay%1.8
82.01.00.31.81
Zn Assay%
23.52.0
77.11.2
23.6
MxA(Pb)t/h
180.0130.829.620.7
181.0
MxA(Zn)t/h
2350.03.2
2279.182.6
2364.9
RecoveryCu,%100.672.716.411.5
RecoveryZn,%100.6
0.1497.0
3.5
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17.4. Circulating LoadThe premise in the methods of assessing the streams so far has been that the circuits were
open, that is, maximum product was obtained at reasonable rates in the concentrate. In actualpractice it is found that all concentrate do not satisfy the required specifications of size andconcentration. Hence the concentrate has to be treated to separate the unwanted fraction. Theout of specification fraction is submitted for further separation by passing on to downstreamprocesses or by adding it to the original feed. In the latter case, a continuous circulating loadis set up in the system as illustrated in Fig 17.3. The recirculation operation results inimproved recovery and grade. Fig. 17.3 illustrates such a situation for a simple grindingcircuit where the coarse underflow fraction from the classifier is circulated for retreatmentwhile the overflow fine fraction is the product. The circulation ratio CR is defined as the ratioof the flowrates of the circulating stream to the flowrate of the new feed to the mill, which atsteady state is equal to the fine product leaving the circuit.
CR = Circulation Ratio, CR = — x 100 (17.26)
When a classifier returns the coarse fraction of its feed material to the mill, then the totalload to the mill is increased and is the sum of the new feed stream plus the coarse returns.Thus in a closed circuit system the circulating load CL according to Austin et al [4] is definedas:
Rate of new feed + Amount recycled=
Rate of new feedx 100
= 100Amount recycledRate of new feed
xlOO (17.27)
NewFeed,Q
Overflow (fines), Q
Classifier
Underflow(coarse), T
Fig. 17.3. Circulating stream in a closed circuit grinding/classification circuit.
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This can be written as:
CL=100 (17.28)
The circulating load CL and the circulation ratio CR are both expressed as a percent. Thereis some confusion by different authors between the circulation ratio and the circulating load.The circulating load in slurry streams is not easily measured without instrumentation such asdensity gauges and flowmeters and hence is usually calculated by mass balancing. For acomminution circuit closed with a screen or classifier, a mass balance can be performed onthe masses in individual size intervals around the size separator or on the cumulative massespassing or retained at a given size. If individual size intervals are used then a weightedaverage should be performed on a number of size intervals.
Bond [4] considered the circulating load associated with two general circuit configurations.In the first (Fig. 17.3) the stream returning from the classifier is to the mill feed. In thesecond (Fig. 17.4) the new feed is classified first and the oversize material sent to the grindingmill.
In both cases the same general formula applies. By a balance of the mass in size interval i,the circulating ratio in the classifier circuit shown in Fig. 17.4 is given by:
Circulating load (CL) =(Classifier under size - New feed to circuit)
(Feed to classifier - Classifier over size)xlOO (17.29)
Thus if mi (F> = mass fraction of size i in the feed to the circuit,nij (CF) = mass fraction of size i in the feed to the classifier,mi (u) = mass fraction of size i in the classifier undersize,mi (o) = mass fraction of size i in the classifier oversize andnij (D) = mass fraction of size i in the mill discharge,
then the circulating load for the circuit in Fig. 17.4 can be written as [4]:
Feed
_ .̂ Product, fines or undersize
Classifier
water
Coarse or oversizeO, m i (o)
Mill
MilldischargeD, f l i (D)
Fig. 17.4. Grinding/classification circuit with recirculating stream.
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c - £ mi{CF) ~ mi(U)
m i (0) mi(CF)
zz
m j (F)-] Ji(CF)
m - m i (
(17.30)
In the case of the circuit in Fig. 17.4, the mass passing through the mill and the massrecirculating in the cyclone underflow are the same, hence the circulation ratio and circulatingload will be the same.
For the circuit in Fig. 17.3, the circulating ratio, by a similar mass balance of size fractionswill be:
CR =m i ( U ) - r
m:fn\ ~xlOO (17.31)
To determine the circulation ratio CR, it is usual to determine the water to solid ratios ofthe streams (masses can also be taken), by taking simultaneous samples for the same duration.Considering the water/solid ratio, R, for the different streams as in Fig. 17.4 and:
RF = New feed,RD = Mill discharge,RCF = Feed to classifier,RQ = Classifier oversize, course stream,Ru = Classifier undersize, fines stream.
Then applying Bond's concept, the circulation load would be:
cK= (Ro - RD ) ( CF - Ro )(17.32)
When more than one circulating load is operating in an integrated circuit, the massbalances have to be established for each circuit.
Example 17.4 and 17.5 illustrates the methods of determining circulating load with andwithout the knowledge of the size distribution of solids in each stream.
Example 17.4An integrated circuit consisted of a crusher, grinding mill and a classifier. The circuitproduced 4800 t of ground ore per day. The underflow from the classifier was returned to themill for re-grinding. The classifier feed contained 45% solids (by mass) and the classifierunderflow and overflow streams contained 80% and 20% solids respectively. Calculate thecirculation ratio and the circulating load.
SolutionSteplDetermine the liquid/solid ratios in each stream.
Step 2Eq. (17.32) may be used to determine circulation ratio CR:
(4.0-1.22)Circulating ratio =•? 4r = 2.33x100 = 233%
(1.22-0.25)
Circulating load = 100 + CR = 100 + 233 = 333%
Example 17.5A rod mill was integrated with a hydrocyclone and produced a grind at the rate of 250 t/h.Samples taken simultaneously from the discharge of the rod mill and the overflow andunderflow streams from the hydrocyclone gave the following results. Calculate thecirculating ratio and circulating load.
Screen Size
-4.0 mm-4+2 mm-2+lmm
-100+420um-420+210 urn-210+105 um-105+74 urn
-74 um
RodMass %
2.040.46.35.116.619.05.55.1
MillCum%
2.042.448.753.870.489.494.9100.0
Hydrocyclone O/FMass %
0.00.21.815.621.220.425.015.8
Cum%
0.00.22.017.638.859.284.2100.0
Hydrocyclone U/FMass %
36.015.28.15.113.818.52.80.5
Cum%
36.051.259.364.478.296.799.6100.0
SolutionSteplLet us choose arbitrarily the following three sizes: -4 +2.0 mm, -1000 +420 um,-210 +105 um instead all the eight sizes, to illustrate the principle of calculations.
Step 2Calculate the circulation ratio for each screen interval chosen. Thus
For size -4.0+2.0 mm42.4-0.251.2-42.4
620620
For size -1000+420 urn CR = 53"8 17"6 = 3.4164.4-53.8
eo 4_5O ?For size-210+105 urn CR = =4.13
^ 97.6-89.4
Average CR for the sizes = 4.11 = 411%
The circulation load is then = 100 + 411 = 511%
A practical but rapid and approximate method to determine the circulating load in agrinding mill and classifying circuit is suggested by Barber-Greene[5]. The procedure is todetermine the percent (by mass) of -200 mesh in the classifier feed (mill discharge) andclassifier overflow and classifier underflow streams. Then for feed mass flowrate, QF, theclassifier underflow (Fig. 17.3) will be given by:
(17.33)
where Q(o> = Mass flowrate of the classifier oversize (underflow)Q(F) = Mass flowrate of the new feed
= % -200 mesh in classifier undersize (overflow),= % -200 mesh in classifier oversize (underflow),
Other screen sizes could be chosen for the calculation as shown in Example 17.5. Asimilar rapid method can be applied by taking the solid/liquid ratios of the streams as given inEq. (17.32) and individual size fractions as given in Eqs. (17.30) and (17.31).
17.5. Problems
17.1A calcite sample is ground in a mill in close circuit with a hydroeyclone. Samples were takenfrom the feed, overflow and underflow streams and their solid to water ratios determined as2.5, 7 and 0.3 respectively. Calculate the circulating load of the circuit.
621621
17.2An iron ore company milled ore at the rate of 150 t/h in a ball mill in closed circuit with aclassifier. The underflow (course) stream was re-circulated to the mill till a steady value wasobtained in the cyclone overflow stream. The specific gravities of each stream were measuredas:1. Mill discharge stream to classifier = SG(MD)2. Product overflow from classifier = SG(OF)3. Product underflow from classifier = SG(upj
Establish a mass balance and derive an expression for the circulating load.
17.3A copper sulphide ore was crushed and milled in close circuit with a classifier. The overflowfrom the classifier fed a rougher cleaner flotation circuit at the rate of 500 t/h. The ore assayed2.75% Cu. The re-circulating load in flotation circuit was 270%. The overall recovery was76% at a grade of 92%. Calculate:
1. Mass flowrates of the cleaner concentrate and rougher tailings,2. Grade of copper in the rougher tailings.
17.4The screen analysis of feed, product and tailings from a classifier were:
Size, (microns)
85050025012575
Feed %
15.28.533.634.28.5
100.0
Overflow
00
2.965.431.8100.0
Underflow
18.310.239.927.83.7
100.0
The classifier was fed with ground silica at the rate of 50t/h. Estimate:
1. Mass (tonnes) of dry ore per day in classifier underflow,2. Mass (tonnes) of dry ore per day from classifier overflow.
REFERENCES[1] J.A. Aylmer, RJ. Holmes, L. Rutherford, International J. of Nuclear Geo Physics, Pre-
print. Private Communication.[2] T.J. Napier-Munn, S. Morrell, R.D. Morrison and T. Kojovic, Mineral Comminution
Circuits, JKMRC, 1999.[3] B.A. Wills, Mineral Processing Technology, Pergamon Press, Oxford, 1981.[4] L.G. Austin, R.R. Klimpel, and P.T. Luckie, Process Engineering of Size Reduction,
SME/AIME, New York, 1984.[5] F.C. Bond, Mineral Processing Handbook, N.L. Weiss (ed), 1985, p. 3A 23.[6] Barber-Greene, Mine and Smelter Application Guide, Bulletin 820-979, 1979.
