Module4 - Work Index Efficiency

The Metcom Engineering and ManagementSystem for Plant Grinding Operations

MODULE #4:

WORK INDEX EFFICIENCY

Metcom Consulting, LLC© 1992 GPD Co. Ltd. / Metcom Consulting LLC (Rev.4, 2005)

© 1992 GPD Co. Ltd. / Metcom Consulting LLC (Rev.4, 2005)

WORK INDEX EFFICIENCY i

page

Objectives 1Introduction 2Circuit arrangements 3

• Grinding circuits with a single mill 3• Grinding circuits with multiple mills 10• Other circuit arrangements 20

PART I - The Operating Work Index 22

The Bond law of comminution 23The operating work index 24

PART II - Work Index Efficiency 30

Work index efficiency 30Comparison of work index efficiencies 35

• Rod milling 35• Ball milling 41

Accuracy of comparative work index efficiencies 46

PART III - Combined Grinding Circuits 50

Operating work index of combined circuits 50• Rod mill/ball mill circuits in series 51• Ball mill circuits in series 54

Work index efficiency of combined circuits 58• Rod mill/ball mill circuits in series 59• Multiple-stage ball mill circuits 64

Work index efficiency of individual ball mill circuits in series 66Work index efficiency of single-stage ball mill circuits 74

Progress Review 1 81

Closing word 89References 91Glossary 92

TABLE OF CONTENTS


WORK INDEX EFFICIENCY ii

LIST OF FIGURES

page

Figure 1. Rod mill in open circuit. 4Figure 2. Ball mill in reverse closed circuit. 6Figure 3. Ball mill in reverse closed circuit with two

stages of classification. 8Figure 4. Circuit containing two ball mills in parallel. 11Figure 5. The "conventional" grinding circuit. 13Figure 6. Two-stage ball mill circuit . 15Figure 7. Single-stage ball mill circuit. 18Figure 8. Two statistically different measurements. 47Figure 9. Two measurements that are not statistically

different. 48Figure 10. Two Bond ball mill work index tests for ball

mill circuits in series. 68



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OBJECTIVES

In this module, you will learn about work index calculations forevaluating grinding circuit efficiency based on the methoddevelopped by Mr. Fred Bond.

After completing this module, you will be able to:

• Identify the boundaries of various grinding circuit arrangements.

• Calculate the operating work index of a grinding circuit.

• Calculate the work index efficiency of a grinding circuit.

• State the accuracy of comparative work index efficiencies of grind-ing circuits.

• Calculate the operating work index and work index efficiency ofgrinding circuits under various arrangements.

The prerequisite module to this one is entitled "Introduction to the Metcom System". To complete the module, you need a scientific calcu-lator. The estimated time for completion is two and a half hoursincluding one Progress Review at the end of the module.



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INTRODUCTION

You must first establish a basis for measuring the overallefficiency of a grinding circuit. From this basis, you will be able tomeasure and compare the effects of various design and/or operatingvariables on overall circuit efficiency.

When changes occur in a grinding circuit, they may be:

• Intentional, e.g. an experiment with water addition rates; or,• Imposed, e.g. a change in the grindability of the ore.

If you can relate the efficiency of the circuit to specific design and/oroperating variables, you will then be able to justify and implementchanges that will lead to performance improvements. Efficiencymeasurements will also allow you to monitor long-term circuit perfor-mance.

This module presents the Bond method for measuring grinding circuitefficiency. This approach is very useful because:

• It is a well known, widely accepted standard throughout the industry around the world.• It is relatively simple and inexpensive.• It provides the important link to grinding economics. This topic will be covered in the module entitled "Grinding and Plant Economics".

The Bond method relates to the overall performance of grindingcircuits. There are several possible circuit arrangements:

• Grinding circuits with a single mill.• Grinding circuits with multiple mills.• All other circuit arrangements.

Here are some definitions and examples of grinding circuits.



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CIRCUIT ARRANGEMENTS

There are two general designs of grinding circuits with a single mill:open and closed.

Open circuit: The most common example of a grinding mill in opencircuit is the rod mill in open circuit. In this case, thecircuit feed is also the mill feed.

The mill discharge is also the circuit product.See Figure 1.

GRINDING CIRCUITS WITH A SINGLE MILL



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Closed circuit: This circuit may consist of one or more stages ofgrinding and classification in variousarrangements.

In this case, the circuit feed is different fromthe mill feed because of circulating loads. Themill discharge is different from the circuitproduct for the same reason.

Figure 2 shows the most common example of aclosed circuit: the single ball mill in reverseclosed circuit with one stage of classification.

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The circuit shown in Figure 2 is called "reverse" because the ore fedto the circuit goes to the classifier before going to the ball mill. In the"forward" closed circuit, the ore goes directly to the ball mill.

Figure 3 gives an example of a closed circuit with multiple stages ofclassification.

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It is important for you to note the difference between a grinding milland a grinding circuit.

The rod mill and ball mill are grinding units. In general:

• Rod mill and rod mill circuit mean the same thing because the feed and discharge to and from the rod mill are the feed and product to and from the circuit.

• Ball mill and ball mill circuit are distinct. Ball mill feed is generally hydrocyclone underflow. Ball mill circuit feed is generally rod mill discharge. A ball mill circuit normally has both a grinding unit and classification equipment.

The Bond method applies to grinding circuits only, such as thosepresented in Figures 1, 2, and 3. In this context, you must considerany circuit as a black box with only a "feed stream" and a "productstream". The equipment and flowsheet inside the black box areirrelevant.



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GRINDING CIRCUITS WITH MULTIPLE MILLS

Mills in parallel: Grinding is sometimes performed in more thanone mill in a single stage of grinding.

The most common example is that of two ballmills in parallel. See Figure 4.

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Rod/ball mill circuit: This arrangement is also called a "conven-tional" grinding circuit.

It consists of an open-circuit rod mill fol-lowed by a closed-circuit ball mill. SeeFigure 5.

The boundaries of the conventional circuit are at the rod mill feed(circuit feed) and at the hydrocyclone overflow (circuit product).

Let's examine which streams constitute "ore" around aconventional grinding circuit. To help us, let's say that in this circuit,"ore" contains 2% copper. If "ore" is fed to the conventional circuit,then we find "ore" in the:

• Rod mill circuit feed;• Rod mill feed;• Rod mill discharge;• Rod mill circuit product;• Ball mill circuit feed; and,• Ball mill circuit product.

Note that "ball mill feed" and "ball mill discharge" are not on the list:the circulating load in the closed ball mill circuit may not contain 2%copper but more or less depending on the hardness (density, etc.) ofthe copper bearing mineral compared to that of the host rock. Soeven though what goes into the ball mill originates from the "ore", it isnot "ore" but simply a mixture of ore components called "ball mill feedmaterial ".

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Multi-stage ball milling: This is also termed "ball mill circuits inseries".

The circuit boundaries are defined as thefeed to the first stage and product from thelast stage. Figure 6 shows a two-stageball mill circuit.

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Note that the rod mill/ball mill and multi-stage ball mill circuits aresimply a combination of several circuits in sequence.

In general, you will determine the efficiency of both individual andcombined circuits. Therefore either the individual or combinedcircuits may be considered for efficiency calculations.



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Single-stage ball milling: This is a special arrangement in whicha single ball mill is used in place of arod mill and ball mill in series.

The single-stage ball mill does thework of a conventional circuit (rod/ballmill) with one grinding unit. It may alsobe followed by further grinding.See Figure 7.

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All previously described circuits may be further combined as theyoccur in actual plant flowsheets for the purposes of the efficiencycalculations presented in this module.



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OTHER CIRCUIT ARRANGEMENTS

There are a few special cases that will not be addressed in thismodule:

Circuits with multiple feed or product streams: These can nor-mally be handled by calculations that combineor eliminate specific streams.

Ball mills in semi-autogenous grinding circuits: In this case,efficiency calculations require that steps be taken toallow for the specific characteristics of SAG millcircuits.

Regrind mills: Bond work index calculations generally cannot bedirectly applied to extremely fine grinding applica-tions.

Discuss any of these special applications with Metcom.



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Let's turn to Part I of this module where you will learn how to deter-mine the operating work index of a circuit.



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PART I - THE OPERATING WORK INDEX

There are four factors that determine the efficiency of a grindingcircuit. They are:

1. The ore throughput rate ("tonnage") to the circuit.2. The grinding mill energy consumption.3. The circuit feed size and the circuit product size.4. The grindability characteristic of the ore.

For a grinding circuit, the efficiency is directly related to tonnage if theother three factors are constant. For example, if you can increasethe tonnage by 10% while energy consumption, circuit feed andcircuit product sizes, and ore characteristics remain constant, thencircuit efficiency has increased by 10%.

Likewise, if you can reduce energy consumption by 10% while allthree other factors remain constant, then circuit efficiency has in-creased by 10%.

In order to account for changes in circuit feed/product sizes and oregrindability, Bond provided us with his "law of comminution" as fol-lows.



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THE BOND LAW OF COMMINUTION

Bond developed an empirical equation from numerous plantobservations that takes the four factors previously listed intoaccount.

First, Bond determined that a complete size distribution could berepresented by the 80% passing size* , K80* , of a material. Herepresented the circuit feed size distribution by F80 and the circuitproduct size distribution by P80.

Secondly, Bond observed that for a given grinding circuit, thefollowing relationship applies when changes in the circuit feed orproduct size, or mill energy input occurs.

The Bond law of comminution is:

W = Constant x 10 - 10šP80 šF80

Where W = Work (energy) input per tonne of solidsprocessed (kwh/t).

Constant = Work (energy) consumed to grind the ore fromF80 to P80 (kwh/t).

F80 = K80 of the circuit feed (microns).P80 = K80 of the circuit product (microns).

( )

The constant in the equation above is also called the operating workindex* . It is discussed next.



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The operating work index gives an overall measure of theperformance of a circuit in terms of the energy consumed to achievea certain amount of size reduction. When a circuit has a high operat-ing work index, a lot of energy is consumed to achieve a certainamount of size reduction. When the operating work index is low, littleenergy is consumed to achieve size reduction.

If you measure W, F80, and P80 for a circuit, then the constant in theBond equation can be calculated. The constant represents theoperating work index of the circuit; it is labelled Wio.

During a plant survey, the ball mill circuit feed rate was 100.0 drytonnes per hour. The ball mill power draw at the pinion was 900 kw.The size of the circuit feed, F80, was 2100 microns and the size ofthe circuit product, P80, was 85 microns. The operating work index,Wio, for this circuit can be calculated as follows.

During the circuit survey, W, the work input per tonne or ore, wasequal to:

W = 900 kw / 100.0 t/h = 9.00 kwh/t

Using the Bond law of comminution, the operating work index, Wio,can be calculated:

W = Constant 10 - 10šP80 šF80

9.00 kwh/t = Wio 10 - 10 š85 š2100

10.4 kwh/t = Wio

Solve the following exercise.

THE OPERATING WORK INDEX

Example

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Exercise

During a plant survey, the rod mill circuit feed rate was 126.6 drytonnes per hour. The rod mill power draw was 427 kw. The size ofthe circuit feed, F80, was 14 870 microns and the size of the circuitproduct, P80, was 1460 microns.

What was the operating work index, Wio, of this circuit?

The answer follows.



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Answer

18.8 kwh/t

Solution:

The first step is always to calculate W:

W = 427 kw = 3.37 kwh/t126.6 t/h

Using the Bond law of comminution, the operating work index, Wio,can be calculated:

W = Constant 10 - 10šP80 šF80

3.37 kwh/t = Wio 10 - 10š1460 š14 870

18.8 kwh/t = Wio

Solve this second exercise.

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Exercise

Some information on the closed ball mill circuit that follows the rodmill presented in the previous example follows.

Dry tonnage: 126.6 t/hBall mill power draw (at the pinion): 955 kwF80 (rod mill discharge): 1460 micronsP80 (hydrocyclone overflow): 126 microns

What is the operating work index of this circuit?

The answer follows.



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Answer

12.0 kwh/t

Solution: W = 955 kw = 7.54 kwh/t 126.6 t/h

Then 7.54 kwh/t = Wio 10 - 10 š126 š1460

12.0 kwh/t = Wio

You may have noticed that the P80 of the rod mill circuit in the firstexercise equals the F80 of the ball mill circuit in the second exercise.The data used in both exercises came from a circuit survey donesimultaneously on the rod mill and ball mill circuits.

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When the value of the operating work index is high, a lot of energyhas been consumed to achieve a certain amount of size reduction. Ifthe ore becomes more difficult to grind, the measured operating workindex will also increase. If the circuit becomes less efficient, theoperating work index will increase again.

Since circuit feed and product sizes are taken into account in theBond equation, the value of the operating work index reflects twothings:

1. The grindability of the ore.2. The efficiency of the grinding circuit.

In order to determine the efficiency of the grinding circuit, it is neces-sary to factor out the grindability of the ore.

Bond has provided us with some "standard" laboratory tests whichallows us to factor out the grindability of the ore from the operatingwork index. This process analysis gives us the work indexefficiency* of a grinding circuit. This topic is covered in Part II of themodule.



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Bond used standard laboratory test procedures to determine thelaboratory test work index of ores. There are two standard tests:one for the size reduction range of solids in rod mill circuits (Bond rodmill test) and one for the size reduction range of solids in ball millcircuits (Bond ball mill test).

The Bond grindability tests are locked-cycle laboratory tests. Closed-circuiting is achieved using a sieve opening size that yields a testproduct size which is close to the plant circuit product size. Youwill learn how to perform these tests in the module entitled "BondGrindability Tests".

Once you can factor out the characteristics of the ore from theoperating work index, you can get the work index efficiency, Eff (WI),of the grinding circuit:

Eff (WI) = Bond work index of the ore (kwh/t) (%) Operating work index of the circuit (kwh/t)

Work index efficiency is a relative value and is not restricted to amaximum of 100%. It can be greater than, equal to, or less than 100%.

When the work index efficiency of a circuit is 100%, the circuit isperforming exactly as predicted by the Bond scale-up method forcircuit design: the Bond laboratory work index of the ore exactlyequals the operating work index of the circuit.

Work index efficiency will be below 100% if the circuit is using moreenergy to reduce the ore than indicated by a Bond test. Similarly,work index efficiency will be above 100% if the circuit is using lessenergy to reduce the ore than indicated by a Bond test.

PART II - WORK INDEX EFFICIENCY




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Note

You may be aware of certain "correction factors" that are applied tothe Bond work index of the ore for sizing a new rod mill or ball mill.(You will learn more about them in later modules.) However, thesefactors are never used in basic circuit efficiency calculations inthe Metcom System.


Exercise

The operating work index of a rod mill circuit was determined to be18.8 kwh/t. The Bond rod mill work index of the ore was measured at17.4 kwh/t [for a sieve opening size of 1700 microns (10 mesh)].

What is the work index efficiency of this circuit?

The answer follows.



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Answer

93%

Solution: Eff(WI) = 17.4 kwh/t = 93%18.8 kwh/t

Solve this second exercise.



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Exercise

Some information from a survey of a ball mill circuit follows:

Dry feed rate: 131.8 t/hBall mill power draw: 924 kwF80 (circuit feed size): 1650 micronsP80 (circuit product size): 149 micronsBond W.I. at 1700 microns (10 mesh): 13.6 kwh/t

Questions

1. Calculate the operating work index of this circuit during the survey.

2. Calculate the work index efficiency of this circuit during the survey.

The answers follow.



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1. 12.2 kwh/t

Solution: W = 924 kw = 7.01 kwh/t131.8 t/h

7.01 kwh/t = Wio 10 - 10š149 š1650

12.2 kwh/t = Wio

2. 111% = 13.6 kwh/t12.2 kwh/t

You can use the values of work index efficiency to monitor if achange to a grinding circuit has improved its overall efficiency. Takea break and we will cover this next.

Answers

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COMPARISON OF WORK INDEX EFFICIENCIES

Work index analysis works for any circuit arrangement. Let's look atit for the most common cases: open circuit rod milling and closedcircuit ball milling.

For most open circuit applications, particularly rod milling, you canuse work index efficiency measurements to observe the net effect ofdesign or operating variables on the overall efficiency of the circuit.

For example, if you want to test the effect of rod mill feed wateraddition rate on circuit efficiency, two surveys can be carried out: oneunder the present operating conditions and a second under theexperimental condition. You will then determine the work index effi-ciency of the circuit during each survey: if the work index efficiencyhas increased under the experimental change in water addition rate,then you have observed a net positive effect of this change on theefficiency of this rod mill circuit.

Solve the following exercise which presents the results from anexperimental study on an open circuit rod mill.

ROD MILLING



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Exercise

The following information was determined from two rod mill circuitsurveys, A and B, at the Horse Shoe Mine.

Survey # A B

Dry solids feed rate (t/h): 68.4 67.1

Rod mill power draw (kw): 209 214

Feed size, F80 (microns): 12 330 12 310

Product size, P80 (microns): 1178 1031

Bond test work indexat 1700 microns (10 mesh): 14.8 15.8

Rod mill discharge % solids: 81.4% 77.1%

The purpose of the two surveys was to study the effect of differentrod mill feed water addition rates. This is illustrated in the followingfigure.

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Exercise (continued)

3. What happened to the efficiency of this circuit when the water addition rate was increased?

The answers follow.

2. Calculate the work index efficiency of this circuit during Survey B.



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Answers

1. Survey A: 97%


3.06 kwh/t = Wio 10 - 10 š1178 š12 330

15.2 kwh/t = Wio

Eff (WI) = 14.8 kwh/t = 97% 15.2 kwh/t

2. Survey B: 110%


3.19 kwh/t = Wio 10 - 10 š1031 š12 310

14.4 kwh/t = Wio

Eff (WI) = 15.8 kwh/t = 110% 14.4 kwh/t

3. The efficiency of the rod mill circuit increased by an absolute 13% (110-97%) while the water addition rate to the mill feed was increased. In relative terms, this also represents:

110% = 1.13 = 13% 97%

In the last section of Part II, you will see if this change in efficiency isstatistically meaningful.



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In both rod milling and ball milling, changes in the ore throughputrate, ore characteristics, F80 and/or P80 from one survey to the otherare all taken into account in Bond's law of comminution. Changes inore characteristics are always assessed by performing Bond testswhile the other three factors are directly measured from survey data.

In open-circuit grinding such as rod milling, a change in a design oroperating variable usually has a direct effect on circuit efficiency.Therefore you can relate an increase or decrease in overall circuitefficiency to the experimental change through work index efficiencymeasurements.

In closed-circuit grinding, however, work index analysis does nothave as much potential as in open-circuit grinding. Let's look at workindex analysis for closed-circuit ball milling.



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BALL MILLING

In closed-circuit grinding such as ball milling, you can use work indexanalysis to monitor and verify overall net changes in ball millcircuit efficiency. However, you cannot normally relate work indexefficiency variations to changes in specific design or operating vari-ables because of complex interactions between grinding and classifi-cation. These complex interactions mean that a change in one vari-able causes several other variables to change.

The module entitled "Functional Performance of Ball Milling" willaddress the issue of relating specific design and operating variablesto overall circuit efficiency in closed-circuit grinding. However, in themeantime, let's see how you can still make use of work indexanalysis in closed-circuit grinding by solving the following exercise.



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Exercise

Variations in water addition rate to the ball mill feed point were alsotested at the Horse Shoe Mine. Hydrocyclone underflow (ball millfeed) is normally diluted to 70% solids. One survey (C) wasconducted under this condition. Subsequently, the ball mill feedwater line was shut off and a second survey (D) was carried out. Thesurvey results were as follows:

Survey # C D

Hydrocyclone underflow % solids: 78.0% 76.0%

Ball mill discharge % solids: 70.0% 76.0%

Operating work index: 13.0 kwh/t 15.8 kwh/t

Bond ball mill work index (at 150 microns): 12.0 kwh/t 14.0 kwh/t

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2. Calculate the work index efficiency of this circuit during Survey D.

3. What happened to the overall efficiency of this circuit from SurveyC to Survey D if you use work index analysis?

The answers follow.



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Answer

1. Eff (WI) for Survey C = 12.0 kwh/t = 92%13.0 kwh/t

2. Eff (WI) for Survey D = 14.0 kwh/t = 89%15.8 kwh/t

3. Overall circuit efficiency decreased by 3%:

92% / 89% = 1.03 = 3% (loss)

The survey results indicate that shutting off the water line to the ballmill had a net negative effect on grinding circuit efficiency. However,we cannot attribute this 3% loss in efficiency to water addition ratealone. Changing the water addition rate has resulted in a change inhydrocyclone underflow % solids. It also resulted in other changeswhich affect overall circuit performance (such as hydrocyclone feedconditions, circulating load ratio, etc.)

In the module entitled "Functional Performance of Ball Milling", youwill see that cutting back on water addition to the ball mill feedactually had a positive effect on some aspects of the circuit but anegative effect on others.

In the previous two exercises, relative changes in overall circuitefficiency were +13% and -3%. Let's see if these changes inefficiency are statistically meaningful.



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ACCURACY OF COMPARATIVE WORK INDEX

There are three causes for the loss of accuracy in any work indexefficiency determination:

• Circuit instability during the survey.• Sampling.• Sample analysis procedures.

To keep these causes to a minimum, you must ensure that:

• Stable circuit operating conditions are maintained during the survey.• Samples are properly collected.• Plant readings are read from the same instruments.• Laboratory analyses are performed using the same equipment and procedures.

Under the most ideal conditions, the total error in comparativework index efficiency determinations is approximately +/- 4%(relative).

The value of +/- 4% represents the 95% confidence interval * of ourmost accurate relative work index efficiency measurements. Underthe best conditions, if the relative difference between two measuredefficiencies is 4% or greater, then we have observed a statisticallymeaningful change in circuit efficiency. This is illustrated inFigure 8.



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Figure 8. Two statistically different measurements.

In Figure 8, you can see that the 95% confidence interval of onemeasurement (mean) is just outside the 95% confidence interval ofthe other. The two measurements are therefore statistically different.

In the exercise on rod milling, the relative increase in efficiency was13%. This means that circuit efficiency increased by a statisticallymeaningful amount through changing the mill feed water additionrate.



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In the exercise on closed-circuit ball milling, the relative loss inefficiency was 3%. This value is less than the minimum 4%. Thismeans that changing the water addition rate to the feed to the ballmill did not have a statistically meaningful effect on overall circuitefficiency. Such a scenario is illustrated in Figure 9.

Figure 9. Two measurements that are not statistically different.

When sources of inaccuracy in your plant are evident (i.e. circuitstability is difficult to attain, instrument readings are taken fromdifferent instruments, sampling and analytical methods areinconsistant, etc.), then the total error in comparative work indexefficiency measurements will be greater than 4%. The value of thetotal error may be assessed on an individual basis for any plant sur-vey.

When comparing efficiencies of circuits in different plants, the rela-tive accuracy is typically in the order of +/- 10 to 20%.



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In the introduction to this module, we have presented several circuitarrangements. While work index analysis can be performed onsimple circuits such as open circuits and closed grinding circuits witha single mill, it can also be performed on circuits which combineseveral "simple" circuits in series. This is covered next.



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PART III - COMBINED GRINDING CIRCUITS

OPERATING WORK INDEX OF COMBINED CIRCUITS

You can combine grinding circuits to evaluate the operating workindex and work index efficiency of the combined circuit. Thistechnique allows you to determine the overall efficiency of severalcircuits in series or of an entire grinding plant. A combined circuitgenerally consists of a rod mill and ball mill in series (conventionalcircuit) or of several ball mills in series.

To obtain the operating work index of a combined circuit, you need toconsider the total power draw of all grinding mills in the combinedcircuit, and the feed and product sizes to and from the combinedcircuit.



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You can calculate the operating work index of a combined rod mill/ball mill circuit using the information on the individual rod mill and ballmill circuits.

Follow the two steps in the procedure.

1. Calculate the work input, W, for the combined circuit:

W = Total power draw of the combined circuit (kw) Tonnage to the combined circuit (t/h)

2. Calculate the operating work index, Wio, for the combined circuit:

W = Wio x 10 - 10 šP80 šF80

where W = Work input per tonne of ore for the combinedcircuit (kwh/t)

Wio = Work (energy) consumed to grind the orefrom F80 to P80 (kwh/t)

F80 = Size of the combined circuit feed (microns) P80 = Size of the combined circuit product

(microns)


ROD MILL / BALL MILL CIRCUITS IN SERIES

Procedure

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Exercise

Information on a rod mill/ball mill circuit follows:

Dry tonnage: 150 t/h

Rod mill circuit:

Rod mill power draw: 975 kwF80: 19 146 micronsP80: 1035 microns

Ball mill circuit:

Ball mill power draw: 1220 kwF80: 1035 micronsP80: 60 microns

If you wish, refer back to Figure 5 on page 13 where this combinedcircuit is illustrated.

What is the operating work index of this combined circuit?

The answer follows.



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Answer

( )

12.0 kwh/t

Solution: W = 975 + 1220 kw = 14.63 kwh/t 150 t/h

14.63 kwh/t = Wio 10 - 10 š60 š19 146

12.0 kwh/t = Wio

Let's look at the operating work index of ball mills in series.



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BALL MILLS IN SERIES

The method presented to calculate the operating work index ofcombined rod/ball mill circuits is also used for ball mills in series.

Answer the questions in the following exercise.

Two stages of ball milling follow rod milling at the Deep Sixty CopperConcentrator. The operating data obtained during a survey of thetwo ball mill circuits were as follows:

Dry circuit feed rate: 109.5 t/hRod mill discharge K80: 1260 microns

Primary ball mill circuit:

Mill power draw (at the pinion): 720 kwP80: 131 microns

Secondary ball mill circuit:

Mill power draw (at the pinion): 692 kwP80: 60 microns

Exercise



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Questions

1. For the appropriate circuit, what is:

Primary Secondary Combined circuit circuit circuit

Power draw:

F80:

P80:

2. What is the operating work index of the primary circuit?

3. What is the operating work index of the secondary circuit?

4. What is the operating work index of the combined circuit?

The answers follow.



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1. Primary Secondary Combined circuit circuit circuit

Power draw (kw): 720 692 1412

F80 (microns): 1260 131 1260

P80 (microns): 131 60 60

2. 11.1 kwh/t


6.58 kwh/t = Wio 10 - 10 š131 š1260

11.1 kwh/t = Wio

3. 15.1 kwh/t


6.32 kwh/t = Wio 10 - 10 š60 š131

15.1 kwh/t = Wio

4. 12.8 kwh/t


12.90 kwh/t = Wio 10 - 10 š60 š1260

12.8 kwh/t = Wio

Answers

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( )

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How did you do in the exercise? Well? Good work!

As you can see, the operating work index of the combined circuit fallsbetween the operating work indices of the individual circuits. Also, inthis example, the second stage of ball milling is doing more work thanthe first stage (15.1 kwh/t versus 11.1 kwh/t). In another module, youwill learn how to balance the work done by several grinding circuits inseries.

Let's turn to the work index efficiency of combined circuits.



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WORK INDEX EFFICIENCY OF COMBINED CIRCUITS

As previously mentioned, a Bond work index test is performed usinga selected sieve opening size. This sieve should yield a test P80which is as close as possible to the circuit P80 in the plant. Don'tworry if the P80 in the plant circuit and that from the Bond test are notexactly the same - they rarely are.

Bond work index testing of the feeds to individual circuits is generallyrequired in order to determine the work index efficiency of the com-bined circuit. In this section, we will show you how to determine thework index efficiency of two combined circuits: the rod mill/ball millcircuit (conventional circuit) and ball mills in series.



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[ ] + [ ]

The above equation can be used to calculate the overall work indexefficiency of any number of grinding circuits in series. For example,for a circuit that combines three individual circuits, the above equa-tion can be reconstructed with three terms in the numerator while thedenominator would then equal the sum of the power draws of allthree individual circuits.

Note

To determine the work index efficiency of rod mill/ball mill circuits,follow these seven steps.

1. Perform a Bond rod mill work index test on the rod mill circuit feed sample.

2. Perform a Bond ball mill work index test on the ball mill circuit feed sample.

3. Determine the operating work index of the rod mill circuit.

4. Determine the operating work index of the ball mill circuit.

5. Calculate the work index efficiency of the rod mill circuit.

6. Calculate the work index efficiency of the ball mill circuit.

7. Calculate the work index efficiency of the combined rod mill/ball mill circuit using the following equation:

Eff (WI) x Power Eff (WI) x PowerEff (WI) = (rm) draw (rm) (bm) draw (bm)

(%) Total power draw of the combined circuit (kw)

ROD MILL / BALL MILL CIRCUITS IN SERIES

Procedure



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Some results from a survey on a rod mill/ball mill circuit follow:

Rod mill power draw: 495 kwBall mill power draw: 961 kwOperating work index of the rod mill circuit: 20.1 kwh/tOperating work index of the ball mill circuit: 8.6 kwh/t

The results from the Bond work index tests were as follows:

Bond rod mill work index at 1700 microns (10 mesh): 15.4 kwh/t Bond ball mill work index at 75 microns (200 mesh): 11.5 kwh/t

Questions

1. Calculate the work index efficiency of the rod mill circuit.

2. Calculate the work index efficiency of the ball mill circuit.

3. What is the work index efficiency of this conventional circuit?

The answers follow.

Exercise



61

Answers

1. 77% = 15.4 kwh/t 20.1 kwh/t

2. 134% = 11.5 kwh/t 8.6 kwh/t

3. 115% = ( 0.77 x 495 kw ) + ( 1.34 x 961 kw ) = 1.15 495 + 961 kw

In this rod/ball mill circuit, you can see that the ball mill circuit isperforming much more efficiently than the rod mill circuit.

Solve this other exercise.



62

Exercise

Some information on a rod/ball mill circuit follows.

Rod mill Ball mill circuit circuit

Power draw: 792 kw 828 kwOperating work index: 10.8 kwh/t 12.0 kwh/tBond work index: 10.3 kwh/t 12.4 kwh/t

What is the work index efficiency of the combined circuit?

The answer follows.



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Answer

99%

Solution: Eff (WI) (rm) = 10.3 / 10.8 kwh/t = 95%

Eff (WI) (bm) = 12.4 / 12.0 kwh/t = 103%

The work index efficiency of the combined circuit is:

( 0.95 x 792 kw ) + ( 1.03 x 828 kw ) = 99% ( 792 + 828 kw)

To determine the work index efficiency of a conventional (rod mill/ball mill) circuit, you need to perform two Bond tests, one for eachstage of milling.

However, to determine the overall work index efficiency of a mul-tiple-stage ball mill circuit, you usually have to perform only oneBond test. Afterwards, if you want to determine the work index effi-ciency of each individual ball mill circuit within the combined circuit,you will need to perform as many tests as there are individual circuits.More on this in the following sections!



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Exercise

MULTIPLE - STAGE BALL MILL CIRCUITS

In order to obtain the overall work index efficiency of a multiple-stageball mill circuit following rod milling, you need to perform only oneBond ball mill work index test.

In the case of a two-stage ball mill circuit (two ball mill circuits inseries), the feed to the primary circuit will be used as Bond test feedwhile the test control size will be based on the P80 of the secondarycircuit. The work index of the ore will therefore reflect the energyrequired to grind one tonne of ore, from the test F80 to the test P80,over the overall ball mill circuit (all stages combined).

The work index efficiency of the multiple-stage circuit is simply theratio of the Bond test work index and of the operating work index forthe multiple-stage ball mill circuit.


The operating work index of a two-stage ball mill circuit (two ball millcircuits in series) is 12.8 kwh/t. The Bond ball mill work index test,performed on the circuit feed to give a test P80 similar to the P80 ofthe overall circuit, was 12.9 kwh/t.

What is the work index efficiency of this multiple-stage circuit?

The answer follows.



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Answer

101% = 12.9 / 12.8 kwh/t

You can now determine the work index efficiency of a two-stage ballmill circuit. Next, you will learn how to determine the efficiency ofeach individual circuit within the combined circuit.



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WORK INDEX EFFICIENCY OF INDIVIDUALBALL MILL CIRCUITS IN SERIES

You can easily calculate the operating work index of individual ballmill circuits in series following Bond's law of comminution. However,to calculate their work index efficiencies, you must perform severalBond ball mill work index tests. In the case of ball mill circuits inseries, there is a special way of testing the ore for grindability.

The feed to a Bond ball mill work index test must meet specific sizerequirements. One of these requirements is that the test feed mustnot be too fine.

Primary ball mill circuit feed is generally adequately sized for Bondtesting; however, the feed to secondary and tertiary ball mill cir-cuits is generally too fine. This means that for a secondary or tertiarycircuit, you cannot subject the circuit feed to Bond testing.

To circumvent this constraint, you will use the feed to the primaryball mill circuit to perform as many Bond tests as there are indi-vidual circuits within the overall ball milling stage. If there are twoball mill circuits in series, two Bond tests are required; if there arethree, three Bond tests are required. The variable that will changefrom one test to the other is the test control size which you willselect accordingly.

For example, to obtain the work index efficiency of each ball millcircuit if there are two ball mill circuits in series, you need to performtwo Bond work index tests on the primary circuit feed:

• The first Bond test is performed (on the feed to the primary ballmill circuit) while selecting the sieve opening size that will give atest P80 close to the P80 of the secondary circuit. This workindex is used (along with the operating work index) to determinethe work index efficiency of the entire two-stage ball mill circuit.

• The other Bond test is performed (also on the feed to the primarycircuit) while selecting the sieve opening size that will give a testP80 close to the P80 of the primary ball mill circuit only. Thiswork index will be used (along with the operating work index) todetermine the work index efficiency of the primary circuit only.



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You therefore determine the work index efficiency of the overall ballmilling stage and that of the primary circuit.

In order to calculate the work index efficiency of the secondary ballmill circuit, you must determine the Bond work index of the ore overthe size reduction that is observed in the secondary ball mill circuit.Since the feed to the secondary ball mill circuit is too fine for Bondtesting, you will use the results from the two Bond tests that you havealready performed to determine the work index of the ore for thesecondary circuit: the difference in energy input per tonne of orebetween the two Bond tests will help you to determine the work indexof the ore for the secondary circuit.

This principle is illustrated in Figure 10.

Administrator

Text Box




69

To determine the Bond work index of the ore for the secondary ballmill circuit, follow the four steps in this procedure.

Use information from Bond ball mill work index tests only in thisprocedure.

1. Calculate the work input, Wc , during the Bond test done over thesize reduction of the ore in the combined two-stage circuit:

Wc = Constant 10 - 10 šP80 šF80

where Constant = Bond ball mill work index of the ore forthe combined circuit (kwh/t)

F80 = Size of the Bond test feed for the com-bined circuit (microns)

P80 = Size of the Bond test product for thecombined circuit (microns)

2. Calculate the work input, W1 , during the Bond test done over thesize reduction of the ore in the primary stage of ball milling:

W1 = Constant 10 - 10 šP80 šF80

where Constant = Bond ball mill work index of the ore forthe primary circuit (kwh/t)

F80 = Size of the Bond test feed for the pri-mary circuit (microns)

P80 = Size of the Bond test product for theprimary circuit (microns)

Procedure

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( )



70

Procedure (continued)

3. Calculate the difference, W2 , between the two test work inputs:

W2 = Wc - W1

4. Calculate the Bond work index of the ore for the secondary stageof ball milling:

W2 = Constant 10 - 10 šP80 šF80

where W2 = Work input by difference to grind the oreover the secondary stage of milling (kwh/t)

Constant = Bond ball mill work index of the ore forthe secondary stage (kwh/t)

F80 = Size of the Bond test product (P80) forthe primary circuit (microns)

P80 = Size of the Bond test product (P80) forthe combined circuit (microns)

Note


If you have a three-stage ball mill circuit in your plant, then you needto perform three Bond tests: one to cover the size reduction in theprimary stage, one to cover the size reduction in the primary andsecondary stages, and one to cover all three milling stages.

In this case, adapt the given procedure accordingly.

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71

Some information on the Bond work index tests performed for astudy of a two-stage ball mill circuit composed of two ball mill circuitsin series follows:

Bond ball Bond ball mill test for the mill test for the combined circuit primary stage

Bond ball millwork index: 12.9 kwh/t 13.5 kwh/t

Bond test F80: 1360 microns 1360 microns

Bond test P80: 59 microns 115 microns

Exercise



72

Questions

1. What is the work input, Wc , from the Bond ball mill test for thecombined circuit?

2. What is the work input, W1 , from the secondary Bond ball milltest for the primary circuit?

3. What is the work input, W2 , for the size reduction of the ore overthe secondary stage of ball milling?

4. What is the Bond work index of the ore over the size reductionrange of the secondary ball mill circuit?

The answers follow.



© 1992 GRINDING PROCESS DEVELOPMENT CO. LTD. (Rev. 1, 1992)

73

1. 13.3 kwh/t = 12.9 kwh/t 10 - 10š59 š1360

Wc = 13.3 kwh/t

2. 8.9 kwh/t = 13.5 kwh/t 10 - 10 š115 š1360

W1 = 8.9 kwh/t

3. 4.4 kwh/t = 13.3 - 8.9 kwh/t = W2

4. 11.9 kwh/t

Solution: 4.4 kwh/t = Constant 10 - 10š59 š115

11.9 kwh/t = Constant

The estimated test work index for this ore from 115 microns to 59microns is therefore 11.9 kwh/t.

Take a break and then we will look at work index analysis ofsingle-stage ball mill circuits.

( )

Answers

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( )



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Procedure

WORK INDEX EFFICIENCY OFSINGLE - STAGE BALL MILL CIRCUITS

A single-stage ball mill circuit performs the tasks of both a rodmill and a ball mill since it immediately follows the crushingplant. This circuit is not often seen in concentrators and it requiresspecial attention for work index efficiency determination. We will notask you any questions on this type of circuit in the next ProgressReview nor in the Certification Test. You should still cover this sec-tion carefully.

For this circuit, you must therefore perform both a Bond rod mill anda Bond ball mill work index test on the ore since this ball mill does thework of both a rod mill and a ball mill.

To determine the work index efficiency of a single-stage ball millcircuit which immediately follows crushing, follow the six steps in theprocedure below. To determine the work index of the ore for thesingle-stage ball mill circuit, use 2100 microns as the reference sizeto perform the Bond rod mill test on the ore. Also, use 2100 micronsin some of your calculations. (Use the product from the Bond rod milltest to perform the Bond ball mill test.)

1. Calculate the operating work index of the single-stage ball mill circuit:

W = Wio x 10 - 10 šP80 šF80

Where W = Work (energy) input per tonne of ore to thecircuit (kwh/t)

Wio = Operating work index (kwh/t)F80 = Size of the single-stage ball mill circuit feed

(microns)P80 = Size of the single-stage ball mill circuit prod-

uct (microns)

( )



75


( )

( )

2. Calculate the work input, Wr , for the size reduction of the ore related to the Bond rod mill test:

Wr = Constant 10 - 10 šP80 šF80

where Constant = Bond rod mill work index of the ore(kwh/t)

F80 = Size of the feed to the Bond rod milltest (microns)

P80 = 2100 microns (do not use the P80from the Bond test)

3. Calculate the work input, Wb , for the size reduction of the ore related to the Bond ball mill test:

Wb = Constant 10 - 10 šP80 šF80

where Constant = Bond ball mill work index of the ore(kwh/t)

F80 = 2100 microns (do not use the F80from your Bond test)

P80 = Size of the product from the Bond ballmill test (microns)

4. Calculate the work input, Ws , for both Bond tests:

Ws = Wr + Wb



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5. Estimate the Bond work index of the ore related to the Bond rod mill and ball mill tests (constant) using Ws from Step (4):

Ws = Constant 10 - 10 šP80 šF80

where Ws = Work input in both Bond tests (kwh/t)Constant = Bond work index of the ore (kwh/t)F80 = Size of the Bond rod mill test feed

(microns)P80 = Size of the Bond ball mill test product

(microns)

6. Calculate the work index efficiency of the single-stage ball mill circuit:

Eff (WI) = Bond work index of the ore (kwh/t) (%) Operating work index of the circuit (kwh/t)


( )



77

Exercise

Solve this exercise while carefully following the previous procedure.

Following a survey of the single-stage ball mill circuit at the GoldenRainbow Concentrator, Bond work index tests on a sample of thecircuit feed yielded the following results:

Survey data:

Dry tonnage: 250 t/hMill power draw: 2000 kwF80: 20 582 micronsP80: 173 microns

Bond test results:

Bond rod mill W.I. test at 2360 microns (6 mesh): 11.8 kwh/t

Test F80: 12 200 micronsTest P80: 2 053 microns

Bond ball mill W.I. test at 212 microns (65 mesh): 9.9 kwh/t

Test F80: 2053 micronsTest P80: 162 microns

Questions

1. What is the operating work index of this single-stage ball mill circuit?



78


2. What is the work input, Wr , for the size reduction of the ore related to the Bond rod mill test?

3. What is the work input, Wb , for the size reduction of the ore related to the Bond ball mill test?

4. What is the total work input, Ws , related to both Bond work index tests?

5. What is the Bond work index of the ore related to both Bond work index tests?

6. What is the work index efficiency of this single-stage ball mill circuit?

The answers follow.



79

( )

( )

1. 11.6 kwh/t

Solution: W = 2000 kw = 8.0 kwh/t 250 t/h

8.0 kwh/t = Wio x 10 - 10 š173 š20 582

11.6 kwh/t = Wio

2. 1.51 kwh/t = 11.8 10 - 10 š2100 š12 200

3. 5.62 kwh/t = 9.9 10 - 10 š162 š2100

4. 7.13 kwh/t = 1.51 + 5.62 kwh/t

5. 10.3 kwh/t

Solution:7.13 kwh/t = W.I. 10 - 10

š162 š12 200

10.3 kwh/t = W.I.

6. 89% = 10.3 kwh/t 11.6 kwh/t

( )

Answers

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80

By now you should be able to determine the operating work indexand work index efficiency of various circuit arrangements. On thejob, you can apply what you have learned in this module by usingdata such as that from circuit surveys.

Review your knowledge in the only Progress Review in this module.



81

1 PROGRESS REVIEWEstimated time for completion: 10 minutes

There are five problems in this Progress Review. Each problemrefers to the figure on the following page.

1. Examine the figure on the following page and associate the numbers there listed to the following list of terms.

Primary ball mill circuit feed

Secondary ball mill circuit

Combined ball mill circuit product

Primary ball mill feed

Secondary ball mill discharge

Combined two-stage ball mill circuit

Secondary ball mill circuit product

Secondary ball mill feed

Primary ball mill circuit

Secondary ball mill circuit feed

Primary ball mill discharge

Combined ball mill circuit feed

Primary ball mill circuit product

© 1992 GPD Co. Ltd. / Metcom Consulting LLC (Rev.4, 2005) WORK INDEX EFFICIENCY

82



83

1 PROGRESS REVIEW(continued)

2. Examine the previous figure again and answer these questions:

a) How many operating work indices can you calculate for this flowsheet?

__________________________

b) How many Bond work index tests can you perform for this circuit?

__________________________

c) Record the number(s) which corresponds to the sampling point where ore must be collected for Bond work index testing:

__________________________

d) How many work index efficiencies can you determine for this flowsheet?

__________________________

e) If the material that flows at point "1" is ore, what are the other points at which ore is known to flow in this flowsheet (as opposed to "material")? (Hint: There are five of them.)

__________________________



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3. If you obtain the following results on the combined circuit previously shown, which of the three circuits is the most efficient using work index analysis?

Operating Bond work index work index (kwh/t) (kwh/t)

Combined circuit 12.1 13.9Primary ball mill circuit 11.3 13.8Secondary ball mill circuit (calculated) 13.2 14.0

Write your answer: ____________________________

4. At which stage is the ore the most difficult to grind?

Write your answer: ____________________________

The answers to the Progress Review follow.



85


Answers

1. The numbers corresponding to the terms in the figure follow:

Primary ball mill circuit feed

Secondary ball mill circuit

Combined ball mill circuit product

Primary ball mill feed

Secondary ball mill discharge

Combined two-stage ball mill circuit

Secondary ball mill circuit product

Secondary ball mill feed

Primary ball mill circuit

Secondary ball mill circuit feed

Primary ball mill discharge

Combined ball mill circuit feed

Primary ball mill circuit product

2

12

10

3

8

13

9

7

11

6

4

1

5



86


Answers (continued)

2. a) Three.

You can determine the operating work index of the primary ballmill circuit, secondary ball mill circuit, and combined two-stageball mill circuit.

b) Two.

You can perform two Bond work index test on the feed to the combined circuit. The first test will cover the size reduction range of the ore in both stages of ball milling. The second will cover the size reduction range of the ore in theprimary ball mill circuit.

c) Point "1" or "2".

Points "1" and "2" correspond to the same sampling point inthe plant even though they can be distinguished on theflowsheet. The ore that flows through these points is thematerial used for Bond work index testing since itis circuit feed of appropriate size.

d) Three.

You can determine work index efficiencies for the same circuits described in the answer to problem (2a).

e) 2, 5, 6, 9, 10.

What flows through points "3", "4", "7", and "8" is material.



87


Answers (continued)

3. The answer is (a): the first-stage ball mill circuit.

The work index efficiency for this circuit is 122% compared to 106% for the secondary ball mill circuit. It is 115% for the combined circuit.

4. The secondary ball mill circuit with a Bond work index of 14.0 kwh/t.



88

How did you do in the Progress Review?

• You scored 100%? Good work!

• If you made some mistakes, study the solutions carefully and talk to your Program Administrator if you have any questions.



89

CLOSING WORD

Congratulations on completing another module of the MetcomInstructional Program. A summary of the contents of this modulefollows.

Bond's law of comminution states that:

W = Constant 10 - 10 šP80 šF80

Where W = Work (energy) input per tonne of ore(kwh/t)

Constant = Work (energy) input to grind the orefrom F80 to P80 (kwh/t)

F80 = K80 of the circuit feed (microns)P80 = K80 of the circuit product (microns)

The "constant" is also called the "operating work index" when W, F80and P80 relate to plant data.

The "constant" can also represent the "Bond work index of the ore"when W, F80 and P80 relate to Bond work index test data.

The operating work index gives a measure of the energy required togrind a specific ore from the circuit feed size to the circuit productsize. It therefore takes into account the grindability characteristics ofthe ore.

By determining the grindability characteristics of the ore throughBond work index laboratory testing, the ore can be factored out of theoperating work index in order to determine the efficiency of the circuit:

Efficiency = Bond work index of the ore (kwh/t) . (%) Operating work index of the circuit (kwh/t)

The work index efficiency of a circuit can be equal to, less than orgreater than 100%. Bond work index analysis can be applied to anyrod mill or ball mill circuit. The circuits can be analysed individually orcombined in series.

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90

The topic of work index efficiency will be further covered in themodule entitled "Functional Performance of Ball Milling" in relation toball mill circuits. In that module, you will see that work index analysiscan be used to verify the results from functional performance analy-sis.



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REFERENCES

Bond, F.C., "Crushing and Grinding Calculations", British ChemicalEngineering, June and August, 1961, pp. 378-385.

Bond, F.C., "The Third Theory of Comminution", Trans. AIME, Vol.193, 1952, pp. 484-494.

Bond, F.C., "Action in a Rod Mill", Engineering and MiningJournal, March 1960, pp. 82-85.

Rowland, C.A., "The Tools of Power Power: The Bond Work Index, ATool to Measure Grinding Efficiency", AIME meeting, Denver,1976.

Rowland, C.A., "Selection of Rod Mills, Balls Mills, Pebble Mills andRegrind Mills", Design and Installation of ComminutionCircuits, SME of AIME, New York, 1982, Chapter 23,pp. 393-438.



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GLOSSARY

Eighty percent passing size: The micron size which correspondsto the 80% passing of a sample on aweight basis. It is also called K80. [p. 23]

K80: See "Eighty percent passing size". [p. 23]

Operating work index: This index gives a measure of theperformance of the circuit in terms of theenergy consumed to achieve a certainamount of size reduction. Its units arekwh/t. [p. 23]

Work index efficiency: Ratio (%) between the Bond work index ofthe circuit feed and the operating workindex of the circuit. [p. 29]

95% confidence interval: For example, when we estimate a valueequal to 10 (mean) with a 95% confidenceinterval of +/- 1.0, we are 95% sure thatthe true value falls between 9.0 and 11.0.[p. 46]

Documents

Module4 - Work Index Efficiency