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The Metcom Engineering and Management System for Plant Grinding Operations

MODULE #4: WORK INDEX EFFICIENCY

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

WORK INDEX EFFICIENCY

i

TABLE OF CONTENTS page Objectives Introduction Circuit arrangements • Grinding circuits with a single mill • Grinding circuits with multiple mills • Other circuit arrangements

1 2 3 3 10 20

PART I - The Operating Work Index

22

The Bond law of comminution The operating work index

23 24

PART II - Work Index Efficiency

30

Work index efficiency Comparison of work index efficiencies • Rod milling • Ball milling Accuracy of comparative work index efficiencies

30 35 35 41 46

PART III - Combined Grinding Circuits

50

Operating work index of combined circuits • Rod mill/ball mill circuits in series • Ball mill circuits in series Work index efficiency of combined circuits • Rod mill/ball mill circuits in series • Multiple-stage ball mill circuits Work index efficiency of individual ball mill circuits in series Work index efficiency of single-stage ball mill circuits

50 51 54 58 59 64 66 74

Progress Review 1

81

Closing word References Glossary

89 91 92

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

WORK INDEX EFFICIENCY

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LIST OF FIGURES page Rod mill in open circuit. Ball mill in reverse closed circuit. Ball mill in reverse closed circuit with two stages of classification. Figure 4. Circuit containing two ball mills in parallel. Figure 5. The "conventional" grinding circuit. Figure 6. Two-stage ball mill circuit. Figure 7. Single-stage ball mill circuit. Figure 8. Two statistically different measurements. Figure 9. Two measurements that are not statistically different. Figure 10. Two Bond ball mill work index tests for ball mill circuits in series. Figure 1. Figure 2. Figure 3.

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

4 6 8 11 13 15 18 47 48 68

WORK INDEX EFFICIENCY OBJECTIVES In this module, you will learn about work index calculations for evaluating grinding circuit efficiency based on the method developped 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 grinding circuits. • Calculate the operating work index and work index efficiency of grinding 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 calculator. The estimated time for completion is two and a half hours including one Progress Review at the end of the module.

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

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WORK INDEX EFFICIENCY INTRODUCTION You must first establish a basis for measuring the overall efficiency of a grinding circuit. From this basis, you will be able to measure and compare the effects of various design and/or operating variables 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/or operating variables, you will then be able to justify and implement changes that will lead to performance improvements. Efficiency measurements will also allow you to monitor long-term circuit performance. This module presents the Bond method for measuring grinding circuit efficiency. 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 grinding circuits. 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.

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

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WORK INDEX EFFICIENCY CIRCUIT ARRANGEMENTS GRINDING CIRCUITS WITH A SINGLE MILL 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 open circuit is the rod mill in open circuit. In this case, the circuit feed is also the mill feed. The mill discharge is also the circuit product. See Figure 1.

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

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WORK INDEX EFFICIENCY

Closed circuit:

This circuit may consist of one or more stages of grinding and classification in various arrangements. In this case, the circuit feed is different from the mill feed because of circulating loads. The mill discharge is different from the circuit product for the same reason. Figure 2 shows the most common example of a closed circuit: the single ball mill in reverse closed circuit with one stage of classification.

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

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

WORK INDEX EFFICIENCY The circuit shown in Figure 2 is called "reverse" because the ore fed to 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 of classification.

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

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

WORK INDEX EFFICIENCY It is important for you to note the difference between a grinding mill and 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 those presented in Figures 1, 2, and 3. In this context, you must consider any circuit as a black box with only a "feed stream" and a "product stream". The equipment and flowsheet inside the black box are irrelevant.

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

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WORK INDEX EFFICIENCY GRINDING CIRCUITS WITH MULTIPLE MILLS Mills in parallel:

Grinding is sometimes performed in more than one mill in a single stage of grinding. The most common example is that of two ball mills in parallel. See Figure 4.

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

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

WORK INDEX EFFICIENCY

Rod/ball mill circuit:

This arrangement is also called a "conventional" grinding circuit. It consists of an open-circuit rod mill followed by a closed-circuit ball mill. See Figure 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 a conventional 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.) of the copper bearing mineral compared to that of the host rock. So even though what goes into the ball mill originates from the "ore", it is not "ore" but simply a mixture of ore components called "ball mill feed material ".

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

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

WORK INDEX EFFICIENCY Multi-stage ball milling: This is also termed "ball mill circuits in series". The circuit boundaries are defined as the feed to the first stage and product from the last stage. Figure 6 shows a two-stage ball mill circuit.

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

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

WORK INDEX EFFICIENCY Note that the rod mill/ball mill and multi-stage ball mill circuits are simply a combination of several circuits in sequence. In general, you will determine the efficiency of both individual and combined circuits. Therefore either the individual or combined circuits may be considered for efficiency calculations.

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

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WORK INDEX EFFICIENCY

Single-stage ball milling:

This is a special arrangement in which a single ball mill is used in place of a rod mill and ball mill in series. The single-stage ball mill does the work of a conventional circuit (rod/ball mill) with one grinding unit. It may also be followed by further grinding. See Figure 7.

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

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

WORK INDEX EFFICIENCY All previously described circuits may be further combined as they occur in actual plant flowsheets for the purposes of the efficiency calculations presented in this module.

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

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WORK INDEX EFFICIENCY OTHER CIRCUIT ARRANGEMENTS There are a few special cases that will not be addressed in this module: Circuits with multiple feed or product streams: These can normally be handled by calculations that combine or eliminate specific streams. Ball mills in semi-autogenous grinding circuits: In this case, efficiency calculations require that steps be taken to allow for the specific characteristics of SAG mill circuits. Regrind mills: Bond work index calculations generally cannot be directly applied to extremely fine grinding applications. Discuss any of these special applications with Metcom.

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

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WORK INDEX EFFICIENCY Let's turn to Part I of this module where you will learn how to determine the operating work index of a circuit.

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

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WORK INDEX EFFICIENCY PART I - THE OPERATING WORK INDEX There are four factors that determine the efficiency of a grinding circuit. They are: 1. 2. 3. 4.

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

For a grinding circuit, the efficiency is directly related to tonnage if the other three factors are constant. For example, if you can increase the tonnage by 10% while energy consumption, circuit feed and circuit product sizes, and ore characteristics remain constant, then circuit efficiency has increased by 10%. Likewise, if you can reduce energy consumption by 10% while all three other factors remain constant, then circuit efficiency has increased by 10%. In order to account for changes in circuit feed/product sizes and ore grindability, Bond provided us with his "law of comminution" as follows.

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

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WORK INDEX EFFICIENCY

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THE BOND LAW OF COMMINUTION Bond developed an empirical equation from numerous plant observations that takes the four factors previously listed into account. First, Bond determined that a complete size distribution could be represented by the 80% passing size* , K80* , of a material. He represented the circuit feed size distribution by F80 and the circuit product size distribution by P80. Secondly, Bond observed that for a given grinding circuit, the following relationship applies when changes in the circuit feed or product size, or mill energy input occurs. The Bond law of comminution is: W

Where

=

Constant x

(

10 šP80

10 šF80

)

W

= Work (energy) input per tonne of solids processed (kwh/t). Constant = Work (energy) consumed to grind the ore from F80 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 work index* . It is discussed next.

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

WORK INDEX EFFICIENCY

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THE OPERATING WORK INDEX The operating work index gives an overall measure of the performance of a circuit in terms of the energy consumed to achieve a certain amount of size reduction. When a circuit has a high operating work index, a lot of energy is consumed to achieve a certain amount of size reduction. When the operating work index is low, little energy is consumed to achieve size reduction. If you measure W, F80, and P80 for a circuit, then the constant in the Bond equation can be calculated. The constant represents the operating work index of the circuit; it is labelled Wio.

Example During a plant survey, the ball mill circuit feed rate was 100.0 dry tonnes 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 of the 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, was equal 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

9.00 kwh/t

=

Wio

10.4 kwh/t

=

Wio

(

( 10 š85

Solve the following exercise.

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

10 šP80 -

10 šF80

10 ) š2100

)

WORK INDEX EFFICIENCY Exercise During a plant survey, the rod mill circuit feed rate was 126.6 dry tonnes per hour. The rod mill power draw was 427 kw. The size of the circuit feed, F80, was 14 870 microns and the size of the circuit product, P80, was 1460 microns. What was the operating work index, Wio, of this circuit?

The answer follows.

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

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WORK INDEX EFFICIENCY

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Answer 18.8 kwh/t Solution: The first step is always to calculate W: W

=

427 kw 126.6 t/h

=

3.37 kwh/t

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

=

Constant

3.37 kwh/t

=

Wio

18.8 kwh/t

=

Wio

(

10 šP80

10 ( š1460

Solve this second exercise.

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

-

10 šF80

10 š14 870

)

)

WORK INDEX EFFICIENCY

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Exercise Some information on the closed ball mill circuit that follows the rod mill presented in the previous example follows. Dry tonnage: Ball mill power draw (at the pinion): F80 (rod mill discharge): P80 (hydrocyclone overflow):

126.6 t/h 955 kw 1460 microns 126 microns

What is the operating work index of this circuit?

The answer follows.

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

WORK INDEX EFFICIENCY

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Answer 12.0 kwh/t Solution:

W

=

955 kw 126.6 t/h

Then 7.54 kwh/t =

Wio

12.0 kwh/t =

Wio

(

= 10 š126

7.54 kwh/t -

10 ) š1460

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

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

WORK INDEX EFFICIENCY When the value of the operating work index is high, a lot of energy has been consumed to achieve a certain amount of size reduction. If the ore becomes more difficult to grind, the measured operating work index will also increase. If the circuit becomes less efficient, the operating work index will increase again. Since circuit feed and product sizes are taken into account in the Bond equation, the value of the operating work index reflects two things: 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 necessary to factor out the grindability of the ore. Bond has provided us with some "standard" laboratory tests which allows us to factor out the grindability of the ore from the operating work index. This process analysis gives us the work index efficiency* of a grinding circuit. This topic is covered in Part II of the module.

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

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WORK INDEX EFFICIENCY PART II - WORK INDEX EFFICIENCY WORK INDEX EFFICIENCY Bond used standard laboratory test procedures to determine the laboratory test work index of ores. There are two standard tests: one for the size reduction range of solids in rod mill circuits (Bond rod mill test) and one for the size reduction range of solids in ball mill circuits (Bond ball mill test). The Bond grindability tests are locked-cycle laboratory tests. Closedcircuiting is achieved using a sieve opening size that yields a test product size which is close to the plant circuit product size. You will learn how to perform these tests in the module entitled "Bond Grindability Tests". Once you can factor out the characteristics of the ore from the operating 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 a maximum 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 is performing exactly as predicted by the Bond scale-up method for circuit design: the Bond laboratory work index of the ore exactly equals the operating work index of the circuit. Work index efficiency will be below 100% if the circuit is using more energy to reduce the ore than indicated by a Bond test. Similarly, work index efficiency will be above 100% if the circuit is using less energy to reduce the ore than indicated by a Bond test.

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

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WORK INDEX EFFICIENCY Note You may be aware of certain "correction factors" that are applied to the 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, these factors are never used in basic circuit efficiency calculations in the Metcom System. Solve the following exercise.

Exercise The operating work index of a rod mill circuit was determined to be 18.8 kwh/t. The Bond rod mill work index of the ore was measured at 17.4 kwh/t [for a sieve opening size of 1700 microns (10 mesh)]. What is the work index efficiency of this circuit?

The answer follows.

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

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WORK INDEX EFFICIENCY

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Answer 93% Solution:

Eff(WI)

=

17.4 kwh/t 18.8 kwh/t

Solve this second exercise.

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

=

93%

WORK INDEX EFFICIENCY

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Exercise Some information from a survey of a ball mill circuit follows: Dry feed rate: Ball mill power draw: F80 (circuit feed size): P80 (circuit product size): Bond W.I. at 1700 microns (10 mesh):

131.8 t/h 924 kw 1650 microns 149 microns 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.

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

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Answers 1. 12.2 kwh/t W

=

924 kw 131.8 t/h

7.01 kwh/t

=

Wio

12.2 kwh/t

=

Wio

Solution:

2. 111% =

= 10 ( š149

7.01 kwh/t -

10 ) š1650

13.6 kwh/t 12.2 kwh/t

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

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

WORK INDEX EFFICIENCY COMPARISON OF WORK INDEX EFFICIENCIES Work index analysis works for any circuit arrangement. Let's look at it for the most common cases: open circuit rod milling and closed circuit ball milling.

ROD MILLING For most open circuit applications, particularly rod milling, you can use work index efficiency measurements to observe the net effect of design or operating variables on the overall efficiency of the circuit. For example, if you want to test the effect of rod mill feed water addition rate on circuit efficiency, two surveys can be carried out: one under the present operating conditions and a second under the experimental condition. You will then determine the work index efficiency of the circuit during each survey: if the work index efficiency has increased under the experimental change in water addition rate, then you have observed a net positive effect of this change on the efficiency of this rod mill circuit. Solve the following exercise which presents the results from an experimental study on an open circuit rod mill.

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

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WORK INDEX EFFICIENCY

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Exercise The following information was determined from two rod mill circuit surveys, 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 index at 1700 microns (10 mesh):

14.8

15.8

81.4%

77.1%

Rod mill discharge % solids:

The purpose of the two surveys was to study the effect of different rod mill feed water addition rates. This is illustrated in the following figure.

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

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

WORK INDEX EFFICIENCY Exercise (continued) 2. Calculate the work index efficiency of this circuit during Survey B.

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

The answers follow.

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

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WORK INDEX EFFICIENCY

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Answers 1. Survey A:

97% W =

Solution:

209 kw 68.4 t/h

3.06 kwh/t = Wio

= 3.06 kwh/t

10 ( š1178

-

10 š12 330

)

15.2 kwh/t = Wio Eff (WI)

2. Survey B: Solution:

= 14.8 kwh/t = 97% 15.2 kwh/t

110% W =

214 kw 67.1 t/h

3.19 kwh/t = Wio

= 3.19 kwh/t

10 ( š1031

-

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

WORK INDEX EFFICIENCY In both rod milling and ball milling, changes in the ore throughput rate, ore characteristics, F80 and/or P80 from one survey to the other are all taken into account in Bond's law of comminution. Changes in ore characteristics are always assessed by performing Bond tests while the other three factors are directly measured from survey data. In open-circuit grinding such as rod milling, a change in a design or operating variable usually has a direct effect on circuit efficiency. Therefore you can relate an increase or decrease in overall circuit efficiency to the experimental change through work index efficiency measurements. In closed-circuit grinding, however, work index analysis does not have as much potential as in open-circuit grinding. Let's look at work index analysis for closed-circuit ball milling.

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

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WORK INDEX EFFICIENCY BALL MILLING In closed-circuit grinding such as ball milling, you can use work index analysis to monitor and verify overall net changes in ball mill circuit efficiency. However, you cannot normally relate work index efficiency variations to changes in specific design or operating variables because of complex interactions between grinding and classification. These complex interactions mean that a change in one variable causes several other variables to change. The module entitled "Functional Performance of Ball Milling" will address the issue of relating specific design and operating variables to overall circuit efficiency in closed-circuit grinding. However, in the meantime, let's see how you can still make use of work index analysis in closed-circuit grinding by solving the following exercise.

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

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WORK INDEX EFFICIENCY

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Exercise Variations in water addition rate to the ball mill feed point were also tested at the Horse Shoe Mine. Hydrocyclone underflow (ball mill feed) is normally diluted to 70% solids. One survey (C) was conducted under this condition. Subsequently, the ball mill feed water line was shut off and a second survey (D) was carried out. The survey 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

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

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

WORK INDEX EFFICIENCY Exercise (continued) 2. Calculate the work index efficiency of this circuit during Survey D.

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

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

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WORK INDEX EFFICIENCY

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Answer 1.

Eff (WI) for Survey C

=

12.0 kwh/t = 92% 13.0 kwh/t 14.0 kwh/t = 89% 15.8 kwh/t

2.

Eff (WI) for Survey D

=

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 ball mill had a net negative effect on grinding circuit efficiency. However, we cannot attribute this 3% loss in efficiency to water addition rate alone. Changing the water addition rate has resulted in a change in hydrocyclone underflow % solids. It also resulted in other changes which affect overall circuit performance (such as hydrocyclone feed conditions, circulating load ratio, etc.)

In the module entitled "Functional Performance of Ball Milling", you will see that cutting back on water addition to the ball mill feed actually had a positive effect on some aspects of the circuit but a negative effect on others. In the previous two exercises, relative changes in overall circuit efficiency were +13% and -3%. Let's see if these changes in efficiency are statistically meaningful.

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

WORK INDEX EFFICIENCY ACCURACY OF COMPARATIVE WORK INDEX There are three causes for the loss of accuracy in any work index efficiency 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 comparative work index efficiency determinations is approximately +/- 4% (relative).

The value of +/- 4% represents the 95% confidence interval * of our most accurate relative work index efficiency measurements. Under the best conditions, if the relative difference between two measured efficiencies is 4% or greater, then we have observed a statistically meaningful change in circuit efficiency. This is illustrated in Figure 8.

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

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WORK INDEX EFFICIENCY

Figure 8. Two statistically different measurements. In Figure 8, you can see that the 95% confidence interval of one measurement (mean) is just outside the 95% confidence interval of the other. The two measurements are therefore statistically different. In the exercise on rod milling, the relative increase in efficiency was 13%. This means that circuit efficiency increased by a statistically meaningful amount through changing the mill feed water addition rate.

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

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WORK INDEX EFFICIENCY In the exercise on closed-circuit ball milling, the relative loss in efficiency was 3%. This value is less than the minimum 4%. This means that changing the water addition rate to the feed to the ball mill did not have a statistically meaningful effect on overall circuit efficiency. 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. circuit stability is difficult to attain, instrument readings are taken from different instruments, sampling and analytical methods are inconsistant, etc.), then the total error in comparative work index efficiency measurements will be greater than 4%. The value of the total error may be assessed on an individual basis for any plant survey. When comparing efficiencies of circuits in different plants, the relative accuracy is typically in the order of +/- 10 to 20%.

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

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WORK INDEX EFFICIENCY In the introduction to this module, we have presented several circuit arrangements. While work index analysis can be performed on simple circuits such as open circuits and closed grinding circuits with a single mill, it can also be performed on circuits which combine several "simple" circuits in series. This is covered next.

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

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WORK INDEX EFFICIENCY PART III - COMBINED GRINDING CIRCUITS OPERATING WORK INDEX OF COMBINED CIRCUITS You can combine grinding circuits to evaluate the operating work index and work index efficiency of the combined circuit. This technique allows you to determine the overall efficiency of several circuits in series or of an entire grinding plant. A combined circuit generally consists of a rod mill and ball mill in series (conventional circuit) or of several ball mills in series. To obtain the operating work index of a combined circuit, you need to consider the total power draw of all grinding mills in the combined circuit, and the feed and product sizes to and from the combined circuit.

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

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WORK INDEX EFFICIENCY

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ROD MILL / BALL MILL CIRCUITS IN SERIES You can calculate the operating work index of a combined rod mill/ ball mill circuit using the information on the individual rod mill and ball mill circuits. Follow the two steps in the procedure.

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

where

=

W

=

Wio

=

F80 P80

= =

Wio

x

(

10 - 10 šP80 šF80

)

Work input per tonne of ore for the combined circuit (kwh/t) Work (energy) consumed to grind the ore from F80 to P80 (kwh/t) Size of the combined circuit feed (microns) Size of the combined circuit product (microns)

Solve the following exercise.

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

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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: F80: P80:

975 kw 19 146 microns 1035 microns

Ball mill circuit: Ball mill power draw: F80: P80:

1220 kw 1035 microns 60 microns

If you wish, refer back to Figure 5 on page 13 where this combined circuit is illustrated. What is the operating work index of this combined circuit?

The answer follows.

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

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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

12.0 kwh/t

= Wio

10 ( š60

-

10 š19 146

)

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

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

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BALL MILLS IN SERIES The method presented to calculate the operating work index of combined rod/ball mill circuits is also used for ball mills in series. Answer the questions in the following exercise.

Exercise Two stages of ball milling follow rod milling at the Deep Sixty Copper Concentrator. The operating data obtained during a survey of the two ball mill circuits were as follows: Dry circuit feed rate: Rod mill discharge K80:

109.5 t/h 1260 microns

Primary ball mill circuit: Mill power draw (at the pinion): P80:

720 kw 131 microns

Secondary ball mill circuit: Mill power draw (at the pinion): P80:

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

692 kw 60 microns

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Exercise (continued) Questions 1. For the appropriate circuit, what is: Primary circuit

Secondary circuit

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

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Answers 1.

Primary circuit

Secondary circuit

Combined circuit

Power draw (kw):

720

692

1412

F80 (microns):

1260

131

1260

P80 (microns):

131

60

60

2. 11.1 kwh/t Solution:

W =

720 kw 109.5 t/h

6.58 kwh/t

=

= 6.58 kwh/t Wio

(

10 š131

-

10 š1260

11.1 kwh/t = Wio 3. 15.1 kwh/t Solution:

W =

692 kw 109.5 t/h

= 6.32 kwh/t

6.32 kwh/t = Wio

10 ( š60

-

10 ) š131

15.1 kwh/t = Wio 4. 12.8 kwh/t Solution:

W =

1412 kw 109.5 t/h

= 12.90 kwh/t

12.90 kwh/t = Wio

(

12.8 kwh/t = Wio

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

10 š60

-

10 ) š1260

)

WORK INDEX EFFICIENCY How did you do in the exercise? Well? Good work! As you can see, the operating work index of the combined circuit falls between the operating work indices of the individual circuits. Also, in this example, the second stage of ball milling is doing more work than the first stage (15.1 kwh/t versus 11.1 kwh/t). In another module, you will learn how to balance the work done by several grinding circuits in series. Let's turn to the work index efficiency of combined circuits.

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

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WORK INDEX EFFICIENCY WORK INDEX EFFICIENCY OF COMBINED CIRCUITS As previously mentioned, a Bond work index test is performed using a selected sieve opening size. This sieve should yield a test P80 which is as close as possible to the circuit P80 in the plant. Don't worry if the P80 in the plant circuit and that from the Bond test are not exactly the same - they rarely are. Bond work index testing of the feeds to individual circuits is generally required in order to determine the work index efficiency of the combined circuit. In this section, we will show you how to determine the work index efficiency of two combined circuits: the rod mill/ball mill circuit (conventional circuit) and ball mills in series.

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ROD MILL / BALL MILL CIRCUITS IN SERIES To determine the work index efficiency of rod mill/ball mill circuits, follow these seven steps.

Procedure 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) = (%)

[

Eff (WI) x Power ] (rm) draw (rm)

(WI) + [ Eff(bm)

x

Power ] draw (bm)

Total power draw of the combined circuit (kw)

Note The above equation can be used to calculate the overall work index efficiency of any number of grinding circuits in series. For example, for a circuit that combines three individual circuits, the above equation can be reconstructed with three terms in the numerator while the denominator would then equal the sum of the power draws of all three individual circuits.

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

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Solve the following exercise.

Exercise Some results from a survey on a rod mill/ball mill circuit follow: Rod mill power draw: Ball mill power draw: Operating work index of the rod mill circuit: Operating work index of the ball mill circuit:

495 kw 961 kw 20.1 kwh/t 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.

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

WORK INDEX EFFICIENCY 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 is performing much more efficiently than the rod mill circuit.

Solve this other exercise.

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

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Exercise Some information on a rod/ball mill circuit follows.

Power draw: Operating work index: Bond work index:

Rod mill circuit

Ball mill circuit

792 kw 10.8 kwh/t 10.3 kwh/t

828 kw 12.0 kwh/t 12.4 kwh/t

What is the work index efficiency of the combined circuit?

The answer follows.

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

WORK INDEX EFFICIENCY 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 each stage of milling. However, to determine the overall work index efficiency of a multiple-stage ball mill circuit, you usually have to perform only one Bond test. Afterwards, if you want to determine the work index efficiency 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!

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

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WORK INDEX EFFICIENCY MULTIPLE - STAGE BALL MILL CIRCUITS In order to obtain the overall work index efficiency of a multiple-stage ball mill circuit following rod milling, you need to perform only one Bond ball mill work index test. In the case of a two-stage ball mill circuit (two ball mill circuits in series), the feed to the primary circuit will be used as Bond test feed while the test control size will be based on the P80 of the secondary circuit. The work index of the ore will therefore reflect the energy required 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 the ratio of the Bond test work index and of the operating work index for the multiple-stage ball mill circuit. Solve the following exercise.

Exercise The operating work index of a two-stage ball mill circuit (two ball mill circuits 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 of the overall circuit, was 12.9 kwh/t. What is the work index efficiency of this multiple-stage circuit?

The answer follows.

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

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WORK INDEX EFFICIENCY Answer 101% = 12.9 / 12.8 kwh/t

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

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

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WORK INDEX EFFICIENCY WORK INDEX EFFICIENCY OF INDIVIDUAL BALL MILL CIRCUITS IN SERIES You can easily calculate the operating work index of individual ball mill circuits in series following Bond's law of comminution. However, to calculate their work index efficiencies, you must perform several Bond ball mill work index tests. In the case of ball mill circuits in series, there is a special way of testing the ore for grindability. The feed to a Bond ball mill work index test must meet specific size requirements. One of these requirements is that the test feed must not be too fine.

Primary ball mill circuit feed is generally adequately sized for Bond testing; however, the feed to secondary and tertiary ball mill circuits is generally too fine. This means that for a secondary or tertiary circuit, you cannot subject the circuit feed to Bond testing. To circumvent this constraint, you will use the feed to the primary ball mill circuit to perform as many Bond tests as there are individual circuits within the overall ball milling stage. If there are two ball mill circuits in series, two Bond tests are required; if there are three, three Bond tests are required. The variable that will change from one test to the other is the test control size which you will select accordingly. For example, to obtain the work index efficiency of each ball mill circuit if there are two ball mill circuits in series, you need to perform two Bond work index tests on the primary circuit feed: •

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

•

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

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

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WORK INDEX EFFICIENCY You therefore determine the work index efficiency of the overall ball milling stage and that of the primary circuit. In order to calculate the work index efficiency of the secondary ball mill circuit, you must determine the Bond work index of the ore over the size reduction that is observed in the secondary ball mill circuit. Since the feed to the secondary ball mill circuit is too fine for Bond testing, you will use the results from the two Bond tests that you have already performed to determine the work index of the ore for the secondary circuit: the difference in energy input per tonne of ore between the two Bond tests will help you to determine the work index of the ore for the secondary circuit. This principle is illustrated in Figure 10.

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

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

WORK INDEX EFFICIENCY

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

Procedure Use information from Bond ball mill work index tests only in this procedure. 1. Calculate the work input, Wc , during the Bond test done over the size reduction of the ore in the combined two-stage circuit: W

where

c

= Constant

Constant F80 P80

(

10 - 10 šP80 šF80

)

= Bond ball mill work index of the ore for the combined circuit (kwh/t) = Size of the Bond test feed for the combined circuit (microns) = Size of the Bond test product for the combined circuit (microns)

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

= Constant

Constant F80 P80

10 ( šP80

-

10 šF80

)

= Bond ball mill work index of the ore for the primary circuit (kwh/t) = Size of the Bond test feed for the primary circuit (microns) = Size of the Bond test product for the primary circuit (microns)

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

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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 stage of ball milling: W2 = Constant where W2

=

Constant = F80

=

P80

=

10 ( šP80

-

10 šF80

)

Work input by difference to grind the ore over the secondary stage of milling (kwh/t) Bond ball mill work index of the ore for the secondary stage (kwh/t) Size of the Bond test product (P80) for the primary circuit (microns) Size of the Bond test product (P80) for the combined circuit (microns)

Note If you have a three-stage ball mill circuit in your plant, then you need to perform three Bond tests: one to cover the size reduction in the primary stage, one to cover the size reduction in the primary and secondary stages, and one to cover all three milling stages. In this case, adapt the given procedure accordingly.

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

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Exercise Some information on the Bond work index tests performed for a study of a two-stage ball mill circuit composed of two ball mill circuits in series follows:

Bond ball mill test for the combined circuit

Bond ball mill test for the primary stage

Bond ball mill work index:

12.9 kwh/t

13.5 kwh/t

Bond test F80:

1360 microns

1360 microns

Bond test P80:

59 microns

115 microns

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

WORK INDEX EFFICIENCY Exercise (continued) Questions 1. What is the work input, Wc , from the Bond ball mill test for the combined circuit?

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

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

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

The answers follow.

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

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Answers 1. 13.3 kwh/t = 12.9 kwh/t

(

10 š59

-

10 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

11.9 kwh/t

= Constant

10

( š59

-

10 š115

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

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

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

)

WORK INDEX EFFICIENCY

74

WORK INDEX EFFICIENCY OF SINGLE - STAGE BALL MILL CIRCUITS A single-stage ball mill circuit performs the tasks of both a rod mill and a ball mill since it immediately follows the crushing plant. This circuit is not often seen in concentrators and it requires special attention for work index efficiency determination. We will not ask you any questions on this type of circuit in the next Progress Review nor in the Certification Test. You should still cover this section carefully. For this circuit, you must therefore perform both a Bond rod mill and a Bond ball mill work index test on the ore since this ball mill does the work of both a rod mill and a ball mill. To determine the work index efficiency of a single-stage ball mill circuit which immediately follows crushing, follow the six steps in the procedure below. To determine the work index of the ore for the single-stage ball mill circuit, use 2100 microns as the reference size to perform the Bond rod mill test on the ore. Also, use 2100 microns in some of your calculations. (Use the product from the Bond rod mill test to perform the Bond ball mill test.)

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

Where

=

W

=

Wio F80

= =

P80

=

Wio

x

(

10 šP80

-

10 šF80

)

Work (energy) input per tonne of ore to the circuit (kwh/t) Operating work index (kwh/t) Size of the single-stage ball mill circuit feed (microns) Size of the single-stage ball mill circuit product (microns)

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

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

W

r

where

= Constant

Constant

=

F80

=

P80

=

10 ( šP80

-

10 šF80

)

Bond rod mill work index of the ore (kwh/t) Size of the feed to the Bond rod mill test (microns) 2100 microns (do not use the P80 from the Bond test)

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

W

b

where

= Constant

Constant = F80

=

P80

=

(

10 šP80

-

10 šF80

)

Bond ball mill work index of the ore (kwh/t) 2100 microns (do not use the F80 from your Bond test) Size of the product from the Bond ball mill test (microns)

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

s

=

Wr

+ Wb

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

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Procedure (continued) 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):

W

s

where

=

Constant

W = s Constant = F80 = P80

=

(

10 šP80

-

10 šF80

)

Work input in both Bond tests (kwh/t) Bond work index of the ore (kwh/t) Size of the Bond rod mill test feed (microns) 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)

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

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Solve this exercise while carefully following the previous procedure.

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

Survey data: Dry tonnage: Mill power draw: F80: P80:

250 t/h 2000 kw 20 582 microns 173 microns

Bond test results: Bond rod mill W.I. test at 2360 microns (6 mesh): 11.8 kwh/t Test F80: Test P80:

12 200 microns 2 053 microns

Bond ball mill W.I. test at 212 microns (65 mesh): 9.9 kwh/t Test F80: Test P80:

2053 microns 162 microns

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

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

WORK INDEX EFFICIENCY Exercise (continued) 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, W , for the size reduction of the ore b related to the Bond ball mill test?

4. What is the total work input, W , related to both Bond work index s 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. © 1992 GPD Co. Ltd. / Metcom Consulting LLC (Rev.4, 2005)

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Answers 1. 11.6 kwh/t Solution:

W

= 2000 kw = 8.0 kwh/t 250 t/h

8.0 kwh/t = Wio x

10 ( š173

-

10 ) š20 582

11.6 kwh/t = Wio 2. 1.51 kwh/t = 11.8

3. 5.62 kwh/t = 9.9

10

-

( š2100 (

10 š162

10 š12 200 )

-

10 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

( š162

10.3 kwh/t = W.I. 6. 89%

= 10.3 kwh/t 11.6 kwh/t

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

-

10 š12 200 )

WORK INDEX EFFICIENCY By now you should be able to determine the operating work index and work index efficiency of various circuit arrangements. On the job, you can apply what you have learned in this module by using data such as that from circuit surveys. Review your knowledge in the only Progress Review in this module.

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PROGRESS REVIEW Estimated time for completion: 10 minutes

There are five problems in this Progress Review. Each problem refers 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

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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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84

PROGRESS REVIEW (continued)

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?

Combined circuit Primary ball mill circuit Secondary ball mill circuit (calculated)

Write your answer:

Operating work index (kwh/t)

Bond work index (kwh/t)

12.1 11.3 13.2

13.9 13.8 14.0

____________________________

4. At which stage is the ore the most difficult to grind? Write your answer:

____________________________

The answers to the Progress Review follow.

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

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PROGRESS REVIEW (continued)

Answers 1. The numbers corresponding to the terms in the figure follow: Primary ball mill circuit feed

2

Secondary ball mill circuit

12

Combined ball mill circuit product

10

Primary ball mill feed

3

Secondary ball mill discharge

8

Combined two-stage ball mill circuit

13

Secondary ball mill circuit product

9

Secondary ball mill feed

7

Primary ball mill circuit

11

Secondary ball mill circuit feed

6

Primary ball mill discharge

4

Combined ball mill circuit feed

1

Primary ball mill circuit product

5

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

WORK INDEX EFFICIENCY

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PROGRESS REVIEW (continued)

Answers (continued) 2. a) Three. You can determine the operating work index of the primary ball mill circuit, secondary ball mill circuit, and combined two-stage ball 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 in the plant even though they can be distinguished on the flowsheet. The ore that flows through these points is the material used for Bond work index testing since it is 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.

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PROGRESS REVIEW (continued)

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.

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WORK INDEX EFFICIENCY 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.

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CLOSING WORD Congratulations on completing another module of the Metcom Instructional Program. A summary of the contents of this module follows. Bond's law of comminution states that: W = Constant Where

W Constant F80 P80

(

10 šP80

-

10 šF80

)

= Work (energy) input per tonne of ore (kwh/t) = Work (energy) input to grind the ore from F80 to P80 (kwh/t) = K80 of the circuit feed (microns) = K80 of the circuit product (microns)

The "constant" is also called the "operating work index" when W, F80 and 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 to grind a specific ore from the circuit feed size to the circuit product size. It therefore takes into account the grindability characteristics of the ore. By determining the grindability characteristics of the ore through Bond work index laboratory testing, the ore can be factored out of the operating 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 or greater than 100%. Bond work index analysis can be applied to any rod mill or ball mill circuit. The circuits can be analysed individually or combined in series.

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

WORK INDEX EFFICIENCY

The topic of work index efficiency will be further covered in the module entitled "Functional Performance of Ball Milling" in relation to ball mill circuits. In that module, you will see that work index analysis can be used to verify the results from functional performance analysis.

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WORK INDEX EFFICIENCY REFERENCES Bond, F.C., "Crushing and Grinding Calculations", British Chemical Engineering, 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 Mining Journal, March 1960, pp. 82-85. Rowland, C.A., "The Tools of Power Power: The Bond Work Index, A Tool to Measure Grinding Efficiency", AIME meeting, Denver, 1976. Rowland, C.A., "Selection of Rod Mills, Balls Mills, Pebble Mills and Regrind Mills", Design and Installation of Comminution Circuits, SME of AIME, New York, 1982, Chapter 23, pp. 393-438.

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WORK INDEX EFFICIENCY GLOSSARY Eighty percent passing size: The micron size which corresponds to the 80% passing of a sample on a weight 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 the performance of the circuit in terms of the energy consumed to achieve a certain amount of size reduction. Its units are kwh/t. [p. 23]

Work index efficiency:

Ratio (%) between the Bond work index of the circuit feed and the operating work index of the circuit. [p. 29]

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

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