Module5 - Functional Performance of Ball Milling

The Me Metc tcom om Eng ngin inee eeri ring ng and Management Management Sys ystem tem for Plant Gri Grindi nding ng Operations Operations

MODULE #5: FUNCTIONAL PERFOMANCE OF B A L L MIL L ING

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

FUNCTIONAL PERFORMANCE OF BALL MILLING TABLE OF CONTENTS Objectives Introduction

page 1 2

PART PAR T I - The Ele Element ments s of the Func Function tional al Per Perform formanc ance e Equ Equatio ation n

11

Circuit output of fines Classification system efficiency Effective mill power draw Ball mill specific grinding rate Ball mill grinding efficiency Progress Review 1

11 16 24 29 33 39

PART II - Functional Performance Analysis

43

Using the functional performance equation Functional performance efficiency Relating design and operating variables to grinding, classification, and circuit efficiencies Relative accuracy of functional performance parameters Progress Review 2

43 47 53 62 67

Closing word References

77 78

Appendix Append ix A - Selection Selection of the grindability grindability value value to use use in functional performance analysis

79

Glossary

81

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

i

FUNCTIONAL PERFORMANCE OF BALL MILLING LIST OF FIGURES AND TABLES

page

Figure 1. Elements contributing to the output of a ball mill circuit.

4

Figure 2. The "effective mill power draw".

6

"specific grinding rate". Figure 3. The ball mill "s

8

Figure 4. The output of a ball mill circuit.

9

Figure 5. The development of the functional performance equation.

38

Table 1. Estimates of the accuracy of functional performance parameters.


63

ii

FUNCTIONAL PERFORMANCE OF BALL MILLING OBJECTIVES In this module, you will learn how to characterize the performance of ball mill circuits. Specifically, after completing this module, you will be able to: • List and and describe describe the four elements elements of of the functional functional performan performance ce equation for ball mill circuits. • Define and calculate calculate the the classification classification system efficiency efficiency of a ball ball mill circuit. • Define and and calculate calculate the grinding grinding efficiency efficiency of the ball ball mill in a ball ball mill circuit. • Relate overall overall ball ball mill circuit circuit output and circuit circuit efficiency efficiency to specific specific design and operating variables. • Compare sets of circuit survey data in terms of the elements of the functional performance equation.

The prerequisite module to this one is entitled: "Work Index Efficiency". You will need a calculator to complete this module. The estimated time for completion is two and a half hours including a Progress Review at the end of each Part. In this module, most terms and expressions included in the Glossary will be identified as such in the Introduction.


1

FUNCTIONAL PERFORMANCE OF BALL MILLING INTRODUCTION In the prerequisite module entitled "Work Index Efficiency", you have learned about work index analysis* to define overall grinding circuit efficiency. In rod milling, you can use work work index analysis to relate design and operating variables to overall circuit efficiency. However, you cannot use work index analysis for the same purpose on ball mill circuits because of the complex interactions between grinding and classification. In this module, you will learn how to relate design and operating variables to ball mill circuit efficiency through functional performance analysis*. This Introduction is seven pages long. It may seem rather lengthy; however, we feel that it is necessary to give you an overview of what functional performance analysis is about so that you can more efficiently cover the contents of this module. Let’s get started...


2

FUNCTIONAL PERFORMANCE OF BALL MILLING In functional performance analysis, you must differentiate between "coarse" and "fine" particles. To do so, you can select a specific particle size as the target grind size for the ball mill circuit; for example, it is convenient to select the desired 80% passing size as the target grind size. You can then use this target grind size to define and distinguish between "coarse" and "fine" particles in any of the given circuit streams.

Coarse particles are therefore larger than the circuit target grind size. Fine particles are therefore smaller than the circuit target grind size. For any process, including ball mill circuits, we can say that output equals input multiplied by efficiency* .

Output = Input x Efficiency

In a ball mill circuit, the "output" can be defined as the production rate of fines of the circuit. As for any output, ball mill circuit output is a function of both its inputs and efficiencies. There are two "inputs" to a ball mill circuit: the ore fed to the circuit and the power delivered delivered by the grinding mill. A ball mill circuit has has two "efficiencie "efficiencies": s": that of the the ball mill grinding ball mill circuit environment* and that of the classification system* . A ball has two efficiencies because it has two main functions: • The grinding of coarse particles; and, • The removal of the fine particles to make room for grinding more coarse particles in the ball mill. The overall efficiency of the ball mill circuit is therefore comprised of two efficiencies: that of the "ball mill grinding environment" and that of the "classification system".


3

FUNCTIONAL PERFORMANCE OF BALL MILLING Note In functional performance analysis, classification system efficiency* refers to the fines removal effectiveness of the classification system of the circuit - it is not just the efficiency of the classifier (normally viewed as hydrocyclone performance). Look up "classification system" in the Glossary if you have not already done so.

The output of a ball mill circuit is therefore a function of two inputs and two efficiencies. This is illustrated in Figure 1.

Figure

Figure 1. Elements contributing to the output of a ball mill circuit.


4

FUNCTIONAL PERFORMANCE OF BALL MILLING Let's look at classification system efficiency. If a ball mill contained only coarse particles, then 100% of the mill grinding volume and power draw would be applied to the grinding of coarse particles. In reality, the mill always contains fines: these fines are present in the ball mill feed and are produced as the particles pass through the mill. For example, when 60% of the solids in a ball mill is coarse, then the coarse solids inventory * in the mill is 60%, and only 60% of the mill grinding volume and power is used for the grinding of coarse particles. The classification system efficiency of the circuit is then only 60%. We can simply define "classification system efficiency" as the proportion of coarse of coarse solids to total solids in a ball mill .

Classification system efficiency (% (%)

=

Coarse solids inventory in the ball mill (%)


5

FUNCTIONAL PERFORMANCE OF BALL MILLING Figure 2 illustrates that the total mill power draw multiplied by the classification system efficiency is the effective mill power draw * . The effective mill power draw is the power draw that is applied to the grinding of coarse particles.

Figure 2. The "effective mill power draw". Now let's see how the remaining two terms, ore grindability and ball mill grinding efficiency * in the above figure, come into the picture.


6

FUNCTIONAL PERFORMANCE OF BALL MILLING Let's define the ball mill specific grinding rate* as the weight of new product (fines) produced per unit of effective energy* (applied to the coarse particles). Ball mill specific grinding rate (t/kwh)

Circuit output = of fines (t/h) Effective mill power draw (kw)

We can then define the grinding efficiency of a ball mill as the ratio between the specific grinding rate of the coarse solids in the ball mill and the grinding rate (grindability) of the ore in a standard laboratory mill. The grindability characteristic of the ore can be measured in a standardized laboratory test mill.

Ball mill grin gr indi ding ng ef effi fici cien ency cy

=

Specific grinding rate of coarse particles (in the plant ball mill) Ore Or e gr grin inda dabi bili lity ty (i (in n th the e la lab b ba ball ll mi mill ll))

The units of "ball mill grinding efficiency" will be covered in detail in the first part of the module. Alternatively, Alternat ively, we can say that: that:

Specific grinding rate of coar ars se part rtic icle les s (in the plant ball mill)

=

Ball mill gri rin ndin ing g efficiency

x

Ore grindability (in (i n th the e lab mi mill ll))

These are the two remaining elements of the four elements that define ball mill circuit output. See Figure 3.


7

FUNCTIONAL PERFORMANCE OF BALL MILLING

Figure 3. The "ball mill specific grinding rate". Finally, we can recombine the effective mill power draw and the ball mill specific grinding rate of coarse particles to once again derive the circuit output :

Circuit output of fines (t/h)

=

Effective mill power draw (applied to coarse particles) (kw)

x

Study Figure 4.


Ball mill specific grinding rate (of coarse particles per unit of energy applied to them) (t/kwh)

8


output ut of of a ball mill circ circuit. uit. Figure 4. The outp

The equations presented in this introduction can be combined to give the functional performance equation for ball milling:

Circuit output

=

Ball mill Classification Ore Ball mill power x system x grindability x grinding draw efficiency efficiency


9

FUNCTIONAL PERFORMANCE OF BALL MILLING This concludes the introduction to functional performance analysis for ball mill circuits. You may wish to take a break at this time. In Part I of this module, you will learn how to evaluate or use each element of the functional performance equation from the operating data and laboratory results from circuit surveys.


10

FUNCTIONAL PERFORMANCE OF BALL MILLING PART I - THE ELEMENTS OF THE FUNCTIONAL PERFORMANCE EQUA EQUATION TION In this part of this module, you will learn how to calculate the following elements of the functional performance equation: • • • • •

Circuit output of fines Class ssiifi fic cat atio ion n sy sys stem effi fic cie ien ncy Effective mi mill po power dr draw Ball mi mill sp specific gr grinding ra rate Ball mill grinding efficiency

CIRCUIT OUTPUT OF FINES The circuit output is defined as the production rate of fines by the circuit. It is calculated from three values: 1. The dry ore feed rate to the circuit (t/h). 2. The % fines in the circuit feed. 3. The % fines in the circuit product. Use this equation to solve for circuit output:

Circuit outtpu ou putt (t/h)

=

(

Fines in the ci circ rcu uit product (fraction)

-

Fines in the th e ci circ rcu uit feed (fraction)

Use this equation in the following two exercises.


)

Circuit x ore feed ra ratte (t/h)

11

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise During Survey #1 at the Camco Mine, the ore feed rate to the ball mill circuit was 67 t/h. The circuit feed contained 29.33% of -106 micron (150 mesh) material (fines) and the circuit product contained 78.54% of -106 micron (150 mesh) material. What was the circuit output of fines during the survey?

The answer follows.


12

FUNCTIONAL PERFORMANCE OF BALL MILLING Answer 33.0 t/h = (0.7854 - 0.2933) x 67 t/h The circuit was therefore producing 33.0 t/h of fines during Survey #1.

Solve the second exercise.


13

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise During a second survey of the same circuit, the ore feed rate was 70 t/h. The feed to the ball mill circuit contained 30.38% fines and the circuit product contained 77.60% fines. What was the circuit output of fines during the second survey?

The answer follows.


14

FUNCTIONAL PERFORMANCE OF BALL MILLING Answer 33.1 t/h = (0.7760 - 0.3038) x 70 t/h The circuit was therefore producing 33.1 t/h of fines during Survey #2.

Next, let's see how to determine the "classification system efficiency" of a grinding circuit.


15

FUNCTIONAL PERFORMANCE OF BALL MILLING CLASSIFICATION SYSTEM EFFICIENCY The classification system efficiency of a grinding circuit is determined by the percentage of coarse particles in the ball mill in relation to the total solids content of the mill. This can also be referred to as the inventory of coarse particles in the ball mill. You can estimate the inventory of coarse particles in the ball mill by taking the average of the % coarse solids in the ball mill feed and ball mill discharge:

Coarse particles = in the ball mill (% (%)

% coarse % coarse solids in the solids in the ball mill feed + ball mill discharge = 2

Solve the following two exercises.


Classification system efficiency of the circuit ( %)

16

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise The size distributions of ball mill feed and ball mill discharge samples collected during Survey #1 at the Camco Mine are shown in the table below.

Mesh #

4 6 8 10 14 20 28 35 48 65 100 150 200 270 400

Sieve opening size (microns) 4750 3350 2360 1700 1180 850 600 425 300 212 150 106 75 53 38

Cumulative size distribution (% passing) Mill feed Mill discharge 100.00 99.02 96.44 91.31 84.59 77.23 68.90 59.25 47.71 37.37 27.67 20.38 15.42 12.56 10.48


100.00 99.17 97.38 94.95 91.48 87.62 82.20 74.84 64.73 54.41 43.14 33.75 26.97 22.67 18.96

17

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise (continued) Questions Based on a circuit target product size of 106 microns (150 mesh): 1. What is the inventory of coarse solids in the ball mill?

2. What is the classification system efficiency of the grinding circuit?

The answers follow.


18

FUNCTIONAL PERFORMANCE OF BALL MILLING Answers 1. The inventory of coarse solids in this ball mill during the survey was 72.9%. The ball mill feed contained 20.38% fines or (100% - 20.38%) 79.62% coarse solids. The ball mill discharge contained 33.75% fines or (100% - 33.75%) 66.25% coarse solids: 72.9% = 79.62% + 66.25% 2

2. The classification system efficiency of this circuit was therefore 72.9% during the survey.



19

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise The size distributions of ball mill feed and ball discharge samples collected during Survey #2 at the Camco Mine are shown in the table below.

Mesh #

4 6 8 10 14 20 28 35 48 65 100 150 200 270 400


Cumulative size distribution (% passing) Mill feed Mill discharge 100.00 99.07 96.64 91.98 85.89 78.92 70.94 61.53 50.41 40.13 29.76 21.85 16.29 12.70 10.12

100.00 99.33 97.95 95.64 92.36 88.78 83.82 76.86 67.33 57.67 46.05 36.19 28.60 23.73 19.11

Based on a circuit target product size of 106 microns (150 mesh): 1. What was the inventory of coarse solids in the ball mill during the survey?

2. What was the classification system efficiency of the circuit during the survey?


20

FUNCTIONAL PERFORMANCE OF BALL MILLING Answers 1. The inventory of coarse solids in this mill was 71.0%.

The mill feed contained 21.85% fines or 78.15% coarse solids. The mill discharge contained 36.19% fines or 63.81% coarse solids: 71.0% = 78.15% + 63.81% 2

2. The classification system efficiency of this circuit was 71.0%.

Now answer the questions in the following exercise.


21

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise 1. What happened to the classification system efficiency of the circuit at the Camco Mine from Survey #1 to Survey #2? It increased.

It decreased.

2. Examine the functional performance equation on page 9. What was the effect of the variation in classification system efficiency efficienc y on the circuit circuit output from the first to the second survey at the Camco Mine? (Assume that all the other elements of the equation have remained constant from the first to the second survey.) It increased.

It decreased.

The answers follow.


22

FUNCTIONAL PERFORMANCE OF BALL MILLING Answers 1.

It increased.

It decreased.

š

The classification system efficiency decreased slightly from Survey #1 to Survey #2 from 72.9% to 71.0%.

2.

It increased.

It decreased.

š

The absolute variation of 1.9% (72.9% - 71.0%) in classification system efficiency represents a 2.7% relative decrease in classification system efficiency: 72.9% / 71.0% = 2.7% In fact, if all the other items in the functional performance equation were to remain constant, this relative decrease in classification system efficiency would cause the circuit output of fines to decrease also by 2.7%.

Now that the classification system efficiency of the grinding circuit has been defined, let's look at the effective power draw of the ball mill.


23

FUNCTIONAL PERFORMANCE OF BALL MILLING EFFECTIVE MILL POWER DRAW Remember that the mill power draw is always measured at the pinion. This was discussed in detail in the module entitled "Power and Charge Level Measurements". The mill power draw is not fully applied to the breaking of coarse particles because fine particles are also present in the mill. For example, if the classification system efficiency of the circuit is 60%, the mill contains 60% coarse particles and 40% fine particles. In this case, only 60% of the available power is effectively used to grind coarse particles. The other 40% of the available power is used to further grind fine particles: this is a waste of energy and creates extreme fines which can have a detrimental effect on mineral recovery processes downstream. Use this equation to calculate the effective power draw of a ball mill:

Effective mill power draw (kw)

=

Mill power draw (kw)

Classification system x efficiency of the circuit (fraction)

Solve the following two exercises.


24

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise During Survey #1 at the Camco Mine, the classification system efficiency of the circuit was 72.9%. The mill power available for grinding (at the pinion) was 527 kw. What was the effectiv effectivee mill power draw for grinding coarse particles during this survey?

The answer follows.


25

FUNCTIONAL PERFORMANCE OF BALL MILLING Answer 384 kw = 527 kw x 0.729 Since the coarse solids inventory in the ball mill was 72.9%, 384 kw out of the 527 kw available were used to grind coarse particles in the ball mill during this survey.



26

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise During Survey #2 at the Camco Mine, the classification system efficiency of the circuit was 71.0%. The mill power available for grinding (at the pinion) was 523 kw. What was the effective mill power draw for grinding coarse particles during this survey?

The answer follows.


27

FUNCTIONAL PERFORMANCE OF BALL MILLING Answer 371 kw = 523 kw x 0.710

By now you can define three items that relate to circuit output. These were highlighted in Figure 2 on page 5.

Next, we will show you how to determine the "ball mill specific grinding rate", and relate its value to "ore grindability" and "ball mill grinding efficiency".


28

FUNCTIONAL PERFORMANCE OF BALL MILLING BALL MILL SPECIFIC GRINDING RATE Recall from Figure 4 that:

Circuit output (t/h)

=

Effective mill power draw (kw)

x

Ball mill specific grinding rate (t/kwh)

Since you can determine the circuit output and the effective mill power draw for your circuit from a set of survey data, you can calculate the specific grinding rate of the ball mill . To obtain the specific grinding rate of a ball mill, you must: 1. 2. 3. 4.

Calculate the circuit output (t/h). Calculate the classification system efficiency of the circuit (%). Calculate the effective mill power draw (kw). Use the results from Steps (1) and (3) in the above equation.

An example example follows. follows.

Example During Survey #1 at the Camco Mine, the following data was collected:

Circuit ore feed rate: % fines in the circuit feed: % fines in the circuit product:

67 t/h 29.33% 78.54%

Mill power draw at the pinion: % fines in mill feed: % fines in mill discharge:

527 kw 20.38% 33.75%


29

FUNCTIONAL PERFORMANCE OF BALL MILLING The first step is to calculate the circuit output: (0.7854 - 0.2933) x 67 t/h = 33.0 t/h

The second step is to calculate the classification system efficiency : (79.62% + 66.25%) = 72.9% 2 The third step is to calculate the effective mill power draw during the survey: 527 kw x 0.729 = 384 kw

You can now calculate the specific grinding rate of the ball mill during this survey: Circui Circ uitt output 33..0 t/ 33 t/h h

0.08 0. 0859 59 t/ t/kw kwh h

= Effe Effect ctiv ive e mi mill ll x Ball Ball mi mill ll sp spec ecif ific ic power draw grinding rate =

384 kw

x Ball mi mill ll spe pec cif ific ic grinding rate

= Ba Ball ll mi mill ll sp spec ecif ific ic gr grin indi ding ng ra rate te

This means that coarse material was being ground into fines at the rate of 0.0859 tonnes for every kwh of effective energy (applied to the grinding of coarse particles).


30

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise During Survey #2 at the Camco Mine, the data collected were as follows:

Circuit ore feed rate: % fines in the circuit feed: % fines in the circuit product:

70 t/h 30.38% 77.60%

Mill power draw at the pinion: % fines in mill feed: % fines in mill discharge:

523 kw 21.85% 36.19%

What was the specific grinding rate of the ball mill during this second survey?

The answer follows.


31

FUNCTIONAL PERFORMANCE OF BALL MILLING Answer The answer is 0.0892 t/kwh. The circuit output was: (0.7760 - 0.3038) x 70 t/h = 33.1 t/h

The classification system efficiency of the circuit was: (78.15% + 63.81%) = 71.0% 2 The effective mill power draw was: 523 kw x 0.710 = 371 kw

And the specific grinding grinding rate rate of the mill was: 33.1 t/h = 371 kw x Ball mill specific grinding rate 0.0892 t/kwh = Ball mill specific grinding rate

Let's look at "ball mill grinding efficiency".


32

FUNCTIONAL PERFORMANCE OF BALL MILLING BALL MILL GRINDING EFFICIENCY Recall from the introduction that ball mill grinding efficiency may be defined as the ratio between the ball mill specific grinding rate and the grinding rate (grindability) of the ore in a laboratory mill: Ball mill grinding efficiency /kwh ( tg/rev )

=

Ball mill specific grinding rate (t/kwh) Grindability of the ore (g/rev)

Note the units of "ball mill grinding efficiency". These units reflect the grinding rate of the coarse solids in the plant ball mill (t/kwh) versus the grindability rate of solids in the lab mill (g/rev). Since each revolution of the lab mill represents a fixed amount of energy, the units in both the numerator and denominator are weight of fines produced per unit of energy. Ball mill grinding efficiency could therefore be considered as a unitless number. However, we recommend that you carry the units in all your calculations; you will see that some of these units cancel out with others when you write the functional performance equation. Solve the following two exercises on ball mill grinding efficiency.


33

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise During Survey #1 at the Camco Mine, the specific grinding rate of coarse particles in the mill was 0.0859 t/kwh. In the lab, the grindability of the ore was found to be 2.08 g/rev. What was the grinding efficiency of the ball mill during this survey?

The answer follows.


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FUNCTIONAL PERFORMANCE OF BALL MILLING Answer 0.0413 t/kwh = 0.0859 t/kwh g/ g/rev 2.08 g/rev

The grindability of the ore can be determined through different types of standard laboratory test procedures as discussed in the module entitled "Introduction to Grindability Testing". Whether you should use the grindability (g/rev) measured in a Bond work index test or in an on-site batch grindability test is discussed in Appendix Append ix A of this this module. You should should read this this appendix appendix after you have covered the main contents of this module. In the following example and exercises, the Bond ball mill grindability values are used.

Solve this second exercise.


35

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise During Survey #2 at the Camco Mine, the specific grinding rate of the ball mill was 0.0892 t/kwh. This time, the grindability of the ore was 2.31 g/rev. 1.

What was the ball mill grinding efficiency for this second survey?

2.

What hap What happe pene ned d to the the bal balll mill mill grin grindin ding g effic efficien iency cy from from the fir first st to the second survey?

The answers follow.


36


0.0386 t/ t/k kwh = 0.08 089 92 t/k /kw wh g/ g/rev 2.31 g/rev

2.

Betwee Betw een n the the two two surve surveys ys carr carried ied ou outt at th the e Camco Camco Min Mine, e, the the ball mill grinding efficiency fell from 0.0413 to 0.0386. The grinding efficiency of the ball mill fell by 7%: 0.0413 / 0.0386 = 7.0%


37

FUNCTIONAL PERFORMANCE OF BALL MILLING In this section, you have learned how to calculate and use the items highlighted in Figure 5.

Figure 5. The development of the functional performance equation.

Time for a Progress Review!


38


1

PROGRESS REVIEW Estimated time for completion: 10 minutes

There is one problem and five questions in this Progress Review.

The results from Survey #1 on the ball mill circuit at Fida Mines are shown in the table below.

Mesh #

4 6 8 10 14 20 28 35 48 65 100 150 200 270 400


Cumulative size distribution (%) Grinding circuit Ball mill Feed Product Feed Discharge 100.00 99.04 96.16 91.28 80.73 69.69 58.85 50.11 44.27 38.93 34.27 31.39 28.24 26.13 23.63

100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 99.86 99.13 96.44 86.07 76.32 67.37

10 1 00.00 99.77 98.74 96.92 93.06 88.54 82.87 76.55 67.77 56.35 39.13 23.55 11.59 7.77 5.49

100.00 99.90 99.93 99.55 98.76 47.55 94.91 90.99 83.60 73.34 56.86 41.18 27.13 21.36 17.24

More information on the survey follows: Circuit solids feed rate: Ball mill power draw: Ore grindability:

60 t/h 500 kw 1.87 g/rev

The target product size in this circuit is 75 microns (200 mesh).


39


1

PROGRESS REVIEW (continued)

Questions 1. What was the circuit output of fines during the survey?

2. What was the classification system efficiency of the circuit (coarse solids inventory in the ball mill)?

3. What was the effective mill power draw ?

4. What was the specific grinding rate of the ball mill ?

5. What was the grinding efficiency of the ball mill ?

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

40


1


Answers 1. 34.7 t/h

= (0.8607 - 0.2824) x 60 t/h

2. 80.6%

= (100% - 11.59%) + (100% - 27.13%) 2

3. 403 kw

= 0.806 x 500 kw

4. 0. 0.0861 t/kwh

= 34.7 t/h 403 kw

5. 0. 0.0460 t/kwh g/rev

= 0.0861 t/kwh 1.87 g/rev


41

FUNCTIONAL PERFORMANCE OF BALL MILLING How did you do? If you scored 100%, good work! Take a break before moving on to Part II of this module.


42

FUNCTIONAL PERFORMANCE OF BALL MILLING PART II - FUNCTIONAL PERFORMANCE ANALYSIS USING THE FUNCTIONAL PERFORMANCE EQUATION The functional performance equation follows:

Circuit = output (t/h)

Ball mill power draw (kw)

x

Classification system efficiency

Ore Ball mill x grindability x grinding efficiency

(fraction)

(g/rev)

(t/kwh) (g/rev)

Let's use the equation to analyse the results from Survey #1 at the Camco Mine. These results were already presented in Part I:

Circuit output (of fines): Ball mill power draw (at the pinion): Classification system efficiency: Grindability of the ore: Ball mill grinding efficiency :

33.0 t/h 527 kw 72.9% 2.08 g/rev 0.0413 t/kwh g/rev

The functional performance equation for this survey looks like this: 33.0 t h

=

527 kw x 0.729

x 2.08 g x 0.0413 t/kwh rev g/rev

Presented in this fashion, we can see that circuit output depends on the four elements of the equation. Perform the calculations on the right-hand side of the equation and compare the result to the circuit output value on the left-hand side to ensure that the equation is balanced.


43

FUNCTIONAL PERFORMANCE OF BALL MILLING You can see that the output of new product (fines) of a ball mill circuit depends on: a) b) c) d)

The power draw of the ball mill. The classification system efficiency. The grindability of the ore. The ball mill grinding efficiency efficiency..

The elements of the functional performance equation can be readily obtained from a circuit survey and through standard laboratory analyses of the samples collected during the survey; all but the last term of the equation (the ball mill grinding efficiency) are directly determined from survey information and laboratory analyses. The efficiency of the ball mill grinding environment can be calculated from the functional performance equation when all the other values are known. In the intermediate steps, the effective mill power draw and the ball mill specific grinding rate are also calculated. Practice using the functional performance equation in the following exercise.


44

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise Write the functional performance equation using the following information on Survey #2 at the Camco Mine.

Circuit output: Mill power draw at the pinion: Classification system efficiency: Grindability of the ore: Grinding efficiency of the ball mill:

The equation follows.


33.1 t/h 523 kw 71.0 % 2.31 g/rev. 0.0386 t/kwh g/rev

45

FUNCTIONAL PERFORMANCE OF BALL MILLING Answer The functional performance equation for Survey #2 is: 33.1 t = h

523 kw x 0.710 x 2.31 g x 0.0386 t/kwh rev g/rev

Next, you will learn how to calculate the functional performance efficiency of a ball mill circuit.


46

FUNCTIONAL PERFORMANCE OF BALL MILLING FUNCTIONAL PERFORMANCE EFFICIENCY Once again, the functional performance equation looks like this:

Circuit output

=

Ball mill Classification Ore Ball mill power x system x grindability x grinding draw efficiency efficiency

This equation shows that for given energy and ore inputs, circuit output is maximised when the product of the two efficiency parameters, i.e. classification system efficiency and ball mill grinding efficiency, is maximised. The functional performance efficiency of a circuit is therefore the product of the two efficiency parameters. This also equals the circuit output of fines per unit of mill power draw for ore of a given grindability:

Functional performance Classification Ball mill efficiency = system x grinding = of the efficiency efficiency circuit or Eff(FP)

Study the following example.


Circuit output . Ball mill x Ore power grinddraw ability

47

FUNCTIONAL PERFORMANCE OF BALL MILLING Example For the first survey at the Camco Mine, the functional performance equation looks like this: 33.0 t = h


The values in the equation can be used directly to calculate the functional performance efficiency of the circuit during the survey: Eff (FP)

= =

0.729 x 0.0413 t/kwh g/rev 0.0301 t/kwh g/rev

Calculate the functional performance efficiency of the second survey in the following exercise.


48

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise For Survey #2 at the Camco Mine, the equation is: 33.1 t = h


Calculate the functional performance efficiency of the circuit during this survey.

The answer follows.


49

FUNCTIONAL PERFORMANCE OF BALL MILLING Answer EFF (FP)

=

0.710 x 0.0386 t/kwh g/rev

=


0.0274 t/kwh g/rev

50

FUNCTIONAL PERFORMANCE OF BALL MILLING To summarize the results from both surveys at the Camco Mine, the equation for Survey #1 was: 33.0 t = h


Survey #2 gave this equation: 33.1 t = h


Assuming that all the Assuming the above figures are are significant significant in terms terms of their their reported accuracy, we can say that during Survey #2 compared to Survey #1: a)

The Th e mill mill pow power er draw draw de decr creas eased ed mar margin ginall ally y (less (less th than an 1%). 1%).

b)

The cla classif ssificat ication ion syst system em effi efficien ciency cy dec decreas reased ed slig slightly htly (les (less s than than 3%).

c)

The ore The ore got got signi signific fican antly tly ea easie sierr to grin grind d (app (appro roxim ximate ately ly 11% 11% higher in grindability).

d)

The grind The grindin ing g effic efficien iency cy of the the bal balll mill mill decr decrea ease sed d (by (by approximately 7%).

The net effect of the variations in the four elements was a negligible increase in the circuit output (0.3%). The two efficiency elements of the equation from Survey #1 to #2, i.e. classification system efficiency and ball mill grinding efficiency , have decreased. This indicates that the overall efficiency of the grinding circuit has also decreased. The functional performance efficiencies that you have just studied and calculated reflect this: 0.0301 versus 0.0274 t/kwh/g/rev.


51

FUNCTIONAL PERFORMANCE OF BALL MILLING To verify that the overall efficiency of the grinding circuit has decreased, you can also compare the work index efficiency* results from both surveys. As a reminder: Work index efficiency = Bond work index of the ore (kwh/t) . (%) Operating work index of the circuit (kwh/t)

In this particular case, the work index efficiency of the circuit decreased from 106% to 101%. This supports the results from functional performance analysis.

Note "Functional performance analysis" and "work index analysis" will not necessarily agree in quantitative terms because they are based on different principles. However, the general trend indicated by one will be reflected in the other. Both analyses are good ways to measure circuit performance; both should be applied to a set of circuit survey data so that you can compare and verify your results.

Both surveys at the Camco Mine were performed under two different but normal operating conditions to provide basic measures of circuit efficiencies. Ball mill grinding efficiency decreased by 7%; a close look at all ball mill parameters would reveal the cause of the decrease. When two or more surveys are conducted in order to study the effects of a specific variable on circuit efficiency, survey results become invaluable in the search for improving circuit performance. Turn the page to find out about exciting applications of functional performance analysis!


52

FUNCTIONAL PERFORMANCE OF BALL MILLING RELATING DESIGN AND OPERATING VARIABLES TO GRINDING, CLASSIFICATION, AND CIRCUIT EFFICIENCIES The goal of the Metcom System is to improve grinding efficiency in your plant. By comparing the results of two or more surveys using functional performance analysis, you can establish which design and/ or operating variables can be manipulated to improve circuit efficiency. From now on, you can plan circuit surveys to study the effect of specific variables on circuit efficiency. An example example follows. follows.

Example Recall the earlier study at the Horse Hair Mine presented in the module entitled "Work Index Efficiency". In this study, water addition rate to the ball mill feed was tested. Have a look at the figure below.

Figure


53

FUNCTIONAL PERFORMANCE OF BALL MILLING If you recall, in this circuit, hydrocyclone underflow (ball mill feed) is normally diluted from 78% to 70% solids. One survey (C) was conducted under this condition. A second survey (D) was conducted with the ball mill feed water shut off. Some results from the surveys were as follows:

Survey # Hydrocyclone underflow % solids: Ball mill discharge % solids: Work index efficiency:

C

D

78% 70%

76% 76%

92%

89%

Work index analysis indicated a net loss in the overall efficiency of the circuit from the first to the second survey: 92% versus 89%. (As you know, this change was not significant.) However, work index analysis could not indicate how and by how much grinding efficiency and classification system efficiency were affected.

Subsequently, the survey data were reviewed using functional performance analysis.

Circuit output (t/h)

=

Ball mill power draw (kw)

Classification Ore Ball mill x system x grindability x grinding efficiency efficiency (fraction)


(g/rev)

(t/kwh) (grev)

54

FUNCTIONAL PERFORMANCE OF BALL MILLING For Survey C, the functional performance equation was: 31.2 t/h = 480 kw x 0.62 x 2.50 g/rev x 0.0 0.0419 419 t/kwh g/rev For Survey D, the equation was: 27.2 t/h = 470 kw x 0.53 x 2.32 g/rev x 0.0471 t/kwh g/rev

You can see that from Survey C to Survey D: 1. 2. 3. 4.

The mill The mill pow power er dra draw w dec decre reas ased ed sl slig ight htly ly (2% (2%). ). Clas Cl assif sifica icatio tion n system system effic efficien iency cy decre decrease ased d substa substanti ntiall ally y (17%). (17%). The Th e ore ore wa was s mor more e dif diffi ficu cult lt to gr grin ind d (8% (8%). ). The Th e grind grinding ing ef effic ficien iency cy of of the the ball ball mill mill inc incre rease ased d (12%) (12%)..

The net effect of all these changes was a relative 15% decrease in the circuit output. The survey results therefore indicate that without water addition to the ball mill, classification system efficiency decreased significantly while grinding efficiency increased. As a result of the changes in these two efficiencies, overall circuit efficiency decreased. This was confirmed by the calculated work index efficiencies (92% versus 89%) and by the calculated functional performance efficiencies (0.0260 versus 0.0250).


55

FUNCTIONAL PERFORMANCE OF BALL MILLING Recall that work index analysis at the Horse Hair Mine did not reveal why the overall efficiency of the circuit decreased following the change in the water addition rate. However, functional performance analysis clearly shows what happened: • The decrease in the classification system efficiency was attributed to poorer hydrocyclone performance, as expected with a reduction in water usage in the circuit.

efficiencyy was attributed • The increase in ball mill grinding efficienc to the increase in ball mill slurry density (which happened to be favorable to grinding in this application). Based on the results from functional performance analysis, water addition should be discontinued at the ball mill feed and it should instead be added at the hydrocyclone feed pump box . This would maintain new and improved ball mill grinding efficiency (0.0471 t/kwh/g/rev) and would restore good classification system efficiency (62%). As a result, the overall efficiency of the circuit would increase significantly. With this new circuit design, you would expect the functional performance efficiency of the circuit to increase to 0.0292: Eff (FP)

=

0.62 x 0.0471 t/kwh g/rev = 0.0292 t/kwh g/rev

This represents a 12% relative increase in overall circuit efficiency from the best previous circuit conditions (Survey C: 0.0260). In addition, if you assume that the inputs to the circuit are the same as those measured during Survey C, you would expect the circuit output to reach 35.0 t/h instead of 31.2 t/h: 35.0 t/h = 480 kw x 0.62 x 2.50 g/rev x 0.0471 t/kwh g/rev


56

FUNCTIONAL PERFORMANCE OF BALL MILLING This means that a simple change in the selection of the water addition point can increase the efficiency and output of this circuit by 12%. Parameters such as hydrocyclone adjustments and ball diameter have not even yet been explored!

So far, we have presented you with only one example of how to study the effect of a variable on overall circuit efficiency through functional performance analysis. With the results from properly conducted plant surveys, you can explore many ways in which to run your grinding circuit more efficiently, thanks to the functional performance equation! Solve the following exercise.


57

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise The metallurgical staff at the Greenfield Concentrator are conducting a long-term study of the effect of media size on the grinding efficiency of the ball mill and on the overall efficiency of their ball mill circuit. So far, they have conducted two surveys: the first when the ball mill contained a worn-in charge of 2-inch (5 cm) balls and the second while the mill contained a worn-in charge of a mixture (50/50) of 1-inch (2.5 cm) and 1 1/2-inch (3.8 cm) balls. During both surveys, the mill liners were at the half-life stage. Other circuit parameters were carefully adjusted to be similar during both surveys. The results are as follows:

Survey G-4 35.8 t/h = 516 kw x 0.68 0.680 0 x 2.83 g/re g/rev v x 0.0 0.0361 361 t/kw t/kwh/g/ h/g/rev rev Eff (FP) = 0.02 0.0245 45 t/kw t/kwh/g/ h/g/rev rev Eff (W (WI) I) = 101%

Survey G-5 38.5 t/h = 511 kw x 0.69 0.691 1 x 2.62 g/re g/rev v x 0.0 0.0416 416 t/kw t/kwh/g/ h/g/rev rev Eff (FP) = 0.02 0.0287 87 t/kw t/kwh/g/ h/g/rev rev Eff (W (WI) I) = 113%


58

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise (continued) Questions 1. Com Compare pare the the ball ball mill grindin grinding g efficienc efficiencies ies for for both surve surveys. ys.

2. Compare Compare the the circuit circuit function functional al performa performance nce efficie efficiencie ncies s for both surveys.

3. Com Compare pare the the circuit circuit work work index index efficie efficiencie ncies s for both both surveys. surveys.

4. Compare Compare the the trends trends from from functiona functionall performan performance ce analysi analysis s to those from work index analysis.

5. From From all all thos those e effi efficien ciency cy res results ults,, wha whatt wou would ld you do at this point about grinding media usage in this plant?

The answers follow.


59


Ball mill grind grinding ing effic efficienc iency y was 15% highe higherr during during the the secon second d survey (0.0361 versus 0.0416). This indicates that a 50/50 mixture of 1-inch and 11/2-inch (2.5 and 3.8 cm) balls are 15% more efficient than 2-inch (5 cm) balls. (Remember that most operating conditions were maintained as much as possible from the first to the second survey.)

2.

The 15% 15% increa increase se in ball ball mill mill grind grinding ing effic efficien iency cy automa automatica tically lly caused a 15% increase in functional performance efficiency. In addition, a small increase in the classification system efficiency during the second survey contributed another 2% increase in circuit efficiency. The total increase in functional performance efficiency was therefore 17% from the first to the second survey.

3.

Work inde index x analys analysis is indicat indicated ed that that circuit circuit perf performa ormance nce incr increase eased d by 12% from the first to the second survey, from 101% to 113%.

4.

Work inde index x analys analysis is suppor supports ts the the results results from func function tional al performance analysis. Work index analysis alone, however, would leave us wondering whether or not the increase in efficiency is due to the change of balls, ore, hydrocyclone performance, etc. Functional performance clearly shows by how much the change in media has affected the ball mill grinding efficiency and the overall efficiency of the circuit.

5.

You would would hop hopeful efully ly contin continue ue using using 1-inc 1-inch h and 1 1/2-inc 1/2-inch h (2.5 (2.5 and 3.8 cm) balls! It may be that 2-inch (5 cm) balls were much oversized for this application.


60

FUNCTIONAL PERFORMANCE OF BALL MILLING Of course, economics plays a major role in decision making whether it is for selecting media size, changing equipment, boosting tonnage, etc. In the following module entitled "Grinding and Plant Economics", you will learn how to deal with economic issues. How accurate are your functional performance values? Find out in the following section.


61

FUNCTIONAL PERFORMANCE OF BALL MILLING RELATIVE ACCURACY OF FUNCTIONAL PERFORMANCE PARAMETERS As discussed discussed in the the module entitled "Work "Work Index Index Efficiency", Efficiency", there there are variations in the accuracy of all measured and calculated performance parameters due to sampling, plant and laboratory measurements, and circuit instability. Table 1 provides estimates of the accuracy (roughly, the 95% ) in the relative values of ball mill circuit confidence interval* ) functional performance parameters as determined under the best conditions. The "best conditions" imply that: •

Comparisons Comparis ons are made made betw between een two two sets sets of of data data collec collected ted on the the same circuit.

•

Circu Cir cuit it stab stabili ility ty has has been been veri verifie fied d in each each cas case. e.

•

All samp sampling ling and ana analysi lysis s were were carri carried ed out out using using the same equipment (including a rotary splitter for sample division) and procedures.


62

FUNCTIONAL PERFORMANCE OF BALL MILLING Table 1. Estimates of the accuracy of functional performance parameters

Parameter

Estimated error a

Based on:

Circuit output (of fines)

< +/- 1%

Circuit feed rate (weightometer readings and % moisture in feed) and size analyses of circuit feed and product streams.

Mill power draw

+/- 2%

Multiple voltmeter, ammeter and power factor readings.

Classification system efficiency

< 1%

Size analyses of ball mill feed and ball mill discharge streams.

Ore grindability

+/- 2%

Combined sampling and experimental errors through all the steps to arrive at the ore laboratory grindability.

Effective mill power draw

+/- 2%

The calculated combined error from the calculation of this parameter from the elements of the functional performance equation.

Specific grinding rate

+/- 2%


Ball mill grinding efficiency

+/- 3.5%


Functional performance efficiency

+/- 3%

The calculated combined error from the calculation of this parameter from classification system efficiency and ball mill grinding efficiency.

a

95% confidence interval for values measured under the best conditions.


63

FUNCTIONAL PERFORMANCE OF BALL MILLING Note Recall that the accuracy (approximate 95% confidence interval) of relative work index efficiency determinations is +/- 3% when determined under the best conditions. Since it is simpler to calculate "functional performance efficiency" than to calculate "work index efficiency", functional performance efficiency is statistically more accurate than work index efficiency.

The difference between parameters evaluated from two circuit surveys must exceed the values listed in Table 1 for them to be statistically different . An example follows.

Example Power draw readings for a ball mill during two surveys were 958 and 931 kw respectively. For these two values to be statistically different, they must vary by more than 2% (use the average of the two values at the denominator): 958 - 931 kw = 2.9% 945 kw This calculation indicates that the two values of power draw are statistically different. Solve the following exercise using the information in Table 1.


64

FUNCTIONAL PERFORMANCE OF BALL MILLING Exercise Determine if the two values of ball mill grinding efficiency, 0.0452 and 0.0466, are statistically different.

The answer follows.


65

FUNCTIONAL PERFORMANCE OF BALL MILLING Answer No. The difference is 3.1%; according to Table 1, it must be at least 3.5%:

0.0466 - 0.0452 = 3.1% 0.0459

These measurements are therefore not statistically different.

Under less than ideal conditions, the relative inaccuracy of measurements will be significantly greater. For example, the use of different sieves of the "same opening size" for sieve analyses can easily introduce an error of +/-1% on sieve analyses. Typically, a variation of +/-10 to 15% will exist between ball mill grinding efficiency determinations from different operations. The actual variation in comparing functional performance parameters must be evaluated for each particular case. Consult with Metcom if you ever need help with this task. You can practice your ability to determine the effects of a design variable on overall circuit efficiency in the last Progress Review of this module.


66


2

PROGRESS REVIEW Estimated time for completion: 25 minutes

There is only one problem in this Progress Review. Refer back to the functional performance equation presented on page 36 if necessary. At the Carrier Carrier Mine, Mine, two grinding grinding circuit circuit surveys surveys were carried out out to determine the effect of grinding media on circuit efficiency. During Survey #1, media A was used. Subsequently, after a lengthy period of charging with media B, Survey #2 was carried out. The target product size in this concentrator is 106 microns (150 mesh). Survey results are summarized bellow:

Survey #

1

2

Grinding media

A

B

Circuit information from the surveys: Tonnage (t/h): % fines (-106 microns) in the circuit feed: % fi fin nes (-106 mic icrron ons s) in the cir ircu cuiit produ duc ct: Ore grindability (g/rev):

70.3 30.3% 77. 7.6 6% 2.31

71.3 26.3% 77. 7.5 5% 1.98

% fines (-106 microns) in the ball mill feed: 21.8% % fines fines ((-106 106 mic micron rons) s) in the the bal balll mill mill disc discha harge rge:: 36 36.1% .1% Power draw (kw): 523

20.5% 35.1% 35 .1% 549

Information on the ball mill:


67


2


Questions 1.

What was the circuit output during each survey? Survey #1: Survey #2:

2.

What was the classification system efficiency during each survey? Survey #1: Survey #2:

3.

What was the effective mill power draw during each survey? Survey #1: Survey #2:

4.

What was the specific grinding rate of the mill during each survey? Survey #1: Survey #2:


68


2 5.

PROGRESS REVIEW (continued) What was the ball mill grinding efficiency during each survey? Survey #1:

Survey #2:

6.

Write the functional performance equation for each survey. Survey #1:

Survey #2:

7.

What was the functional performance efficiency of the circuit during each survey? Survey #1:

Survey #2:


69


2 8.

PROGRESS REVIEW (continued) Comment on an increase or decrease decrease of the following items from Survey #1 to Survey #2.

Increased Circuit output Ball mill power draw Classification system efficiency Effective mill power draw Ore grindability Ball mill specific grinding rate Ball mill grinding efficiency Functional performance efficiency


Decreased

70


2


9. Assuming that all the comparative data were generated under ideal conditions, select the items which varied enough to be statistically different. Use the space below for your calculations.

Circuit output Ball mill power draw Classification system efficiency Effective mill power draw Ore grindability Ball mill specific grinding rate Ball mill grinding efficiency Functional performance efficiency


71


2


10. What do you conclude about the effect of using media B over media A on the ball mill grinding efficiency of this circuit from this testwork? ______________ _______ _______________ _______________ ______________ __________ ___

The answers follow.


72


2


Answers 1. Survey #1: 33 33.3 .3 t/ t/h h

= (0.7 (0.776 76 - 0.3 0.303 03)) x 70.3 70.3 t/ t/h h

36.5 t/ t/h h Survey #2 : 36.5

= (0.77 (0.775 5 - 0. 0.26 263) 3) x 71 71.3 .3 t/ t/h h

2. Survey #1: 71.1% = (100.0% - 21.8%) + (100.0% - 36.1%) 2

Survey #2: 72.2% = (100.0% - 20.5%) + (100.0% - 35.1%) 2 3. Survey #1: 372 kw = 523 kw x 0.771

Survey #2: 396 kw = 549 kw x 0.722 4. Survey #1: 0.0895 t/kwh = 33.3 t/h / 372 kw

Survey #2: 0.0922 t/kwh = 36.5 t/h / 396 kw 5. Survey #1 : 0.0387 t/kwh = 0.0895 t/kwh g/rev 2.31 g/rev 0. 0466 t/kwh = 0.0922 t/kwh Survey #2: 0.0466 g/rev

1.98 g/rev

6. Survey #1: 33.3 t/h = 523 kw x 0.711 x 2.31 g/rev x 0.0387 t/kwh g/rev

Survey #2: 36.5 t/h = 549 kw x 0.722 x 1.98 g/rev x 0.0466 t/kwh g/rev © 1992 GPD Co. Ltd. / Metcom Consulting Consulting LLC (Rev.4, 2005)

73


2


Answers (continued) 7.

Surv Su rvey ey #1:

0.027 0.0 275 5 t/k t/kwh wh/g/ /g/rev rev = 0.71 0.711 1 x 0. 0.038 0387 7 t/k t/kwh wh/g/ /g/rev rev

Survey #2:

0.0336 t/kwh/g/rev = 0.722 x 0.0466 t/kwh/g/rev

Increased

8. Circuit output

š

Ball mill power draw

š

Classifi Clas sificati cation on system efficienc efficiency y

š

Effective mill power draw

š

Decreased

š

Ore grindability Ball Ba ll mi mill ll sp spec ecif ific ic gr grin indi ding ng ra rate te

š

Ball mi mill gr grinding efficiency

š

Functional performance efficiency

š


74


2


Answers (continued) 9. All changes were statistically meaningful:

š

Circuit output:

36.5 - 33.3 = 9.2% 34.9

Ball mill power draw:

549 - 523 = 4.9% 536

Classif Cla ssificat ication ion syst system em effi efficien ciency: cy:

72.2% 72.2 % - 71.1 71.1% % = 1.5% 71.7%

š

Effective mill power draw:

396 - 372 = 6.3% 384

š

Ore grindability:

2.31 - 1.98 = 15.3% 2.15

š

Ball Ba ll mi mill ll sp spec ecif ific ic gr grin indi ding ng ra rate te::

0.09 0. 0922 22 - 0. 0.08 0895 95 = 3.0% 3.0% 0.0909

š

Ball mil illl gri rind ndiing ef effi fici cie enc ncy y:

0.0 0. 0466 - 0.0 .03 387 = 18.5% 0.0427

š

Functional performance efficiency: 0.0336 - 0.0275 = 20.0% 0.0306

š

š

10. The use of media B has a positive effect on the efficiency of this grinding circuit: ball mill grinding efficiency increased by 20%.


75

FUNCTIONAL PERFORMANCE OF BALL MILLING The circuit work index efficiency during the two surveys presented in this Progress Review was also calculated: the results showed that work index efficiency increased from 101% to 112%. This supports the trend of increased efficiency observed through functional perfomance analysis. Note that the (112% - 101%) 11% change in work index efficiency does not identify the cause(s) of the improvement in overall circuit efficiency in this study. Many things changed from the first to the second survey (the ore, the circulating load, hydrocyclone performance, etc.) which could affect overall circuit efficiency. Only through functional performance analysis was it possible to identify an increase in the efficiency of the breakage environment of the ball mill, and thus relate the increase in overall circuit efficiency to the change in grinding media. How did you do in this Progress Review? • Well? Fantastic! • Not so well? It may take some time and practice on information from your own plant before you can really feel comfortable with the new terms of functional performance analysis. You have completed all the work in the module. Congratulations!


76

FUNCTIONAL PERFORMANCE OF BALL MILLING CLOSING WORD We hope that you have enjoyed completing this module. We also hope you will successfully use functional performance analysis (and work index analysis) on the grinding circuit(s) in your plant. Before quitting, go to Appendix A where a short review on the selection of the appropriate grindability test for functional performance analysis is presented.


77

FUNCTIONAL PERFORMANCE OF BALL MILLING REFERENCES McIvor, R.E., "Classification Effects in Wet Ball Milling Circuits", Mining Engineering, August 1988, pp. 815-820. McIvor, R.E., Lavallée, M.L., Wood, K.R., Blythe, P.M. and Finch, J.A., "Functional Performance of Ball Milling", Mining Engineering, March 1990, pp. 269-276. McIvor, R.E., "Technoeconomic Analysis of Plant Grinding Operations", Ph. D. Thesis, McGill University, Montreal, 1989.


78

FUNCTIONAL PERFORMANCE OF BALL MILLING APPENDIX A SELECTION OF THE GRINDABILITY VALUE TO USE IN FUNCTIONAL PERFORMANCE ANALYSIS The topic of "grindability" will be covered in detail in the module entitled "Introduction to Grindability Testing". What you need to know at this point in time is that "grindability" is expressed in grams per revolution (of fines or new product) created in a laboratory test mill. "Grindability" can be determined by performing either a: • •

Bond ball mill work index (locked-cycle) test on circuit feed (ore). On-site grindability test (single batch) on the coarse solids in the ball mill feed.

Throughout this module on functional performance analysis, we compare the grinding rate of the material in the plant ball mill to the grindability of the circuit feed in a Bond ball mill test to obtain "ball mill grinding efficiency":

Ball mill grinding effi ef fici cien ency cy t/kwh ( g/rev )

=

Ball mill spec sp ecif ific ic gr grin indi ding ng ra rate te (t (t/k /kwh wh)) Ore grindability (g/rev)

To date, the Metcom System has almost exclusively used the grindability of circuit feeds measured in a Bond ball mill work index test for functional performance analysis since the Bond work index test has been traditionally performed on circuit feeds from detailed plant surveys. (The Bond work index of the ore is needed for work index analysis.)


79

FUNCTIONAL PERFORMANCE OF BALL MILLING However, you can always use the grindability of the plant b a l l m i l l feed as measured in an on-site batch grindability test . This grindability value reflects the ease of grind of the coarse particles that actually go into the ball mill . On-site batch grindability is therefore the ideal parameter for determining ball mill grinding efficiency. Simply be aware that the value in the functional performance equation would not be "ore grindability" but rather "ball mill feed grindability". To compare two or more functional performance equations, the values of "ore grindability" must be of the same origin : from a Bond ball mill test or on-site batch grindability test . In addition, if you use the Bond grindability of ore (circuit feed) for your comparisons, circuit feeds in the analyses must be similar in size (K80).


80

FUNCTIONAL PERFORMANCE OF BALL MILLING GLOSSARY Ball mill grinding efficienc efficiencyy : Ratio between the specific grinding rate of the ball mill and the grindability of the ore defined in a standard laboratory test. [p. 6]

Ball mill grinding environment : Collectively, the prevailing conditions inside the ball mill which affect the rate at which coarse particles are ground into fine particles. [p. 3]

Ball mill specific grinding rate : Weight of new product (fines) produced per unit of effective energy in the ball mill (effective mill power draw). [p. 7]

Classification system : Collectively, all factors which influence the fines content (or inversely, the coarse solids content) of the ball mill in a closed grinding circuit (classifier performance, pumping, circuit design, etc.). [p. 3]

Classification system efficiency : Proportion of coarse solids to total solids in the ball mill. This is also called "coarse solids inventory". [p. 4]

Coarse solids inventory : See "classification system efficiency". [p. 5] Effective energy : Energy provided by a ball mill which is strictly used for grinding coarse particles. [p. 7]

Effective mill power draw : Total ball mill power draw multiplied by the classification system efficiency. [p. 6]

Efficiency : Output divided by input. [p. 3] Functional performance analysis : Analytical procedure for ball mill circuits in which ball mill power draw, classification system efficiency, ore grindability, ball mill grinding efficiency, and circuit output of fines are considered or evaluated. [p. 2]

Work index analysis : Evaluation of overall grinding circuit performance on the basis of comparative work index efficiencies. (See "work index efficiency".) [p. 2] © 1992 GPD Co. Ltd. / Metcom Consulting Consulting LLC (Rev.4, 2005)

81

FUNCTIONAL PERFORMANCE OF BALL MILLING GLOSSARY (continued) Work index efficiency : Ratio (%) equal to the Bond work index of the circuit feed divided by the operating work index of the circuit. [p. 52]

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 of the mean falls between 9.0 and 11.0. [p. 62]


82

Module5 - Functional Performance of Ball Milling

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