The SMC Test's® versatility allows it to be used for a range of comminution optimization and modelling applications.

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The last 20 years has seen an increasing awareness of the need for detailed ore characterization data with which to map orebody hardness, regardless of the nature of the project. In the case of new project development the need to understand the breakage characteristics of the orebody is paramount if the comminution circuit is to be sized correctly for the duration of the life-of-mine. The need is no less different in geometallurgy projects where it is required to forecast the performance of comminution circuits. Regardless of the nature of the project, when planning the undertaking of an ore comminution characterisation programme the first question that needs answering is: “what test(s) should be used?”.

To arrive at a satisfactory answer to this question it must be determined whether the chosen test(s) satisfy the following criteria:

  1. Do the chosen ore comminution test(s) relate to the equipment/circuit in question?
  2. Can the chosen ore comminution test(s) be used with the available sample?
  3. Are the equations/models that use the comminution test results accurate and hence fit for purpose?

Considering each of the questions in turn:

1.            Do the chosen ore comminution test(s) relate to the equipment/circuit in question? 

This may be seen as stating the obvious but it is the author’s experience that in some cases this has not been fully thought through.  For example in a circuit design project, say a characterisation programme has been executed in which it was decided to carry out Bond crushing and ball mill work index tests. However, the design project includes a trade-off study between SABC and Crushing/HPGR/ball mill circuits.  Hence in this particular example, as Bond crushing and ball mill work index tests cannot be used to size SAG mill and HPGR circuits the project cannot be carried out and the ore charcaterisation programme has to be re-done with more appropriate choices of tests.

2.            Can the chosen ore comminution test(s) be used with the available sample? 

Most circuit design and geometallurgy projects rely on data from drill core.  There are a range of drill core diameters that are used, the most common diameters being nominally 50mm (NQ), 65mm (HQ) and 85mm (PQ).  As the cost to extract core is proportional to its diameter, NQ and HQ cores tend to be by far the most commonly available. As there is a range of data that need to be extracted from the drill cores it is quite common to find that whole core is not available for comminution testing purposes.  Hence sometimes only half or even quartered (slivered) core is available. In addition it may also be that the overall mass that is made available for testing is also limited.  These constraints influence what laboratory test can be physically carried out. For example, if a comminution test is initially chosen and it requires 40 kg of -75mm+50mm of rock to be carried out yet only 20kg quartered NQ sample is available it will be unusable on the grounds that the size of rock available is too small and also, even if the rock size was appropriate, there is insufficient quantity.

Table 1 provides guidance for such situations and shows the most popular comminution tests commercially available, what comminution machines/circuits they can be used for, what sample quantity is usually required and what rock size is necessary.  For the purposes of Table 1 “most popular” is defined as tests where more than 5000 have been carried out to date world wide and where there are recognized published details of how the tests can be used for the purposes of comminution machine/circuit modelling.

Table 1 – Most Popular Commercially Available Laboratory Comminution Tests

Test

Use

Sample mass (kg)

Material Size

Minimum Core

Bond crushing

Conventional crushers

40

-75+50mm

Whole HQ

Bond rod mill

Rod mills

15

100% -12.7 mm

¼ NQ

Bond ball mill

Ball mills

10

100%  -3.35 mm

¼ NQ

SPI®

SAG mills

12

100% -19 mm

¼ NQ

JK Drop-weight

AG/SAG mills

100

-63+13.2 mm

Whole HQ

JK Drop-weight

Conventional crushers

100

-63+13.2 mm

Whole HQ

SMC Test®

AG/SAG mills

5-20**

28,20 or 14mm*

¼ NQ

SMC Test®

Conventional crushers

5-20**

28,20 or 14mm*

¼ NQ

SMC Test®

HPGR

5-20**

28,20 or 14mm*

¼ NQ

*nominal 28mm is preferred but either 20mm or 14mm particles can be used if sample size is limited

**lower mass requirement is for when sample pieces are prepared using a diamond saw; sample can be re-used for Bond ball work index tests

3.      Are the equations/models that use the comminution test results accurate and hence fit for purpose?

This question is often omitted in reviews of the suitability of tests and their commercial availability, yet it is one of the most important questions of all. In simple terms there is little point, for example,  in selecting a laboratory test that may be cheap, needs little sample, is labelled as being suitable for a specific comminution circuit/equipment but either cannot be demonstrated to have been used over a wide range of conditions to accurately predict the specific energy, or even worse, has been shown to give very inaccurate results. In such cases the results from the laboratory test are effectively meaningless at best or grossly misleading at worst.   Hence to answer the question of fit-for-purpose the equations/models associated with the laboratory test in question must be able to convincingly demonstrate they have a high degree of accuracy for the comminution machine/circuit they are being applied to.  This can only be done through validation using an extensive data base of real plant data. The 2019 SME Mineral Processing & Extractive Metallurgy Handbook1 is particularly useful in providing such data together with the associated statistics on the models’ accuracy.  These are summarised in Table 2.  Equations/models are divided into power-based and simulation types.  Two statistics are presented.  One is the standard deviation of the relative error and the other is the mean of the relative error.  The relative error is the difference between the observed and predicted specific energies divided by the observed value, expressed as a percentage.  The mean of the relative error reflects how much bias the equation/model has, ie based on all of the available data, it indicates on average how near or far the predicted specific energy is to the observed one.  The standard deviation of the relative error indicates how much scatter there is about the mean of the relative error.   Hence, for example, if we consider the Bond crushing accuracy data in Table 2, it indicates that if this test is used to predict the crusher specific energy, the results on average will be 39.9% different to the true value.  However, if we consider the 90% confidence interval of approximately 1.65 standard deviations, individual results can as much as (39.9% + 1.65 x 22.9%) = 77.7% different to the true value.  Such a potentially large error renders this test unsuitable for practical purposes.  If we contrast this with Bond’s ball mill work index the equivalent maximum error is 17.1%, which is far more acceptable, being close to the typical accuracies required by mining companies at the feasibility level of design studies.  Most design studies are divided into at least 3 stages and as the study progresses the required accuracy for predictions/estimations gets tighter and tighter. All companies are different in terms of the accuracies they require for each stage as well as what each stage is called.  However, Table 3 gives the typical accuracy ranges applied by most of the larger mining companies.  These need to be viewed in conjunction with the “max error at 90% conf. level” column in Table 2 to determine which comminution tests satisfy the accuracy requirements for which stages in the design study.

Table 2 – Accuracy of Models and Their Associated Laboratory Comminution Tests

Test

Use

Type of model

Relative error stdev (%)

Relative error mean (%)

Max error at 90% conf. level (%)

Bond crushing

Conventional crushers

power-based

22.9

39.9

77.7

Bond rod mill

Rod mills / ball mills

power-based

12.6

21.8

42.6

Bond ball mill

Ball mills

power-based

9.3

1.8

17.1

SPI®

SAG mills

power-based

17.3

2.3

30.8

JK Drop-weight

AG/SAG mills

simulation

6.4

3.5

14.1

JK Drop-weight

Conventional crushers

simulation

n/a

n/a

n/a

SMC Test®

AG/SAG mills

simulation

6.4

3.5

14.1

SMC Test®

Conventional crushers

simulation

n/a

n/a

n/a

SMC Test®

HPGR

simulation

n/a

n/a

n/a

SMC Test®

AG/SAG mills

power-based

8.6

0.6

14.8

SMC Test®

Conventional crushers

power-based

18.1

1

30.9

SMC Test®

HPGR

power-based

8.5

1.6

15.6

SMC Test®

Total comminution circuit

power-based

6.5

0.2

10.9

Table 3 – Typical Accuracies Required by Mining Companies in Design Studies

Stage

Accuracy

Scoping/Conceptual/Identification

+/- 30-50%

Pre-feasibility/Selection

+/- 20-35%

Feasibility/Definition

+/- 10-15%

References

12019 SME Mineral Processing & Extractive Metallurgy Handbook, Dunne, R, C., Kowatra K S., and Young C A (Editors), Society for Mining, Metallurgy and Exploration.

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