Size does matter

Sample dimensions

Power models generally operate with a series of calculations at different size classes. Each size class typically has a specific test that returns the characteristic hardness of that class.

Breakage mechanisms by size classes

The mechanism of breakage tends to change as the size of a rock changes. In general:

• Breakage in coarse rocks is dominated by impact (crushing) action.
• Breakage in the medium (intermediate) size class is dominated by attrition (compression and breaking angular chunks of rock).
• Breakage in the fine size class is dominated by abrasion (rubbing of particles against other particles).

Modelling of breakage

Which tests correspond to which size classes varies by the type of model used, but these can be generalized into the follow categories based on the dimensions of the samples tested:

Model	Fine size	Medium size	Coarse size
Bond/Barratt	WiBM	WiRM	WiC
Morrell Mi (SMC)	Mib	Mia	Mic †
SAGDesign	WiBM(modified)	SAGDesign	—
CEET 1	WiBM	SPI	—
CEET 2 ‡	WiBM	SPI	CI
JK SimMet ‡	WiBM, ta	A, b	—

^† The Mi_c is not a true measurement of coarse hardness because the measurement is conducted at a medium size and extrapolated based on a database.

^‡ JK SimMet is actually a population-balance model rather than a power model. CEET 2 is a hybrid model having properties of a population-balance model and a power model. Both tend to be more complicated and have more "tuning factors" that are appropriate to fitting mill surveys as opposed to initial design. Specialized software is needed to operate both models.

Extrapolating across size classes

Orebodies tend to have relationships between the different size class breakage types, and once enough data has been collected, is is possible to project breakage across size classes.

Models that do not have a coarse test generally extrapolate grindability results from a medium size class using the model practitioner's database. These extrapolations are valid for the ore types represented in the database, but should be used with caution for orebodies that have unknown characteristics (pre-feasibility level studies) or where the orebody does not match the type that dominates the practitioner's database. For example, the SMC test does not have a coarse impact test, and instead extrapolates the breakage character from a drop weight test on specimens in the medium size class by way of a database calibration. For example, an Andean ore deposit (commonly soft in the coarse size fraction) would predict excessively hard properties for the coarse size class if the database used for extrapolation is dominated by Archean-age Australian ore types that tend to be hard in the coarse size fractions.

Comments on size classes

• The CEET2 model is a hybrid population-balance and power model. The CI measurement is not used directly in the power modelling; it is used to predict the particle size distribution (F₈₀ and F₅₀) sizes of the SAG mill feed. The net effect of adjusting the particle size distribution is similar to what is observed in the Bond/Barratt model by adjusting the crushing work index which dictates the hardness of the coarse size class.
• The CI measurement is conducted on particles similar to the 'medium' size class in the Bond/Barratt model, but published information ^{Doll & Barratt, 2011} suggests that it is a reasonable proxy for the crushing properties typically measured in coarser particles. The CI test is particularly useful as it can be conducted on much smaller core sizes than the Bond crushing work index, making it particularly suitable for pre-feasibility programs with limited availability of whole-diameter HQ or PQ size samples.
• The Bond/Barratt model uses a series of hidden 'calibration transfer sizes' to determine the overall grindability of a sample. These transfer sizes control the degree of weighting that each of the tests has on the overall grindability result. In general, the default size classes in the model match the transfer sizes observed in the laboratory tests; but these can be adjusted by the engineer (setting the min/max T₈₀ limits) if there are other 'natural' transfer sizes observed in the rock (example: a porphyritic rock type with 1.5–2.5 mm clasts can reasonably be expected to produce a 1.5–2.5 mm T₈₀ range).
• The JK DWT and SAGDesign tests blend results of several size classes together to predict a composite grindability prediction. Composite samples are a valid approach that avoids the need to set 'transfer sizes', but do require correctly constructed 'feed composites' containing the correct proportions of the size fractions. Laboratory bench-scale testing is limited in the top size that can realistically be tested, and care is required to correctly represent the proportion of this coarse fraction in a composite.
  • The JK DWT performs a mathematical compositing of the results of several different size classes to predict model parameters A and b.
  • The SAGDesign test mixes a feed charge to a small SAG mill consisting of several different size classes. The exact behaviour of each size class is not determined; only the composite grindability of the mixture is determined.
  • Pilot plant samples are an extreme variant of this type of test that uses composites. Pilot plants can both handle coarser feed (up to 150 mm) and can create circulating loads of 'pebbles' (critical size) that can not be observed in laboratory bench-scale tests.