Geometallurgy Course & Geometallurgical Modelling

Geometallurgy Course & Geometallurgical Modelling

Basic Geometallurgy Short Course for mineral processing applications


Geometallurgy Short Course
Geometallurgy Training Course by

Geometallurgy and grinding

  • It is often desirable to be able to load ore hardness information into the mine block model.
  • Allows the mining engineers to better schedule ore delivery to the plant, and to run more sophisticated net present value calculations against ore blocks.
  • Requires hundreds of samples from drill holes distributed across the orebody.

Geometallurgy and plant recovery

  • It is often desirable to be able to load leaching information into the mine block model.
  • Allows the mining engineers to run more sophisticated net present value calculations against ore blocks.
  • Requires hundreds of samples from drill holes distributed across the orebody.



Geometallurgy Course
Geometallurgist -> Geologist + Metallurgist


Used in Geometallurgy Training
geometallurgical Block modelling

Block model

Geologic systems can be modelled as a structure of equally sized blocks arranged in a regular grid.


Interpolation is the mathematical method used to estimate a parameter in the spaces between known positions with known values.

  • A simple interpolation method could be a linear weighted average of the two nearest points.
  • Geo-statisticians use more complex methods, such as kriging.
  • Consider the same 1-dimensional model with measurements at points A&B.
  • Try an inverse distance-squared weighting.
geometallurgical modelling
Geometallurgy Book
  • Consider a 3-dimensional model with measurements at points A,B,C,D
  • A ‘polygon’ displays the rock unit that X belongs to.

geometallurgical modelling polygon

Interpolation by kriging

  • The most common interpolation is some form of kriging.
  • Kriging uses nonlinear, directional interpolation constrained by domains.

Interpolation by kriging

Check the domains

  • Domains determined for assay data may not apply for process parameters
  • Geostatisticians should re-domain the process data to verify.

Example: Grade may be determined by alteration, but grindability may be determined by tectonic stress fields.

  • You must check!


  • Example grinding data, top from a ‘hematite’ domain and bottom from a ‘magnetite’ domain.
  • Shapes are different – confirms each must be interpolated separately.

geometallurgical Domains

Example domain definitions

geometallurgical modelling


A variogram plots the average difference between two arbitrary points and the distance between the points.


  • Warning: oversimplified!
  • Plotting the example grade difference VS distance from earlier slide

Variogram geometallurgy

  • Slightly more correct version
  • Y-axis shows variance
  • The population variance is shown as the “sill”


A published variogram from Adanac Moly suggests that the maximum spacing between samples should be 200 m or less.


How many samples?

Area of influence of a sample

  • How “close by” must a sample be to have importance in geostatistics.
  • Observed as the location of the“sill” of a variogram of grindability versus distance.
  • So you should know the variogram result of a geometallurgy program to plan a geometallurgy program.

Additive parameters


  • Geostatistics only works if the values you are “mixing” have a linear mixing characteristic.
  • A parameter is “additive” if you can combine two samples of a known value, and the blend test results in the arithmetic average of the two.
    – Eg. mix one sample “10” and a second sample “20”
    – The blend should give a result of “15”
  • Values suitable for block modelling
    – Not all grindability results are suitable for block model interpolation, they must be “additive” • e.g. mixing two samples with “10” and “20” should give “15”. Work index, SGI and A×b results do not have this property.
    – Specific energy consumption is generally additive, so Etotal, ESAG and/or Eball can be interpolated.

Additivity of process parameters

A variety of process models exist. You will need to evaluate which models are useful for your mine.
– The process models need to make useful predictions of process behaviour.
– The process models need to have additive parameters suitable for geometallurgy.

Geometallurgy program

Procedure for a geometallurgy program:

  • collect samples distributed around the orebody
  • test in the laboratory, use at least 2 methods
  • run all samples through comminution models
  • distribute specific energy values into block model
  • run geostatistical checks (variograms) and repeat (do a second, in-fill, sample collection program)
  • provide mining engineers with a model populated with grindability values; run annual production forecasts.

The block model

A block model containing geometallurgical data will include:

  • grindability information suitable for estimating the maximum plant throughput,
  • recovery information suitable for estimating the metal production,
  • (flotation plants) concentrate grade predictions for smelter contracts.

Grindability models

  • Specific energy consumption models determine how much energy is required to grind a sample.
    – E given in kW·h/t {alternative notation: kW/(t/h)}
  • Mill power models determine the amount of grinding power available
    – P given in kW
    • Dividing P by E gives the circuit throughput
    – t/h = kW ÷ (kW·h/t)

Throughput predictions

  • Grindability, in the form of specific energy, will be interpolated for a block.
    – in this example, ESAG = 6.0 kWh/t
  • The metallurgists will supply the typical power draw of the SAG mill (at the pinion).
    – Yanacocha is about 14,000 kW
  • Throughput = 14,000 kW ÷ 16.0 kW = 875 t/h

Recovery models

flotation Recovery models

Net Smelter Return prediction

  • The mining engineer can estimate the revenue of a block using the recovery equation(s) and the block model parameters.
    – Gold recovery R is known by interpolation.
    – Revenue=block mass (t) × grade (g/t) × recovery
  • If there are penalty elements in the block model, is may be necessary to estimate their recovery, too.

Block value prediction

  • Determine the value of a block
    – Revenue
    include penalties, if applicable
    – Operating costs ($/t)
    • include mill power draw, kWh/t × t/h × $/kWh
    • include other operating costs
    – Processing time can be included as a cost penalty
    • revenue form harder blocks worth less than revenue from softer blocks.

New cut-off calculation

  • The variable revenue benefits blocks with good recovery characteristics.
  • The variable grindability benefits blocks with lower power consumption.
  • Applying a penalty for difficult to process blocks benefits easy to process blocks.

Benefits of geometallurgy

  • Permits future production to be accurately predicted. Future sales can be estimated.
  • Identifies “problem” areas within the mine where throughput may be low or recovery may suffer.
  • Allows better optimized mine plans with more accurate NPV predictions per block.

Variable mining rate

  • Operate the mine to keep the SAG mills full.
  • A grinding geometallurgy database allows mine planners to schedule more ore to the mill.
    – Do not plan a “nominal” throughput rate for the whole mine life.
    – mine more in years with soft ore, and
    – mine less in years with hard ore.
    – If possible, defer hard ore until later in the mine life.

Variable gold production

  • The gold production in each year of a mine life will be different, and can be calculated from
    – block gold grade,
    – block gold recovery,
    – block throughput calculated from the grindability.
  • The pit optimization software will pull the pit towards softer ore with better recovery.

Summary of benefits

  • The pit shape and equipment fleet will change due to the new NPV equations,
  • the pit will probably be mined more rapidly,
  • production is advanced into earlier mine years,
  • a more optimal pit shape will all result from a fully applied geometallurgy program, and
  • no nasty surprises.

Stages of a geometallurgy program

  • Decide which process parameters to collect
    – plant surveys, fitting models to plant data
  • Conduct a drilling program to obtain samples of future ore
  • Conduct a laboratory program determining parameters for samples
  • Supply geostatisticians the parameters and their spatial locations
  • Interpolate the parameters into the block model
    – check variograms, conduct in-fill drilling and recycle
  • Generate a mine plan with a variable ore throughput
  • Generate a cash flow with a variable gold production rate

Cost of a geometallurgy program

  • Plant surveys, engineering time fitting models to plant data
  • drilling program to obtain samples of future ore
  • laboratory program determining parameters for samples
  • Geostatistician time to interpolate parameters into the block model
    – check variograms, conduct in-fill drilling and recycle
  • Mine engineering time to generate a mine plan
  • Sustaining capital cost of mine fleet needed to support variable throughput rates

Geometallurgy for scoping studies

  • Early project evaluation will not use a full program:
    – Use about 5-15 intervals of half-core (from the resource drilling program).
    – Do laboratory work for one set of process models.
    – Unlikely enough data will exist to do variograms or kriging. Work with cumulative distributions instead of geometallurgy.

Geometallurgy for prefeasibility

  • Collect at least 50 more half-core samples from the resource drilling.
    – The quantity should be sufficient to permit creation of variograms.
    – Do the first circuit of the geometallurgy program stages, but exclude the recycle.
    – Determine how much of the orebody is unrepresented by samples.
    – Do the variable rate mine plan and gold production schedule.

Geometallurgy for full feasibility

  • Using the variograms from pre-feasibility, determine how many more samples are needed
    – These extra samples should be dedicated metallurgical drilling. Use the whole core for a greater variety of metallurgical tests.
  • Do the “recycle” loop and determine updated variable rate mine plans and gold production.

Geometallurgy for operation

  • Do the program indicated for pre-feasibility and feasibility to establish the initial mine plans.
  • Do annual drilling to keep extending into the next 5 years of future ore.
  • Revise the process models (did they work?).
  • Revise the mine plans based on the updated geometallurgy database.

Examples of geometallurgy

  • Los Bronces, Confluencia (Chile)
    – Design of pit for an expansion project included plant recovery and ore grindability parameters.
  • Collahuasi (Chile)
    – Monthly throughput predictions are within 5% of actual.
  • Freeport-McMoRan study
    – Geometallurgical database used to compare SAG milling to HPGR in a detailed study.
  • Andina, Piuquenes tailings (Chile)
    – Recovery and regrind energy for re-mining a tailings pond.

Escondida variograms


geometallurgy short course
Escondida variograms

Examples of geometallurgy used in training

Examples of geometallurgy

  • Adanac Molybdenum, Canada
    Flotation model using interpolated parameters:
    • k, Rmax value for molybdenum
    • k, Rmax value for non-sulphide gangue
    – Different models run at different grind P80 sizes
    • k, Rmax values change at each P80.


  • Grade proxies and process mineralogy are often called geometallurgy, but they are different
    – Grade proxy is where a process variable (eg. recovery) is closely related to a grade (%Cu)
    – Process mineralogy is a careful mapping of minerals (rather than elements)
  • useful to predict recoveries, rate constants, etc.


Presented by: Alex Doll, Consultant of

More great articles

– Brissette, M. & de Souza, H. (2012) `Metallurgical testing of iron ore from the Labrador Trough`, Mineral Resources Review Conference.
– Bulled, D. (2007) `Flotation circuit design for Adanac Moly Corp using a geometallurgical approach`, Proceedings of the 39th Canadian Mineral Processors Conference, Ottawa, Canada.
– Preece, R. (2006) `Use of point samples to estimate the spatial distribution of hardness in the Escondida porphyry copper deposit, Chile`, Proceedings of International Autogenous and Semi-autogenous Grinding Technology 2006, eds.
Allan, M., Major, K., Flintoff, B., Klein, B. & Mular, A., Vancouver, Canada. Slide 51 2015-11-12
• References
– Rocha, M., Ulloa, C. & Díaz, M. (2012) `Geometallurgical modelling at Los Bronces mine`, Proceedings of the International Seminar on Geometallurgy (GEOMET 2012), eds. Barahona, C., Kuyvenhoven, R. & Pinto, K., Santiago, Chile.
– Suazo, C., Hofmann, A., Aguilar, M., Tay, Y. & Bastidas, G. (2011) `Geometallurgical modelling of the Collahuasi grinding circuit for mining
planning`, Proceedings of the 8th International Mineral Processing Conference, eds. Kracht, W., Kuyvenhoven, R., Lynch-Watson, S. & Montes-Atenas, G., Santiago, Chile. Slide 52 2015-11-12
• References
– Suazo, C., Muñoz, C., & Mora, N. (2013) `The Collahuasi geometallurgical modelling and its application to maximizing value`, Proceedings of the 10th International Mineral Processing Conference, eds. Álvarex, M., Doll, A., Kracht, W. & Kuyvenhoven, R., Santiago, Chile.
– NI43-101 report, Zafranal project

Adanac Moly variogram should be referenced as “Bulled et al, 2007”

The Escondida variograms should be references as “Preece, 2006”