Geometallurgy Course & Geometallurgical Modelling

Table of Contents

Basic Geometallurgy Short Course for mineral processing applications
Geometallurgy program

Basic Geometallurgy Short Course for mineral processing applications

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.

Sampling

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

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.

Interpolation by kriging

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

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!

Domains

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

Example domain definitions

geometallurgy — geometallurgical modelling

Variogram

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

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

Additivity

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

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

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.

CONCLUSION

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.

Most important concept! ALL MODELS ARE WRONG, BUT SOME ARE USEFUL

Presented by: Alex Doll, Consultant of SAGmilling.com