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Grade control sampling andSMU size optimization using

conditional simulation

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Choose a grade control sampling grid that maximizes recovery

and minimizes dilution.

Optimize the Selective Mining Unit (SMU) size to ensure mineable

envelopes can be designed with adequite recovery and minimum

dilution.

Definition of the problem

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Grade control is a fundamental part of the mining cycle.

Base of the decision Ore/Waste.

Usually it is based on what is done in similar operations.

Normaly left to inadequate or subjetive criteria.

Very little bibliography on the subject.

Starting point

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Estimation looks after local precision with the available

information.

Simulation is a technique that looks after reproducing not the

known values but the internal structure.

Simulation reproduces the sample variograms and histograms.

Not so estimation.

Estimation vs Simulation (I)

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Estimation vs Simulation (II)

Real Kriging (40 samples)

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Estimation vs Simulation (and III)

Real Simulation (40 samples)

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Based on the principles delineated in Journel and Kyriakidis

(2004)

Planning is usually done in estimated grade maps that are

normally skewed and present a softened distribution of grades.

Inadequate image of SMUs.

Traditional practice does not have the formality to analyze the

uncertainty associated to the reserve or grade control calculations.

Proposed method: Background (I)

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Method proposed will use conditional simulation to generate

possible alternatives for grade distribution.

These alternatives will be artificially sampled with GC holes and

the results used to calculate a new grade model that will be

compared with the original.

Proposed method: Background (and II)

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Proposed method: Algorithm

Analize initial data (Histogramand variogram)

Simulate n denseocurrences SGS. True

values.

Reblock to differentSMU sizes. Real

selection models

Drill with GC Holes. Futuresamples

Add errors to samples.Lower quality samples.

Calculate new blockmodel with worsened

GC holes.

Compare estimated valueswith real values and real

selection models.Results and Conclusions

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Application: Step 1

Domain 1 Acid Volcanic Rocks

Domain 2 Basic Volcanic Rocks

Domain 3 Filon Sur

Domain 4 Filon Norte

Domain 5 Oxides

Domain 6 Slates

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Application: Step 2

Samples Base de datos

Histogram Base de datos

Variogram Snowden

Parameters Snowden

50 Times

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Application: Step 3

Simulation 1 (12.5 x 12.5)

These are the real values of the mining units. Not known in paractice.

Simulation 1 (6.25 x 6.25)

Simulation 1 (4.2 x 4.2)

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Application: Step 4

9m x 9m 6m x 6m 3m x 3m

These are the real values of the GC holes. Not known in practice.

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Application: Step 5

The GC holes done over the real model do not include sampling

or assay errors.

Quality of data must be worsened.

Error model was developed with the use of historical GC data.

The model error for this case is heteroscedastic. It will depend on

the grade of the environment of the sample.

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Application: Step 6GC Holes + Errors

=

Real GC holes

Estimation

Kriging

Kriging for simulation 1 GC holes on 3x3 with errors on 6.25 x 6.25

blocks

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Application: Step 7

Simulation 1 vs

Kriging for simulation 1 GC holes on 3x3 with errors on 6.25 x 6.25 blocks

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Results (I)

50 simulations

7 grade control sampling meshes

2 error fields

3 SMU sizes (12.5m, 6.25m and 4.16m)

Total of 2,100 comparatives with real models

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Results (I)

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Results (and II)Statistical limit due to nugget effect and sampling errors to the dilution and

ore loss that can be controlled.

Dilution diminishes with sampling, ore loss does not.

SMU must be smaller than 12.5m, 6.25 m is a good compromise between size

(production rate) and reserve recovery, 4% better.

Statistical limit to the unit that can be correctly sampled. SMU below 6.25 do

not appear to have advantage. What is gained in selectivity is lost due to the

impossibility of sampling (and classifying) the blocks correctly.

Sampling mesh should be in the range of 5 x 5 m.

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Future workAnalisys of flitch mining.

Optimal bench height selection

Waste zones sampling

Underground sampling

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Thank You