The Affect Of Radiometric Truck Discrimination On Reconciliation

Th Aff t f R di t i T k The Affect of Radiometric Truck Discrimination on

ReconciliationReconciliationJ Carpenter, S Hackett, N AndersonInternational Uranium ConferenceInternational Uranium Conference

Perth, 2011

ENVIRONMENT GEOLOGY MINING PROCESSING VALUATION RISK TECHNOLOGIES

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Introduction• The intention of this

presentation is to:Di th i t – Discuss the importance of sample support to grade control

– Demonstrate some methods that can be used for “change of used for change of support”

What is change of support?• Support is another name for volume• The most obvious support change in a mining operation is the

difference in support between the block model used for planning and the truck volumes that are actually mined

Planning using a Block Model... ...mining using Trucks

Mining is a selection process• Mining is a selection process;

– Define a cutoff– Using this criterion select material above the cutoff and send it Using this criterion, select material above the cutoff and send it

to the mill, and – Send material below the cutoff to the waste stockpile.I t i i di t i t k • In some open cut uranium mines, radiometric truck discriminators are used to sort each truckload leaving the pit

• This creates a situation where “Perfect Selection” may be assumed

Why is support important?• Example:

100 tonne blocks;1600 tonnes at

0.35 % Cutoff0.4%

400 tonne blocks;1600 tonnes at

0.35 % Cutofftonnes at 0.4%

Why is support important?

• The outcome of applying the selection applying the selection criteria (a cutoff of 0.35%) has a pronounced effect on pronounced effect on the mined grade and tonnages

• Fewer tonnes, higher gradehigher grade

Real Data

• Some real data comes from ERA’s Ranger #3 Uranium mine, located approximately 250km east of Darwin, Northern Territory, Australia at latitude 120 41’ S, longitude 1320

55’

• Ranger 1 Anomaly 3 (colloquially g y ( q yknown as Ranger #3) is situated in Early Proterozoic sediments of the South Alligator Groupg p

Table adapted from Kendall (1990)

Real DataLarge blocks are the Large blocks are the block model

Small blocks are trucks

Global Results• The results show that the estimate of what will be mined is

very close to what was actually mined• This is an excellent outcome:This is an excellent outcome:

Blocks: 8.08 million tonnes at 0.043 % U3O8

Trucks: 8.02 million tonnes at 0.042 % U3O8

Support and selection criteria• However, when we apply a cutoff grade of 0.12% U3O8 we

find that there is a deviation away from what the block model has predictedp

Blocks: 803,120 tonnes at 0.232% U3O8

Trucks: 774,800 tonnes at 0.278% U3O8

• Outcome: Fewer tonnes, higher grade

Predicting the tonnes and grade• Before a new area is mined it would be highly desirable to

predict the tonnes and grade that will be mined on the truck scale

• How do we predict the tonnes and grade of material on a t k t b t ff d ?truck support above a cutoff grade?

How to predict the tonnes and grade

• We can use Geostatistics

• I will demonstrate 2 methods:– Affine Correction– Conditional Simulation

Demonstration of change of support• In order to demonstrate some

examples of change of support, a data set has been created by ysimulation. It is necessary to do this for a few reasons:

Confidentiality of company – Confidentiality of company data

– Real data has additional complexities

Simulated Data• A data set has been created by a geostatistical simulation

• There is a single bench with a mining height of 5 metres and a g g gbulk density of 2.8 t/m3

• There is a cutoff grade of 0.12% U3O8There is a cutoff grade of 0.12% U3O8

• The mine is mined by open cut using 130 tonne trucks (which equates to a support of 3 by 3 by 5 metres)equates to a support of 3 by 3 by 5 metres)

• The simulation has been sampled on 25 by 25 metre and 50 by 50 metre centres this is the drillhole data50 metre centres – this is the drillhole data

Simulated Data – 1 metre spacingN = 354,690

Mean U3O8 grade = 0.152%

Minimum value = 0.023%

Maximum value = 0.278%

Variance = 2.13 x 10-3 (%)2

Simulated Data – Reblocked to 3 by 3 mN = 39,480




Variance = 1.51 x 10-3 (%)2

Simulated Data – Reblocked to 25 by 25 mN = 574




Variance = 0.79 x 10-3 (%)2

Grade and Tonnage at Cutoff 0.12% U3O8

• Applying a cutoff of 0.12% U3O8 for the three supports of simulations:

• Point support: 3.66 Mt at 0.173% U3O8

• 3 by 3m support: 3.93 Mt at 0.167% U3O8

25 b 25 t 4 38 Mt t 0 159% U O• 25 by 25m support: 4.38 Mt at 0.159% U3O8

We ill call these the “TRUE” al es• We will call these the “TRUE” values

Sample DataN = 329




Variance = 2.24 x 10-3 (%)2

Semi-Variograms for U3O8

Cross validation:Mean of error = 0.0003%

SAMPLES SIMULATED VALUES

Mean squared error = 0.0021(%)2

Mean kriging variance = 0.0019(%)2

(small mean error, theoretical variance within 10% of true variance)

Kriged estimate over benchN = 574




Variance = 1.00 x 10-3 (%)2

Kriged estimate over bench

• Applying a cutoff of 0.12% U3O8 for the kriged estimate:

• Kriged 25 by 25m support: 4.37 Mt at 0.159% U3O8

• “True” 25 by 25m support: 4.38 Mt at 0.159% U3O8y pp 3 8

First method of change of support – Affine Correction

• Using an Affine Correction to predict the tonnes and grade:


• “True” 3 by 3m support: 3.93 Mt at 0.167% U3O8

• Close! But no thumbs up

Discussion on Affine Correction

• The Affine correction is rarely used in practice

• The reason behind this is that estimates are always “normalised” – the histogram of the estimates are more “bell shaped” than the samplesbell shaped than the samples

• The normalising effect is due to the Central Limit Theorem

• The change in the shape of the histogram makes this method less reliable

Second method of change of support –Conditional Simulation

• Using the sample data, 10 conditional simulations were made

• A conditional simulation is any method that maintains the following 5 conditions:

h l h h h d– The simulation has the same statistics as the data– The simulation has the same spatial statistics as the data– The simulation has the same multivariate statisticsThe simulation has the same multivariate statistics– The simulated value and the data value are the same at the

same locationTh i l t d i bl id th l– The simulated variable considers the geology


• If we make a simulation with a sufficiently dense grid of points we can re block the simulations on different points, we can re-block the simulations on different supports

• The 10 conditional simulations are on a 1 by 1 m grid, same as the original simulation, then re-blocked to the 3 and 25m dimensionsdimensions


• We don’t have one answer –we have 10 equally probable we have 10 equally probable answers!

Conditional Simulation – 25 by 25m reblock

0.163

25 by 25m blocks from simulation - Grade Comparison

4550000

25 by 25m blocks from simulation - Tonnage Comparison

0 159

0.160 0.160

0.161

0.162 0.162

0.16

0.161

0.162

by

5m

blo

cks

4,322,500

4,348,750

4,410,0004,427,5004,427,500

4,471,2504,488,750

4,370,0004,380,000

4350000

4400000

4450000

4500000

by

5m

blo

cks

0.157

0.159 0.159 0.159 0.159 0.159 0.159

0.157

0.158

0.159

cted

Gra

de

for

5 b

4,182,500

4,243,750

4,287,500

4150000

4200000

4250000

4300000

cted

Gra

de

for

5 b

0.154

0.155

0.156

Pre

dic

4000000

4050000

4100000

Pre

dic

Conditional Simulation – 3 by 3m reblock

0 1680.168

3 by 3m blocks from simulation - Grade Comparison

4100000

3 by 3m blocks from simulation - Tonnage Comparison

0 165 0.1650.166

0.166 0.166

0.167

0.167 0.168

0.167

0.166

0.167

by

5m

blo

cks

3,951,864

3,969,378

3,987,0183,988,656

4,005,4144,012,344

4,047,7504,049,136

4,030,000

4000000

4050000

by

5m

blo

cks

0.164

0.165

0.165

0.165

0.164

0.165

cted

Gra

de

for

5 b

3,859,2543,865,806

3,951,864

3,930,000

3850000

3900000

3950000

cted

Gra

de

for

5 b

0.162

0.163Pre

dic

3750000

3800000Pre

dic

Conclusions

• It is important to consider the change of support for mine planning purposesplanning purposes

• It is possible to perform change of support using geostatistical methods; e g Affine correction Uniform geostatistical methods; e.g. Affine correction, Uniform Conditioning, Multiple Indicator Kriging, Disjunctive Kriging, Conditional Simulation to name a few

• They all do the same thing – predict the tonnes and grade above a cutoff for a certain support

Final Comment

• If we want to know the support on 3 metres, why don’t we just estimate into 3 metre blocks?just estimate into 3 metre blocks?

• Why not? Because the answer will be about the same as if we estimate into 25 metre blocks!!


K i d 3 b 3 t 4 26 Mt t 0 159% U O• Kriged 3 by 3m support: 4.26 Mt at 0.159% U3O8

• Affine corrected 3 by 3m support: 4.03 Mt at 0.165% U3O8Affine corrected 3 by 3m support: 4.03 Mt at 0.165% U3O8

ReferencesKENDALL, C. J. (1990). Ranger Uranium Deposits. In: Geology of the Mineral Deposits of

Australia and Papua New Guinea. Vol 1 ed. F. E. Hughes, pp. 799 – 805. The Australian Institute of Mining and Metallurgy, Melbourne.

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The Affect Of Radiometric Truck Discrimination On Reconciliation