Presentation from 2011 Uranium Conference in Perth, Australia. Focuses on selection and the support effect using a case study.

1. The Aff t f R di
Th Affect of Radiometric T
t i Truckk
Discrimination on
Reconciliation
J Carpenter, S Hackett, N Anderson
International Uranium Conference
Perth, 2011
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2. Introduction
• The intention of this
presentation is to:
– Di
Discuss th i
the importance
t
of sample support to
grade control
– Demonstrate some
methods that can be
used for “change of
change
support”

3. 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

4. Mining is a selection process
• Mining is a selection process;
– Define a cutoff
– Using this criterion, select material above the cutoff and send it
criterion
to the mill, and
– Send material below the cutoff to the waste stockpile.
• In
I some open cut uranium mines, radiometric truck
t i i di t i t k
discriminators are used to sort each truckload leaving the
pit
• This creates a situation where “Perfect Selection” may be
assumed

5. Why is support important?
• Example:
100 tonne
blocks;
1600 0.35 % Cutoff
tonnes at
0.4%
400 tonne
blocks;
1600 0.35 % Cutoff
tonnes at
0.4%

6. Why is support important?
• The outcome of
applying the selection
criteria (a cutoff of
0.35%) has a
pronounced effect on
the mined grade and
tonnages
• Fewer tonnes,
higher grade

7. 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 y
known as Ranger #3) is situated in
Early Proterozoic sediments of the
South Alligator Group
g p
Table adapted from Kendall (1990)

8. Real Data
Large blocks are the
block model
Small blocks
are trucks

9. 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:
Blocks: 8.08 million tonnes at 0.043 % U3O8
Trucks: 8.02 million tonnes at 0.042 % U3O8

10. 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 predicted
p
Blocks: 803,120 tonnes at 0.232% U3O8
Trucks: 774,800 tonnes at 0.278% U3O8
• Outcome: Fewer tonnes, higher grade

11. 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
truck support above a cutoff grade?
t k t b t ff d ?

12. How to predict the tonnes and grade
• We can use Geostatistics
• I will demonstrate 2 methods:
– Affine Correction
– Conditional Simulation

13. Demonstration of change of support
• In order to demonstrate some
examples of change of support,
a data set has been created by y
simulation. It is necessary to do
this for a few reasons:
– Confidentiality of company
data
– Real data has additional
complexities

14. 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 g
bulk density of 2.8 t/m3
• There 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)
• The simulation has been sampled on 25 by 25 metre and 50 by
50 metre centres – this is the drillhole data

15. Simulated Data – 1 metre spacing
N = 354,690
Mean U3O8 grade = 0.152%
Minimum value = 0.023%
Maximum value = 0.278%
Variance = 2.13 x 10-3 (%)2

16. Simulated Data – Reblocked to 3 by 3 m
N = 39,480
Mean U3O8 grade = 0.152%
Minimum value = 0.023%
Maximum value = 0.276%
Variance = 1.51 x 10-3 (%)2

17. Simulated Data – Reblocked to 25 by 25 m
N = 574
Mean U3O8 grade = 0.152%
Minimum value = 0.074%
Maximum value = 0.238%
Variance = 0.79 x 10-3 (%)2

18. 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 by 25m support: 4.38 Mt at 0.159% U3O8
b 25 t 4 38 t 0 159%
• We will call these the “TRUE” values
ill al es

19. Sample Data
N = 329
Mean U3O8 grade = 0.152%
Minimum value = 0.024%
Maximum value = 0.278%
Variance = 2.24 x 10-3 (%)2

20. Semi-Variograms for U3O8
SAMPLES SIMULATED VALUES Cross validation:
Mean of error = 0.0003%
Mean squared error =
0.0021(%)2
Mean kriging variance =
0.0019(%)2
(small mean error,
theoretical variance within
10% of true variance)

21. Kriged estimate over bench
N = 574
Mean U3O8 grade = 0.153%
Minimum value = 0.092%
Maximum value = 0.220%
Variance = 1.00 x 10-3 (%)2

22. 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% U3O8
y pp

23. First method of change of support – Affine
Correction
• Using an Affine Correction to predict the tonnes and grade:
• Kriged 3 by 3m support: 4.03 Mt at 0.165% U3O8
• “True” 3 by 3m support: 3.93 Mt at 0.167% U3O8
• Close! But no thumbs up

24. 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 samples
bell shaped
• The normalising effect is due to the Central Limit Theorem
• The change in the shape of the histogram makes this
method less reliable

25. 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:
– The simulation h the same statistics as the data
h l has h h d
– The simulation has the same spatial statistics as the data
– The simulation has the same multivariate statistics
– The simulated value and the data value are the same at the
same location
– Th simulated variable considers th geology
The i l t d i bl id the l

26. Second method of change of support –
Conditional Simulation
• If we make a simulation with a sufficiently dense grid of
points,
points we can re-block the simulations on different
re block
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
dimensions

27. Second method of change of support –
Conditional Simulation
• We don’t have one answer –
we have 10 equally probable
answers!

28. Conditional Simulation – 25 by 25m reblock
25 by 25m blocks from simulation - Grade 25 by 25m blocks from simulation - Tonnage
Comparison Comparison
0.163 4550000
0.162 0.162 4,488,750
4500000
0.162 4,471,250
cted Grade for 5 by 5m blocks
cted Grade for 5 by 5m blocks
4450000 4,427,5004,427,500
0.161 0.161
4,410,000
4400000 4,370,000
4,380,000
0.160 0.160
0.16 4,348,750
4350000 4,322,500
0.159
0 159
b
b
0.159 0.159 0.159
0.159
0.159
0.159 4300000 4,287,500
4,243,750
0.158 4250000
0.157
4200000 4,182,500
0.157
4150000
Predic
Predic
0.156
4100000
0.155
4050000
0.154 4000000

29. Conditional Simulation – 3 by 3m reblock
3 by 3m blocks from simulation - Grade 3 by 3m blocks from simulation - Tonnage
Comparison Comparison
0.168 4100000
0.167 0 168
0.168
4,047,7504,049,136
0.167 4050000
cted Grade for 5 by 5m blocks
cted Grade for 5 by 5m blocks
0.167 0.167 4,030,000
4,012,344
4,005,414
4000000 3,987,0183,988,656
0.166 0.166 0.166 3,969,378
0.166
0.165 3,951,864
0.165
0 165
b
b
3950000 3,930,000
0.165
0.165 0.165
3900000
0.164
3,865,806
3,859,254
0.164
3850000
Predic
Predic
0.163
3800000
0.162 3750000

30. Conclusions
• It is important to consider the change of support for mine
planning purposes
• It is possible to perform change of support using
geostatistical methods; e.g. Affine correction, Uniform
eg correction
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

31. Final Comment
• If we want to know the support on 3 metres, why don’t we
just estimate into 3 metre blocks?
• Why not? Because the answer will be about the same as if
we estimate into 25 metre blocks!!
• Kriged 25 by 25m support: 4.37 Mt at 0.159% U3O8
• Kriged b 3
K i d 3 by 3m support: 4.26 Mt at 0.159% U3O8
t 4 26 t 0 159%
• Affine corrected 3 by 3m support: 4.03 Mt at 0.165% U3O8

32. References
KENDALL, 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.