Assessing Uncertainty with Drill Hole Spacing Studies – Applications to Mineral ... ·...

Assessing Uncertainty with DrillHole Spacing Studies – Applicationsto Mineral ResourcesGeorges Verly1, Tomasz Postolski2, Harry Parker1

(1) AMEC; (2) Goldcorp Inc

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90

% C

I

Drill spacing (m)

Q90%: Mineralogy

Enargite

Chalcocite

Chalcopyrie

Cu Leach Recovery

Content

Introduction

Principles and limitations

Formulation

Block size and sample locations Sensitivity study

Software issues

Historical antecedents of confidence intervals for classification

Conclusions

1

Introduction

Assessing uncertainty in mineral resource estimation is required for best practice and is implied by public reporting codes.

Conditional simulation is an ideal tool for uncertainty and risk assessment. Drill spacing studies (DHSS), however, are worth considering for the following reasons: A good simulation is not straightforward. It requires planning, time and

careful validation. DHSS are generally simpler and faster to execute. They also offer some

flexibility, though less than simulation. There are cases when the risk assessment requirements are not so

complex as to necessarily require simulation, or when time to complete a simulation is lacking.

2

Introduction

When the requirement is limited to an assessment of the uncertainty of some estimated attribute within large production blocks, drill hole spacing studies can be useful.

The results provide an indication of risk given the current of future drill hole spacings. This can be used as a guide for classification, a justification for additional drilling, or simply as a heads-up to be followed by a more comprehensive simulation.

The principles behind DHSS have been around for quite some time. The practice of these studies, however, is not readily available.

This presentation is essentially about the practice of DHSS.

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Principles

4

0

90% ConfidenceInterval (CI)

Principles

Compute an estimation variance of an attribute within a large production block

The production block can be regular or irregular

The samples can be at conceptual or actual locations

Assume that the error is normally distributed

Deduce relative confidence intervals (CIs) Usually a 90% CI

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Principles

Which attributes?

Depending on where the risks are, the attribute(s) could be one or several of the following: Grade; Deleterious element; Tonnage related:

– Thickness– Proportion of ore Indicator variable

Metal = tonnage * grade Etc.

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Wittichenite at Antamina; a Cu-Bi sulphide;

Courtesy P. Gomez(Parker, 2014)

Principles

The results can be presented in a number of different ways

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0 25 50 75 100 125 150 175

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CI

Drill spacing (m)

Q90%: Mineralogy

Enargite

Chalcocite

Chalcopyrie

Cu Leach Recovery

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Q1 Q2 Q3 Q4 Q5

90%

CI

Quarterly production volumes

Q90%: Tonnes, Grade, Metal

Tonnage Metal Content Grade Ni

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0.00 0.20 0.40 0.60 0.80

90%

CI

Ore Type Proportion

Y90% As in Ore Type "A"

100 m

75 m

50 m

Limitations

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Limitations

1. Not as flexible as simulation.

2. CIs are approximations because: Calculated estimation variances do not depend on sample values; and Normal distribution assumed for the error.

This is reasonable for variables with quasi-symmetrical distributions, but not for variables with skewed distributions, which is the case most base and precious metal deposits.

Practical solution (but still an approximation): Use large blocks with many samples (central limit theorem) Use relative confidence intervals

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Formulation

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Formulation

Formula of the estimation variance

Notes: Sample values are not needed. Blocks can be of any shape. Different estimation methods can be used to provide the estimation weights.

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2

1 1 12 ( , ) ( , )

N N N

Err block i i j iji i j

S w Block i w w Block Block

N : Number of sampleswi : Sample “i ” estimation weight, : various variogram values

Formulation

Estimation variance for a period:S2

Err period = S2Err block / N

N is the number of blocks in the period. Blocks must be such that their errors of estimation can be considered

independent.

Standard error is square root of estimation variance SErr period

90 % relative confidence interval (CI): 90% relative CI = 1.645 * SErr period / Mean This assumes a normal distribution of the error

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Impact of Sample CV

Relative error CIs are proportional to the sample coefficient of variation (CV).

An indicator is often used as proxi for an ore type proportion or tonnage As Prob(Ind) , CV , CI

This is an important consideration for low proportion ore types.

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Ore Type Proportion

Y90% As in Ore Type "A"

100 m

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50 m

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Q1 Q2 Q3 Q4 Q5

90% CI

Q90% ‐Ni

Case of Metal

Metal content = tonnes * grade

Uncertainty on metal can be driven by grade, tonnes, or both.

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Y 1 Y 2 Y 3 Y 4 Y 5

90% CI

Y90%: Ta2O5

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25%

90% CI

Y90% ‐ Ag

Block Size & Samples

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Block Size & Samples

Initial Block size: Should be large such as when

combined can be considered to be spatially independent

May represent monthly or quarterly increments

Samples Once blocks are combined, the

“final” block should be surrounded with samples

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QuarterlyBlock

YearlyCave

Sensitivity Study

Objective: Get the estimation variance of a large quarterly block with samples within

and outside the block.

Note: Quarterly block size: 300 x 150 x 45 m Two drill hole grids are considered:

– 150 m and 50 m grids The variogram has relatively long ranges

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Quarterly Block

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90%

CI

Scenario

150 m50 m

Grid

Sensitivity – Scenario 1

Scenario 1 The quarterly block is directly

estimated with samples within as well as outside the block.

No issues.

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Quarterly Block


Monthly block. Samples within and outside the block. Issues:

– Sharing of samples when combining blocks to get quarterly block S2

Err quarter lower than it should

– Vertical dimension of block is small S2


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Quarterly BlockMonthly blocks

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90%

CI

Scenario

150 m50 m

Grid

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90%

CI

Scenario

150 m50 m

Grid


Monthly block. Samples within block, no sample outside. Issues:

– Implies that no samples outside quarterly block are considered S2

Err quarter higher than it should



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90%

CI

Scenario

150 m50 m

Grid


Monthly block. Samples within block + a lateral fringe Issues:

– Implies that no samples above and below quarterly block are considered S2




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1 5

90%

CI

Scenario

150 m50 m

Grid


Block size is such that there is one sample per block Issues:

– Implies that no samples outside quarterly block are considered S2


– Starting block size is very small S2


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Quarterly BlockBlocks with one sample

Sensitivity

Recap

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90%

CI

90% CI vs. Scenario

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‐20%

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% C

hang

e

%Change from Scenario 1

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Guidelines

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Block Size & Samples - Guidelines

Preference is to use large production blocks

Think about the number of large “panels” mined per year. For example: Production: 50 KT/d Bench height: 15 m Two long panels of size:

– 500 x 150 x 45 m

Suggested “initial” block sizes: 500 x 150 x 45 m; or 250 x 150 x 45 m

25Oct-2014

Yearly production(2 panels)

Block Size & Samples - Guidelines

It helps to use large actual blocks with actual drilling.

26Oct-2014

Provided courtesy of OT LLC; designs have been superseded; parker, 2014

Software Issues

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Software Issues

Actual production block shapes are irregular

The number of samples can be large: Example:

– 500 x 150 x 45 m block; 25 x 25 m DH grid 1,400 samples

Issues: Most commercial software do not calculate

estimation variances for irregular blocks Limitation on maximum number of samples Numerical inaccuracies creeping-up

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Software Issues

Possible solutions Eventually consider an initial smaller block Discretize the irregular block Ordinary kriging

– Use public domain kriging software– Regroup the samples by groups of 2 or 3– Modify kriging system to account for:

» block discretization» groups of samples

Inverse distance– Compute ID weights using “sample – block discretized point” distances.– Inject these weights in the estimation variance formula.

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Historical Antecedents

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USBM – USGSMeasured ore:

within ±20%

1976

1982

Diehl & David95% CI:

• “A” : 40 d – 8 m: ± 20% • “B” : 8m – 2y: ± 40% • “C” : 2 – 4 years: ± 80%.

1983

Harrison – Exxon90% CI (annual basis):

• “I” : ± 16% • “II” : ± 33% • “III” : ± 66%.

1993

Wober and Morgan 90% CI (annual basis, economic expectation):• “A” : ± 8%• “B” : ± 9 - 13 % • + 2 other categories

Valee & CoteGold deposits;

90% prob. grade > lower limitGlobal & local error margins

Four classes are defined

1992 1998

Stephensen - JORC‘the accuracy ... measured resource estimate might

range up to ±15%’.


A number of principles were evolving: The use of confidence limits in resource/reserve categorisation The consideration of the volume over which the confidence limits are applied Recognition that feasibility level estimates require resources/reserves defined with

tighter confidence limits than prefeasibility studies Economics should be taken into account A gradual tightening of confidence limits applicable to feasibility studies

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MRDI/AMEC Guidelines

Inferred: Insufficient geological information to establish confidence levels

Indicated: ± 15% accuracy with 90% confidence over annual production. When these stated confidence limits are met, cross-sectional and level plan

interpretations show continuity with respect to orebody outlines and grade. Annual production increments are typically used for Pre-feasibility and Feasibility cash

flows. Can stand one year in 20 as being below 85% of the estimate – normal business risk. If actual is less than 85%, very often the mine will run a loss.

Measured: Same but over quarterly or monthly production increments Quarterly or monthly production increments are typically used for Operating Budget

cash flows. If error is less than 15% can usually rework the mine plan and prevent a loss.

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Conclusions

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Conclusions

Drill hole spacing studies involving estimation variances are relatively simple and very fast to execute.

The results are not as complete or flexible as those that could be obtained by conditional simulation.

But if the aim is to provide reasonable confidence intervals on an estimated attribute over medium to long time periods, drill hole spacing studies are a valid option.

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Conclusions

Various situations can be accommodated such as: Conceptual or actual block shapes Conceptual or current drill hole spacings, impact of future drill holes Different attributes can be considered:

– Tonnage, grade and metal content– Ore type proportion, deleterious element, etc.

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Conclusions

Although simple to complete, careful planning is recommended. In particular, the main risks should be identified first

– Grade, deleterious element, volume of high-grade shells, etc. Finding out where the risks are requires an understanding of the geology

and anticipated mining method.

Attention must be paid to the way blocks/samples are combined to get longer production periods. Large blocks are preferred.

The CIs obtained should be considered as approximate rather than strict CIs.

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