Theory of Sampling and Geostatistics for twin drill holes analysis in a niobium mine in Araxá, Brazil
M T G C M A R Q U E S , T M E L H A J J , J M B R A G A J R , A C C H I E R E G AT I A N D H D E L B O N I J R
Day 1 - Tuesday 9 May 2017
Session 4: Drill and Blast Hole Sampling - 4.40pm -
5.00pm
Presenter: Thammiris M. El Hajj – Professor in the Mining Department of the Federal University of Alfenas in Brazil.
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Maria T. G. C. Marques Thammiris M. El Hajj José Marques B. Jr.
Ana Carolina Chieregati Homero Delboni Jr.
INTRODUCTION
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• Main niobium producer (85% of the world consumption).
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Brazil 94%
Canada 5%
Other 1% Niobium production (t)
Reserves (t)
2014 2012 2013 2014 (%)
Brazil 10.827.843,00 82.214,00 76.899,00 88.771,00 93,67
Canada 200.000,00 4.710,00 5.260,00 5.000,00 5,28
Other countries nd 375,00 1.000,00 1.000,00 1,05
TOTAL 11.027.843,00 87.299,00 83.159,00 94.771,00 100,00
Production (t)Country
Niobium Ore Discovery Djalma Guimarães.
Carbonatite Complex in Araxá.
CBMM Alphanumeric campaign.
Twin Drill Holes campaign.
FIG 1 – Djalma Guimarães.
Available at: Federal University of Minas Gerais Journal, 2007 ed.
INTRODUCTION
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Niobium Ore Discovery Djalma Guimarães.
Carbonatite Complex in Araxá.
CBMM Alphanumeric
campaign.
Twin Drill Holes campaign.
INTRODUCTION
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FIG 2 – CBMM and CODEMIG Mine Rights. Available at: Google Earth, 2016 - SIGMINE.
INTRODUCTION
The importance of sampling procedures aligned with reserves estimation.
“The importance of sampling is emphasised especially while considering the evaluation of mineral deposits, the process control and the product marketing. It should be noted that poor sampling can result in sizeable losses or distortions of results with unpredictable technical and financial consequences. Sampling is one of the most complex operations and it can easily introduce errors in the metallurgical and mining industries.”
(Luz et al., 2004)
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Original Content (%)
X Y Z W
Sample Content (%)
X Y Z W
Sampling
INTRODUCTION
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OBJECTIVE
The objective of this work was to asses whether the data from the 70s campaign is suitable to be used in the pit modeling.
Lithology.
Grade.
Nugget effect.
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OVERVIEW
Why apply QA/QC procedures during a twin drill hole campaign
validation?
QA (quality assurance)
Planning: comprises all the measures that need to be planned and materials that need to be
previously acquired;
QC (quality control)
Implementation: consists of all verification procedures required during and after the drilling
program.
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OVERVIEW Representativeness “The representativeness must be maintained at all stages of the sampling procedure. By ensuring the precision and accuracy of the samples taken at all stages of the mining chain, the results will be auditable and reproducible.”
(Gy, 1998)
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OVERVIEW Twin Drill Holes Technique
“Commonly, the twin holes drilling technique is applied for verification of grades provided by previous drilling. It is important to use it when the reliability of previous campaigns data is questionable, especially when data are collected without rigorously applying the relevant QA/QC procedure.”
(Abzalov, 2009)
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F FG
Parameters:
1. Same slope and azimuth;
2. Distance between collar holes less than 5 metres.
Drill Hole Campaigns
OVERVIEW Geostatistics
“When sampling involves two directions (x, y), the most suitable instrument to estimate the dependence between samples is the variogram. The variogram is a basic tool to support the kriging techniques, which allows representing the variation of a regionalised phenomenon in space.”
(Huijbregts, 1975)
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sill
Nugget Effect Sample Reproducibility
METHODOLOGY CBMM Geological Model
(“Alphanumeric” Campaign); Twin drill holes location within the
limit of the current pit; Drilling identical samples interval;
Geological domains: soil, orange
weathered ore, brown weathered ore, saprolite and fresh rock.
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FIG 4 – Google Earth’s view of the current campaign inside the actual pit and its 11 drill holes chosen to
validate the previous campaign.
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Horizontal sections
Vertical sections
3D Geological
Model 490 DDH;
Geological domains: soil, orange weathered ore, brown weathered ore, saprolite and fresh rock.
Software MS3D (Minesight).
METHODOLOGY
Quality Assurance / Quality Control Insertion of control samples;
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SAMPLES Duplicate Blank Standard
FREQUENCY 20 35 25
METHODOLOGY
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Precision Accuracy
REPRESENTATIVENESS
m²(SE) + σ²(SE) = r²(SE)
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DATA BASE
Twin Drill Holes Alphanumeric Holes
Statistical Analysis Statistical Analysis
QA/QC
ASSESMENT
Collar Directory
Assay Directory
Geology Directory
Estimate variance between duplicates
Calculation of the error linked to the sampling
protocol
ASSESMENT METHODOLOGY
+
{
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Content Analysis ASSAY
Coordinates Analysis COLLAR
Lithology Analysis GEOLOGY
Horizontal distance between holes
𝑫 = 𝒙𝟏 − 𝒙𝟐 ² + 𝒚𝟏 − 𝒚𝟐 ²
Difference of the elevation between holes (axis z)
+
Statistical analysis of the variable 𝒙𝟏
(𝑵𝒃𝟐𝑶𝟓)
Software SGeMS: Analysis of the grade range variation between pairs
of samples to obtain the nugget effect from semivariogram
0.5*γ(h)
Use the previous value to calculate the standard
deviation σ(h)
Applying stacked column charts to generate drill hole geological profiles
Comparison between the lithological profiles
boundaries
RESULTS AND DISCUSSION
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Relative difference between duplicate samples QA/QC
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
Ore
co
nte
nt (%
) -
Dup
lica
te
Ore content (%) - Sample
Quality Control Program DDH Campaign - FG
Lab. SGS - Global
Tendency Line
Sample
Upper Limit 15%
Lower Limit 15%
Refused
Samples
0.00%
ϒ(h)=σ(ℎ)
2
ϒ(h) – estimated semivariogram; σ(ℎ) – standard deviation.
21
Relative standard deviation of the fundamental sampling error during the sample preparation
Stage Mass per lot Sample mass d95 IHL FSE2 FSE (%)
Primary Sample
Selection 30000 15000 3.2 14.65 0.000488477 2.21%
Primary Comminution 15000 15000 0.2 0.01 0 0.00%
Rotary Sampler 15000 2000 0.2 0.01 3.02093E-06 0.17%
Rotary Sampler 2000 250 0.2 0.01 2.43998E-05 0.49%
Pulverization 250 250 0 0.00 0 0.00%
Chemical Analysis 250 50 0 0.00 0.000000128 0.04%
Total 0.00051 2.26%
S² (QFE) = S²(FSE) + S²(GSE) = 2 x s2 (FSE) 0.00103 3.20%
Regarding the fundamental sampling error (FSE) associated to the sampling protocol, a value of 3.20 per cent was obtained and it is in
accordance with the standards adopted by the company. QA/QC
RESULTS AND DISCUSSION
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Coordinates Validation COLLAR
Comply with the maximum spacing (horizontally) of 5
metres between the pair of drill holes.
DHID DHID
Horizontal
distance
(cm)
Elevation
difference
(m)
F-0IXM0 FG-0IXM0 1.41 72.4
F-0XM9 FG-0XM9 1.7 43.06
F-0XN0 FG-0XN0 1.26 61.88
F-2IXK5 FG-2IXK5 1.17 50.23
F-2VIIK0 FG-2VIIK0 0.22 2.99
F-3VIIK7 FG-3VIIK7 1.8 27.8
F-5IXK5 FG-5IXK5 2.66 51.1
F-5XIJ3 FG-5XIJ3 1.55 9.42
F-7IXH5 FG-7IXH5 1.35 -2.32
F-8.5VIIL9.5 FG-8.5VIIL9.5 0.99 21.39
RESULTS AND DISCUSSION
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Coordinates Validation COLLAR
The twin drill hole FG-7IXH5 was performed on a landfill, and due
to this fact, its height is above the old drill hole
level.
DHID DHID
Horizontal
distance
(cm)
Elevation
difference
(m)
F-0IXM0 FG-0IXM0 1.41 72.4
F-0XM9 FG-0XM9 1.7 43.06
F-0XN0 FG-0XN0 1.26 61.88
F-2IXK5 FG-2IXK5 1.17 50.23
F-2VIIK0 FG-2VIIK0 0.22 2.99
F-3VIIK7 FG-3VIIK7 1.8 27.8
F-5IXK5 FG-5IXK5 2.66 51.1
F-5XIJ3 FG-5XIJ3 1.55 9.42
F-7IXH5 FG-7IXH5 1.35 -2.32
F-8.5VIIL9.5 FG-8.5VIIL9.5 0.99 21.39
RESULTS AND DISCUSSION
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Drill Holes Percentage of accepted
samples
F/FG - 0IXM0 samples at different intervals
F/FG - 0NX0 55.4%
F/FG - 0XM9 69.3%
F/FG - 2IXK5 91.7%
F/FG - 2VIIK0 64.4%
F/FG - 3VIIK7 57.1%
F/FG - 5IXK5 75.0%
F/FG - 5XIJ3 58.3%
F/FG - 7IXH5 52.5%
F/FG - 8.5VIIL9.5 samples at different intervals
F/FG - 8VIIK0 57.9%
Content Validation
ASSAY
Variogram applying spherical function
Nugget Effect
0.45 Variance
Standard Deviation
47.4 per cent.
=
{ Upper Limit
Lower Limit
RESULTS AND DISCUSSION
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Drill Holes Percentage of accepted
samples
F/FG - 0IXM0 samples at different
intervals
F/FG - 0NX0 55.4%
F/FG - 0XM9 69.3%
F/FG - 2IXK5 91.7%
F/FG - 2VIIK0 64.4%
F/FG - 3VIIK7 57.1%
F/FG - 5IXK5 75.0%
F/FG - 5XIJ3 58.3%
F/FG - 7IXH5 52.5%
F/FG - 8.5VIIL9.5 samples at different
intervals
F/FG - 8VIIK0 57.9%
FIG 5 – Scatterplot of the comparison between F-2IXK5 and FG-2IXK5 drill holes that contain the largest quantity of
samples within the deviation limit of 47.4 per cent.
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Drill Holes Percentage of accepted
samples
F/FG - 0IXM0 samples at different
intervals
F/FG - 0NX0 55.4%
F/FG - 0XM9 69.3%
F/FG - 2IXK5 91.7%
F/FG - 2VIIK0 64.4%
F/FG - 3VIIK7 57.1%
F/FG - 5IXK5 75.0%
F/FG - 5XIJ3 58.3%
F/FG - 7IXH5 52.5%
F/FG - 8.5VIIL9.5 samples at different
intervals
F/FG - 8VIIK0 57.9%
FIG 6 – Comparison between the grades of the variable x1 in the drill holes F/FG-2IXK5 and its average. Both holes
have samples at identical intervals; the graph only illustrates the spacing of every 5 m for better visualisation.
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FIG 7 – Alphanumeric drill holes that showed better results regarding the conformity with their respective twin drill holes.
Lithology Validation GEOLOGY
Applying stacked column charts to generate drill hole geological
profiles
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FIG 8 – Twin drill holes which did not reach a satisfactory depth to be described.
Lithology Validation GEOLOGY
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FIG 9 – Twin drill holes with slight discrepancy among its respective original hole, which ranged from 2.5 to 5.0 metres between the lithological contact.
Lithology Validation GEOLOGY
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FIG 10 – Pair of drill holes with significant discrepancy between the lithology’s delimitation involving brown wethearing ore, the saprolite and the rock.
Lithology Validation GEOLOGY
RESULTS AND DISCUSSION
As previously reported, the accepted representativeness value is 1.0.
Although, some samples resulted in different values, they are not inadequate when referring the average of 𝑁𝑏2𝑂5 content in both drill holes.
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CONCLUSIONS
Effectiveness of the applied methodology.
Distance between the holes regarding the coordinates validation.
High value expected for the nugget effect.
QA/QC procedures benefits.
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CONCLUSIONS
The objective of this paper was to provide helpful information regarding the use of a methodology that associates the TOS with Geostatistics to validate old drilling campaigns, along with its economic benefits and practicality.
The new campaign samples, which were obtained following a QC campaign, are suitable to evaluate the old campaign data.
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CONCLUSION
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Twin Drill Hole Campaign
New Campaign
ACKNOWLEDGEMENTS
The authors kindly thank the support and permission to publish the paper by CBMM. Moreover, the researchers express their
sincere gratitude to the company’s mine planning department, especially the geology team.
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