segregation free analysis (sfa) for calibrating the ... · segregation free analysis (sfa) for...
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Segregation Free Analysis (SFA) for calibrating the constants K and Alpha
for use in Gy’s formula
Richard Minnitt School of Mining Engineering, University of the Witwatersrand, Private Bag 3, WITS. 2050. Telephone: +27 11 717 7416. Fax: +27 11 339 8295.
Email: [email protected]
Dominique Francois-Bongarcon PhD, President, AGORATEK International, 1720-B Marina Ct., San Mateo, CA 94403, USA. Telephone: +1 650 574 5411. Fax: +1 650 574 5244. Email: [email protected]
Francis Pitard President, Francis Pitard Sampling Consultants, 14800 Tejon Street, Broomfield, CO 80023, USA. Telephone: +1 303 451 7893. Fax: +1 303 280 1396:
Structure of the presentation
• CONTEXT AND CONCERNS
• A new approach
• Underlying theory
• Experimental results– Calibration curve
– Liberation size
– Nomogram
• Conclusions
Types and sources of sampling errors
• Random errors (INE, FSE, GSE, no bias) must be managed
• Systematic errors (DE, EE, PE, AE, cause bias) can be eliminated
• Random errors - Constitutional Heterogeneity - differences in
grade between particles in the lot
• A given lot, a given fragment size, a given sample mass
• Reduce the error - reduce the particle size
• Random errors can only be managed and maintained at
acceptable levels through appropriate sampling protocols
Managing Random Sampling Errors
• Causes poor ore/waste selection decisions, profit/loss decisions, poor reconciliations, poor metal accounting
• Sampling error can be reduced by maximising the sample mass, reducing fragment size, minimising steps
Sampling Error CharacteristicsSampling error
typeRandom Systematic
Other names In-situ Nugget Effect (INE), Fundamental Sampling Error (FSE)
DE, EE, PE, WE, introduce a Bias
Sources Sub-sampling Faulty technique
Measurement approach
Heterogeneity Test, Duplicate Sampling Analysis
Test against alternative techniques
Measure Variance, Coefficient of Variation Relative difference
Quality assurance target
Field duplicate sampling imprecision less than 50%
Less than 3%
Improvement strategy
Increase sample mass, decrease fragment size, decrease sampling steps
Change or improvetechniques
Concerns about current methods
• A range of calibration methods used for establishing the sampling parameters for use in Gy’s formula for the FSE
• Heterogeneity Test proposed by Gy and championed by others, uses a single fragment size, may not be applicable to other fragment sizes.
• The Duplicate Sampling Analysis (Sampling Tree Experiment) method proposed by Dominique Francois-Bongarcon
• QEM-Scan methods could, - depending on costs and sample representivity, - replace the fire-assay-type methods of calibration
Three problem areas1. Introduction of Grouping and
Segregation Error during riffle splitting
2. Inaccuracies in fragment size classification for each series, and;
3. Removal of outliers from the data (undermines the integrity of the method)
Used with permission, Eduardo Magri 2011
Shakespearian aside: Research the GSE
• Pierre Gy performed 124 experiments to investigate the behaviour of the granulometric factor
• Did he ever anticipate this outcome?
• We have new technologies to research the GSE problem
• X-Ray tomography and geostatistics as a means of characterising and parameterising the GSE
Used with permission, Eduardo Magri 2011
Structure of the presentation
• Context and concerns
• A NEW APPROACH
• Underlying theory
• Experimental results– Calibration curve
– Liberation size
– Nomogram
• Conclusions
Used with permission, Eduardo Magri 2011
Sieve analysis of the oresPassing but not Mass (g) Relative Percent Cumulative Percent
>25000 >25000 2626 1.28% 1.28%
25000 19000 12936 6.30% 7.58%
19000 16000 17956 8.74% 16.32%
16000 13200 32986 16.06% 32.38%
13200 11200 19286 9.39% 41.77%
11200 9500 17866 8.70% 50.47%
9500 8000 16956 8.26% 58.72%
8000 6700 16086 7.83% 66.55%
6700 4750 16496 8.03% 74.58%
4750 3350 13886 6.76% 81.34%
3350 2000 12036 5.86% 87.20%
2000 1000 9156 4.46% 91.66%
1000 710 3936 1.92% 93.58%
710 500 1674 0.82% 94.39%
500 212 5641 2.75% 97.14%
212 150 3237 1.58% 98.72%
<150 2637 1.28% 100.00%
Total 205397
Relative and cumulative mass of fragment sizes comprising the lot
Average fragment sizes passing between two screen sizes
Seventeen screen sizes,
25.0cm to 0.015cm, used
to screen 205.80 kg of
crushed ore
Riffle splitting protocol
for each screened
fraction to produce 32
samples (RHS of
diagram)
448 samples submitted
for 50g fire assay
Mitigates two problems
1. Mitigates Grouping and Segregation Error during riffle splitting
2. Eliminates the need to classify each Series for fragment size
Structure of the presentation
• Context and concerns
• A new approach
• UNDERLYING THEORY
• Experimental results– Calibration curve
– Liberation size
– Nomogram
• Conclusions
Modification of some parameters
2 3
R e lative M A X
S
1cfg ' d d
M
Where g’ is the Granulometric Factor derived in this case for closely sieved materials
Ratio r = dMAX/dMIN for different fragment sizes
Granulometric factor g’ versus r (for closely sieved materials, r = dMAX/dMIN))
Used with permission, Dominique Francois-Bongarcon, AGORATEK, 2011
Modification of some parameters
2 3
R e lative M A X
S
1cfg ' d d
M
2 3
R e la tive S M A XL n * M L n d L n cfg ' d
cmxy
Ln[K]]αLn[d]M*Ln[ σ
)]Ln(cfg')α)Ln(d[(3]αLn[d]M*Ln[ σ
MAXS
2
Rel
MAXS
2
Rel
(1)
(2)
(3)
(4)
Structure of the presentation
• Context and concerns
• A new approach
• Underlying theory
• EXPERIMENTAL RESULTS– Calibration curve
– Liberation size
– Nomogram
• Conclusions
Histogram and descriptive statistics - 448 gold assays
Statistic Value
Mean 1.06 g/t Au
Standard Error 0.025 g/t Au
Median 0.98 g/t Au
Mode 0.85 g/t Au
Standard Deviation 0.53 g/t Au
Sample Variance 0.28 g/t Au2
Coeff of Variation 0.50
Kurtosis 59.52
Skewness 5.04
Range 7.82 g/t Au
Minimum 0.01 g/t Au
Maximum 7.83 g/t Au
Count 448
Average gold grade versus fragment sizes
Structure of the presentation
• Context and concerns
• A new approach
• Underlying theory
• Experimental results
• CALIBRATION CURVE– Liberation size
– Nomogram
• Conclusions
Primary data reduction
Parameter Value
Mean (g/t) 1.02
Variance (g/t2) 0.09
Std Dev (g/t) 0.31
Relative Std Dev 0.30
Top screen (cm) 0.67
Bottom screen (cm) 0.48
Size (cm) 0.59
Average Mass (g) 302.18
Relative variance versus nominal fragment size
Variance versus Nominal fragment size
Variance versus Nominal fragment size (Sichel’s t estimator)
Comparison of the three calibration curves
Establishing K and Alpha ()
• The constant K is determined using the formula:
• The slope is determined from the slope of the calibration curve
3
L n K L n cfg ' d
Calibrated values of K and Alpha
DFB Grubbs Test Sichel’s t estimate
Correlation Coefficient (R2) 0.96 0.97 0.96
Number of data points
removed77 6 1
LnK 2.9 3.64 4.88
K 18.17 38.09 131.6
Alpha 1.4 0.94 1.04
Gold grain liberation size
(microns)4 23 42
Structure of the presentation
• Context and concerns
• A new approach
• Underlying theory
• Experimental results– Calibration curve
• LIBERATION SIZE– Nomogram
• Conclusions
Calculation of Liberation Size
Parameters Value
Grade (g/t) 0.80
g/g (100000) 0.000000803
/g* 19933261.44
K (calibrated) 131.6
f 0.5
g’ 0.6
c 19933261.44
Alpha (calibrated for SFA) 1.04
(1/(3-)) 0.51
cfg’ 5979978.43
sqrtdl (K/(f*c*g’)) 2.20119E-05
* = Density for gold-silver alloy ~ 16g/cc
Calculation of Liberation Size3
1
3
. . ' .
. . '
K c f g d
Kd
c f g
1
3 1 .0 3 8
1
1 .9 6 2
1 3 1 .61 0 0 0 0
1 9 9 3 3 2 6 1 .4 0 .5 0 .6
0 .0 0 0 0 2 2 0 0 6 7 1 0 0 0 0
0 .0 0 4 2 2 8
4 2 .3
l
l
l
l
d
d
d cm o r
d m icro n s
d (cm) 0.00423007
d (m) 42.30
Structure of the presentation
• Context and concerns
• A new approach
• Underlying theory
• Experimental results– Calibration curve
– Liberation size
• NOMOGRAM
• Conclusions
Fundamental Sampling Error (2FSE)
Size (cm) Mass(g) DFB Grubbs Test Sichel’s t
7.5 1000000 0.00047 0.00063 0.00121
5.5 1000000 0.00034 0.00046 0.00085
5.5 300000 0.00112 0.00155 0.00283
1.9 300000 0.00036 0.00056 0.00084
1.9 30000 0.00361 0.00557 0.00842
0.5 30000 0.00087 0.00154 0.00184
0.5 5000 0.00522 0.00923 0.01103
0.1 5000 0.00094 0.00196 0.00176
0.1 500 0.00938 0.01960 0.01760
0.0075 500 0.00059 0.00162 0.00092
0.0075 50 0.00593 0.01618 0.00919
Sampling nomograms for a hypothetical ore
Nomograms trend lines
Structure of the presentation
• Context and concerns
• A new approach
• Underlying theory
• Experimental results– Calibration curve
– Liberation size
– Nomogram
• CONCLUSIONS
Conclusions
• Segregation Free Analysis (SFA) method improves on the DSA method in three ways:
1. It overcomes the GSE introduced during riffle splitting of the series;
2. It overcomes the need for inaccurate fragment size classification; calibration of fragment sizes using
closely spaced screens is very accurate
3. It overcomes the need for eliminating outliers
• SFA data yield a straight line;
• SFA is a point-by-point estimate of the relative variance at different size fractions;
• SFA allows for better determination of the liberation size;
• SFA simplifies the calibration process:
1. Crush 40kg of run of mine ore, and screen large, intermediate, and small size fractions;
2. Riffle split each size fraction into 32 samples, and;
3. Assay the samples and plot the calibration curve
Thank You!