segregation free analysis (sfa) for calibrating the ... · segregation free analysis (sfa) for...

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: Richard.Minnitt@wits.ac.za

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: dfbgn@att.biz

Francis Pitard President, Francis Pitard Sampling Consultants, 14800 Tejon Street, Broomfield, CO 80023, USA. Telephone: +1 303 451 7893. Fax: +1 303 280 1396:

Email: fpsc@aol.com www.fpscsampling@aol.com

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!