Page 268 - Introduction to Mineral Exploration

10: EVALUATION TECHNIQUES 251

Sphalerite contains 67% zinc with a specific Chalcopyrite contains 33% copper with a den-
−3
−3
gravity of 4.0 kg m . sity of 4.2 kg m .
(a) Fundamental variance of each sampling (a) Fundamental variance of each sampling
stage (see also Box 10.1). Critical content stage.
(a L ) = 7% zinc = 10.5% sphalerite as a fraction Critical content (a L ) = 0.7% = 2.1% chalcopyrite
= 0.105. as a fraction = 0.021.
Constitution factor (c): Constitution factor (c)

0
− .105
1
( 0 ) 1 − .021
= [(1 − .105 ) .0 + ( .105 ) . ] = [(1 − 0.105)4.0 + (0.105)2.7]
2
7
0
0
4
. 0 105 . 0 021
= 8.52(3.58 + 0.28) = 32.89, say 33. = 46.62(4.11 + 0.06) = 194.4, say 195.
Heterogeneity constant (C) Heterogeneity constant (C) = cβfg = 195 × 1 ×
0.5 × 0.25 = 24.38.
= cβfg = 33 × 1 × 0.5 × 0.5 = 4.13. Fundamental variance:
Fundamental variance: C
−3
= = 24.38/125,000 = 195 × 10 .
C K
= = 24.38/125,000 = 33 × 10 −6
K (b) Total variance (TE) of the sampling scheme.
As above but, suppose, the system consists of
(b) Total variance (TE) of the sampling scheme.
At each reduction stage the total variance is five reduction stages each ending on the safety
equal to double the fundamental variance. The line. The total error variance now equals 10
complete sampling scheme consists of four times (2 × 5) the fundamental variance.
reduction stages (Fig. 10.5a) each ending on the −6
safety line (see text). Consequently, the total Total variance (TE) = 10 × (195 × 10 )
−6
variance equals eight times (2 × 4) the funda- = 1950 × 10
mental variance as calculated above.
Relative standard deviation = (1950 × 10 ) =
−6 −2
−3
−6
−6
Total variance (TE) = 8 × (33 × 10 ) = 264 × 10 . 44 × 10 = 4.4%.
Absolute standard deviation as % of
Relative standard deviation = (264 × 10 − 6 ) mineral = 2.1% chalcopyrite × 4.4% = 0.09%
= 16.2 × 10 −6 chalcopyrite.
Absolute standard deviation as % of metal =
Absolute standard deviation as % of mineral = 0.09% × 33% = 0.03% copper.
10.5% sphalerite × 1.6% = 0.17% sphalerite. The confidence at 95% probability is ±2 SD =
Absolute standard deviation as % of metal = ±2(0.03%) = 0.06% copper.
0.17% sphalerite × 67% = 0.11% zinc. The two-sided confidence level is then 0.7% ±± ±± ±
The confidence level at 95% probability is ±2 0.06% copper at 95% probability, which is an
SD = ±2(0.11%) = 0.22% zinc. acceptable result. Generally a relative standard
The two-sided confidence level is then 7% deviation of <5% is acceptable.
± ± ± ± ± 0.22 zinc at 95% probability, which is an
acceptable result. Generally, a relative stand- 4 Calculation of the weight of a sample (M) to
ard deviation of <5% is acceptable. be taken knowing the confidence interval.
(a) Introduction (see section 10.1.4)
3 Calculation of total variance (TE) and
3
2
double-sided confidence interval: chalcopyrite M = Cd /S (FE)
mineralisation.
A prospect contains chalcopyrite mineralisa- (b) Sphalerite mineralisation.
tion of grade 0.7% copper (X) in gangue of Sphalerite mineralisation assays 7% zinc and
−3
density 2.7 kg m . the confidence level required is ± 0.2% zinc at