Page 226 - Introduction to Mineral Exploration

10: EVALUATION TECHNIQUES 209

Cd 3 total error can be calculated and compared with
=
M the initial assumption (see later).
S 2
M is the minimum sample mass in grams, d
is the size of the coarsest top 5% of the sample Graphical solution of sample reduction
in centimeters, C is a heterogeneity constant
characteristic of the material being sampled, Introduction
2
and S is the variance. Consequently, in reduc- Sample preparation is essentially an alterna-
ing the mass of a sample there is a cube rela- tion of size and mass reduction within the
tionship between this reduction and its particle parameters of the Gy formula given above
size if the variance is to remain constant. which provides for a control of the variance.
In practice the observed variance of a Such reduction is best shown graphically with
sampling system is larger than that calculated log d (top particle size) contrasted with log M
from the above model. This is because the (sample mass), where a horizontal line repres-
observed variance comprises the total sampling ents a size reduction and a vertical line a mass
error (TE) while the above model calculates a reduction (Fig. 10.5).
particular component of this totality, the fun- These reductions have to be completed
damental error (FE). This important point has within an acceptable variance which can be
2
2
already been referred to, where S (TE) = 2S (FE). taken as a relative standard deviation of less
than 5%. Ideally what is required is a safety
line which divides the above graph into two
Design of a sample reduction system parts, so that on one side of the line all reduc-
tion would be safe (i.e. with an acceptable vari-
The choice of suitable crushing, grinding, dry-
ing, and splitting equipment is critical and sys- ance) while on the other side unacceptable
tems are best designed and installed by those errors occur. Gy (1992) provides a mathemat-
with appropriate experience. The design of a ical expression for such a line as:
reduction system is often neglected but it is of 3
prime importance particularly in dealing with Mo = Kd
low grade and/or fine-grained mineralisation.
In particular, equipment may have to handle Empirically Gy (1992) suggests a value of
wet, sticky material with a high clay content 125,000 for K but emphasizes that for low con-
which will choke normal comminution equip- centrations of valuable constituents (<0.01%) a
ment. Also the creation of dust when pro- higher K value should be used of up to 250,000.
cessing dry material is an environmental and Consequently:
health hazard and may also contaminate other
3
samples. Dust has to be controlled by adequate Mo = 125,000 d or log Mo = log K + 3 log d
ventilation and appropriate isolation.
In any reduction system the most sensit- This relationship on log–log graph paper
ive pieces of equipment are the crushers and (Fig. 10.5) is a straight line, with a slope of
grinders. Each such item works efficiently 3.0, which divides the graph into two areas.
within a limited range of weight throughput 1 To the left of this safety line Mo is greater
and size reduction and there has to be a real- than M and, consequently, from the Gy for-
2
istic assessment in the planning stage of the mula the fundamental sampling variance So is
2
expected number and weight of samples to less than S , and is acceptable.
2
2
be processed each hour or shift. The use of 2 On the line, Mo = M and So = S , which is
inadequate comminution equipment at best acceptable. All points on the safety line cor-
may introduce excessive preparation errors and respond to a constant fundamental variance.
at the worst can close the entire system. 3 To the right of the line Mo is less than M and
2
2
The calculation of TE from twice the FE the sampling variance is too high (So > S ) and
provides a safe estimate (see previously) from unacceptable and either Mo has to be increased
which a flexible reduction system can be or d decreased to place the reduction point to
designed. When it is in operation its actual the left of the safety line.