Geoscience Reference
In-Depth Information
Multiple variants of the indicator kriging approach have
been used. A common application considers a single indica-
tor estimated at the ore/waste boundary of interest, thus pro-
viding the probability of any block or point within the blast
being ore or waste. Generally point kriging is performed,
usually at a larger-than necessary grid spacing. Occasionally,
block kriging may be done, ignoring the fact that the aver-
age of estimated probabilities within a block is not the same
as the point probability derived from the ore/waste indica-
tor (Chap. 9). Nonetheless, the practice is to analyze equal-
probability contour lines for several values and decide based
on visual observations which one adjusts better to prior pro-
duction. Commonly, in gold operations that use this method,
probabilities of being ore of about 30-40 % are used to define
ore/waste boundaries.
A method that has proven successful in several operations
is the “Breakeven Indicator Method” (BEI), as described
in Douglas et al. (
1994
). It was implemented first at Inde-
pendence Mining Company's Jerritt Canyon, north of Elko,
Nevada, in the early 1990s.
The BEI grade control method uses a combination of both
indicator and grade kriging. An ore/waste indicator vari-
able is used to predict the probability of ore occurrence at
a given location
P
o
(
x
)
,
which is obtained by kriging the ore/
waste indicator variable. The ore-grade blast holes are then
used to krige an ore grade
Z
o
(
x
) for the location
x
. Similarly,
the waste-grade blast holes are used to krige a waste grade,
Z
w
(
x
)
,
for the same location. Then, the expected revenue
is estimated from the kriged probability
P
o
(
x
) and ore and
waste grades:
lower grade ore will not pay for much overbreak. Thus, the
method requires that the low grade be most surely higher
than the economic cutoff. This can be seen by calculating
the probability that corresponds to the economic breakeven
cutoff,
E
(
R
)
= 0
:
−
RZ
()
P
(
BE
)
=
w
(13.2)
o
RZ
() ( )
−
RZ
o
w
The method should be applied on small blocks, one third to
one half of the blast hole spacing, allowing the grade con-
trol engineer to define dig lines based on revenues. The BEI
method is designed to improve grade control performance
most along contacts of ore/waste zones. If the panels to be
mined are very large (wide), the ratio of contact surface area
per ton of ore is small. The opposite is true for panels that
are narrow for which this method would provide the most
improvements.
If compared to the single indicator kriging method out-
lined before, the BEI is equivalent to working on a variable
probability of being ore, which is dependent on the revenue
function defined.
13.3.3
Example: Grade Control Study
A comparison of several grade control methods was per-
formed for the copper-molybdenum Ujina open pit mine in
Northern Chile. It is summarized here, courtesy of Compa-
ñía Minera Doña Inés de Collahuasi (CMDIC). The company
mines a Cu-Mo porphyry deposit with a significant Cu enrich-
ment blanket, which was the main target of mining at the time.
As a massive, disseminated-type deposit, it could have been
assumed that grade control is a simple process; however, there
are factors that made grade control at Ujina a complex process.
The differences observed among the methods tested will be
larger if the grade distributions being modeled are more vari-
able. Also, if there are many different possible destinations
for ore and waste, the grade control process is more compli-
cated: the grade ranges that are used to separate the material
become narrower. Table
13.1
shows the possible destinations
for ore coming out of the Ujina pit at the end of 1999.
A quick inspection of Table
13.1
suggests that a large
degree of accuracy and precision is required of the grade
control method, since the mining method and metallurgical
processing requirements are very specific.
The methods tested included the inverse distance cubed
(ID
3
) as used at the time by the mine; ordinary kriging (OK);
the breakeven indicator method described above (BEI); and
the maximum revenue method, based on conditional simula-
tions and loss functions as described further below. Only a
short summary of a long and detailed study is presented here
ER
(
)
=
P RZ
×
(
)
+−
(1
P
)
×
RZ
(
)
(13.1)
o
o
o
w
The revenue function is traditionally calculated as
(
) (
)
R
=
gold price
*
metallurgical recovery
(
) (
)
*
grade
-
costs
where “costs” generally imply metallurgical processing costs
only. The method offers the flexibility of adding additional
costs if desired, to work on what would amount to a higher
ore/waste cutoff grade.
If the expected revenue from Eq. 13.1 is negative, the
material at the location is waste. If the expected revenue is
positive, the material at the location is ore. If the grade of ore
is high, the corresponding revenue will be high, allowing for
a block with a low probability of being ore to be sent to the
mill. In this case, the ore pays for large amounts of waste,
which ensures all high grade ore is recovered. Alternatively,
if the ore grade is low, the revenue will tend to zero and the
estimated probability of ore will have to be close to 1: the
