Geoscience Reference
In-Depth Information
is done to irregular polygonal boundaries. Isolated blocks
cannot be freely extracted and thus assuming free selection
is optimistic. The simulation of the grade control process,
feasible if using CS models from a pre-feasibility stage on-
wards, allows for an early understanding of the information
effect, selectivity, dilution and ore loss.
Another useful application of simulation is forecasting
metal recovery and other related metallurgical performance
variables. This is done by visiting each location over one re-
alization for all variables and applying a transfer function
that accounts for the known metallurgical processes and
translates grades for multiple metals into a recovery at that
location. This is repeated for all realizations to create mul-
tiple recovery models. These recovery models can be used to
produce distributions of uncertainty for both local and global
recovery. This process requires a clear understanding of the
metallurgical processes, including the non-linearity of some
of the geometallurgical properties involved.
The production of probability maps is easily achievable
using the results of simulation. This is done by visiting each
location over multiple realizations to determine local dis-
tributions of uncertainty. We then calculate the probability
to exceed a cutoff grade from this local distribution. This
is done at all locations. A map of probabilities can then be
plotted. Specific quantiles of interest can be analyzed, such
as 10, 50, or 90 %. Any areas that are high on the p10 map
will surely be high grade. Any areas that are low on the p90
map will surely be low. The same technique can also be used
for classification of resources; for example, yearly volumes
within X% of predicted value Y% of the time can be called
proven.
Simulation models can also be used to simulate stockpiles
(see Boucher et al.
2005
, among others). A large volume con-
sistent with blast patterns is selected. This volume is applied
to a simulated realization to determine the average grade for
the stockpile. This is repeated for all realizations to get aver-
age grades from each. This information can be used to de-
termine the probability that the volume will satisfy blending
criteria or economic cutoff.
The results of simulation are also able to determine global
reserves and their uncertainty. The global reserves are calcu-
lated using all the relevant metal grades, recovery models,
and the economic cutoff. This is done for each realization.
The uncertainty in the reserves can now be found.
Another post-processing application of a simulation-
generated model is assessing the link between equipment
size and mine selectivity, and thus to determine the value/
cost of selective mining. This is applicable to both open pit
and underground settings; however, stope design and extrac-
tion methods are less flexible than the open pit counterpart,
and thus this study should be done well in advance of mine
development. In open pit, CS models are used to evaluate
equipment selectivity in relation to the available sampling,
Fig. 10.19
Example of error bounds for a time period
bench height, ore/waste boundary definitions, blast hole
spacing, blast heave, and so on. The process always involves
one or more transfer functions that allow incorporating rel-
evant economic assessments and cost/benefit curves.
Reporting the results of studies from CS models is usu-
ally done by zone (time period, bench, stope, and so on) and
reporting common quantiles (P
10
; P
50
; P
90
) or (P
5
; P
50
; P
95
).
The uncertainty in NPV/ROI type statistics can be shown
as error bounds derived from the multiple realizations. In the
example in Fig.
10.19
, P90 is exceeded 10 % of the time,
while the value of interest falls below P10 10 % of the time.
Usually there is a need to rank the simulated values. By
definition, all realizations are equi-probable, but have differ-
ent impact to the problem being studied. Often, ranking is
necessary to limit the number of realizations used in the ap-
plications, since considering the entire model of uncertainty
may be impractical.
An increasingly popular post processing of uncertainty
from uniform conditioning, indicator kriging and simula-
tion is localization (Abzalov
2006
; Hardtke et al.
2011
). One
value is chosen per block in a manner that reproduces the
block distribution within larger panels.
The most common criterion used for ranking is total
metal content; for example, in pit or stope optimization what
matters is the total dollar value of the block, which is in turn
a function of the metal content in the block. Occasionally,
ranking by total variability (by stationary domain) may be an
option, especially if overall local uncertainty measures are
desired. The chosen realizations should fairly represent the
full space of uncertainty for the variable that is deemed of
highest consequence.
10.8
Summary of Minimum, Good and Best
Practices
Minimum practice is to thoroughly check and validated the
realizations obtained. The details of the validation procedure
are given in Chap. 11, but it is a more involved and demand-
ing process than for any estimated block models.
Realizations are more difficult to report and to communi-
cate than any other model, because they contain much more
