Geoscience Reference
In-Depth Information
1.3.6
Recoverable Resources: Simulation
boundaries and the quality are predicted using closely spaced
data. The information at the time of resource estimation is
quite different than at the time of mining, for which esti-
mates will be much better.
The traditional approach to block modeling is to estimate a
single value in each block of the model, obtaining the best
possible prediction in some statistical sense. This estima-
tion can be done using non-geostatistical methods, or more
commonly, some form of kriging. Although there is a need
for a single estimate in each block, there are some important
shortcomings in attaching only the estimated value to each
block.
An alternative approach to resource evaluation is the use
of conditional simulation that provides a set of possible val-
ues for each block, which represent a measure of uncertainty.
The idea is to obtain a number of simulated realizations that
reproduce the histogram and the variogram of the original
drill hole information. The realizations are built on a fine
grid. Reproducing or honoring the histogram means that the
realizations will correctly represent the proportion of high
and low values, the spatial complexity of the orebody, the
connectivity of high and low values, and the overall grade
continuity in three dimensions. These characteristics of the
mineralization are important aspects that play a signifi-
cant role in designing, planning, and scheduling a mining
operation.
A number of issues have to be adequately resolved for the
realizations to be representative of the grades of the deposit.
These include, among others, choosing among several simu-
lation techniques available, such as Sequential Gaussian
(Isaaks
1990
), Sequential Indicator (Alabert
1987
), or oth-
ers. Also, decisions about grid size, conditioning data, search
neighborhoods, and treatment of high grade values must be
made. It is a similar process to developing a kriging block
model. Some discussions about practical implementations
can be found in Deutsch and Journel (
1997
) and Goovaerts
(
1997
), among others.
When a number of these realizations have been created
and checked, then, for each node defined in the grid, there will
be a corresponding number of different grades available. This
set of multiple grades is a model of uncertainty for that node.
These simulated points can be re-blocked to any block size
desired such as the Selective Mining Unit SMU size of the
operation. These results are used further by mining engineers.
Important parameters can be obtained from the distribu-
tions of local uncertainty such as the mean, median, and prob-
ability of exceeding of exceeding a specified cutoff grade.
Therefore, the information provided by a simulation model
is significantly more complete than the single estimate pro-
vided by an estimated block model. The simulation models
can provide recoverable resources for any selectivity by re-
blocking the simulated grades to the chosen SMU block size.
It is likely that, in due time, simulation models will replace
estimated block models, since they not only provide a single
estimate, but also a full range of possible values.
1.3.5
Recoverable Resources: Estimation
The importance of calculating recoverable resources and re-
serves was recognized early on in geostatistics (Matheron
1962
,
1963
), but it was M. David's early work (
1977
) that
demonstrated the practical significance of estimating recov-
erable reserves, while Journel and Huijbregts (
1978
) pro-
vided the theoretical and practical foundations for the most
common methods used to estimate at different volumes.
Block model resources estimated from exploration or de-
velopment drill holes (long-term models) and mine produc-
tion predictions (short-term models) may show significant
discrepancies. The discrepancies are even larger when com-
pared to actual production figures which may or may not be
reliable. It is desirable to minimize these discrepancies for
evaluation and planning purposes. It has been shown that in-
correct accounting for the volume of prediction (the volume-
variance effect) is a major contributor to the discrepancies
usually encountered.
The resource model contains blocks with dimensions
that should relate to the spacing of the data, hopefully de-
termined based on the quantity of information available to
predict grades. Block sizes may be larger than the selective
mining unit (SMU) of the operation. The smoothing effect
of kriging will generally result in a grade distribution that
does not match the distribution of grade of the SMUs. In
addition, in-pit selection is not perfect. The grade-tonnage
predictions based on blast holes may need to be corrected
for unplanned dilution and other errors of estimation in the
short-term model.
An integrated approach to predicting reserves and mine
performance is required for more accurate predictions. Spe-
cifically, the volume-variance relationship, the selectivity of
the mining operation, planned dilution and ore loss must be
accounted for. Additionally, incorporating an allowance for
unplanned dilution at the time of mining is reasonable.
The traditional estimation techniques provide limited
flexibility to account for these factors. The estimation of re-
coverable resources is based on limited information about
the SMU distribution of grades. There are a number of meth-
ods and techniques that help estimate point distributions,
but relatively little research has been done to develop robust
methods for estimating block distributions. It is a difficult
task, since little is known a-priori about the SMU distribu-
tion. An important option available is the use of conditional
simulation models to resolve the issues related to recover-
able resources.
