Geoscience Reference
In-Depth Information
1.3.11
Grade Control
tion and the grade that can be achieved. Inverse distance and
nearest-neighbor methods became popular in the early days of
computer-aided mapping. The computer was used to mimic
what was done by hand calculations, but hopefully faster. The
implementation aspects of these techniques evolved as more
sophisticated computer tools became available.
Mineral resource modeling evolved further with ad-
vances in drilling and assaying techniques, and with greater
awareness of the possible pitfalls related to sample prepara-
tion and analysis. Methods used for geologic interpretation
and modeling also evolved, mostly through the section-by-
section interpretation and into three-dimensional modeling
(wireframes and solids modeling for visualization). The oc-
casional use of three-dimensional hand-made models was
made common with the availability of computers.
Grade estimation techniques have evolved through the
years, beginning with early geostatistics (Sichel
1952
; Krige
1951
; Matheron
1962
,
1963
) that attempt to predict single
values into blocks. Advanced versions of these techniques
are pervading industry practice and are the most commonly
used methods.
The estimation of probability functions developed next,
although using the same basic linear regression tools. As-
sumptions about statistical properties and variable transfor-
mations led to the development of probabilistic estimation of
a distribution of possible values for any given block.
In more recent years the use of simulation for modeling
uncertainty has become important. Geological processes
have important patterns and structure, but also have uncer-
tainty due to the chaotic nature of the processes. Characteriz-
ing the natural heterogeneity and the uncertainty that results
from incomplete sampling is an important goal of mineral
resource estimation.
Grade control is an important task performed at the mine on
a daily basis. It is a basic, economic decision that selects the
destination of each parcel of material mined. Mistakes at this
stage are costly, irreversible, and can be measured in terms of
cash flow losses and increased operational costs.
Grade control models are based on a large number of
samples. In underground mines, production data is usually a
series of tightly drilled holes, channel samples, or short holes
to test production stopes. In an open pit environment, blast
holes samples are obtained on closely spaced grids, accord-
ing to blasting requirements. Less frequently, grade control
drilling is performed separate from blast hole drilling, for
example using dedicated reverse circulation (RC) drilling. In
some geologic settings, surface tranches and channel sam-
ples are used as well.
Production samples are used to select ore from waste, and
are affected by several sampling issues. Often, blast hole
samples are not as reliable as samples obtained from explo-
ration or RC drill holes. This is explained by a combination
of drilling and field sampling methods. Sometimes, the large
quantity of samples available will tend to minimize the im-
pact of the error of a single blast hole sample.
Geologic variables are mapped in the pit or stopes, but
are not always used in production control. Procedures for
extracting some benefit from the local geology mapped
should be implemented. The goal is to find practical ways
of mapping and quickly processing geological information.
The typical turnaround time for a grade control model in an
open pit is 24-48 h.
Conventional grade control methods include defining
grade outlines and using inverse distance, polygonal estima-
tion, or more commonly kriging of blast hole grades. These
methods do not account for the uncertainty in prediction.
Alternatively, simulation of multiple realizations provides
the basis for different optimization algorithms, such as the
minimum-loss/maximum profit method.
In general, improvements from the simulation-based
methods are evident in more erratic grade distributions and
in more marginal mixed ore-type zones. More complicated
grade control scenarios, such as those including multiple
processing options and stockpiling, will also lend themselves
to optimization through simulation based methods.
References
Alabert FG (1987) Stochastic imaging of spatial distributions using
hard and soft information. MSc Thesis, Stanford University, p 197
David M (1977) Geostatistical ore reserve estimation. Elsevier,
Amsterdam
Deutsch CV, Journel AG (1997) GSLIB: geostatistical software library
and user's guide, 2nd edn. Oxford University Press, New York,
p 369
François-Bongarçon D, Gy P (2001) The most common error in
applying 'Gy's Formula' in the theory of mineral sampling, and
the history of the liberation factor. In: Edwards AC (ed) Mineral
resource and ore reserve estimation—the AusIMM guide to good
practice. The Australasian Institute of Mining and Metallurgy, Mel-
bourne, p 67-72
Goovaerts P (1997) Geostatistics for natural resources evaluation.
Oxford University Press, New York, p 483
Gy P (1982) Sampling of particulate materials, theory and practice,
2nd edn. Elsevier, Amsterdam
Isaaks EH (1990) The application of Monte Carlo methods to the anal-
ysis of spatially correlated data. PhD Thesis, Stanford University,
p 213
1.4
Historical Perspective
Hand-calculated sectional estimates continue to have a place
in resource and reserve estimation. They have the advantages
of directly accounting for expert geological interpretation and
providing a first order approximation; however, they also tend
to be optimistic with respect to continuity of the mineraliza-
