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By D. E. Ranta, M. G. Hester

The ore reserve modelling of stratiform uranium deposits to be mined by selective underground mining methods must be done with consideration of the erratic nature of the ore-forming processes that produced the mineralization. Estimation methods that model the uranium grade as a smooth transition between high-grade and low-grade drill hole intercepts tend to greatly overestimate the ore tonnage. Care must be taken to first establish realtistic ore pod geometries and then estimate the grade of the reserve units within the pods.

Jan 1, 1992

By M. G. Hester

The ore reserve modeling of stratiform uranium deposits to be mined by selective underground mining methods must be done with consideration of the erratic nature of the ore forming processes that produced the mineralization. Estimation methods that model the uranium grade as a smooth transition between high grade and low grade drillhole intercepts tend to greatly overestimate the ore tonnage. Care must be taken to first establish realistic ore pod geometries and then estimate the grade of the reserve units within the pods.

Jan 1, 1985

By G. H. Blackwell, A. J. Sinclair

"The main components of a ""PC” -based mineral inventory system are described in a sequence common to many real reserve/ resource estimation projects and in the practical context of problems and decision-making typically encountered in such studies. Some components are designed particuarly to improve the geostatistical instructional capability of the package. An important part of this approach involves the use of widely available software for data manipulation and evaluation in the design of a mineral inventory study progressing to mine design and feasibility. A variety of more or- less fixed routines written in high level languages provide acceptable computational speeds on a personal computer. These critical segments are linked by simple, short, compiled Basic programs easily adjustable to various data configurations and needs. IntroductionGeostatistical mineral inventory estimation has progressed greatly since its slow dissemination during the 1960s. The mining industry generally has accepted the benefits of the technique, notably the quantification of grade and geology, an indication of error in grade estimation, and of the mined volume / grade variance relationship (Clark, 1979, Isaacs and Srivastava, 1989).Acceptance has been slowed, first by complexities of geostatistical theory and second by a bewildering variety of computer systems and applications programs. Continuing improvements in education will facilitate a better understanding of the underlying theory.The purpose of this paper is to describe, in a practical context, the development of a geostatistical-based approach to reserve/resource estimation. The approach integrates various existing commercial software packages with a wide selection of programs developed by the authors for personal computers which estimate mineral inventories and educate users in the techniques applied; that is, the QMIN system.It is hoped that the approach presented here will convince mining and geological engineers concerned with resource estimation, of the soundness of geostatistical methods and its broad potential to their problems."

Jan 1, 1992

By Oy Leuangthong

The McMurray formation in the Athabasca oil sands deposits of Northern Alberta is part of the world?s second largest proven crude oil reserves. The formation is characterized by stratigraphic layers that correspond to three different depositional environments: Marine, Estuarine and Fluvial facies. Resource estimation for oil sands has traditionally relied on polygonal and inverse distance schemes. These techniques are simple and straightforward in practice, but they do not permit reliable uncertainty assessment. This paper describes the modeling of the McMurray formation using modern geostatistical techniques. Geostatistical modeling should be performed within homogeneous geological facies. The methodology for geostatistical simulation within each of the identified facies involves: (1) assessing the most appropriate stratigraphic transformation for optimisation of the correlation structure, (2) determining representative distributions with declustering and debiasing techniques, (3) modeling spatial continuity of the bitumen grade, fines grade, water saturation and other petrophysical variables, (4) performing estimation and cross validation as checks against simulation results, (5) performing simulation for uncertainty quantification of bitumen and fines grade, and (6) model checking of simulation results against the input data and comparisons against the kriged models. These steps are described in detail. The application of these models for uncertainty quantification in support of resource classification is also discussed.

May 1, 2004

By O. Babak, J. G. Manchuk

ABSTRACT A significant factor in evaluating bitumen recovery from an oil sands mine is the particle size distribution (PSD). Increased understanding of mined ore quality and improvement in predictions of recovery can be achieved through PSD modeling. This paper addresses PSD modeling using geostatistics. PSDs may be described using many discrete particle sizes, making this a challenge. The approach parameterizes PSDs with a few statistics. A lookup table is used to reconstruct the PSDs based on models of the statistics. The workflow is applied to Total E&P Canada’s Joslyn Lease and yields good results that reproduce input statistics without introducing artifacts.

Jan 1, 2013

By John S. F. Dunlop

One of the more difficult problems frequently facing geologists and mining engineers is that of estimating the ore reserves of mineral deposits. Cost conscious mining operations invariably require an accurate knowledge of tonnage and grade for both short and long term planning. A case study is presented, showing how a classical frequency distribution was fitted to a population of drillhole assays. Using these results, a grade- tonnage curve is derived using the Lasky expressions, and the results discussed. A geostatistical analysis is then presented. First, variograms are drawn, models fitted to them and analyses made of drift and anisotropy. Second, simple block kriging is carried out and the results plotted on large 1000 scale plans, suitable for overlay with routine .mine plans. Kriging results are verified using two independent techniques: random kriging on a regular grid and inverse distance weighting. Finally an attempt is made to optimize the drilling grid, and to fully tabulate the total computer running costs for the work described.

Jan 1, 1979

By Isobel Clark

The increasing complexity of modern mining technology makes it ever more difficult to decide on the 'best* way to solve problems in mine planning. Yet with escalating costs it becomes increasingly more important for the mining engineer to be able to evaluate quantitatively the implications of the 'what happens if' postulation on the efficiency and economics of exploitation. The use of a model of the orebody can yield an estimate, not just of overall expected results, but also of the sensitivity of these results to possible variations in the orebody. Estimation techniques, such as Kriging, will produce the expected value for the grade of ore at any given point, or over any given volume within a deposit. However, the actual grades mined during production will - of necessity - differ from the predicted values. These possible variations, and the sensitivity of the management decisions to them, can be investigated in detail by the use of simulation. An orebody can be simulated which follows the known characteristics of the deposit at any given stage in development. These properties might be the histogram of grade values, the semivariogram from the samples, the actual borehole assays, geological constraints and/or interpretation, topography, lease boundaries etc. This would be one possible 'realisation' of the deposit as dictated by the currently known data. If several of these simulations are carried out, each conditioned to the current knowledge of the orebody, then it is possible to gain an idea of the range of possible outcomes of any mining procedure or decision taken - all of which are equally likely. Not only can the best decision then be taken, but its sensitivity to the inherent variation within the orebody, and to the ever present estimation errors may be thoroughly studied.

Jan 1, 1977

By W Patton, I Minniakhmetov, H Talebi, U Mueller

The sustainability of mining projects is linked to informed investment decisions based on public reporting of exploration and mineral resource estimation results. In Australia, public reporting guidelines are established by the Joint Ore Reserves Committee reporting code through the JORC Code (2012). Although the assessment of uncertainty in the results reported is a requirement, this is often communicated qualitatively and evaluated subjectively. This can become a liability particularly in the early stages of mining projects when spatial domains of geological interpretation and mineralisation envelopes inform resource estimations’ reliability. A recent review of JORC reports found no reports used quantitative assessments of the geological interpretation or mineral resource estimation envelopes, and 27 per cent of reports did not address the question of quality of geological interpretation. Reports that did address the quality used 19 different terms to communicate quality. This work presents methodologies for quantitative uncertainty assessment and communication and explores how they could be applied in public reporting practice. Quantitative uncertainty reporting would benefit mine planning and financial modelling as they normally assume the geology is 100 per cent right (since no error is reported or only a single deterministic model is provided). The complexity, cost, and additional work of doing a quantitative assessment could hinder a straightforward implementation. This could be overcome if mining companies budget for quantitative uncertainty assessment and associated professional development. A compulsory requirement for the inclusion of uncertainty assessments in public reporting or adopting standardised subjective language would improve industry practice.

Mar 22, 2022

By C V. Deutsch

"Geometallurgical variables often cause problems to conventional geostatistical workflows. There are many variables; some are compositional and some are non-additive. They often show: complex multivariate relationships undersampling relative to conventional grade variables unequal sampling; that is, all variables are not available at all data locations.A variety of approaches have been developed over the years, but geostatisticians remain mostly focused on modelling rock types and a few grade variables with an abundance of data. The problems are reviewed and a chained workflow is presented where appropriate techniques are employed in sequence to permit reliable spatial prediction of geometallurgical variables. The spatial models may be used to assess the value of additional data, for prediction of process performance, for improved mine planning and other optimisation tasks. The chained workflow will include data transformations such as ratios and normal scores that make the variables amenable to geostatistical modelling. Data imputation techniques to account for missing values are considered with special consideration to spatial correlation with the available data. Decorrelation techniques such as the principal components, min/max autocorrelation factors and projection pursuit multivariate transformation are employed to manage massively multivariate modelling. Full distribution modelling must be considered to avoid biases in the prediction of non-additive variables. The post-processing of geometallurgical models must be streamlined for robustness and efficiency. The precise workflow varies according to the specific purpose of the study. Guidelines and thoughts on best practice are presented.CITATION:Deutsch, C V, 2013. Geostatistical modelling of geometallurgical variables - problems and solutions, in Proceedings The Second AusIMM International Geometallurgy Conference (GeoMet) 2013, pp 7-16 (The Australasian Institute of Mining and Metallurgy: Melbourne)."

Sep 29, 2013

By Kalyan Saikia

An integrated statistical-geostatistical modelling of gold exploration data of Gurahar Pahar prospect of Mahakoshal greenstone belt in Central India has been attempted. Statistical modelling of gold accumulation and width reveal a positively skewed 2-parameter lognormal distribution fit with an estimate of mean gold as 0.84 gram/tonne. Geostatistical modelling provided a spherical semi-variogram function fit with mean kriged estimate and mean kriging variance of gold as 0.76 gram/tonne and 0.23 (gram/tonne)2 -respectively. Ore inventory and grade-tonnage relationships for a selected part provided an estimate of 3,36,000 tomes of ore with an average gold of 0.76 gram/tonne at 0.5 gram/tonne cutoff grade.

Jan 1, 2002

By P Landeros, D Benado, J Cornejo, A Pinochet, C Caviedes

In 2005, El Teniente mine began preconditioning the primary rock mass by hydraulic fracturing (HF). The major perceived benefits of this process are a decrease in the magnitude of the expected maximum seismic event and improved cave propagation. In addition, HF has resulted in new information on the propagation pressures of each fracture. Previous studies have attempted to relate propagation pressure to minor principal stress or confining stress.Considering the spatial continuity of propagation pressure and the significant quantity of collected data since the incorporation of the HF technique, minimum requirements for geostatistical modelling have been reached, permitting robust estimates inside the representative volume with acceptable errors (Cornejo, Muñoz and Rojas, 2012; Cornejo and Landeros, 2013). These results are then used to identify zones with higher magnitudes, which are mostly related to more complex geotechnical zones (intrusive and major faults) and caving singularities, making it possible to estimate the spatial extension of these zones.Finally, these results are integrated with other geomechanics aspects to support risk analysis of the mining plan.CITATION:Cornejo, J, Landeros, P, Benado, D, Caviedes, C and Pinochet, A, 2016. Geostatistical modelling of hydraulic fracturing pressures at El Teniente Mine, in Proceedings Seventh International Conference and Exhibition on Mass Mining (MassMin 2016), pp 183–190 (The Australasian Institute of Mining and Metallurgy: Melbourne).

May 9, 2016

By O. Leuangthong, E. Schnetzler

"The McMurray formation in the Athabasca oil sands deposits of northern Alberta is part of the world’s second largest proven crude oil reserves. The formation is characterized by stratigraphic layers that correspond to three different depositional environments: Marine, Estuarine, and Fluvial facies. Resource estimation for oil sands has traditionally relied on polygonal and inverse distance schemes. These techniques are simple and straightforward in practice, but they do not permit reliable uncertainty assessment. This paper describes the modelling of the McMurray formation using modern geostatistical techniques.Geostatistical modelling should be performed within homogeneous geological facies. The methodology for geostatistical simulation within each of the identified facies involves: 1) assessing the most appropriate stratigraphic transformation for optimization of the correlation structure; 2) determining representative distributions with declustering and debiasing techniques; 3) modelling spatial continuity of the bitumen grade, fines grade, water saturation, and other petrophysical variables; 4) performing estimation and cross validation as checks against simulation results; 5) performing simulation for uncertainty quantification of bitumen and fines grade; and 6) model checking of simulation results against the input data, and comparisons against the kriged models. These steps are described in detail. The application of these models for uncertainty quantification in support of resource classification is also discussed."

Jan 1, 2006

Plurigaussian simulation allows constructing lithofacies or rock type models that reproduce the contacts between facies in accordance with the geologist?s interpretation. Its implementation requires inferring the local facies proportions, but the uncertainty in the true proportions is not accounted for. The simpler model with constant facies proportions may not yield realistic results, due to the possibility of obtaining facies at locations where it is geologically unlikely to find them. This article presents a variation of the plurigaussian model, in which the facies proportions are represented by random fields. The realizations can be made conditional to soft geological informati onto account for local changes in the facies proportions. The model is illustrated via a case study of a porphyry copper deposit where four Gaussian random fields are simulated conditionally to drill hole data and to constraints on the probability of finding a given facies at specific locations (control points) in the deposit. Then the first two fields are truncated using the random thresholds defined by the last two, generating a three-facies model. The proposed random proportion model proves to be simple to use and to account for spatial variations of the geological characteristics and for the uncertainty in the facies proportions. Keywords: categorical variable; lithofacies; truncated plurigaussian simulation; regionalized proportions

Jan 1, 2008

By Raymond G. F

Geostatistics - a tool used by geologists and mine planning engineers to estimate grades and rapidly evaluate alternative mining strategies has reached an advanced stage of development for the silver-lead-zinc orebodies at Isa and Hilton Mines. Geostatistics has been used for over a decade in the massive copper orebodies but the stratiform lead-zinc orebodies are much more complex and provided a completely different set of challenges. Recent increases in computer processing speed and power provided by the Integrated Mine Planning System (IMPS) has aided the development of the geostatistics package. Also the formation of a project team and the subsequent in-house development which has drawn together the expertise of geologists, engineers and system analysts has contributed significantly to the success of the project.The most important feature of any approach to modelling the lead-zinc orebodies is that the kriging search must consider estimate and sample points according to their positions relative to bedding surfaces. By transforming co-ordinates as perpendicular offsets from a plane representing the local strike and dip, it is possible to elongate the ellipsoidal influence to parallel bedding. By interactively modelling surfaces using CAD facilities and then specifying these surfaces as 'hard' or 'soft' boundaries, the geologist has complete control over the kriging process.

Jan 1, 1993

For practical reasons all basic input data for the gold mines of the Anglovaal Group conform to a regular grid of averages of sample values within 25-ft squares in the plane of the ore body; individual sample values with their metric co-ordinates are input and converted by a computer program to the basic 25-ft square averages. At the Prieska copper mine the bore- hole data are forced on to a regular grid of 15-m squares corresponding to the coordinates of the grid points nearest to the actual borehole intersections. As for the gold mines the Prieska ore body, although some 3 to 30 m thick, is also dealt with on a two-dimensional basis (Krige, 1973). On the gold mines the data subjected to geostatistical analysis cover: gold values (in cm g/t), uranium values (cm kg/t), and channel widths (cm). The gold and uranium values are normalised on the basis of log (value plus constant) and all the geostatistical analyses are performed on these transformed values. The channel widths usually conform reasonably well to the normal distribution and are, therefore, not transformed. At Prieska the metal grades analysed cover the two main products, copper and zinc, as well as the impurities lead and bismuth; in addition the specific gravity values and the hanging- and foot-wall deviations from a projection plane are also handled. These were all previously used on an untransformed basis but because of problems associated with the proportional effect the lognormal-de Wijsian model is now used for some of the grade variables. The key computer pro- grams can be summarised briefly as follows:

Jan 1, 1981

By Roger A. Blais, Michel David

"Matheron's geoslalislical method for the estimation of ore reserves has been developed to the point at which real-life problem may be handled effectively. The steps involved in the method are:(i) obtalning the variogram,(ii) fitting a model, and(iii) producing block estimates.All three steps may cause difficulty, and would-be users need a deep understanding of the theory if failure is to be avoided.To illustrate these points, specific cause are considered:(i) two almost equidimensional porpbyry deposits, one drilled randomly and the other regularly; and(ii) two iron formation, one drilled extensively and being mined, while the other is still at the stage of early estimation."

Jan 1, 2014

By Marc Lavigne

"The Lac Knife graphite deposit was estimated, as part of a feasibility study, using a geostatistical ore reserve estimation method: ordinary kriging. Based on the geology and its interpretation, the results of a variogram study, and the statistical parameters of the grade distribution of the core samples and the composites through the mineralization, the deposit was divided into three separate zones (west, centre and east), and each of these zones was then analyzed and kriged independently.The geological ore reserve estimation results of ordinary kriging are compared to the results of a conventional method (sections) used previously. The two methods gave almost similar reserve figures. The conventional method provided a +2% estimation for tonnage and + 10% for grade because it ignored the spatial relation between sections and samples, and ordinary kriging gave a more accurate longitudinal definition of the deposit.Finally, the paper concludes with the advantages of proceeding with ordinary kriging, namely: higher flexibility (change of cut-off grade), better deposit resolution and enhanced selectivity for the design of the open pit.IntroductionWithin the context of a complete feasibility study for the Société d' Exploration Minière Mazarin Inc., specialists of the Mines and Geology Division of Roche Ltd., Consulting Group, defined a modelling method appropriate to the graphite deposit of the Lac Knife property near Fennont. Many patterns were considered. Based on the geology of this deposit, the planned mining method, the statistical parameters of grade distribution and the variogram study, the process of reserve estimation retained was to use the ordinary kriging in a selective way. It was required because the geometry of the deposit is such that it was unthinkable to apply ordinary kriging without restrictions.This paper gives a detailed explanation of the observations and interrogations which led to the choice of this ore reserve estimation method, and the calculation procedure itself."

Jan 1, 1991

By Leahey T. A

The variability of gold mineralization in the Warrego Gold Pod is described by classical statistical techniques using sample distrib- utions and analysis of variance; and by the use of geostatistical variogram analysis to define the spatial variability and anisotropy of the mineralization. Comparison is made between declared mine production from the Nineteen Stope and a series of ore reserve estimates derived by manual, numerical and disjunctive kriging methods.

Jan 1, 1979

By Indranil Roy

Gua supergene enriched iron ore deposit from Jharkhand, India has been geostatistically modeled. Population modeling shows a negatively skewed 3-parameter log-normal fit for Fe and positively skewed 3-parameter log-normal fit for Al2O3 and SO2. Semi-variographic studies for Fe indicate spherical function fit using point kriging cross-validation technique with Co=4.06(%)2, C5.11 (%)2, Co+C=9.1 7(%)2 and 'a'=348m. Kriging with 50mx50mx 10m block size at 740mRL led to a global mean kriged estimate of 61.98% and kriging variance of 4.04(%)2 for Fe with central 90% geostatistical confidence limits at 61.39% and 62.24% for that level. This led to an ore inventory at 740mRL as 7.29 million tonnes of ore.

Jan 1, 2002

By Sarkar B. C, Sen A. K

India is well endowed with vast reserves of banded hematite ore, about 12 billion tonnes, estimated by some conventional methods. Various authors have assessed this huge reserve using some advanced geostatistical methods. A Banded Iron Formation (BIF) belt named the `Singhbhum-Keonjhar-Bonai' belt in India has been chosen as a case study. In this paper, the experiences of Chiria iron ore, in particular, have been described. This study will finally create a dynamic mineral inventory after standardising the geostatistical parameters which will help to cater for the needs of the stringent quality requirements of the Indian steel industries.

Jan 1, 1995