Search Documents

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 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

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 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

Types of structure found in 'Jest Australian beach sands are described. Their recognition by geostatistical methods follows nth a discussion of the effectiveness of sampling patterns. Examples of structures are given, and an account of their effect on valuation procedures.

Jan 1, 1977

By Mehmet Guney

[The Atlantis-II-Deep is a hydrothermal mineralization located along the median valley of the Red Sea at a water depth of about 2200 m. Extensive exploration of the metal-rich brine deep revealed a potentially mineable deposit on economic interest consisting of oxides, silicates and sulphides with considerable concentrations of zinc, copper, cadmium and silver. Geostatistics was applied to assess the most likely in-situ vague of the metal potential for economical exploitation. Semi-variograms were constructed to characterize the structure of the regionalized distribution of the geological parameters. Volume grades and thicknesses were determined by the kriging technique, avoiding systematically biased high or low grades, and then block .tonnages were computed. The estimation variances, distribution of errors and histograms of observed and kriged values in each grid Mock were also produced.]

Jan 1, 1983

A case study for the application of a novel geostatistical technique for resource estimation of a narrow steeply dipping, gold-silver mineralized quartz vein deposit is presented. The technique is novel in two respects. First, mineral grades are kriged directly rather via the accumulation method more often applied to vein deposits and, second, a modified 2D ordinary kriging algorithm is used that allows the calculation of a single grade and variance for irregular shaped blocks of varying sizes. The objective of this investigation was to evaluate the suitability of this novel geostatistical technique for resource estimation of the Poura mine deposit and, if appropriate, to lay a firm foundation for future geostatistical work at the mine. The reserve estimation concentrated on the remnant ore blocks and pillars in both underground and surface workings. The data, which was collected in 2D coordinates with grade and vein thickness values, was first analyzed statistically and used to compute experimental semi-variograms. Appropriate semi- variogram models were fitted and various aspects of the estimation technique were evaluated using cross-validation error analysis, with acceptable results. A block kriging computer program called Krige2D was developed to implement the modified 2D kriging algorithm and calculations. Production data were not available to evaluate the computed block resources, but they were compared with a previous resource data determined using an arithmetic approach. The geostatistical technique estimated slightly higher grades but lower overall tonnages as compared to the earlier arithmetic estimates.

Feb 1, 2004

By P. K. Frempong, S. D. Butt

"A case study for the application of a novel geostatistical technique for resource estimation of a narrow steeply dipping, gold-silver mineralized quartz vein deposit is presented. The technique is novel in two respects. First, mineral grades are kriged directly rather via the accumulation method more often applied to vein deposits and, second, a modified 2D ordinary kriging algorithm is used that allows the calculation of a single grade and variance for irregular shaped blocks of varying sizes. The objective of this investigation was to evaluate the suitability of this novel geostatistical technique for resource estimation of the Poura mine deposit and, if appropriate, to lay a firm foundation for future geostatistical work at the mine.The reserve estimation concentrated on the remnant ore blocks and pillars in both underground and surface workings. The data, which was collected in 2D coordinates with grade and vein thickness values, was first analyzed statistically and used to compute experimental semi-variograms. Appropriate semivariogram models were fitted and various aspects of the estimation technique were evaluated using cross-validation error analysis, with acceptable results. A block kriging computer program called Krige2D was developed to implement the modified 2D kriging algorithm and calculations. Production data were not available to evaluate the computed block resources, but they were compared with a previous resource data determined using an arithmetic approach. The geostatistical technique estimated slightly higher grades but lower overall tonnages as compared to the earlier arithmetic estimates."

Jan 1, 2004

By J. -M. Chautru

A geostatistical simulation of a typical mining site for polymetallic nodules in the North Pacific Ocean is presented. This is the first stage in the design of an industrial mining system. Two variables which have a major effect on the orebody's economic potential are considered, namely: the maximum slope of the ground inside a mining block of 50 x 100 m; and the average quantity of nodules on the same support. Two geostatistical problems have emerged in this study. The first is due to the lack of a change of support model for the maximum of a variable. A provisional solution, considering an experimentally accessible 'equivalent' support, is proposed. The second is due to a non-linear link between the two variables. To be able to take this into account in the simulation, we propose a new method based on the decomposition: X = E(X/Y) + Residue (X). Satisfactory results were obtained with this approach.

Jan 1, 1987

By J. A. McLennan

Nickel laterite deposits are typically formed from tropically weathered mafic-ultramafic complexes. The resulting nickel concentration is found within soil horizons and is mineable with regular dozer units. At the time of mining, digging elevations are needed at selective mining units (SMUs). Moreover, for mine planning, the costs due to dilution and lost ore require mining elevations to be specified. A conditional simulation approach is used to calculate ?optimum? SMU mining elevations. Multiple realizations of the ore base surface are simulated. For a single bottom surface realization, dilution and lost ore costs are calculated over the entire vertical extent of each SMU. The optimum mining elevation is the elevation where the lowest summed cost of ?accepting dilution? and ?wasting ore? occurs. The reported SMU dilution is the cost of mining the volume of waste located below the bottom surface and above the optimum mining elevation and the reported SMU lost ore is the cost of not mining the volume of ore above the bottom surface and below the optimum mining elevation. For all ore bottom surface realizations, optimum SMU mining elevations and their associated dilution and lost ore costs are calculated and compiled to represent production uncertainty.

Apr 1, 2005

By J. A. McLennan, J. M. Ortiz

Nickel laterite deposits are typically formed from tropically weathered mafic-to-ultramafic complexes. The resulting nickel concentration is found within soil horizons and is mineable with regular dozer units. At the time of mining, digging elevations are needed at selective mining units (SMUs) or representative dozer regions (RDRs). Moreover, for mine planning, the costs due to dilution and lost ore require mining elevations to be specified. A conditional simulation approach is used to calculate “optimum” RDR mining elevations. Multiple realizations of the ore base surface are simulated. For a single bottom surface realization, dilution and lost ore costs are calculated over the entire vertical extent of each RDR. The optimum mining elevation is the elevation where the lowest summed cost of “accepting dilution” and “wasting ore” occurs. The reported RDR dilution is the cost of mining the volume of waste located below the bottom surface and above the optimum mining elevation. The reported RDR lost ore is the cost of not mining the volume of ore above the bottom surface and below the optimum mining elevation. For all ore bottom surface realizations, optimum RDR mining elevations and their associated dilution and lost ore costs are calculated and compiled to represent production uncertainty.

Jan 1, 2006