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By S. Banisi, A. Ghasemi, E. Nematollahi

Discrete element method (DEM) has been used as a popular simulation method to verify designs by visualising how material will flow through complex equipment geometries. Although DEM simulation is a powerful design tool, finding a DEM model which includes real material properties (e.g., shape, cohesion and friction coefficients) is not computationally feasible. In order to obtain more realistic results, particle energy loss due to rolling friction has been highlighted by many researchers. To implement a reverse torque to account for rolling friction, various models have been proposed. On account of the complexity of the problem, there is no unique model for all applications (i.e. dynamic and pseudo-static regimes). In this paper, an in-house developed DEM software (KMPCDEM ©) was used to assess the robustness of three commonly used models by comparing the repose angle of iron ore pellets obtained through the draw down test in a laboratory setup and then the elastic–plastic spring dashpot model was modified based on considering the individual parameters instead of relative parameters of two contact entities. Results showed that the modified model could produce higher repose angle. The modified model was used to calibrate DEM simulation of repose angle of iron ore pellets in a laboratory setup of the draw down test. Comparison of the calibrated DEM simulation and laboratory results showed 2° differences between the predicted and measured angle of repose. This difference was attributed to considering the particle shape effects by assuming a spherical shape for particles. Keywords: DEM, rolling friction,particle shape, repose angle

Jan 1, 2020

By L. Pretorius, S. Uludağ

This paper explores how to apply system dynamics principles to surface mining problems towards understanding the consequences of mining efficiencies. Some simulation examples related to machine and people performance have been used to demonstrate systems engineering concepts to mining engineers. The simulation tool used is Vensim, which is widely used in industrial engineering applicable to systems thinking, and systems dynamics. The science and mathematics behind the system dynamics as well as benefits and typical challenges are discussed to explore the applicability to mining problems. The benefit of having one less drill is easily quantifiable with the developed model which is one of many other measurable benefits, using the developed model. Some of the benefits of the improved quality of drill holes are not fully quantified as this depends on the mine specific inputs. There are examples of quantifying this in the other industries using system dynamics tools.

Sep 1, 2021

By N. Snyders, I. Mwandawande, S. M. Bradshaw, M. Karimi

"Computational fluid dynamics (CFD) was applied to predict the average gas holdup and the axial gas holdup variation in a 13.5 m high cylindrical column 0.91 m diameter. The column was operating in batch mode. A Eulerian-Eulerian multiphase approach with appropriate interphase momentum exchange terms was applied to simulate the gas-liquid flow inside the column. Turbulence in the continuous phase was modelled using the k-_ realizable turbulence model. The predicted average gas holdup values were in good agreement with experimental data. The axial gas holdup prediction was generally good for the middle and top parts of the column, but was over-predicted for the bottom part of the column. Bubble velocity profiles were observed in which the axial velocity of the air bubbles decreased with height in the column. This may be related to the upward increase in gas holdup in the column. Simulations were also conducted to compare the gas holdup predicted with the universal, the Schiller-Naumann, and the Morsi-Alexander drag models. The gas holdup predictions for the three drag models were not significantly different. IntroductionColumn flotation is an important concentration technology that is used in the mineral processing and coal beneficiation industries. The growing interest in the use of column flotation in mineral processing has been attributed to the simpler flotation circuits and improved metallurgical performance compared to conventional flotation cells (Finch and Dobby, 1990). Flotation columns have also found other applications outside mineral processing, such as de-inking of recycled paper (Finch and Hardie, 1999).In column flotation, a rising swarm of air bubbles generated by means of air spargers is employed to collect the valuable mineral particles and separate them from the gangue minerals in a countercurrent process. Wash water, which is continuously fed at the top of the column, is used to eliminate entrained particles and stabilize the froth. The column volume can be divided into two sections – the collection zone in which the bubbles collect the floatable mineral particles, and the cleaning zone (or froth zone) where product upgrading is enhanced through the removal of unwanted particles entrained in the water mixed with bubbles from the collection zone."

Jan 1, 2019

By J. Hadjigeorgiou, Y. Potvin

In a benchmarking paper published in the SAIMM Journal, Potvin and Hadjigeorgiou (2008) reviewed ground control strategies to manage large deformations in underground hard rock mines. Significant differences were identified in the design and acceptable tolerance between civil and mining engineering practice for squeezing ground conditions. Variations were also noted in ground support strategies between Australian and Canadian mines. In this paper we review progress in design methodology and ground support practice since 2008, including the availability of more effective deformation monitoring, new design tools, greater access to yielding ground support elements, and better installation practices. An improved understanding of technical and practical issues associated with squeezing conditions has led to the development of ground support guidelines for a range of squeezing ground conditions in hard rock mines.

Jul 5, 2023

Orange Free State Branch Minutes of a General Meeting held at the Welkom Mine Canteen on Wednesday, 21st November, 1973, at 4-.00 p.m. Present Mr E. T. Wilson (Chairman) in the Chair, 15 Fellows and Members, 12 Associates, Graduates, and Students, and 11 Visitors (Total 38). Book review Symposium on Environmental Engineering in Coal Mining The 20 papers presented at the symposium cover some 14 subjects related to environmental engineering in coal mines, such as dust, heat, gas emissions, ventilation, noise, and lighting. Competition for students Each year the Institute offers a prize (or prizes should the entries warrant it) of up to Rl00 for the best paper or dissertation on a topic appropriate to the interests of the Institute. A.8. & T.8. Trust The A.S. & T.S. Trust has been formed with the specific object of establishing a worthwhile source of funds which can be used to further the progress of science and technology in South Africa. Nim reports Report No. 1573 A pilot-plant investigation of a flotation model. Report No. 1597 The role of sulphur in the flotation of sulphide minerals. Report No. 1599 The analysis of silicate rocks and metallurgical slags by X -ray-fluorescence spectrometry. Report No. 1607 The analysis of ion-exchange resins by X-ray- fluorescence spectrometry. Report No. 1617 An electronic differential precision thermometer.

Jan 6, 1974

By J. van der Walt, A. Whillier

Reference is made to the approach to mine cooling in which the service water is used as one of the means of distributing refrigeration, and attention is drawn to various engineering disciplines or functions necessary for effective distribution and reticulation of cold water from refrigeration plant. The demand for service water is intermittent, the peak flow-rates being typically two to three times the average flowrate. The refrigeration plant, on the other hand, must preferably be operated steadily throughout the day and night, with the result that a large storage dam for cold water must be incorporated into each system in order to even out the surge in demand for water. These dams should be operated as constant-temperature, variable-volume reservoirs. The conventional cascade system involving dams on each level is not the best for sending water down mines, and schemes are described that avoid the need for such dams. Reference is made to various tests that were carried out, and to several large systems that were installed. Management and organizational problems that could arise as a result of new technological developments in mine cooling are referred to, and cost figures are quoted to indicate the large potential savings, In addition to the improved environmental conditions, that can be achieved through the use of integrated water systems.

Jan 1, 1979

An evaluation was made of the wear and performance characteristics of liter bars, and the cost-life effectiveness of backing materials for rotary-mil liners. In a large run-of-mine mil in which the liter bars were mounted on grid liners of austenitic manganese steel (AMS), the liners had an average life that was five to six times that of equivalent unprotected liners. For a single mil, this is equivalent to annual savings in the cost of materials of up to R320 000, and to a downtime of 100 hours. Of the five materials tested in a large pebble mil grinding quartzitic ore, AMS grids and 'white iron' blocks performed best on a cost-life basis, with possibly improved performance from a real white cast iron. (The 'white iron' was shown by microstructural analysis to contain flake raphite and pearlite, being in reality a grey cast iron.) The high-chromium white iron had by far the longest predicted life, with mild steel a surprising second. Rubber was shown to last well in this type of mil. The wear rates of liners change during their lifetimes. The protective effect of liter bars was clearly illustrated by the reduction of over 40 per cent in the wear rates of the liners when the lifter bars were renewed to a height of 80 mm from a fully worn height of 35 mm.

Jan 1, 1991

By P. J. H. de Graaf, S. D. N. Wessels

"Rio Tinto’s Western Australian expansion, combined with mining within structurally complex geology and increasingly below the water table, presents challenges in effective slope management to ensure safe and economic mining.The Geotechnical Management System (GMS) was developed by Rio Tinto Iron Ore (RTIO) to manage geotechnical risks identified during the design process and implementation, and to ensure feedback based on the ‘as-found’ conditions. The GMS utilizes a risk-based approach to geotechnical risk management and is centred on the geotechnical risk and hazard assessment management system (GRAHAMS). GRAHAMS is used to assess pre- and post-control risk for future potential risks (planned slopes), current risks (as-built slopes), and actual geotechnical hazards (realized risks) identified in the pit. This serves as a core operational risk management tool in identifying and prioritizing key risk sectors and management of critical controls. The system’s database reporting functionality supports effective communication of operational risks to operational personnel, as well as reporting the risk profile across operations to management.A rigorous engagement process between design engineers and sitebased engineers is implemented to ensure that key design assumptions, limitations, risks, and opportunities are understood by the site teams. This information, together with mine plan schedule details, is used to assess the design risk and develop appropriate controls. These controls typically include slope performance monitoring and slope reconciliation. The design feedback loop is closed through sharing of key slope performance and reconciliation data with the design teams.The GMS has been successfully implemented in RTIO pits and is fundamental to successful geotechnical slope management. Improved characterization of design assumptions has allowed for re-assessment of the pit design and improved hazard management in high-risk pits. The GMS, GRAHAMS, and other processes reduce the incidence of unexpected slope instability. Improved understanding of rock mass conditions has allowed for economic optimization through redesign of slopes, allowing for an improved understanding of risk and fewer unexpected conditions (surprises), hence an increased realized value."

Jan 1, 2016

By M. M. Bwalya, F. K. Mulenga

"SynopsisThe application of the attainable region (AR) technique to the analysis of ball milling is currently limited to batch data. This paper introduces the use of the technique to continuous milling.To this end, an industrial open milling circuit processing a platinum ore was surveyed. Samples were collected and later characterized by means of laboratory batch testing. On site, several milling parameters were varied systematically so as to collect data for modelling purposes. These paramters included ball filling, slurry concentration, and feed flow rate. After data analysis, a simulation model of the open milling circuit was developed under MODSIM®, a modular simulator for mineral processing operations. The mill was then simulated and the data generated was analysed within the AR framework.Initial findings reveal an opportunity to gain valuable insight by studying milling using the AR technique. From an exploratory perspective and inasmuch as this study is concerned, feed flow rate, ball size, and ball filling were identified as being pivotal for the optimization of open ballmilling circuits. Mill speed, on the other hand, had only a limited effect on the production of particles in the size range -75 +10 µm.IntroductionGlasser and Hildebrandt (1997) propounded the attainable region (AR) as a technique for the analysis of chemical engineering reactor systems. Results have since been produced and tested on both the laboratory and pilot scales. The method results in a graphical description of chemical reactions by considering the fundamental processes taking place in the system, rather than the equipment. From the plotted graphs, the process and the reactors can be synthesized optimally into a flow sheet.The use of the AR method still has a long way to go as far as mineral processing is concerned. For instance, several articles have reported the application of the AR technique to ball milling: Khumalo et al. (2006, 2007, 2008); Khumalo (2007); Metzger et al. (2009, 2012); Metzger (2011); Katubilwa et al. (2011); Hlabangana et al. (2012). Their main shortcoming has been the exclusive use of laboratory batch grinding data.To address this deficiency, Mulenga and Chimwani (2013) proposed a way by which the technique could be extended to continuous milling. In effect, the batch milling characteristics of a platinum-bearing ore (Chimwani et al., 2013) were used and scaled up to an open milling circuit. Then, with simplifying assumptions, an attempt was made to optimize the residence time of particles inside the mill. Later, Chimwani et al. (2014a) presented some optimization examples involving various milling parameters. The sequence of published articles then paved the way for the study of industrial milling systems with the AR methodology."

Jan 1, 2015

By D. F. Malan, W. J. Theron

Practical mining aspects should be considered when conducting pillar designs for bord-and-pillar layouts. The current methodology for pillar design will result in increasing pillar sizes with depth. This affects the extraction ratio and will result in onerous ventilation requirements when cutting large pillars. A holistic approach, including all mining engineering requirements, is required to ensure that the rock engineering designs are optimized to ensure efficient mining operations and sustainable production. Bord widths should not only be a function of the rock mass ratings, but should also be selected to fit the specifications of the mechanized equipment. The use of a ‘squat pillar’ formula for hard rock is discussed in the paper and the formula based on the exponents of the Hedley and Grant pillar formula, is explored. The effect of abutments and geological losses on average pillar stress is also explored. These factors must be considered when designing layouts at increasing depths.

Nov 27, 2024

1. New books Australian Institute of International Affairs. Uranium - energy source of the future? Canberra, thelnstitute (Box E181, P.O., Canberra, A.C.T. 2600, Australia), 1979. 202 pp. A$4,95 (postage 50c). Euroeconomics. The steel industry in Western Europe.. industrial and financial indicators. Paris, Eurofinance (9 Avenue Hoche, 75008 Paris, France), 1979. 167 pp. FF4,500 (Available in English and French.) M. B. Piggott. Load-bearing composite materials. Oxford, Pergamon Press, 1979. $15,00. J. H. E. Olaf. Automation and remote monitoring and control in mines. Essen (West Germany), Verlag Gliickauf GmbH, 1979. 200 pp. DM36. (In English.) J. P. Jenkins and E. T. Brown (eds). KWIC index of rock mechanics literature. Oxford, Pergamon, 1979. 742 pp. £60. R. J. Wakeman (ed.). Progress in filtration and separation 1. Amsterdam, Elsevier, 1979. 346 pp. Dfl.llO,OO. 2. New journal As from 1980, Coal Calendar is being published as a separate monthly periodical. 3. Proceedings L. E. St Pierre and G. R. Brown (eds). Future sources of organic raw materials. Oxford, Pergamon, 1979. 612 pp. £22,50. P. Haasen, V. Gerold, and G. Kostorz (eds). Strength of metals and alloys. Oxford, Pergamon, 1979. 3 vols., 1800 pp. $200. K. J. Miller and R. F. Smith (eds). Mechanical behaviour of materials. Oxford, Pergamon, 1979. 3 vols., 1800 pp. U.S.$200. 4. Tax relief? The Publishers' Association of Great Britain recently issued a circular to a number of professional bodies drawing their attention to a court decision in favour of tax allowances on the purchase of textbooks. In January Electroheat The International Union for Electroheat, which com. prises a score of highly industrialized countries, every four years organizes a congress at which experts discuss the technicalities and economics of the latest applications of electroheat in industry and other sectors. Corrigenda: March issue The following amendments should be made to Table II of the paper 'Commodity analysis:

Jan 1, 1980

By C. G. Goncalves

The Gautrain rapid rail link project is currently Africa?s largest infrastructure project connecting South Africa?s major airport (OR Tambo), Johannesburg and Pretoria. Phase one is planned for completion in time for the 2010 FIFA Soccer World Cup and involves 80 km of track and 15 km of underground tunnels. The key shaft sinking blasting issues revolve around maximising advance and improving blasting cycles to meet the tight deadlines as well as environmental control which, in some cases takes place only 15m from the city infrastructure. To achieve success, DetNet South Africa supplied a range of electronic detonator systems to cater for the different blasting applications involved (tunnels, portals, shafts and viaduct foundations). One such product, QuickShot, was used for the first time in a major civil engineering project and has been used in most of the shaft sinking blasts to date. The QuickShot system combines pre-programmed electronic detonators with special on-bench components that enable the user to quickly and easily design the firing sequence solely by using the order of connections. This precludes the user from having to deal in absolute delay times. The connecting system enables benches to be hooked-up speedily by multiple users who have differing levels of experience. This paper provides details of how, after 33 months, the system has been embraced by the project by aiding in maximised advances, improved cycle times and meeting the required environmental constraints.

Jan 1, 2009

By C. G. Goncalves

The Gautrain rapid rail link project is currently Africa?s largest infrastructure project connecting South Africa?s major airport (OR Tambo), Johannesburg and Pretoria. Phase one is planned for completion in time for the 2010 FIFA Soccer World Cup and involves 80 km of track and 15 km of underground tunnels. The key shaft sinking blasting issues revolve around maximising advance and improving blasting cycles to meet the tight deadlines as well as environmental control which, in some cases takes place only 15m from the city infrastructure. To achieve success, DetNet South Africa supplied a range of electronic detonator systems to cater for the different blasting applications involved (tunnels, portals, shafts and viaduct foundations). One such product, QuickShot, was used for the first time in a major civil engineering project and has been used in most of the shaft sinking blasts to date. The QuickShot system combines pre-programmed electronic detonators with special on-bench components that enable the user to quickly and easily design the firing sequence solely by using the order of connections. This precludes the user from having to deal in absolute delay times. The connecting system enables benches to be hooked-up speedily by multiple users who have differing levels of experience. This paper provides details of how, after 33 months, the system has been embraced by the project by aiding in maximised advances, improved cycle times and meeting the required environmental constraints.

Jan 1, 2009

By C. J. Tonkin

Compressed air is widely used on South African gold mines. However, due to recent and proposed future electricity tariff increases it is quickly becoming too expensive to produce and use. Boxfront chute systems at ore passes were focused on during this study, and a number of alternative power sources were examined. After comparing primarily costs, and secondarily safety and practicality, of a number of systems based on water and hydraulic oil, a system making use of either air or water was determined to be the most cost effective. A payback time of 8 years was calculated, which will be significantly less taking into account the avoidance of failures due to electricity and water shortages, which would not affect this system due to its ability to swap between either air or water. It was recommended that this system be installed at all boxfront chutes as soon as possible so that the company can begin to benefit from the cost savings.

Jan 1, 2013

By G. Blight

As part of an investigation of possible water-saving measures at Anglo American Platinum's Mogalakwena Mine in Limpopo, South Africa, a study was made of conditions on the wet beaches of two adjacent tailings dams, each serving a separate plant on the mine. For one of the dams, a special catamaran was designed and constructed to enable the full length of wet beaches to be accessed and sampled immediately after a layer of tailings had been deposited. For the other dam, the wet beach was accessed using conveyor belting and scaffold planks. The length of the beaches was 400 m on the first dam, and 200 m on the second, and each was sampled at 50 m intervals. The parameters reported in this paper, for both beaches, are: > Water content profiles along each beach from the surface to as deep as 2.5 m, at times ranging from 12 hours to 6 weeks from the end of deposition > Particle size distributions at the surface, down the full length of the beaches > Measurements of feed relative density, tonnage and volume, decant and drain flow volumes, as well as rainfall and evaporation for both dams. The surface water contents shortly after deposition have been used to establish the relative density of the settled, decanted tailings and its variation down the beach. This data, combined with the decant and drainage flows, is used to establish the calculated and actual water recoveries from both dams.

Jan 1, 2012

By A. M. Bauristhene

Ti-64, which accounts for more than 50% of the worldwide titanium tonnage, has found commercial importance in industries requiring components with high specific strength and resistance to corrosion. Investment casting is the preferred production method due to the difficult machinability of the alloy. This study was aimed at investigating the mechanism and the extent of alpha case formation on Ti-64 components cast using the investment casting method with YFSZ (yttria fully-stabilized zirconia) shell moulds after vacuum induction melting. The extent of the reaction between the mould hot face and the molten metal has been studied by varying parameters such as soaking temperature and mould hot face composition, and examining their effects on the reaction with the mould. An increase in the soaking temperature had an effect on the alpha case, both in appearance and hardness, but had no effect on contamination levels by carbon, oxygen, and nitrogen. The depth of alpha case increased with soaking temperature, increasing from 35 µm to 161 µm with an increase in temperature from 1200°C to 1400°C. The micro-hardness profiles provided insight into the effect of the alpha case on the mechanical properties of the Ti-64 alloy by displaying hardness values of 1000 HV0.1 and above, but could not be solely utilized to determine the alpha case penetration depth due to microstructural differences in the unaffected Ti-64, in particular the martensitic microstructure that formed with a fast cooling rate from a higher temperature. Levels of expected contaminants such as Zr, Y, 0, and C were low. The addition of the colloidal zirconia binder affected the interfacial reactions. YFSZ proved to be a thermodynamically stable refractory material, with the alpha case possibly forming as a result of segregation.

Jan 1, 2013

By J. F. Lupo

One of the earliest records of metal recovery by solution leaching is described by Agricola as 'juice of rock' in the 1550s. In these early years of hydrometallurgy and civil engineering, few controls and systems were employed to enhance recovery and protect the environment. Since that time, leaching (dump or heap) operations have made significant strides in increasing metal and solution recovery while protecting the environment, all goals of a sustainable operation. It is now recognized that the design and operation of modern heap leach facilities requires contributions from many fields of study, including hydrometallurgy, civil engineering, geotechnical engineering, unsaturated-flow hydrology, mine planning, geosynthetics engineering, geochemistry, process engineering, mechanical engineering, and electrical engineering. While advancements in these fields have resulted in more sustainable heap leach operations, challenges in the industry still exist. A number of heap leach operations exhibit poor or lower-than-predicted metal recovery, loss of solution flow and control within the ore heap, loss of ore heap stability under leach, failure of liner and/or solution recovery systems, and overtopping of process water ponds. A number of these issues may be the result of several compounding conditions. For example, poor metal recovery may be due to an inadequate scale-up assumption (scaling laboratory tests to field-size heaps), lack of control of the in-heap geochemical environment, changes in ore mineralogy from the original design, changes in mechanical and hydraulic properties of the ore from the original design, ore handling and pre-treatment, inadequate solution management system, and inadequate solution application. The purpose of this paper is to present and discuss issues that may affect the sustainability of a heap leach operation. Since sustainability encompasses a broad range of topics and issues, the focus of this paper will be on issues affecting metal and solution recovery, solution flow and containment, and stability of the ore heap.

Jan 1, 2012

The development of short- and medium-term mine production schedules in isolation from each other has meant that only a local optimum can be achieved when each scheduling phase is carried out. The globally optimal solution, however, can be achieved when integrating scheduling phases and accounting for the interaction between short-term and medium-term activities simultaneously. This paper addresses the task of integrating short- and medium-term production plans by combining the short-term objective of minimizing deviation from targeted mill feed grade with the medium-term objective of maximizing net present value (NPV) into a single mathematical optimization model. A conceptual sublevel stoping operation comprising 30 stopes is used for trialling segregated and integrated scheduling approaches. Segregated medium- and short-term scheduling using separate models achieved an NPV of $42 654 456. The final scheduling approach involved integrating the two scheduling horizons using the newly-developed globally optimal integrated production scheduling model to achieve an NPV of $42 823 657 with smoother mill feed grade. The larger the stope data set, the larger the difference between the two scheduling approaches is likely to be. At the very least, an integrated approach ensures feasibility across the two scheduling horizons, which cannot always be assumed when using a segregated approach.

Jan 1, 2012

By C. Montoya

This paper shows, through a case study, the impact of multivariate grade modelling upon mine design and mine planning. A deposit explored by drill holes is considered, in which the grades of five elements (copper, silver, molybdenum, arsenic, and antimony) are of interest. Forty alternative models of the deposit are constructed by fitting the joint correlation structure of the grade variables and using conditional cosimulation. In addition, a reference model, obtained by averaging the alternative models, is also considered. The study shows that the resulting mine design (final pit characteristics and production schedules) is sensitive to the grade model under consideration, and that the design based on the reference model may not be optimal when compared to the alternative models based on cosimulation. However, when assuming a given long-term plan and extraction sequence, the grades and net present value (NPV) calculated on the reference model are unbiased with respect to those calculated on the alternative models with the same extraction sequence. The latter allow assessing the possible dispersion of the actual grades and NPV around their expected values, and are useful for the planner in order to determine the probability of meeting given production targets and of exceeding or falling short of given threshold grades. Additionally, unlike cosimulation, the separate simulation of each grade variable leads to unrealistic resource models and to biased results in mine design and mine planning. This approach should therefore be avoided, unless the grade variables are spatially uncorrelated.

Jan 1, 2012

By M. Cuba

Geostatistical modelling aims at providing unbiased estimates of the grades of elements of economic interest in mining operations, and assessing the associated uncertainty in these resources and reserves. Conventional practice consists of using the data as error-free values and performing the typical steps of data analysis - domaining, semivariogram analysis, and estimation/simulation. However, in many mature deposits, information comes from different drilling campaigns that were sometimes completed decades ago, when little or no quality assurance and quality control (QA/AC) procedures were available. Although this legacy data may have significant sampling errors, it provides valuable information and should be combined with more recent data that has been subject to strict QA/QC procedures. In this paper we show that ignoring the errors associated with sample data considerably underestimates the uncertainty (and consequently the economic risk) associated with a mining project. We also provide a methodology to combine data with different sampling errors, thus preserving the relevant global and local statistics. The method consists of constructing consistent simulated sets of values at the sample locations, in order to reproduce the error of each drilling campaign and the spatial correlation of the grades. It is based on a Gibbs sampler, where at every sample location, the actual sample value (with error) is removed and a conditional distribution is calculated from simulated values at nearby sample locations. A value is drawn from that distribution and kept only if it satisfies some statistical requirements-specifically, the global relative error and local means and variances must be reproduced. All sample locations are visited and simulated sample values are generated iteratively, until the required statistics are satisfactorily attained over all sample locations. This generates one realization of possible sample values, respecting the fact that the actual samples are known to carry an error given by the global relative error. Multiple realizations of simulated sample values can be obtained by repeating the procedure. At the end of this procedure, at every sample location a set of simulated sample values is available that accounts for the imprecision of the information. Furthermore, within each realization, the simulated sample values are consistent with each other, reproducing the spatial continuity and local statistics. These simulated sets of sample values can then be used as input to conventional simulation on a full grid to assess the uncertainty in the final resources over large volumes. The methodology is presented and demonstrated using a synthetic data-set for clarity.

Jan 1, 2012