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Mixed integer programming (MIP) has been used for optimizing production schedules of mines since the 1960s and is recognized a shaving significant potential for optimizing production scheduling problems for both surface and underground mining. The major problem in long-term production scheduling for underground orebodies generally relate to the large number of variables needed to formulate a MIP model, which makes it too complex to solve. As the number of variables in the model increase, solution times are known to increase at an exponential rate. In many instances the more extensive use of MIP models has been limited due to excessive solution times.

Jan 1, 2010

By J. A. Maree

After the South Deep complex was purchased by Goldfields in 2006a re-feasibility study was done and the life of mine (LOM) was extended to 52 years. This also implied that the mine?s infrastructure would have to be enhanced. One of the changes was the proposal of five new main orepass systems to be excavated before the mine reaches full production in 2013. Excavations started to show signs of scaling, and in some cases, whole new excavations were lost. This particular area was exposed to very high stresses and the geology was prone to body delimination rendering the relevant areas unstable. This paper investigates the conditions at the location of one of the proposed orepass systems, and the best possible orientation was suggested to ensure that the orepass system would be stable and have a practical life. It was, however, found that the fourth leg of the orepass system would require further support to be classified as stable by the chief rock engineer and the section geologist of South Deep. Several support methods and orepass system linings would then be analysed and evaluated to give calculated recommendations on how to productively and practically support an orepass system. Keywords Main orepass system, stresses, body delamination, impact and abrasion, rock support, concrete lining.

Jan 1, 2011

By L. M. Tavares, T. M. Campos, P. M. Faria, R. M. Carvalho

Recent advances in mechanistic ball mill modelling are expected to allow for more accurate predictions that overcome the well-known limitations of phenomenological approaches, including their inability to predict the effect of liner geometry and their wear, in grinding. Although able to describe continuous operation, the UFRJ model of ball mills has only been validated in the past in mills that operate in batch mode, either in laboratory or pilot scale. The present work demonstrates the application of the mechanistic UFRJ ball mill model to predict fine grinding of iron ore in a pelletising plant in Brazil, the first application of such a mechanistic modelling in continuous mode. It shows that the model provides accurate descriptions of flows after iterations in a closed-circuit with hydrocyclones. Keywords: Ball mill, iron ore, grinding, modelling, particle breakage

Jan 1, 2020

By K. Lomberg

In this paper the process of sampling and assaying as it relates in particular to the platinum group elements (PGEs) is presented. A discussion of the geology of PGE deposits is included to provide an understanding of the mineralization that is considered necessary prior to sampling, as this has a direct bearing on the mineral resource estimate and also the selection of an appropriate mining cut. The discussion includes the selection of the sampling technique (drilling or face sampling), the size of the sample relating to the requirements of the laboratory, the potential mining cut, as well as a reference to sampling theory. The selection of an assay technique that is appropriate and will yield the optimal result based on sample turnaround, precision, accuracy, and cost is then considered. Examples are drawn from work undertaken on the Bushveld Complex (Merensky Reef, UG2 Chromitite Layer, Platreef) and Great Dyke (Main Sulphide Zone). A discussion of the appropriate QA/QC programme includes the chain of custody, CRM selection and the QA/QC process. Keywords sampling, assaying, QA/QC, platinum group elements.

Jan 1, 2014

Spiral concentrators are compact, cost-effective and generally efficient gravity concentration separators for a wide range of applications (for example: coal, beach sands, iron ore, chromite and tantalite). Large mineral processing plants consist of thousands of spiral concentrators resulting in large plant footprints (capital intensive) and the adjustment of splitters is time consuming, impractical and is in many cases neglected?high capacity (HC) spiral concentrators aim to address these shortcomings. As a result Exxaro Namakwa Sands is currently investigating high capacity spiral technology for the spiral circuit upgrade at the primary concentrator plants (PCPs). This article summarizes the rougher spiral performance evaluation that was conducted on different types of spiral concentrators (the traditional MG4 spiral concentrator and the high capacity (HC) spiral concentrator) under different feed conditions. In addition, the effect of slimes on the spiral concentrator performance was also investigated. Slimes rheology was linked to the poor concentrator performance at the higher slimes concentrations. The test campaign shows a sacrifice in recovery under design-feed conditions can be expected when using high capacity spiral concentrators in the rougher stage when compared to traditional spiral technology currently in use. Both spiral concentrators show a detrimental impact of slimes on the performance, but the high capacity spiral concentrator is more sensitive to the higher slimes conditions.

Jan 1, 2010

Statistics is essentially a study of variability, the use of some suitable mathematical model representative of such variability, and the application of this inferred pattern of behaviour to practical problems. Probability theory is the mathematical structure devised for providing models for chance happenings. Perhaps the simplest example of a chance happening is the result obtained in tossing a coin. Although the result of a single toss can never be predicted with certainty, there is no reason why in repeated tosses the expectancy of heads and tails should not be equal. In such a case the outcomes of the experiment are said to be equally likely, so that the probability of obtaining heads (or tails) is 1 in 2, that is, 0,5. This simple probability .model refers to a 'mathematical' or 'unbiased' coin. Whether such probabilities are meaningful for actual coins tossed in any particular way is a matter for experience to determine. Probability models have also provided the basis for representing observed variability in cases where the actual under- lying probabilities are only partly known or defy analysis. A typical example of the latter case is the variability observed in the values obtained from gold or other ore samples. The interacting natural forces which gave rise to this variability are obviously very complex and are unlikely ever to be unravelled completely. In spite of this, probability theory and the more recent geostatistical theories have provided us with models which can represent this variability on a reasonable basis. Applied statistics and geostatistics must therefore never be accepted as exact mathematical sciences. Furthermore, a basic and essential concept is that in the type of applications covered in these notes, no model must ever be accepted as necessarily the final and exact answer to the problem; thus, any model must prove and continue to prove its appropriateness in practice, preferably by follow-up comparisons.

Jan 1, 1981

By H. Vuthaluru, O. Kavianipour, C. -Z. Li, N. Suresh, D. Sahu

The paper describes a CFD model developed for 76mm Dense Medium Cyclone (DMC) using Ansys Fluent Software to gain insights into the separation of particles according to their size and density. The simulation used in this paper includes the Reynolds stress model to predict the turbulence inside the cyclone body. An Eulerian-Eulerian multiphase CFD model was applied to model a number of physical aspects such as the separation of coal particles and the segregation of magnetite media solids. The experimental results generated in a laboratory scale DMC were used for the validation purpose and the predicted results of CFD have been validated for the flow splits of water, magnetite and coal. The simulation results obtained from the Eulerian-Eulerian multiphase model revealed that the prediction agreed with experimental results, and matched reasonably well in terms of the mass flow rates of water, magnetite and coal. Furthermore, the partition curve of the DMC when mapped for the separation of - 3.0+0.50 mm size also showed to be in agreement with the experimentally obtained curves. The gravity of cut (SG50), also predicted by the Eulerian-Eulerain multiphase CFD model, was found to be in the vicinity of observed experimental value of SG50. Keywords: Dense medium cyclone, Eulerian-Eulerain multi-phase modelling, computational fluid dynamics, cut gravity (SG50)

Jan 1, 2020

By M. B. Díaz Aguado, I. Á. Fernández, C. González Nicieza, B. S. Menéndez

This paper summarizes the works that the Research “Group of Ground Engineering”, belonging to the Mining Department of the University of Oviedo, Spain, has been developing in close cooperation with the Regional Mining Department, since 2001, in order to control and monitor an experimental underground limestone exploitation by the room and pillars method. The aim of the current research is not only the geotechnical characterization of the rock mass (by means of laboratory and site tests) or the instrumentation of its displacements and stress changes (using convergence meters, INCREX probe, extensometers and rigid inclusion cells), but, moreover, to undertake intensive monitoring and control of such pilot mine, which is mined exclusively in order to accomplish this research. The data transmission was made on line via Internet, to achieve a full understanding of the behaviour of the experimental mine, to access data from remote locations and to visualize results from a website. All the collected information becomes input data for several numerical models using finite differences under a program developed in the research Group, ALMEC. The simulation and a final economical analysis lead to a design of an underground exploitation, at production scale, for a resource that is traditionally mined by means of open-pit process methods that could be worked underground with less environmental impact. The main purpose achieved by this exhaustive analysis is the technical and economic viability of such mine, for their optimisation for a future productive exploitation.

Jan 1, 2003

By Z. Saw, C. Poveda, N. L. Mai

Optimising the throughput of a mining network comprising all equipment from shovels to semi-autogenous grinding (SAG) mills is a complicated task, yet the potential benefits can be significant. Key modelling challenges stem from the sheer number of possible routes which material can travel, different equipment operating under different constraints, and the rate of SAG mills being calculated through a nonlinear function of the blended materials’ rock attributes. Nevertheless, this is an ideal onapplication area of mathematical programming, a branch of operations research. This paper describes an application of mixed integer linear programming (MILP) to optimise the mining equipment network of one of the world’s largest copper mines.The model takes as input a year-long monthly mine schedule of shovels in different pits, pushbacks, sequences and faces which produce material to be moved through a network of crushers, conveyors, silos, distributors, stockpiles and SAG mills, ultimately outputting a daily operational plan for all equipment that maximises the throughput of the network. All operational constraints and business rules are considered, including three quality attributes of copper ore. Comparing model results with actual data shows an improvement of 4.47% in network throughput tonnage. Additionally, although the model is solved using a free, open-source solver, optimal solutions are still achieved within a practical timeframe.

Sep 1, 2021

By T. M. Chagwedera, A. E. Lewis, J. Chivavava

Eutectic freeze crystallisation is a novel separation technique that can be applied to treat brine solutions such as reverse osmosis retentates, which are often a mixture of different inorganic salts. The treatment of calcium sulphate-rich brine solutions through eutectic freeze crystallisation has resulted in gypsum scale formation on the walls of the crystallisers and ancillary equipment. In order to prevent gypsum scaling on equipment surfaces, it is essential to understand the mechanism of gypsum scaling on cold surfaces. This paper focused on the interaction between gypsum crystallisation in the bulk solution and scaling on the crystalliser walls in the presence of gypsum seeds. A cooled, U-shaped stainless-steel tube suspended in the saturated solution was employed as the scaling surface. Preliminary results showed that the scale layer was predominantly composed of needle-type and hexagonal prismatic crystals. The rate of scale deposition was highest during the first 24 hours, thereafter it decreased. A thin scale layer was observed to have coated the tube within the first hour of the experiment. Seeding, using reagent grade gypsum crystals, was effective in reducing scale layer formation through providing a surface for growth. The highest scale reduction, 81%, was realised at a seed loading of 0.50 g/L. At a high seed loading of 4.01 g/L, the seed material adhered to the tube. Keywords: Gypsum, eutectic freeze crystallization, seeding, scaling, cooling crystallisation

Jan 1, 2020

By W. Wittke, D. Schröder, H. Polczyk

ABSTRACT: The Urft dam, the Diemel dam and the Eder dam are three old masonry damslocated in Germany. The paper describes the rehabilitation measures and the correspondingstability analyses carried out to adjust the dams to today's standards. Remedial works such as theexcavation of inspection galleries, the installation of a grout curtain with a downstream drainagescreen as well as the installation of pre-stressed permanent tendons were carried out. In all threecases the stability of the upgraded dam could be proven on the basis of finite element analyses. ZUSAMMENFASSUNG: Die Urft-, Diemel- und Edertalsperre sind drei alte deutscheSchwergewichtsmauern aus Bruchsteinmauerwerk. Im Beitrag werden Instandsetzungsmaß-nahmen und Standsicherheitsnachweise beschrieben, die erforderlich waren, um die Staumauernan den heutigen Stand der Technik anzupassen. Hierzu wurden Kontrollgänge aufgefahren,Dichtungsschleier mit luftseitiger Dränage sowie vorgespannte Daueranker hergestellt. In allendrei Fällen konnte unter Berücksichtigung der Instandsetzungsmaßnahmen die Standsicherheit derMauer auf der Grundlage von Berechnungen nach der Methode der finiten Elemente nachgewiesenwerden. RÉSUMÉ: Les barrages de Urft, Diemel et Eder sont trois barrages-poids vieux allemandsconstruit de maçonnerie de moellon. Dans cet article, opérations de remise en état et preuves destabilité sont décrits, qui étaient nécessaires pour adapter les barrages à l'état de la techniqueactuelle. À cet effet, des galeries de contrôle étaient creusés, voiles d'étanchéité avec des drains àla face aval et tirants précontraints permanents étaient fabriqués. Dans tous les trois cas, tenantcompte des opérations de remise en état, la stabilité de la barrage pouvait être prouvée à partir decalculs selon la méthode des éléments finis.

Jan 1, 2003

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 B. Kweto, W. Legodi, C. van Buuren, R. F. Sandenbergh

Biooxidation, and especially the BIOX® process, is a viable, economical and environmentally attractive process to liberate gold hosted in refractory sulfides by oxidatively leaching the sulfides as soluble sulfates. The moderate to high cyanide consumption during the subsequent cyanidiation of the washed biooxidation residue is probably caused by the retention on the solids of labile sulfur species formed during the multi-electron oxidation process of sulfide to sulfate. In this work the nature and mode of transport of the cyanicides in the products from the mesophile BIOX® process, as well as that of the combined mesophile and thermophile bioxidation process, were considered and strategies to reduce cyanide consumption evaluated. It was found that labile sulfur species were the major cyanide consumers in the mesophile biooxidation product, forming predominantly thiocyanate during cyanidation. The transfer of labile sulfur species was only marginally decreased by more intensive and thorough washing of the biooxidation products with warm and hot water, intense stirring and warm caustic leaching. A major reduction in cyanide consumption was however achieved by using a combined mesophile and thermophile biooxidation process. Keywords: Biooxidation, refractory sulfide gold ores, cyanide consumption

Jan 1, 2020

By R. G. Votteler, A. C. Brent

"The first in this series of two papers, on the potential of renewable electricity sources for mining operations in South Africa, investigated the internal structure of mining corporations to evaluate feasible alternative electricity sources that were identified as through earlier research. The purpose of this paper is to combine current knowledge about the external macroeconomic and the internal environments to produce a clear picture of how renewable sources of electricity could perform from the perspective of mining corporations in South Africa. The multi-attribute value theory (MAVT) approach was adapted to structure the research and results. The model was fed with real-time data provided from five different energy companies and four mining corporations operating in South Africa. The results show that the performance of hybrid versions of the currently used electricity sources (diesel generators and Eskom grid connection) with solar PV and onshore wind is favourable compared with the current sources alone. The advantage of diesel generators is significantly greater than that of the Eskom grid connection. By combining the macroeconomic influences with the MAVT results, hybrid solar PV versions are identified as having the greatest potential. In second place are hybrid wind solutions, which have the shortcoming that good wind conditions occur only in coastal regions where there are fewer mining activities. Geothermal hybrid versions are the least favourable owing to the lack of service infrastructure and high initial investment costs.IntroductionRecent developments in the macroeconomic environment necessitate an investigation of the internal structure of mining corporations to evaluate possible alternative electricitygenerating sources (Roehrl and Riahi, 2000). To be able to combine current knowledge of macroeconomic factors and the internal structure of mining corporations, the research process is presented in two papers. The first paper (Votteler and Brent, 2016) investigated the internal structure and argued that a strategic tool should be used to evaluate electricity sources from the perspective of mining corporations. The multi-criteria decision analysis (MCDA) approach was selected as the most appropriate strategic tool. Based on a literature review of previous similar MCDA approaches in energy planning, it was concluded that no adaptation of MCDA methods could be found from a corporate, mining, or South African perspective. Finally, the paper investigated the internal evaluation structure in collaboration with mining corporations, by identifying the criteria they use to evaluate electricity sources."

Jan 1, 2017

By T. Szendrei and S. Tose

Historical approaches to the problem of flyrock based on correlation studies and regression analysis, including artificial neural networks and similar techniques, are inherently incapable of addressing two core issues – root causes of flyrock and projection velocity. A further shortcoming of correlation techniques is that they give no information on the influence of rock size and shape on the flight distance. The scaled depth of burial model for crater blasting in the collar zone and bench face does not specifically address the question of flyrock velocity. A third approach, based on flight trajectory calculations, often neglects the very significant effects of air resistance on the trajectory. Some trajectory models incorporate air resistance but use an implausible fragment velocity model that cannot propel sizeable rocks to distances much beyond 150 m. Nonetheless, trajectory calculation incorporating the effects of air drag affords the most promising approach to the prediction of flyrock range. A unique and insightful feature of the proposed realistic flight modelling is that it collapses all suspected causes of flyrock, many of which are not well understood, to just a single parameter – the launch velocity. This indicates that the root causes of flyrock lie in the mechanisms of momentum transfer to broken rock and suggests new avenues of study.

Dec 13, 2022

By A. Ndibalema

Blasting is one of the primary functions in any mining operation. Despite the fact that it generally constitutes between 30% to 40% of the mining cost, blasting also affects the cost-effectiveness of down steam activities such as load and haul, safety, tyre life for haul trucks, crushing and milling. Over the past three decades, significant progress has been made in the development of new technology in an attempt to reduce costs and increase efficiencies and productivities of blasting activities. Mine to mill project concepts have paved the way for such developments. Other advancements have included sophisticated computer modelling technologies for blast design and performance analysis. There are many factors that affect the cost of blasting. These can be divided into two categories; controllable and uncontrollable. The latter includes costs related to depreciation, exchange rates and government legislation with the former category including contractor versus owner blasting costs, efficiency and productivity issues and product quality. Controllable factors have one common denominator which can determine their outcome; direct site management influence. Excavator digging rates and final floor conditions give a good measure of blasting performance, and alternatively cost effectiveness. This paper is aimed at benchmarking against a blast optimisation database, understanding the relationship between costs and identifying opportunities for improvement. Understanding the cost drivers allowed a typical cost model to be developed for the current mining operation at Geita and this was used to drive continuous improvement with emphasis on closing the information loop.

Jan 1, 2008

The influence of Harold Hotelling?s work in the field of mineral economics is both unusual and outstanding. In the 66 years since its development, theory surrounding the economics of exhaustible resources has only been significantly researched since the early 1970s. At that time a wave of research into the economics of exhaustible resources arose from the threat of global resource scarcity and continued into the late 1990s. Current East Asian and global demand for natural resources as well as mineral and metal commodities, has stimulated interest in the optimal and sustainable exploitation of exhaustible resources to the point that the subject is worthy of review. Hotelling?s theory and the assumptions that he made in establishing a model for the optimal exploitation of mineral resources at the industry level and at the level of the individual mine owner, are examined. He showed that the rate of increase inexhaustible resource prices should be equivalent to the market rate of interest and that in a market with rising prices the rate of extraction should be constant. In markets where demand is stable optimal exploitation requires that the rate of extraction should decline over time, while in a monopoly market he showed that the rate of extraction is retarded. In addition, the effects of cumulative production on costs and prices, the uncertainty associated with estimates of the resource stock, the impact of exploration and issues of intergenerational equity are examined. An analysis of the optimal price path, extraction costs and mineral rents at an industry level is presented as a model. An analysis of the rates of production and optimal benefits at the individual mine level including total, average and marginal costs on the optimal rate of production, is considered. Optimal extraction rates for a mine with a clearly defined concave positive cost equation vary according to the position on the marginal cost curve. The influence of discount rates and the size of the ore reserves on the rates of mineral extraction are also examined and could define the frontier of usefulness for the ?economics of exhaustible resources?.

Jan 1, 2007

By T. Feroze, B. Genc

"The ventilation of underground coal mines plays an important role in minimizing the risk of methane and coal dust explosions. The ability of ventilation, with the use of line brattices (LBs), to remove methane and coal dust in empty headings is dependent on the amount of air leaving the LB and entering the heading. The quantity of this air depends on the associated system variables, namely heading dimensions, settings of the LB, and velocity of air in the last through road (LTR). However, the exact effect of these system variables on the flow rate at the exit of the LB in an empty heading is not known. The installation of LBs in South African coal mines is generally carried out based on experience. This can result in overor under-ventilation and may increase the cost of providing ventilation or cause accidents, respectively. In this paper, using computational fluid dynamics (CFD), the air flow rate at the exit of the LB in an empty heading was estimated using full-scale three-dimensional models. The CFD model used was validated using experimental results Firstly, the settings of these three system variables were varied, the flow rates at the exit of the LB were measured, and finally the results were used to calculate the effect of each system variable. The outcome is a mathematical formula that can be used to estimate air flow rate at the exit of the LB in empty headings for any practical scenario.This paper will help the coal mining sector in South Africa by providing estimation models based on scientific reasoning for the installation of LBs, and will also serve academia as part of the curriculum towards educating future mining engineers."

Jan 1, 2016

By M. C. Bekker, T. Govindasamy

The potential benefits of implementing the Last Planner System (LPS) on mining infrastructure projects were explored through two case studies in the South African mining industry. The first part of the study involved measurement of the impact of LPS through earned value techniques on secondary project data. The second part sought to establish the lean construction success factors leading to improvements in construction performance. This was done by means of a research questionnaire distributed to the project owner’s teams, contracted parties, and the LPS facilitators. The results revealed a positive correlation between LPS application and planned percentage complete. However, the performance achieved during the LPS pilot was not sustained. The success factors and benefits considered most evident in the case study pilot differed among the three stakeholder groups. The findings are expected to guide construction stakeholders to better define performance measures and focus on factors required to make LPS implementation more effective in the South African mining sector.

Feb 12, 2024

Many industries base their decisions on the assaying of tiny analytical sub-samples. The problem is that most of the time several sampling and sub-sampling stages are required before the laboratory provides its ultimate assays using advanced chemical and physical methods of analysis. As long as each sampling and sub-sampling stage is the object of due diligence using the Theory of Sampling it is likely that the integrity of the sought after information has not been altered and the generated database is still capable to fulfil its informative mission. Unfortunately, more often than not, unawareness of the basic properties of heterogeneous materials combined with the unawareness of stringent requirements listed in the theory of sampling, lead to the conclusion that massive discrepancies may be observed between the expensive outcome of a long chain of sampling and analytical custody, and reality. There are no areas that are more vulnerable to such misfortune than sampling and assaying for trace amounts of constituents of interest in the environment, in high purity materials, in precious metals exploration, food chain, chemicals and pharmaceutical products. Without the preventive suggestions of the theory of sampling serious difficulties may arise when making Gaussian approximations or even log-normal manipulations in the subsequent interpretations. A complementary understanding of Poisson processes injected in the theory of sampling may greatly help the practitioner understand structural sampling problems and prevent unfortunate mistakes from being repeated over and over until a crisis is reached. This paper presents an overview of the theoretical, practical and economic difficulties often vastly underestimated in the search for quantifying trace amounts of valuable or unwelcome components.

Jan 1, 2009