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[Consider a square block W in an ore body S2, to be valued from one centre sample w, and one corner sample w2 (Fig. 9.1). The sample set is ws = Iw,;w21. We can estimate the block average µw by the average of the sample values x, and x2: µw = 'z (x, + xz). (9.1) The error made is measured by the estimation variance: o' (ws to W) = 2 - (ws; W) - - (ws;ws) - - (W; W). (9.2) However, we know that the centre sample w, gives more information about the block value than the corner sample w2. In the example studied in § 8.4, where w, and w2 were considered to be points, we found that of (w, to W) was nearly one third smaller than o2E (w2 to W), therefore when estimating W one should give more weight to w, than to w2. In general, when evaluating a block W from a set of n samples ws, where WS = l w;w2; ... wn1, a better estimator of µw can be obtained if we give different weights to the sample values, depending on the size and the positions of the samples. Some desirable properties of such an estimator µw are: ? It should be a linear function of the sample values xi: n µw = bi xi (9.3) =t where bi = weight given to sample x . ? It should be unbiased, i.e. its expected value should be equal to the true block value: E [µw - µw] = 0. (9.4) ? The mean squared error of estimation of µw should be a minimum E [(µw - µw)2] = a minimum. (9.5) The estimator which satisfies these properties is a minimum variance, linear and unbiased estimator, and is known as the kriging estimator. The corresponding error of estimation is the kriging error. This estimator is also known as the BLUE (for Best Linear Unbiased Estimator) estimator. This was named by Matheron in acknowledgement of the early work of Krige's in the optimization of the evaluation of the South African gold mines. The following notations will be used: µK kriging estimator. o2k = o2K (w,, to W) kriging error.]

Jan 1, 1978

In many practical situations, calculation of the point semivariogram is not necessary. Such a case is analysed in this chapter. The purpose of this analysis is to give a better understanding of the meaning of the mathematical formulae developed in the previous chapters. A similar problem will be studied in Chapter 11, using the point semivariogram.

Jan 1, 1978

By T. Puhakka

Simulation is a way to obtain quickly today future information on how planned systems will most likely behave in various selected situations. This information may then be used to optimize the system and its components and maximize the performance and output. Simulation is a way to fine-tune the layout, match the mobile fleet and optimize the schedule and the way of working to meet the desired production requirements. Simulation provides a glimpse of the upcoming operation, ‘future today’ and helps to predict its restrictions and sensitivity to various aspects. OptiMine™, the Sandvik Tamrock Corp. and CyberCube Oy developed simulation tool is designed to simulate underground rock flow and match suitable technology with various layout options. This tool can be used to view what-if situations and determine what kind of impact mastered changes have to production. The findings of critical points in the layout and working procedures at an early stage of a new mine can help to optimize the layout and material flow. OptiMine™is modular based simulation tool that combines the supplier machine knowledge and traffic guidance with mine operational know-how and mine environment. It is developed to work in a way that an effect of an individual incident, such as the effect of one additional turn in a continuous loading cycle to the daily capacity can be identified. The reported output can be used for economical impact evaluation of selected options. This paper discusses the use of simulation in general and the way the OptiMine™ simulation tool operates and how it may be used for operation, technology and material flow optimization.

Sep 1, 2001

By B. Mbuya, A. F. Mulaba-Bafubianda, J. M. Mvita

The paper explains the main effects of input leaching parameters, such as addition of a reducing agent, acidity, agitation, temperature, and leaching system potential, in relation to observed and predicted yields of sought-after cobalt. An artificial neural network coupled with graphical probability networks was developed wherein the abovementioned input parameters were used to predict the percentage of dissolved cobalt. Furthermore, similarities and differences between the Bayesian and neural network approaches in terms of their key outcomes are compared with respect to study of the dissolution of cobalt in sulfuric acid. Key results indicate that there is a need to use neural network results to predict conditions for dissolution of cobalt, while using Bayesian network to explain inferences about conditions of the input parameters, thereby achieving realistic predictions.

Jan 1, 2023

By M. K. Sichone

Anglo Platinum?s Waterval smelting complex based in South Africa operates the Anglo Converting Process (ACP) that produces SO2 offgas. This SO2 offgas is treated in a double-contact, double-absorption acid plant allowing for conversion efficiencies higher than 99.90 %. The catalytic converter used in the acid plant to convert the SO2 to SO3 is a 4-bed reactor loaded with a combination of cesium-promoted and conventional vanadium pentoxide catalysts. In June 2008 there was a shutdown, in which one of the main activities was to screen the catalyst. Before this shutdown, the operator would control the converter pass temperatures manually, via the SCADA, especially during plant start-ups after which some of the automatic temperature controllers were used. After the shutdown, the control philosophy was revisited and all temperature controllers were put on auto mode during plant start up. Furthermore the set points of the pass inlet temperatures were reduced to maximize conversion in the first two passes. The result has been a reduction of SO2 emissions, from a daily average of 50 ? 70 ppm to as low as 20 ppm for similar sulphur dioxide and oxygen concentrations. Further work has been done to maintain high bed temperatures in the third and fourth passes at low SO2 strengths by splitting the gas stream between pass 1 and 2 thus increasing the SO2 content in the gas to pass 2. This increases the temperature of the gas exiting the second pass, which results in higher temperatures in passes 3 and 4. Comparison of the converter performance prior to and after the changes is made. The benefits of partially bypassing the first pass to increase the SO2 content in the gas to the second pass are shown. Conclusions and scope for further work have been drawn from the comparisons.

Jan 1, 2009

By Fadeela Saloojee, Frank K. Crundwell

"Pressure leaching is an option for copper recovery from chalcopyrite. Leaching takes place at high temperatures and pressures in the presence of an oxidising agent. This work shows how the performance of pressure leaching circuits may be improved by optimising the configuration of autoclaves and the heat-removal method. The objective was achieved by creating an autoclave model by combining mass balances, energy balances and population balances. A base-case circuit consisting of a single autoclave was chosen, and this base case was compared with options for increasing capacity by adding more autoclaves to the circuit. These capacity–increase options include circuits in which the additional autoclave is added in parallel, in series and in series with thickening between the two autoclaves. The copper extraction, productivity and cooling requirements for these options are compared. The series circuit with inter-stage thickening has the highest extraction and productivity, however, the cooling duty in the first autoclave is high. In addition to comparing circuit options, three options for heat removal were investigated: cooling coils, quench water and flash recycling. The flash-recycle option results in the highest copper extraction, and the quench-water option gives the lowest copper extraction. INTRODUCTION Background Copper sulfide ores and concentrates containing chalcopyrite are typically hard to leach under atmospheric conditions. Smelting of these ores may also be a challenge, due to the inability of smelting processes to handle low-grade ores, as well as impurities such as arsenic and antimony. Alternative hydrometallurgical routes to treating chalcopyrite are therefore required. One option is pressure leaching, which is the focus of this work. In the pressure leaching process, sulfide ores and concentrates are leached in autoclaves at temperatures of 200 to 220°C and a pressure of about 3000 kPa (Schlesinger et al., 2011). An oxidising agent, usually oxygen, is required to oxidise sulfide ions to sulfate ions. The oxidation of sulfur to sulfate is exothermic; consequently, a method of heat removal is necessary in order to maintain the temperature in the autoclave."

Jan 1, 2015

Two column flotation cells have been installed as single-stage rougher cleaners at Batu Hijau. The objective was to provide additional residence time in the cleaner circuit to maintain maximum recovery during high mill throughput and high feed grade periods. Installation of the columns has allowed the relatively coarse, well-liberated rougher concentrate and the relatively fine, low-grade scavenger concentrate to be treated separately, improving metallurgical performance in the cleaner circuit. Plant results show that the columns produce a high-grade concentrate at an average stage copper recovery of approximately 80 per cent. There is also indication of increases in both overall plant copper recovery and final concentrate copper grade. In addition, the operability and stability of the cleaner circuit has greatly improved.

Jan 1, 2007

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 J. Griesel, P. H. F. Bouwer, K. Bisaka

Transalloys produces 160 000 tons of SiMn per annum from five AC submerged-arc furnaces. The lime-ore melt from two AC open-arc furnaces is contacted with SiMn to produce 50 000 tons of medium carbon FeMn per annum. Metallics in the slag are reclaimed in a jigging plant, which has been in operation since 1999. The flow of materials between the jigging plant and furnaces has been optimised. The amount of recycle slag in the feed of the SiMn furnaces has been decreased by more than 30% which still provides satisfactory stability of the furnace operation. The jigging plant has absorbed all the additional slag generated, to recover SiMn metal. A review of the raw materials used and operating parameters for SiMn production was also undertaken. Slag to metal ratios were decreased by more than 30% by reducing the slag recycle, removing magnesite from the recipe and introducing high-grade ore. Electrode penetration was improved by reducing coke levels and by utilising more reactive coal. The pitch circle diameter (PCD) was reduced to get a better operating stability on furnace no 5 using the MINSTRAL Control System. Energy consumption on the furnaces improved by more than 15% while SiMn production increased as a result by more than 18%.

Jan 1, 2004

By S. Ranganathan

Production of ferro-chromium in the submerged-arc furnace is highly energy-intensive. Several process rates have been attempted to reduce the specific energy consumption in the production of this alloy. An exhaustive understanding of the thermo-chemical features of the production process can be used to reduce the specific power consumption significantly. The knowledge can be used to reduce the energy drain through undesired reactions in the process can be minimised. Plant trials have shown that specific energy consumption up to 100kWh/tonne of hot metal can be obtained by adopting this strategy. The process requires modification in operation practice and does not require any capital investment unlike other processes adopted for reducing power consumption. The principle of thermo-chemistry involved in this process development and results of plant trials are discussed in detail.

Jan 1, 2007

By P. Ramsaywok, S Ndanduleni, G. Legodi

The objective of this paper is to share the optimisation journey of a pilot Reflux classifier (RC) circuit in the Exxaro GG1 plant, at Grootegeluk beneficiation complex in Lephalale, South Africa. The RC circuit was commissioned in 2016 to produce semi-soft coking coal at its fines circuit; however the stability of operation as well as the quality control of the coal product was not fully achieved. Various test campaigns and optimisation studies were conducted to understand and optimise the RC circuit at GG1. The studies revealed circuit design inefficiencies; provided an improved technical understanding of the current pilot circuit and the parameters required for the circuit to reach a stable operation. The operation was stabilised with its current inefficiencies to produce an average 12.5% ash semi-soft coking coal product for sustained periods, above the initial target of 10.3% ash. Keywords: Reflux classifier, coal

Jan 1, 2020

By J. Sehata, J. Tshilongo, I. Govender, S. Pikinini, T. L. Moodley, M. Raedani

In the face of dwindling Merensky ore reserves in the early 1990s, Mintek developed the MF2 flotation circuit to economically recover platinum group metals from the shallow upper group-2 chromitite reef. By aligning the primary and secondary grind to the platinum group metal liberation kinetics, excessive fine chromite generation was avoided, and thus one could consistently produce high-grade concentrates (>200 g/t platinum group metals) with low chrome content (<3% Cr2O₃), well within smelter tolerances. This, coupled with upper group- 2's low-cost open-pit mining, made it particularly attractive to investors and mining houses alike. As a result, deeper lying reefs like middle group and lower group with lower platinum group metals grades and complex mineralogy, were primarily mined only for chromite using density-based separation processes (like spirals), of which the waste tailings are best classified as secondary platinum group metals resources. Today, with global platinum group metal demand rising and high grade upper ground-2 reserves rapidly diminishing, the industry must revisit these middle group and lower group tailings. Mineralogical analysis reveals several challenges: Middle group tailings feature platinum group metals locked within silicate matrices, while lower group tailings contain fine chromitite fragments, and are hosted within non-floating laurite grains, each presenting liberation and gangue issues. Smelter constraints still demand concentrates below 3% Cr₂O₃, requiring solutions that consider both platinum group metals recovery and chrome entrainment. To develop a solution, two lower group chrome spiral tailings samples were obtained from a large chrome mine: Sample A (+425 μm – 106 μm) and Sample B (−106 μm). Initial assays showed Sample B contained higher platinum group metal grades but also higher Cr₂O₃. As such, different blends of flotation feeds were evaluated using ratios of 90:10 (C1) and 80:20 (C2) of Sample A to Sample B, targeting the coarse fraction's lower chrome content while recovering valuable platinum group metals from the fines. This work proposes a practical route for mining houses to unlock additional platinum group metal value from lower group ore spiral tailings. By optimising blending ratios and reagent suites, it is possible to meet smelter chrome and platinum group metal grade thresholds, whilst still obtaining economically viable PGM recoveries.

Mar 6, 2026

By G. Whittle

An important aspect of the project evaluation process is the achievement of a clear and quantitative understanding of the primary drivers influencing project value and risk. A business scenario-based approach is required to ensure that the project meets value and risk hurdles over the short, medium and longer term. Adopting an optimising approach can aid significantly in the development of a project concept into a business that is optimal and sustainable in the longer term. Through the application of case studies, based on work performed with various mining organisations during the last five years, this paper will demonstrate how project value and robustness can be optimised. Experience has demonstrated that applying this approach results in significant value improvements and risk reduction - primarily by application of a rigorous, fact-based analysis and optimisation process that rapidly increases management team understanding and insight of key driver of value and risk.

Jan 1, 2007

By A. M. Hearn, J. G. Roos

Energy consumption, being a large proportion of the input of the ferroalloy production process, can be measured in terms of the efficiency with which the energy is utilized and the effectiveness with which it is used. The efficiency of the usage of energy revolves around the specific consumption of the energy for the production of the alloy, which encompasses the thermodynamic aspects of the process and is more of a metallurgical function that will not be addressed further in this paper. The effectiveness with which the energy is utilized is determined by the optimisation of the electricity supply from the utility (in this case Eskom). The South African electricity supply industry is on the brink of considerable restructuring, implying changes in ownership, structure and regulation. In other countries, however, restructuring has often seen higher prices. Owing to the diversity of growth prospects in South African markets, Eskom is turning to new market management and generation strategies. In future, Eskom will develop pricing strategies to increase demand from attractive customer segments such as paper & pulp, iron & steel, aluminium, and other metallurgical industries. There will be a broader spectrum of product offerings, including dynamic pricing options and demand-side management incentives. In a future electricity market that will become more dynamic and demanding, it will become increasingly important for electricity consumers to optimise their electricity supply. There are many facets in optimising the electricity supply, which include optimal utilisation of the tariff, integrating energy cost management into the production planning process, implementation of demand-side management actions, modelling, scenario planning (.what-ifs?.), optimisation, maintenance scheduling coordinated with the tariff periods, etc. This paper gives consideration to the status of the development of technology at the manganese alloy works of Samancor at Meyerton, South Africa in order to increase the effectiveness with which energy is utilized.

Jan 1, 2004

By I. Kaabachi, F. Meunier, N. Morales

In open pit mining, ore and waste are hauled outside of the excavation area by trucks that move along a system of ramps. The design of these ramps must be carefully addressed because they have to comply with geomechanical constraints to ensure the stability of the pit walls, provide access to the different levels and phases, but also maximise the value of the extracted ore and reduce the extraction of waste. Because an optimisation approach able to deal with the design of the full ramp system seems to be out of reach at the moment, this paper addresses the problem of designing one ramp providing access to a single pushback, which has been determined beforehand. The optimisation objective is therefore to find a ramp that gives access to one given potential volume, while minimising its impact on the economic value of the volume. Two versions of the problem are formalised. One version allows the extraction of ore and waste only if this extraction is necessary for the ramp system. This version somehow minimises the intrinsic value of the ramp system. In the second version, it is possible to extract more than is needed by the ramp system. For instance, this takes into account the possibility of attaining ore on the wall opposite to the ramp as soon as the ramp reaches its level. In the setting mentioned above, the contribution of this work is three-fold. First, the computational complexity of the two different versions of the problem is presented and discussed; in particular, they are shown to be NP-hard. Second, compact integer programs modelling these two versions are proposed. Third, an efficient GRASP algorithm able to cope with the large instances of the problem is proposed. To assess the proposed approaches, the models and algorithms are applied to real instances with an off-the-shelf solver, illustrating and discussing their potential and relevance for the two versions of the problem. They are also compared with other approaches from the literature in terms of value and resulting designs.

Sep 1, 2021

By P. Saayman

The mining industry has much potential for automation. A great deal of work has been done on this subject and is still ongoing. With automation comes the possibility for optimization, because more information is available and actions can be repeated with more accuracy. This paper looks at possible solutions to the problem of optimizing the autonomous vehicle dispatch system in an underground mine. Possible optimization strategies are evaluated using a simulated environment. The majority of the results indicate that improvements on current methods are possible. Keywords: mining automation, simulation, vehicles, dispatching strategy, optimization.

Jan 1, 2006

By R. Ciccu

This paper examine the optimization of a beneficiation plant for recovering marketable barites from crude ores of different characteristics. The plant, part of a mining complex in Sardinia, consists of a jig section integrated with a flotation line. The problem has been studied using a suitable model of the process, based upon experimental and field data pertaining to both the characteristics of the feed material and the performance of machinery. Data have been automatically processed with the aid of a computer to find the optimum setting of each section, in order to maximize profit for each kind of ore separately fed to the plant. Moreover, the advantages of blending the various concentrates - not all of them individually marketable - are also demonstrated. The overall economic result can be improved provided suitable proportions of each kind of ore are fed to the plant. Such information is fundamental for the long-term planning of exploitation of available reserves, and provides guidelines for further prospecting. The paper illustrates the washability characteristics of the ore&apos;s and describes in detail the model adopted. The results of data processing are then presented in the form of computer graphs and discussed. Finally, conclusions are drawn regarding the advantages of resorting to Operations Research as an aid to management.

Jan 1, 1987

By F. Ntuli, T. V. Nyangadzayi

Chromium green is an essential metal with various applications in the paints, construction, electronics, and aerospace industries. The main source of chromium green is the carbo-thermic reduction of chromite ores, however, chromite ores are being heavily depleted on a global scale, hence the need to find alternative or secondary sources for the chromium. In order to meet the global demand for chromium there is a need to implement principles of the sustainable circular economy to keep chromium within the material loop. Ferrochrome slag and stainless steel slags are secondary resources that are potential sources of chromium. In this work, recovery of chromium from ferrochrome slag was investigated. The ferrochrome slag was alkaline leached using sodium hydroxide- sodium hypochlorite solution to reduce the use of potent reagents that have a potential negative environmental impact. The leachate produced by oxidative alkaline leaching of ferrochrome slag contained hexavalent chromium, which was used to recover the extracted chromium through a two-stage process involving reduction and precipitation. Reduction of hexavalent Cr to trivalent Cr was investigated using anhydrous FeSO4 at concentrations of 5 g/L, 10 g/L, and 15 g/L. Precipitation was conducted by dosing the reduced leach solution with 1 M sodium hydroxide at dosages of 5 ml/L, 10 ml/L, and 15 ml/L. The experiments were designed using the Taguchi (L9) orthogonal array and analysed according to the ANOVA, general linear model. The optimized conditions for the reduction step were ferrous sulfate dosage of 5 g/L with a pH of 12, and for the precipitation step, 1 M sodium hydroxide at a dosage of 15 ml/L with a setting time of 90 minutes and pH of 7. Physical changes were observed during the two-step chromium recovery, with solution changing from a yellowish colour to dark green colour indicating completion of the reaction. The chromium recovery was found to be 93.3%.

Dec 11, 2024

"Pressure leaching is an option for copper recovery from chalcopyrite. Leaching takes place at high temperatures and pressures in the presence of an oxidizing agent. This work shows how the performance of pressure leaching circuits may be improved by optimizing the configuration of autoclaves and the heat removal method. The objective was achieved by creating an autoclave model that combines mass balances, energy balances, and population balances. A base case circuit consisting of a single autoclave was chosen, and this base case was compared with options for increasing capacity by adding more autoclaves to the circuit. These capacity increase options include circuits in which the additional autoclave is added in parallel, in series, and in series with thickening between the two autoclaves. The copper extraction, productivity, and cooling requirements for these options are compared. The series circuit with interstage thickening has the highest extraction and productivity; however, the cooling duty in the first autoclave is high. In addition to comparing circuit options, three options for heat removal were investigated: cooling coils, quench water, and flash recycling. The flash recycle option results in the highest copper extraction, and the quench water option the lowest copper extraction. IntroductionBackgroundCopper sulphide ores and concentrates containing chalcopyrite are typically hard to leach under atmospheric conditions. Smelting of these ores may also be a challenge, due to the inability of smelting processes to handle low-grade ores, as well as impurities such as arsenic and antimony. Alternative hydrometallurgical routes to treating chalcopyrite are therefore required. One option is pressure leaching, which is the focus of this work.In the pressure leaching process, sulphide ores and concentrates are leached in autoclaves at temperatures of 200 to 220°C and a pressure of about 3000 kPa (Schlesinger et al., 2011). An oxidizing agent, usually oxygen, is required to oxidize sulphide ions to sulphate ions. The oxidation of sulphur to sulphate is exothermic; consequently, a method of heat removal is necessary in order to maintain the temperature in the autoclave."

Jan 1, 2016

By A. M. Bryukhanov, A. G. Mnukhin

The report states accident rates for gassy/dusty coal mines represented as an ergatic system "man – machine - environment" with further analysis by the method of conditional probabilities. A coal mine has been analyzed with allowance for the attending personnel, equipment and environment as a sequence of events and states. Probabilities of operational states have been determined and prediction of mine behavior has been made on the basis of investigation findings for equipment and the personnel states, and analysis of the environment (i.e. mine and mining conditions). Utilization of expert estimation methods has been considered for determining major operational parameters of gassy/dusty mines. The importance of standardized values of permissible occupational risks (permissible probability of accident, PA) is demonstrated. It is also stated that a procedure is essential to determine these values, involving regular check-ups of the integral safety criterion at all mines and further development of customized recommendations for individual mines on efficient improvement of accident situations. Methodology to determine the assessment criteria has been developed and scientifically substantiated for permissible accident rates in hazardous industries.

Jan 1, 2003