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By M. B. Cortie

An account is given of the development of ferritic stainless steels since their discovery in the early years of this century. The alloys became very widely used in the 1950s, the market during that decade being driven strongly by a demand for automobile trim made of ferritic stainless steel. The production of ferritic stainless steel declined as a proportion of the total at the end of the 1950s as consumer preferences changed. However, the market is now growing strongly again, this time driven by a demand for oxidation-resistant alloys for motor-vehicle exhaust systems. The tonnages produced, applications, and market shares of the various alloys are discussed and compared. Trends in world stainless-steel production, product forms, technological development, and usage are examined.

Jan 1, 1993

By P. G. H. Pistorius, D. S. Konadu, G. Lubbe

The aim of this investigation was to determine whether the composition of a shielded-metal arc-welding electrode coating affected the low-temperature impact toughness of austenitic stainless-steel weld metal. It is generally accepted that increases in the δ-ferrite and nitrogen contents result in a decrease in toughness at low temperatures. Weld metal from electrodes with a basic coating also generally exhibit better toughness than those from rutile (acidic) electrodes. An increase in basicity was expected to decrease the number and size of inclusions, which in turn provides a tougher weld metal. Three commonly available potassium–rutile E308L electrodes were used, complying with the E308L-16 and E308L-17 specifications. Analysis of the electrode coatings showed very similar chemistry and basicity. Significant differences in the inclusion contents of the weld metals were observed: the E308L-17 weld metal had a lower inclusion content (1.4% by volume) than the E308L-16 weld metal (3.7%). The former had higher impact toughness at all temperatures, despite a slightly higher nitrogen content. Regression analysis confirmed that the inclusion content had a significant effect on the impact toughness at all temperatures.

Jul 2, 2022

By G. A. Bezuidenhout, J. P. T. Kapusta, D. K. Chibwe

"Peirce-Smith converters (PSCs) are extensively used in the copper, nickel, and platinum group metals industries to remove iron and sulphur from the molten matte phase. This technology has not changed significantly since its inception in the early 20th century. The typical converting operation involves lateral purging of air/oxygen-enriched air into molten matte through a bank of tuyeres. This blowing operation occurs at low air pressure from the blowers, and the induced bubbling regime is considered inefficient from both a process and an energy utilization perspective. Inherent drawbacks include recurrent tuyere blockage, inevitable tuyere punching operation to clear airways, and low oxygen efficiency as a result of substantial air losses due to leakages.Investigations in the 1980s demonstrated1 that jetting into Cu and Ni converters could reduce or eliminate some of the process difficulties. In spite of these findings, very little progress has been made in the application of these concepts for converting of non-ferrous melts on a commercial scale.As part of its operational improvement and energy reduction initiative, Western Platinum embarked on a full-scale industrial evaluation of generating a jetting regime by using sonic injection. Prior to full-scale industrial evaluation, a numerical assessment was conducted to ascertain the feasibility of implementing sonic injection on Lonmin converters. The work included flow characterization at high injection pressures achieving sonic velocity at the tuyere exit. The 2D and 3D simulations of the three-phase system were carried out using the volume of fluid (VOF) and realizable k- e turbulence models to account for the multiphase and turbulence nature of the flow, respectively. These models were applied using the commercial CFD numerical code FLUENT.This paper discusses the key findings regard ing understanding of gas plume extension, velocity distribution, shear wall stress analysis, and phase distribution characteristics in the system. Plant trials are also discussed with reference to the commercial aspects of a fullscale implementation of sonic injection in the smelter."

Jan 1, 2014

By C. Liu, F. Ye

"To extend the variety of lump ores that are used in the COREX shaft furnace and to optimize iron ore blending, the original evaluation method for iron ores that was proposed by Voestalpine AG has been improved. Physicochemical and metallurgical properties of iron ores, including Sishen lump ore and CVRD pellets, which are currently used in the COREX process, and three other lump ores, were assessed and compared. Ore matching principles were proposed and five optimized iron ore blending schemes designed and verified by laboratory experiments to prove the effectiveness of the improved evaluation method. The replacement of Sishen lump ore by the alternative L2 and L3 lump ores without varying the proportion of CVRD pellets could improve the degree of reduction and rate of metallization, and decrease the bonding index. Based on the results of laboratory test work and industrial- trials, an ore blending scheme of 60% CVRD, 20% L2, and 20% L3 is recommended for use in the COREX process. IntroductionIn recent years, problems such as environmental pollution and a shortage of coke and coal resources for blast-furnace ironmaking have become increasingly apparent. Based on sustainable developments in the iron- and steelmaking industries, the environmentally friendly COREX smelting-reduction process with low energy consumption was developed and introduced (Zhou and Du, 2013; Song, Lv, and Yin, 2015; Xu et al., 2016; Kurunov, 2010). The evaluation system for lump ore that was proposed by Voestalpine AG recommends that only Sishen lump ore from South Africa be used in the COREX process, because of the stringent physicochemical and metallurgical property requirements. This situation significantly hampers improvements to the technical and economic aspects of the COREX ironmaking process, especially in China (Eberle, Siuka, and Bohm, 2006). No theoretical or technical basis has been provided for the evaluation system, and the assessment approach for iron ores also presents problems that need to be discussed and resolved.The COREX process consists of two reactors: the prereduction shaft furnace and the melting gasifier as shown in Figure 1 (Wu et al., 2017). Pellets and lump ores which are charged to the prereduction shaft should have a good reducibility and metallization with a low degradation index (Li et al., 2016; Wu et al., 2011; Kumar et al., 2009; Kang, Gupta, and Sahajwalla, 2007). The properties and microstructure of the iron ore pellets which are required to achieve a high productivity and a lower fuel rate in the COREX process have been investigated (Umadevi et al., 2011). Some efforts have also been made to investigate the behaviour of lump ores in the COREX shaft furnace, including the disintegration characteristics and the reduction degradation (Umadevi et al., 2011; Zhou et al., 2015; Xu et al., 2013; Li, Feng, and Zou, 2013; Hou et al., 2014). However, few studies have focused on the optimization of ore blending for partial or total substitution of the expensive Sishen lump ore by other, cheaper lump ores to reduce the production cost. The technology for the utilization of blended lump ores in the COREX process is still in its early development stages (Zhou et al., 2017; You et al., 2017)."

May 1, 2019

By K. Basaure, S. Palma, R. L. Castro

"Mud rushes are sudden inflows of fine wet ore within underground mines; they can harm people and equipment as well as cause production delays. Block and panel caving mines are prone to mud rushes in their production levels, with mud flowing from the drawpoints. Different mines have developed methods to control drawpoint conditions and thus perform safe ore extraction. The aim of this study is to develop a decision matrix and apply it to samples from drawpoints for the Diablo Regimiento mine, Codelco, El Teniente Division (Chile). The Abrams’s Cone was used to perform slump tests on mud samples and characterize their consistency by setting the saturation degree and packing. The unconfined strength for different saturation degrees and packing was then evaluated. The results show that conditions for fluid response in slump tests correspond to conditions for low strength in unconfined compression tests. We also found the water content value at which the flowing consistency changes from plastic to soft behaviour according to the slump test classification for each sample. This value varied between 12.2% and 16.9%, depending on the sample tested. Finally, a fluid security factor was defined in order to design an extraction pattern for the samples tested, based on the water content. We conclude that a very densely packed ore is not prone to flowing. The flow properties depend strongly on the specific properties of the ore tested, and consequently a specific criterion should be developed for different types of ore at a particular mine. The criterion developed for Diablo Regimiento ore provides critical water content values from 11% to 15%, depending on the ore type. IntroductionBlock/panel caving has the lowest cost and the highest production rates of all underground methods (Heslop, 2000; Hubert et al., 2000). Good management of the risks is important to ensure the security of personnel and infrastructure. Operational risks for the method include rockbursts, air blasts, and mud rushes (Hubert et al. 2000). A mud rush is defined as a sudden inflow of mud from a drawpoint or other underground opening into the mine (Butcher, Joughin, and Stacey, 2000; Butcher, Stacey, and Joughin, 2005). Mud rushes can cause dilution, production delays, and damage to equipment as well as injuries and fatalities. The elements necessary for mud rushes are mud-forming material, disturbances, a discharge point, and water (Butcher, Joughin, and Stacey, 2000). All these elements are present in block/panel caving mines. Mud-forming material comes from ore milled by the caving process; water comes from underground and surface sources. Drawpoints in the production level are discharge points for the mud. Finally, several types of disturbance could trigger the mud rush phenomena: blasting, earthquakes, operation of equipment (Call & Nicholas, Freeport McMoRan, and Hydrologic Consultants, 1998; Jakubec, Clayton, and Guest, 2012), arch collapse above drawbells (Butcher, Joughin, and Stacey, 2000; Butcher, Stacey, and Joughin, 2005; Jakubec, Clayton, and Guest, 2012) and ore drawing (Butcher, Joughin, and Stacey, 2000; Butcher, Stacey, and Joughin, 2005; Call & Nicholas, Freeport McMoRan, and Hydrologic Consultants, 1998; Jakubec, Clayton, and Guest, 2012)."

Jan 1, 2017

By M. Faure

The experiment with backfill at Harmony was mainly an attempt to improve the ground conditions in a particularly tricky section of the mine. A deslimed tailings system was selected for financial reasons, ease of installation, ease of operation and its low level of mechanization. The design of the system has three aspects: firstly, to define the parameters of the backfill material itself; secondly, to design a reliable plant which could consistently produce the desired material in sufficient quantities; and, thirdly, to design a fill distribution system for maximum reliability in the shaft, minimum pipe line velocity, pressure and cost in the horizontal sections and consistency and reliability at the delivery end. The system was successfully constructed and commissioned in a short space of time at a relatively low cost. It has now reached its full potential, and very encouraging results have been achieved with regard to cost savings, ground conditions, ventilation and accident statistics.

Jan 1, 1988

By P Clive Hart

DRA - BACKGROUND [MULTI MINERAL DESIGN & BUILD COMPANY FOUNDED 1984 ENGINEERING FOCUSED CORE ENGINEERING DISCIPLINES INCLUDE: ?PROCESS ?MECHANICAL ?E&I CONTROL PRIVATE COMPANY, INDEPENDENT & INTERNATIONAL]

Jan 1, 2006

The role of research and development In the South African gold-mining industry Presidential Address given by M. D. G. SALAMON, Fellow, Dipl. Eng. (Mining) (Hungary), Ph.D. (Durham) The decision of the gold-mining industry in 1974 to embark on a major ten-year research and development programme was widely publicized at the time. In choosing a subject for this address, I felt almost obliged to use this opportunity to give an account of the progress of this undertaking. On reflection, however, I felt that a simple progress report would not suffice. It seemed important that the programme should be shown in persepective, and that its aims should be outlined to the mining and metallurgical engineering community, many of whom are vitally concerned with the well-being of the gold-mining industry.

Jan 10, 1976

By J. van der Walt, W. Spiteri

Flyrock remains a significant threat to the health and safety of mine employees and integrity of infrastructure, as well as to the safety of the neighbouring communities and their property. This investigation was motivated by the general lack of fundamental research and mathematically quantifiable data in the literature regarding the relationship between blast design parameters and their impact on flyrock. The focus was to develop a concept that can be used to mathematically quantify the trajectory of flyrock resulting from a blast, which can be used for future research. The ultimate goal for this technique, once it has been fully developed, is to: ➤ Enable mining operations to generate a database with accurate historical flyrock measurements resulting from their blasting operations ➤ Allow research teams to conduct scientific investigations into flyrock and the impact of various blast design parameters ➤ Generate point-cloud data to visualize blasts and flyrock in a virtual reality environment for training and education purposes. This paper summarizes a conceptual technique and preliminary fieldwork that was carried out to determine the technique’s feasibility and motivate further development. The results show conclusively that a modified photogrammetric technique is capable of capturing flyrock data for further processing and analysis. The data acquisition procedure can, at this point, be used to meet the first aim of the project, namely to gather a field database of historical flyrock generation. Further development of the technique is ongoing and it is envisioned that the scientific-based technique will provide a method whereby future flyrock studies will be comparable and that assumptions will be limited.

Apr 5, 2023

By M. J. Deats

Your article on page 202 of the August 1993 Journal refers. I was surprised to read that this grant was first introduced in 1984 as it was awarded to me (albeit under the auspices of The Institution of Mining and Metallurgy, London) as long ago as 1964, and I spent two very profitable months in Sweden at that time. Training in job-skills * A South African mine is leading the way in providing alternative job-skills to staff in a bid to upgrade services in local communities and create greater economic empowerment. In recent months, 85 employees of the Associated Manganese Mine (ASSMANG) in the Western Cape have learnt skills as diverse as candlemaking, shoemaking, concrete-product manufacturing, and brick production through a newly established community training centre.

Jan 1, 1993

By S. Annavarapu

"Fragment size distributions play an important part in the design and planning of block cave mining operations. Though several methods have been proposed for estimating fragment size distributions in advance of mining, the calibration of these estimating procedures to field measurements has been a challenge. The Block Size Estimator (BSE) program was developed for providing an assessment of primary fragmentation expected in a block cave mine using drill-core piece length data and joint characteristics from the exploration and geotechnical evaluation programmes. In order to validate the results from the BSE program, the drill-core piece length data and the joint characteristics in different rock types from the DOZ block cave mine in Indonesia were used to help generate fragment size distributions in different areas of the mine. The predicted fragment size distributions were compared with the fragmentation observed at the drawpoints during operation of the mine.This paper presents the details of the validation of the fragment size estimates by the BSE program using fragment size distribution data from the drawpoints at the extraction level at the DOZ block cave mine, and the challenges encountered in developing reasonable correlations between the estimated and measured fragment size distributions. IntroductionThe assessment of fragmentation is an important aspect of the design and planning of the block cave mining method, and forms an integral part of the design of the excavations at the extraction level and the selection of material handling systems for transporting the ore to the processing stations. Secondary blasting requirements can also be estimated based on the fragment size distributions developed for the block cave (Laubscher, 1994).Several methods of estimating fragment size distributions in block cave mines have been developed based on joint set parameters estimated from structural data from oriented core drilling campaigns and mapping of available excavations and outcrops. The BCF program (Esterhuizen, 1999) estimates the fragmentation using a combination of empirical, analytical, and rational methods to model the behaviour of materials during the primary and secondary fragmentation processes. The program JKFrag uses advanced tessellation of joint traces to create rock blocks and then generate fragment size distributions (Brown, 2002). Nickson, Coulson and Hussey (2000) presented the details of processing of the geotechnical data from the Mont Porphyre project, including an assessment of block sizes from the data collected on the core logging sheet. The distance between natural fractures was used to create distributions of block lengths, and a distribution of potential block sizes was estimated assuming that the blocks had equal dimensions in all directions. The results agreed closely with the results of the BCF program. Hadjigeorgiou, Grennon, and Nickson (2002) demonstrated the use of oriented borehole data to provide characteristic block size distributions for a mining project using a software package called Stereoblock, which generates a three-dimensional joint network for a given volume and calculates the volumes of blocks created by the intersections of these joints, simulated as circular planes. The distributions of joint orientation and joint spacing generated from statistical analysis of the oriented core data are used for the creation of the Stereoblock model. The diameter of the circular planes representing the joints is determined based on the mean and standard deviation of the joint trace length obtained from scan-line mapping."

May 1, 2019

By H. Von Michaelis

The world is rapidly becoming more ?green? i.e. energy conscious. Since mining and mineral processing are massive energy users, the mining industry is seeking ways to reduce its energy footprint. In mining and mineral processing operations, energy is often the most expensive cost item. Comminution, i.e. grinding, is frequently the most energy-intensive step between mine and metal. High pressure grinding rolls (HPGR) are being installed in a rapidly growing number of ?hard rock? mineral processing operations. In the energy conscious cement industry, HPGR grinding has been standard practice for decades. HPGR is known to be energy-efficient; the question is how energy efficient? How can the energy efficiency of HPGR be enhanced? This paper reviews recent HPGR applications for the processing particularly of copper, gold, platinum, PGM-Ni-Cu and iron ores. HPGR technology is discussed with respect to energy efficiency. The harder the ore the greater the energy savings are likely to be. Typical energy savings of 10?20% can be expected when installing HPGR vs. a SAG mill. Wipf(2005) showed why conventional Bond Work index tests on HPGR product is likely to under-estimate the energy savings that can be achieved by installing HPGR. Energy efficiency of HPGR is, however, ore-specific. The biggest energy savings of HPGR tested thus far is 9.5 kWh/tonne claimed for Vista Gold?s Mt. Todd gold ore from Western Australia, a savings of over one-third of conventional SABC comminution energy. Several commercial scale iron-ore pellet feed plants install HPGR for fine-grinding of concentrate to increase the surface area of pellet feed in a manner that reduces overall energy consumption. Energy-consumption in comminution is, however, only part of the energy savings benefit story. HPGR typically also reduces the amount of steel lost through wear of mill liners and media. Marsden(2008) showed that when the energy that would have been consumed to produce the steel that is saved by applying HPGR is factored in, then the overall energy savings of HPGR is considerably greater. Johnson et al.(1988, 2005) tested HPGR in a flowsheet in which energy savings of around 50% can be expected if HPGR product screen oversize is recirculated to the HPGR. Innovative flowsheets have been proposed by Rule et al.(2008) and by Morley (2008) which are expected to result in significantly increased energy savings. HPGR applied in flowsheets in conjunction with coarse ore separation devices, e.g. ore sorting or DMS to remove barren waste from HPGR feed promises significantly greater energy efficiencies. Fine-grinding and ultra-fine grinding of ore or concentrates in conventional ball mills results in energy consumptions that increase exponentially with product fineness. Wipf (2009) presented a flowsheet in which he proposed the installation of HPGR ahead of the Aerosion ?Disintegrator? for ultra-fine grinding of ores and/or concentrates. This dry grinding arrangement is expected to achieve ap80 = 7 µm using up to 100 kWh/t less energy than could be achieved by wet ball milling. Using conventional comminution, an ore might require grinding to p80 = 45µm (? 325 mesh), for example, to liberate the valuable components, e.g. magnetite, from gangue, e.g. silica. Inter-particle comminution in HPGR may break some ores along grain boundaries thereby liberating valuable minerals from gangue at a much coarser particle sizes. Early magnetic separation rejection of silica gangue liberated from magnetite by HPGR at coarser grain sizes could further reduce downstream comminution energy consumption.

Jan 1, 2009

By J. D. Stone, I. D. Brumby, J. D. Inch, C. J. Beukes

A. Continuous miners, and their operation at Bosjesspruit Colliery J. D. INCH*, B.Sc. (Min.), M. I. Min. E. (Visitor) A brief description is given of the main types of continuous miner and their incidence of application in South Africa. Definitions and descriptions of the design parameters and components of the main cutting head are given. together with an outline of the modifications carried out to improve machine cutting performance. An account is given of experience with the application of water infusion to suppress airborne dust during continuous-miner operations. B. The selection and performance of continuous miners at Matla Coal by J. D. STONE, B.Sc. Eng. (Min.,) M.B.L. (Graduate) The reasons for the choice of continuous miners for the development of accesses and the winning of coal in a modern underground coal mine are discussed. It is shown that, at relatively low depths, the extraction rate as well as the costs are more favourable than those of proved total extraction methods. The selection of a continuous miner is largely dictated by factors such as production rate, capital and running costs, imported content and the extent to which local content and manufacturing are to be increased, manpower requirements, seam thickness, expected floor and roof conditions, and maximum cutting height. The present inherent shortcomings of continuous miners, such as inefficient continuous transportation of coal away from the miner and the lack of an infinitely variable traction to match the sumping speed with the feasible penetration speed, are pointed out. Specific problems encountered and the methods of solving them, as well as a planned trial with a heavy-duty continuous miner, are discussed. C. Continuous mining within the Tavistock Group of collieries I. D. BRUMBY.Dip. Min. (Visitor) The Tavistock Group of collieries is situated some 25 km south of Witbank. The three collieries comprising the Group are Tavistock Colliery, Phoenix Colliery, and South Witbank Coal Mines. Continuous mining is practised to some degree at all three collieries. This system of mining was introduced at Phoenix during 1976, South Witbank during 1978, and Tavistock during 1979. For the twelve months ended June 1979, continuous mining accounted for 1,7 Mt of the 4,5 Mt hauled from underground. All the continuous miners introduced to date have been of the rotary-drum type. D. Pillar extraction at Usutu Collieries using continuous miners by c. J. BEUKES(Visitor) In 1969 Usutu Collieries began pillar extraction with conventional mechanized equipment. This was very successful, but certain disadvantages could be eliminated if continuous miners were used instead. In 1976 the first continuous miner was introduced for this purpose; this proved so successful that a second unit was introduced in 1977, and pillar extraction by conventional equipment was discontinued. By the end of 1978, 1,3 Mt had been mined from pillar extraction by continuous miners. This paper describes the method in some detail, and indicates that the operational costs are lower than for conventional bord-and-pillar mining. Defect solid state A one-day multidisciplinary symposium entitled 'The Defect Solid State '80' will be held under the auspices of the Solid State Physics and Materials Science Subcommittee of the South African Institute of Physics at the University of the Witwatersrand on Monday, 14th July, 1980, following the Twenty-fifth Annual Conference of the South African Institute of Physics.

Jan 1, 1980

A decision by joint-venture partners Anglo American, Gencor, and the Industrial Development Corporation to proceed with the expansion of the Columbus Stainless Steel plant in Middelburg will contribute significantly towards the economic growth that South Africa needs so desperately. The expanded facility, expected to come on-line in 1995, will be the largest single-plant producer of stainless steel in the world, and the company will rank sixth overall in world production.

Jan 1, 1993

Balance Sheet at 30 June 1990 ACCUMULATED FUNDS Balance at 30 June I989 . Excess of income over expenditure for the year ended 30 June 1990

Jan 1, 1990

Letter to the Editor With reference to the recent questionnaire in the December 1980 issue on 'The Contents of Journals', I have made the following observations.

Jan 1, 1981

By D. V. J. W. Groenewald, T. M. Louw, L. Auret, S. M. Bradshaw, A. V. Cherkaev

Unexpected equipment failures lead to financial losses due to production disruption. Time-based maintenance, based on checks over regular time periods, has been employed to minimise disruption. However, the improvements it can offer are limited as it may lead to unnecessary service of healthy equipment or missed failures occurring between service intervals. Condition-based maintenance (CBM) provides a further improvement to equipment reliability by detecting faults and predicting remaining useful life (RUL) based on equipment health monitoring. Its application in the mineral processing industry is hindered due to the high cost of health monitoring equipment. In this study, two stochastic process models, the adaptive auto-regressive model and the gamma process, are compared in their ability to forecast the degradation state and to provide RUL prediction. The gamma process model was found to be effective in both tasks. Due to its simplicity and minimum hyperparameters requirements, it is proposed to use the gamma process as a baseline for comparison with other models. Keywords: Condition-based maintenance, remaining useful life, slurry pump, adaptive autoregressive mode, gamma process

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

[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

By O. A. W. Strydom, J. C. M. Wethmar, P. R. Jochens, D. D. Howat

Liquidus temperatures in the Cr-Fe-Si system in the composition range representative of ferrochromium-silicide produced in South Africa J. C. M. Wethmar, B.Se. (Eng.) Rand D. D. Howat,U B.Se. (Glas.), Ph.D.. F.I.M. P. R. Joehens, Pr.Eng., M.Sc. (Eng.) Rand, Ph.D., A.I.M. O. A. W. Strydom, M.Sc., Ph.D. Alloys in the composition range of chromium, 20 to 50 per cent, iron, 10 to 30 per cent, and silicon, 25 to 55 per cent, were subjected to both differential thermal analysis and the classical quench method so that the liquidus temperatures of ferrochromium-silicide alloys could be determined. The results are presented as liquidus curves on pseudo-binary sections at various ratios of chromium to iron and as liquidus isotherms in the ternary section.