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[Consider the situation where we wish to estimate the value of a block of ore W from the values of n samples wt (i = 1, 2.... n). The samples can be located anywhere inside or outside W. The blocks and the samples can have any size or shape (Fig. 8.1). We define ws as the set of all the samples wi: WS = Iw1; W2; W3.. . wn and we wish to estimate the block W using the samples ws. Let xi be the value of the ith sample and µw the unknown average value of the block. We can estimate µw from the average value of all the samples. Let µw be the estimator of µw. As the samples need not be of equal size, the sample average is: µw = wi xi/~ wi. (8.1) The mean squared error made when estimating µw by µw is known as the variance of estimation of W by ws. It is the error made when giving the value of the sample set ws to the block W and is written o2E (WS to W). By definition: o2E (ws to W) = E [(µw - µw)2]. (8.2) If n = 1, this error is known as the extension variance. Since the sum of the weights given to the sample values is equal to 1,0, the estimator µw is unbiased (the question of the absence of bias is studied in more detail in Chapter 9): E [( µw - µw)1 = 0. (8.3) The error (µw - µw) has zero mean and a variance o2E = E (W8 to W). If we assume that this error is normally distributed, we can define confidence limits for µw. Let tP be the value of the standardized normal variance t such that the probability that t is less than tP is p: (t,) = .\/27T f exp (- t2/2) dt = p (8.4) The probability that µw is larger than µw + t1-P oE is p. The probability that µw is smaller than µw- t1-P oE is p. The following approximation formulae are often used to calculate 2p central confidence limits for the block value: 68% central confidence limits (p = 16%): µw - o2E, and µw + o2E. 95 % central confidence limits (p = 2,5 %): µw - 2 oE, and µw + 2 oE. Tables of the function 0 can be found in any textbook on statistics (for example, Fraser, 1958, p. 388) (see Table 7.2). [ ] The last line of Table 2.2, corresponding to f = 00, also contains the value of tP for p = 80, 90, 95 and 97,5 %.]

Jan 1, 1978

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 Q. G. Reynolds

The presence of dust and fume suspended in the freeboard region is a common feature of the operation of direct current (DC) plasma smelting furnaces. This occurs primarily as a result of the use of fine feed materials together with the open-arc, open-bath operation of such smelters, and is exacerbated by the high velocities and turbulent mixing of the gas in the vicinity of the arc jet. Dust and fume losses into the furnace off-gas system can be significant in some cases and may have economic, operational, and environmental impacts on the process. A computational modelling study is presented in which the concentration of dust material was considered as a continuous field subject to a governing partial differential equation. Settling behaviour was calculated as a function of particle size, local gas/plasma temperature, and other physical properties. Development of the coupling between the concentration field and a magneto-hydrodynamic description of the arc is shown, and the resulting models were used to compute various aspects of the behaviour of the concentration field in the arc region for a variety of furnace conditions. Time-averaged as well as transient models of the arc were used to generate the results presented. Qualitative case studies produced several practical suggestions for furnace operation, including increased dust capture by the bath when feed ports are located closer to the electrode, and the possible effects of feed segregation in the furnace freeboard based on dust particle size and density.

Jan 1, 2014

By B. Yu, M-H. Cao, C. Zhou, X-Z. Zhang

The transient infiltration and lubrication behaviour of slag during continuous casting of steel is important for billet quality. A two-dimensional coupled mathematical mould model was developed to investigate these phenomena. The accuracy of the model was verified by comparing the calculated slag consumption with measurements by the plant. The results show that the liquid slag is consumed from the middle and late period of positive strip time to the next early period of positive strip time, including the entire negative strip time. The maximum downward infiltration velocity and positive pressure in the slag channel is at the middle of the negative strip time. Increasing the positive pressure of the slag channel is conducive to lubrication. The shear stresses acting on the shell surface and at the mould side were determined by the lubrication slag consumption and total slag consumption, respectively, and gradually decreased with increasing slag consumption. The negative strip time was lengthened to increase the slag consumption and prolong the time near the maximum downward shear stress, so as to be conducive to the demould.

Apr 16, 2024

By D. G. Krige

D. G. Krige: The stimulating contributions from Messrs Cooke, Curtis, Martus, Johnston, Van Wyk, Van Rensburg and Wroth are appreciated by the author and provide clear evidence of the importance not only of the principle of assistance to gold mines, but also of its scope and form. In general all the arguments, raised by Messrs Cooke, Martus and Johnston in favour of extending the scope of the new assistance scheme can be accepted as sound.

By N. C. Joughin

A simplified economic model is derived for the financial return from a new gold mining project. The model is used to analyze the effects of changes in the mining rate, capital costs, working costs, value of the reef and the stoping width. The most effective avenues for improving the return from a new project are indicated. It is shown that those technological innovations which would improve the return significantly, and therefore make it possible to open more mines, are the use of smaller mines, means for improving the mining rate to capital costs ratio for smaller mines, planning and control of mines by computer simulation, an improved mine valuation procedure and means for mining at a decreased stope tramming width.

Jan 1, 2014

By S. W. Jacobsz, E. P. Kearsley, N. K. Schoeman

A physical modelling approach was adopted to simulate the process of cave mining propagation at various horizontal to vertical stress state ratios, and image data was captured and used to characterize the resulting failure mechanisms. Image processing was integrated into the study to determine minor principal strains in models to identify where critical extensional strains had been exceeded relative to crack propagation. The study exhibited a scale factor magnitude of 119 using a calculated critical extensional strain value of 0.014% for the modelling material used. It was perceived that cave propagation occurred through successive parallel extensional ‘fracture bands’ in all cases, as noticed in models of prior studies, deviating from that described by the Duplancic model. Cracks tended to bisect regions of minor principal strain equal to the critical extensional strain, which suggests ‘fracture banding’ is an acceptable failure mode for brittle, rock-like materials. Moreover, it was found that models with lower horizontal to vertical stress ratios (K ratios) showed a greater degree of vertical development of the caving mechanism (at similar vertical stresses), while the vertical extent of the cave was suppressed in models with higher K ratios. Models subjected to larger vertical stresses experienced slower cave formation in latter time-steps. These models exhibited larger two-dimensional caved perimeters and areas, respectively.

Nov 30, 2022

By K, J. MAUNDERS

This paper briefly describes a computerised model of the South African electricity system which has been developed jointly by the Atomic Energy Board and the Electricity Supply Commission. The results of an analysis of this system have been subjected to a fairly extensive sensitivity analysis which reveals that up to the year 1990 between 680 and 700 million tons of coal will be required for electric power generation, together with between 7 000 and 10 000 tons of uranium. This result is fairly insensitive to data variations, but the prediction of a cumulative requirement up to the year 2000, of between 1 300 and 1 800 million tons of coal and 25 000 to 70 000 tons of uranium, proves to be very data-sensitive.

Jan 1, 2014

By A. G. Royle

The reasons for constructing a model of an orebody for which both the parent population and the sampling distribution are known are discussed and details of the model are given. A brief summary of Matheron's theory of regionalized variables is included, with particular reference to his kriging estimators and their variances. Using the model, a comparison is then made between these kriging estimators and other commonly-used estimators. These are compared to find the one with the minimum variance, and an analysis is included to investigate whether any of the estimators is biased. Also included is a comparison between theoretical and experimental variances for some of the estimators.

Jan 1, 2014

By J. M. Stewart, C. H. Wyndham

Suggested thermal stress limits for safe physiological strain in underground environments by J. M. STEW ART M.Sc. (Eng) (Witwatersrand) (Visitor) and C. H. WYNDHAM M.B., D.Sc. (Witwatersrand), F.R.C.P. (Land) (Fellow) A comparison of safe temperature limits, based on Mitchell and Whillier's equations for specific cooling power (SCP), with similar limits determined experimentally shows the SCP-based limits to be unnecessarily conservative. It is argued that, while a small part of this conservatism may be attributed to an erroneous extrapolation of the heat transfer dependence on wind speed, the major part is probably due to the use of too Iowa limiting mean skin temperature in the calculation of SCP. A combination of Mitche/l's basic data with results available in the literature permits the derivation of modified heat transfer equations based on data that fully cover the range of wind speeds of interest. These equations, using a mean skin temperature of 36°C as the basis for the calculation of safe temperature limits, are then shown to agree favourably with those determined empirically. Furthermore, values of SCP based on these equations are shown to correlate reasonably well with wet kata readings, giving positive support to the wet kata thermometer as a heat stress meter.

Jan 8, 1975

The March General Meeting of the Institute was held in Kelvin House, Johannesburg on 18th March, 1970, at 4.30 p.m. Mr J. K. E. Douglas (President) was in the Chair. There were also present fifteen Fellows, Messrs H. Britten, R. C. J. Goode, Prof D. D. Howat, Mr T. C. A. Meyer, Dr R. E. Robinson, Messrs V. C. Robinson and P. W. J. van Rensburg (Council Members), S. K. de Kok, Dr N. P. Finkelstein, Messrs K. W. Findlay, H. N. Hepker, J. Levin, Dr K. A. Murray and Mr A. H. Mokken. Four Members including Mr D. Ayres, Dr M. I. Britten and Dr A. Granville. One Associate: Mr G. S. Stander. One Student, Mr R. N. Guest. Four Visitors, Messrs S. A. Allison, C. N. Leibb, C. J. Kooij and A. Mavrogordato. Secretary: Mr D. C. Visser. Total present: Twenty-seven. OBITUARY The President: "It is my sad duty to announce the death of Henrik Johannes Van Eck, Honorary Life Member, who joined the Institute in 1929 and passed away on 18th February, 1970. Dr van Eck started life as a chemist and chemical engineer and, as we all know, he rose to become one of our most distinguished leaders of industry in the country. On many important occasions we, in this Institute, have been privileged to have him address us on subjects which were always of great importance and relevance to the developments in this country. He was a man of great vision and imagination and could put across his ideas in a most eloquent and convincing manner. In his important position as chairman of the Industrial Development Corporation and of Iscor, whatever he said carried great weight. Busy as he was he always found time to participate not only in the affairs of this Institute but in many other technical and public bodies. His passing is a great loss to South Africa and we in this Institute wish to associate ourselves with the many other tributes which have been paid to this great man. We extend our sympathy to his wife and family and as a mark of respect I would ask you to rise and observe a few moments silence." MEMBERSHIP The President: "I have much pleasure in announcing that the names of the undermentioned candidates, having been published in accordance with By-Law 5.2.2, Council has elected them to membership of the Institute in the following grades: Fellow: Ian Douglas Bruce Corner, Joachim Bernhard Rolfes. Member: Michael Vernon Nolan. Associate: Karl Franz Wilhelm Eick. MEMBERS TRANSFERRED TO A HIGHER GRADE From Member to Fellow: Nilo Zolezzi. From Graduate to Member: Roger Billingham. I welcome the newly elected members to the Institute and congratulate the members who have been transferred to a higher grade." PAPERS FOR PRESENTATION The President: (i) "Mr Lee, may I call on you to deliver your paper entitled 'A new bubble pick-up technique as a rapid flotation test method'." After the presentation of the paper the President said: "The paper which Mr Lee introduced this afternoon was a short one but was nonetheless important in that it described a new tool for use in flotation test work. Those of us who have experienced the frustration of trying to solve flotation problems by trial and error methods know what this means. I well remember 25 years ago at T.G.M.E. trying to improve the recovery from the flotation plant there by trying various combinations of reagents and then having to wait a couple of days for the assay office to give results. Even then, on the small scale laboratory tests which had to precede full scale tests one could never be sure that the results obtained were reproducible on the full scale. Here it seems we have a relatively simple apparatus which can measure instantly the effectiveness of various reagents under different concentrations and pH values, etc. It is most important, I believe, that developments of this kind be reported in our journal for the benefit of all involved in such work, not only so that we know about it but also in order to provoke constructive discussion which might lead to further developments. I would like to invite members, therefore, to submit papers or notes on important

By D White, L. Lorenzen

Sampling and metallurgical testwork during various phases of engineering studies is of paramount importance for a robust processing plant design. When developing a process flowsheet, risks in achieving desirable financial outcomes are minimised by ensuring that appropriate sampling and adequate metallurgical testwork support the engineering and cost estimation at each phase of project development. The quality and type of samples used for metallurgical testwork are just as important as the metallurgical testwork itself. The key characteristic required of any sample is that it represents some defined portion of a mineral deposit. Representivity should consider the spatial orientation, lithology, alteration, degree of oxidation, mineralogy, and competency of the ore such as hardness and abrasiveness. Statistically representative sampling procedures and an appropriate metallurgical testwork program should be designed to bring metallurgical understanding up to feasibility study standard and to give a basis for process plant design. The authors have observed that the quality of sampling and quantity of metallurgical testwork carried out during the various phases of engineering studies are often insufficient to truly support a robust plant design. Some designs are based on benchmarks of apparently similar ore bodies or rely on buoyant metal prices supporting cash flows until rectifications can be implemented. The paper will discuss important aspects of sampling and testwork required for engineering studies in designing process plants. Keywords: Sampling, metallurgical testwork, studies, design

Jan 1, 2020

By A. Kapito

The ferrite-pearlite microstructure is the most popular microstructure for alloys used in structural applications, including railway wagon wheels. These alloys have been designed through alloying and thermo-mechanical processing to have a refined microstructure. Ferrite-pearlite alloys are low cost, weldable, have good fabricability, and are reliable under extreme conditions. Given these performance attributes, it seems unlikely then that their dominant position as structural steels would ever be challenged by alternative microstructures. One major achievement in the development of ferrite-pearlite steels has been in the refinement of their interlamellar spacing to very fine distances of the order of < 0.3 µm. A refined microstructure increases the hardness of the alloy, thus increasing its life under wear conditions. The interlamellar spacing in pearlitic steels has, however, been refined almost to its theoretical limit. The increasing demand for speed and increased axle loading on railway wagons requires the use of stronger, tougher, and more durable materials. This has opened the window for the development of novel bainitic steels. Bainitic alloys have a higher level of microstructural refinement than pearlitic ones. They have shown to have good wear resistance and rolling-contact fatigue resistance, and high toughness. This paper will discuss the progress to date on the development of bainitic railway wheel alloys. Four alloy chemistries have been chosen for possible further development.

Jan 1, 2012

By B. Orgilbayar, B. Unursaikhan, S. Sukhbat, Ts. Zagarzusem, D. Baasanjav, L. Jargalsaikhan, E. Otgonjargal, N. Sugir-Erdene, Ts. Soyolmaa

This study has investigated the efficacy of the gravity beneficiation method based on gravitation and centrifugal forces for manganese ore. Powdered samples of manganese ores from the Unagad deposit in Mongolia were analysed for their element and mineralogical composition using ICP-MS and X-ray powder diffraction (XRD). The analysis presented the mineralogical compositions of the ores as hydro goethite, manganese minerals and magnetite, gangue minerals as quartz, albite, orthoclase and microcline of manganese ore. Manganese minerals are white in colour and have micro-veinlet, fine grained-aggregates associated with gangue minerals. The most important manganese minerals are hausmannite, pyrolusite, rhodochrosite, and manganosite. The composite of feed containing 17.31 % Mn and 36.3 % SiO2 was processed in a shaking table. In the experiment, a concentrate assaying 41.37% Mn was obtained from this composite with 65% recovery. In another experiment, f80=0.074 mm particle size ore was used in the MGS concentration test. A concentrate containing 38.34 % Mn with 75.2% recovery was produced in this experiment. The results showed that it is possible to obtain concentrate through gravity processing of manganese ore, which is an economically beneficial process for producing a product of a standard requirement. Keywords: Manganese ore, gravity separator, centrifuge, shaking table 1. Introduction

Jan 1, 2020

By J. L. Havenga

South Africa produces about 400 Kt zircon (ZrSiO4) per annum. This represents about 30 percent of the global demand. However, very little is beneficiated locally and more than 95 percent is exported with little or no value addition. Zircon is a very inert material and needs to undergo high-temperature alkaline melting processes to produce valuable zirconium products. The conversion of zircon to plasma-dissociated zircon (PDZ) produces a chemically reactive species (ZrO2.SiO2) which consist of finely divided submicron monoclinic ZrO2 crystals dispersed in a SiO2 matrix. In this paper, an in-flight, non-transferred arc pilot plasma plant with a capacity of 100 kg/h and which consists of three 150 kW DC plasma torches, is described. The optimization of the plant, which includes the use of different zircon concentrates, the influence of particle size, feed rates, plasma gas, and energy utilization, is discussed.

Jan 1, 2012

By L. S. Linda, P. G. H Pistorius

Ferritic stainless steel is utilized to fabricate automotive exhaust systems using a ferritic weld metal. Ductility of the weld metal is higher if its microstructure contains a significant proportion of equiaxed grains. The formation of equiaxed (rather than columnar) grains is favoured by a higher titanium weld metal content. In this study, the Ti content of ferritic stainless steel weld metal was changed by using Tifree (Type 436) and Ti-containing (441) ferritic stainless steel as base metals. The metal-cored welding consumable contained 0.4% Ti. Gas–tungsten arc welding and gas–metal arc welding processes were compared. The weld metal Ti content ranged from zero to 0.5% Ti, as determined from scanning electron microscopy supplemented by inductively coupled plasma optical emission spectroscopy. Cross-sections of the weld beads were subjected to point counting (to estimate the fraction of equiaxed grains) and image analysis (to estimate the average grain size). Point counting proved to be more reliable. The fraction of equiaxed grains was sensitive to the Ti content, but not to the welding process. Below 0.4% Ti, the fraction of equiaxed grains gradually increased with an increase in the weld metal Ti content; above 0.4% Ti, the fraction of equiaxed grains rapidly increased with increasing Ti content. The transition in behaviour at 0.4% Ti corresponded to a Ti content at which Ti-rich precipitates became stable at the estimated liquidus temperature of the weld metal.

Jul 2, 2022

By W. P. C. Duyvesteyn, J. R. Cutland, J. R. L. Russell

In 1970 it was decided to build a large new plant at the Chingola Division of N.C.C.M., Ltd., to treat concentrator tailings and leach residues with a low copper content by a leach-solvent extraction-electrowinning process. In order to assist in the establishment of the design parameters for the new plant, and to study the interaction of this plant with the existing leach-electrowinning plant, mathematical models, formulated as linear programs, have been developed and used extensively. The paper outlines the metallurgy of the plants and describes briefly the way in which the models have been formulated and used. The formulation involved the use of separable programming to form the products of some variables.

Jan 1, 2014

By Ronald J. Roman

All mining and milling complexes can, within limits, operate at a variety of production rates. Factors of economic importance that are affected by production rates are costs per unit production, recovery and product grade. Once the relationship between the production rate and cost is established, dynamic programming techniques can be used to define the optimum production schedule (that is, the production schedule that maximizes the present worth of the operation) for the life of the deposit. In general, assuming that the capacity and efficiency of the physical plant remain unchanged throughout the life of the deposit, the optimum production rate is not constant for the life of the deposit, but declines gradually as the deposit is being exhausted.

Jan 1, 2014

By D. F. Malan, J. A. L. Napier

A number of shallow coal or hard rock mines employ pillar mining systems as a strategy for roof failure control. In certain platinum mine layouts, pillars are designed to ‘crush’ in a stable manner as they become loaded in the panel back area. The correct sizing of pillars demands some knowledge of the pillar strength and the overall layout stress distribution. It is particularly important to understand the impact of the layout geometry on the effective regional ‘stiffness’ of the rock mass around each pillar. An important design strategy is to model relatively detailed layout configurations which include a precise representation of the local pillar layout geometry and to analyse multiple mining scenarios and extraction sequences to select optimal pillar sizes and barrier pillar spacing. Although computational solution techniques are now impressive in terms of run time efficiency, a major difficulty is often encountered in assigning suitable material properties to the pillars and in devising an effective material description of the layered rock strata overlying the mine excavations. This paper outlines an efficient numerical strategy that can be used to assess large-scale pillar layout performance while retaining the ability to modify individual pillar constitutive behaviour. The proposed method is applied to selected layouts to compare estimated average pillar stress values against values determined by detailed modelling and against observed behaviour.

May 3, 2023

By M. Timucin

High-temperature phase relations in the Pb-PbS system were established by the quenching of samples equilibrated in evacuated and sealed silica capsules. The liquid-miscibility gap seen in some previously published phase diagrams was not observed. The thermodynamic activities of PbS in liquid solutions of this system were derived at 1473 K from the isopiestic equilibration of samples belonging to this solution series with Cu2S-PbS melts of known PbS activities. The behaviour of Pb-PbS melts was found to be compatible with a subregular solution model. This model also made it possible to obtain an analytical liquidus for PbS that was in excelent agreement with the experimental determination.

Jan 1, 1988