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By Q. Cheng

This paper introduces the multi fractal interpolation method (MIM)developed for handling singularities in data analysis and for data interpolation. The MIM is a new moving average model for spatial mapping and interpolation. The model decomposes the raw data into two components: singular and nonsingular components. The former can be characterized by a localized singularity index that quantifies the scaling invariance property of measures from a multifractal point of view. The latter is a smooth component that can be estimated using ordinary kriging or other moving average models. The local singularity index characterizes the concave/convex properties of the neighbourhood values. The paper utilizes a binomial multiplicative cascade model todemonstrate the generation of one- and two-dimensional data with multi-scale singularities which can be modelled by asymmetrical multifractal distribution. It then introduces a generalized moving average mathematical model for analysing and interpolating data with singularities. Finally, it is demonstrated by a one-dimensional case study of de Wijs’ data from a profile in a zinc mine, that incorporation of spatial association and singularity can improve the interpolation result, especially for observed values with significant singularities.

Jan 1, 2015

By I. Matsunaga, K. Aoki, W. -j. Jung

Blasting is widely used in mining and basic construction because of its speed and economy to destroy the rocks. Blasting has the advantages of reduced excavation costs and shorted construction time when compared to the use of heavy machinery for excavation and cutting such as that with a tunnel boring machine. There are numerous problems with blasting, including the noise, vibration and fly rock. So it is necessary to accurately evaluate fracture mechanics of rocks on the dynamic loading condition to control the fracture process of the blasting. The tests using Hopkinson's effect for the dynamic condition using the precise detonators were performed for various strain rates on three different kinds of rocks. In the tests using Hopkinson's effect for the dynamic condition, the high-speed camera was used to observe the fracture process of the test sample rocks. As the results of experiments there was an increase in the tensile strength of rock with an increase in the strain rate for three kinds of rock on the dynamic loading. The tensile strength of rocks with high porosity on the water saturation condition was decreased on the both static and dynamic condition. It is clear that the strain rate and water saturation were influenced to the tensile strength of the rocks.

Jan 1, 2003

By J. Dvorácek

Similar to the case of any other business venture, the activities of mining industries are profit-oriented. Nothing will stop successful businesses in their quest for new localities to be prospected for minerals of their choice, because the useful economic life of any mine is limited. Before starting the process of land acquisition, it is important for any mining company to be able to forecast the profitability of the venture. The focus of this paper has been on the prospects of success, concerning the case of the opencast extraction of aggregates for construction. A set of 70 successful and loss-making quarries was subjected to investigation. An international company owns the quarries, which are located in seven European countries. The method of discriminate analysis provided the criteria for assessing future economic performance. The same criteria served the purpose of classifying other quarries belonging to the company.

Jan 1, 2012

By C. N. Harman, N. S. S. Rama Rao

Production of Ferro-alloys through submerged electric arc furnace involves use of electric power as one of the major inputs. Hence the production by this power intensive process can be made economically more competitive if the specific power requirement for smelting each ton of the product is brought down. This becomes all the more necessary where the power cost is comparatively high, like in India. Since the day FACOR started production of Ferro Chrome in 1968, briquetted chromite fines along with lumpy ores were used as feed. Subsequently the increase in the proportion of briquettes and reduction in lumpy ore helped in increasing the use of chromite fines and also brought down the specific power requirement. Meantime FACOR had been closely watching the technical development of use of sintered pellets in Outokumpu and SRC Processes which need still lower specific power. But the high capital requirement for a pelletisation plant kept FACOR from introducing pellets feed to their Ferro chrome furnaces. So this was postponed to be adopted in future. In February 2004 in the ?1st Ferro-Alloys India?, a paper [1] was presented by Dr. Amit Chatterjee. In the questions period after the presentation of the paper there came up a discussion in which it was revealed that with the Indian high grade chrome ores it was not possible to make sufficiently strong pellets, unless a larger percentage of bentonite is used as binder. This is because the Indian high grade Chrome ores have different mineralogy of gangue content compared to low grade ores in Finland and South Africa. Higher usage of bentonite gives rise to higher slag volume and this would result in increased specific power. Since FACOR had plans to go in future for sintered pellets feed, this gave rise to a doubt on success of pelletisation for Indian high-grade chrome ores. This prompted FACOR to take up experimental production of sintered chromite pellets and use of the same in one of their existing furnaces for production of high carbon Ferro chrome. The results are encouraging and are summarized in the paper.

Jan 1, 2007

By F. Lombard

We consider the Grubbs estimation of the precision of an online gauge. Typically, this type of estimation involves independent results from two or more reference instruments (sampling and laboratory analysis operations). The properties of the estimator are then independent of the product variability. However, the use of more than one reference instrument entails significant additional costs. The two-instrument Grubbs estimator, which is based on results from a gauge and a single reference instrument, has the disadvantage that its standard error is heavily dependent on the degree of product variability. We propose a new estimator that has a variance that is more or less independent of product variability. In fact, the variance is typically less than that of the Grubbs estimator based on the use of two reference instruments. In order to function successfully, our methodology requires some prior knowledge of the extent of product variability and of gauge precision. In practice, such prior knowledge is often available and it is a weakness of the traditional two - and three-instrument Grubbs methods that no use is made of such knowledge. The efficacy and robustness of the new method is illustrated by Monte Carlo simulation.

Jan 1, 2012

By K. Y. Lee, J. M. Park, C. W. Park

Laboratory-scale experiments were carried out to investigate the effect of ladle slag composition on the decreasing behaviour of aluminum content in steel, i.e., reoxidation of molten steel in contact with slag, using a vertical tube furnace. The steel composition and the slag system chosen were for ultra low carbon and CaO-Al2O3-FeO-MnO-MgO based to simulate ULC steel grades. It has been observed that the reoxidation rate shows a good relationship with (T. Fe) content in slag. In case of (T. Fe) content higher than 1.5 weight per cent, the reoxidation rate increases linearly with increasing (T. Fe) content. For a given (T. Fe) content, it decreases with the increasing (CaO)/(Al2O3) ratio of the slag. However, in the case of (T. Fe) content lower than 1.5 weight percent, no particular relationships are observed between the reoxidation rate and (T. Fe) content or the (CaO)/(Al2O3) ratio of the slag. These results were used to propose for an aim a slag composition for the ULC steel grades in a steelmaking plant. Keywords: slag deoxidation, slag killing, slag composition control, IF steel, ULC steel grade

Jan 1, 2004

By L. K. Smith

The position of Australia as a continuing long-term supplier of mineral sands, and their upgraded products, has been reinforced with the discovery of the extensive mineral reserves in the Murray Basin, an area covering parts of South Australia, New South Wales and Victoria. A major impurity in the Murray Basin is chromium, mainly present in ilmenite concentrates as individual chrome spinel grains. Magnetizing roast treatments are being evaluated as a means of removing the chrome spinel impurity from the ilmenite and as a result of the roast and magnetic separation treatments, the chrome spinels can be expected to be concentrated in the non-magnetic reject fractions. It is from these fractions that attempts were made in this study to recover a chromium-rich product by magnetic fractionation and by application of flotation. The high gauss non-magnetic rejects from the roasting of a primary and a secondary ilmenite fraction were magnetically fractionated to obtain a product with 40.5 and 28.7 per cent Cr2O3,respectively. From the high gauss non-magnetic reject from the roasting of a primary ilmenite, flotation produced a chromium-rich product assaying 29.5 wt per cent Cr2O3at 69.0 per cent recovery. In another test a magnetic fraction assaying 32.9 wt per cent Cr2O3was floated to yield a chromium-rich product with 39.7 wt per cent Cr2O3at 96.4 per cent recovery. X-ray diffraction patterns of all the products indicated that the spinel concentrated was a ferroan magnesiochromite with rutile, ilmenite and hematite as impurities. Since all products were from a single pass, further processing can be expected to remove the impurity minerals and yield higher grade products. The material produced from the Murray Basin ilmenites in this study had similar compositions to commercial chromite ores, except for titania levels that were much higher. The high titania levels were due to residual rutile in the products, but it is expected that this can be removed with further processing. The mineral sand deposits in the Murray Basin are scattered over a wide area and the amount of chromite that may be produced from each of these deposits is unlikely to be sufficient to support an export market. Consequently, any chromite produced in the Murray Basin will most likely need to be processed locally to value added products for a niche market such as chemicals production. Keywords: Murray Basin, ilmenite, chrome spinel, roasting, magnetic separation, chromite ore

Jan 1, 2003

1. New publications International minerals/metals review - 1982. Washington D.C., McGraw-Hill, 1983.720 pp. U.S.$1l7. Mining subsidence engineering, by Helmut Kratzsch. New York, Springer, 1983.580 pp. U.S. $63,20. Papers presented at the 6th International Symposium on Jet Cutting Technology, Guildford, England: April 6-8, 1982, edited by H. S. Step hens and E. B. Davies. Cranfield (England), BHRA Fluid Engineering, 1982. £40. 2. Mintek reports Report M95 Modern applications of polarography and voltammetry to inorganic analysis. Report M96 The mathematical modelling of the reduction behaviour of chromite from the Upper Chromitite Layer of the Bushveld Complex. Report M113 The selective flotation of South African chromite. Conference on copper The International Conference 'Copper 83', to be held in London on 1st and 2nd November, 1983, will provide a valuable forum for all connected with the manufacture and use of copper. Underwater mining The 14th Underwater Mining Institute will be held in Madison, Wisconsin, on 7th and 8th November, 1983. Asian mining The Institution of Mining and Metallurgy, in conjunction with the Chamber of Mines of the Philippines, will hold an international conference, Asian Mining '84, in Manila, Philippines, from 6th to 8th November, 1984. Apcom '84 The Eighteenth International Symposium on the Application of Computers and Mathematics in the Minerals Industries will be held in London in the week 26th to 30th March, 1984. The Symposium is being Jet cutting Another Symposium on the very successful and popular series of international conferences on Jet Cutting Technology is being arranged by BHRA.

Jan 1, 1983

By S. J. Frank

Ferroalloy furnaces are well known to be extremely difficult to control from a metallurgical perspective. Mostly metallurgical control is still reactive in nature, causing a significant amount of reworking and product blending to achieve a proper product specification. Despite numerous efforts towards the model based control of primary smelting operations, actual metallurgical feed forward control seems to remain elusive. One of the key reasons in the failure to model these metallurgical reactors well, is that fundamentally orientated pyrometallurgists, statisticians, data miners and control engineers very often have diverging ideas how to model these systems. Furthermore, metallurgists have often come to rely on their ability to develop empirical regression models of furnace behaviour, as they have lost their faith in the ability of thermochemical and metallurgical engineering fundamentals to accurately predict the outcomes from furnaces. This paper shows how good thermochemical modelling can be combined with proper technological and systems analysis, as well as a proper inventory model, to predict the alloy and slag chemistry with good accuracy one tap into the future, at a time horizon of typically around 4 to 6 hours. For this modelling approach, a number of tools will be used, such as data reconciliation, thermodynamic modelling using Fact Sage®, inventory and heel estimation, neural networks and statistical data exploration. Furthermore, systems identification theory will be combined with the approaches given above to develop a truly dynamic predictive model. This paper seeks to demonstrate the need for a hybrid approach, which incorporates plant data and readily accessible thermodynamic data to develop a proper dynamic model.

Jan 1, 2004

Rock mass classification systems are extensively used in rock engineering design work, and mine design is no exception. Among the systems most widely used for mining-related design work are the NGI 0-system (Barton et al., 1974), the RMR system (Bieniawski, 1976), the MRMR system (Laubscher and Taylor, 1976) and, more recently, the GSI system (Hoek et al., 1998). Classifying the rock mass is widely seen as being the fieldwork required to characterize the rock mass and enable the application of empirical design methods associated with the different classification systems. This paper argues that it is fundamentally important to recognize the distinction between rock mass characterization and rock mass classification. These two processes should, in most cases, be separated from each other. Rock mass characterization should be used to determine the intrinsic properties of the rock mass independently of the application; i.e. independent from the infrastructure to be designed, the size, shape, and orientation of the excavation(s) or pillar(s), etc. Rock mass characterization should also be compatible with most classification systems and empirical design methods to be used. Rock mass characterization is the background fieldwork required to perform rock mass classification and/or engineering design work. Rock mass classification is the subsequent step to the characterization, and an integral part of the design process. Parameters that vary according to the design, such as the relative orientation of geological structures compared to the opening or the mine-induced stresses, should be calculated as part of the rock mass classification and design process, rather than during the rock mass characterization process. The failure to distinguish between rock mass characterization and rock mass classification can lead to major design errors and poor results.

Jan 1, 2012

By J. N. Van der Merwe

Due to the approaching depletion of reserves in the Witbank Coalfield, and the fact that the Waterberg Coalfield is as yet under developed, there is increasing pressure to extend the lives of the operating coal mines in the Witbank Coalfield. One potential source of coal is the old pillars, often small and at shallow depth, that were not left with secondary extraction in mind. At face value, some of these pillars appear to be suitable for secondary mining due to their high safety factors. However, it is known that over time, these pillars have scaled and the current sizes are smaller than the as-mined dimensions. It is also known that at shallow depth, the overburden is often less likely to fail during secondary mining, resulting in high abutment loads on the unmined pillars. The paper proposes a systematic method to pre-evaluate those old pillars for the possibility of stooping. The method consists of elements of fundamental methods and newly developed technology. In essence, it revolves around using empirical methods to estimate current pillar dimensions, followed by numerical modelling to investigate the probability of progressive pillar failure and then fundamental methods to determine the limits of applicability of the numerical model.

Jan 1, 2012

By H. Moosberg-Bustnes

In cement-based products, such as concrete and mortars, a balance between the particle sizes of the components must be kept in order to obtain the required material properties, such as workability and strength. Sometimes the aggregates lack the necessary amount of fines, hence fine particles, i.e., filler materials, have to be added. Large quantities of filler material are needed in the production of modern concrete types; one principle of self-compacting concrete (SCC) is, for instance, the use of large amounts of fillers to reduce the friction between the coarser aggregates. Use of by-products such as slag, dust or sludge from the metallurgical industries as filler materials in concrete may help to conserve natural resources and at the same time be an economically positive option. However, to be able to successfully use the available materials they must be suitable for the planned purpose, i.e., they must be compatible with cement. In this paper three different experimental studies of steel-slags will be discussed. The aim of the studies has been to investigate if it is possible to improve the steel-slags properties, by selective screening, fine wet grinding or remelting, so that the steel-slags can be used as mineral-addition/filler material in concrete. Keywords: concrete, filler, steel-slag, modification

Jan 1, 2004

By M. Royker

Gold has been demonstrated as a possible catalyst for oxidation reactions. Some evidence for a possible promotion effect of platinum has also been recorded. The influence of platinum as promoter for Au/?-Al2O3 prepared via anionic ion-exchange for the oxidation of glycerol was investigated in a batch reactor at 60°C. It is inferred that the addition of platinum reduces the catalytic activity and therate of deactivation, resulting in an overall higher final conversion of glycerol with increasing platinum loading. The addition of platinum to the catalyst favours the formation of the desired product, glyceric acid.

Jan 1, 2012

By Willem Le Roux

Occupational health and safety is regulated by statute and common law. South Africa has, like many other countries, legislated extensively on occupational health and safety. Despite the body of legislation, the common law continues to play an important role as far as it concerns contractual, delictual and criminal liability. Two major Acts regulate occupational health and safety viz. the Occupational Health and Safety Act, No. 85 of 1993 (?OHASA?) and the Mine Health and Safety Act, No. 29 of 1996 (?MHSA?). The MHSA applies to mines and works as defined and related aspects. OHASA applies to other industries but does not apply to employers and workplaces to which the MHSA and certain matters covered by the Merchant Shipping Act, No. 57 of 1951 apply. See section 1(3) of OHASA. 2 The employer?s health and safety obligations in terms of the MHSA 2.1 Section 2(1) of the MHSA provides amongst others, as follows: ?The employer of every mine that is being worked must: (a) ensure, as far as reasonably practicable, that the mine is designed, constructed and equipped: (i) to provide conditions for safe operation and a healthy working environment (ii) ... (b) ensure, as far as reasonably practicable, that the mine is commissioned, operated, maintained and decommissioned in such away that employees can perform their work without endangering the health and safety of themselves or of any other person?.

Jan 1, 2011

By C. Tan, C. Detournay

Wellbore stability is a major concern for drilling in naturally fractured formations. The infiltration of drilling mud into the fractures is a factor, which may compromise wellbore integrity due to the loss of strength experienced by the fractures. The reduction in the fracture frictional and cohesive properties is attributed to weakening of the infill materials and lubrication of fracture asperities by the mud filtrate. One way to investigate the influence of mud infiltration on wellbore stability in fractured formations is to use a numerical modeling approach. A requirement for the numerical model is the ability to predict the region of mud infiltration. This paper describes a numerical technique to model the extent of mud infiltration for application in coupled fluid-mechanical simulations in densely fractured rock masses using the computer code, UDEC. Several factors are considered including fracture pattern, in-situ stresses, reduction in joint frictional angle and cohesion, viscosity of the mud filtrate and fracture plugging. Results of numerical simulations are presented to illustrate the technique and show the influence of these factors on the extent of mud infiltration. Un des problèmes importants posés par le forage en milieu fissuré saturé, est celui du maintient de la stabilité du puit. L’infiltration de boue de forage dans le massif peut avoir pour effet de réduire les propriétés frictionnelles et cohésives des fractures et de compromettre ainsi la stabilité du puit de forage. Le radoucissement des propriétés des fractures est attribué à la dégradation du materiau de remplissage et au pouvoir lubrifiant des boues. L’analyse numérique offre un moyen d’investiguer l’influence jouée par l’infiltration de boue sur la stabilité du puit. Un des critères de sélection du modèle numérique sera son pouvoir de prédiction du domaine d’infiltration de boue. Cet article décrit une technique numérique permettant de modéliser l’infiltration de boue de forage dans le cadre de simulations hydro-mécaniques, en milieu à haute densité de fractures, effectuées avec le logiciel de calcul UDEC. Parmis les facteurs tenus en compte, on trouvera la nature du réseau de fractures, les contraintes in-situ, le radoucissement en friction et cohésion des joints, la viscosité de la boue et le bourrage des fractures. Des résultats de simulations sont présentés pour illustrer la technique et montrer l’influence de ces facteurs sur la taille du domaine d’infiltration de boue. Bohrlochstabilität ist ein wichtiger Aspekt für das Bohren in geklüfteten Gebirgsformationen. Das Eindringen der Bohrlochstützflüssigkeit in die Klüfte kann die Bohrlochintegrität wegen des Verlustes der Festigkeit des Kluftsystems gefährden. Die Reduktion der Reibung und kohäsiven Eigenschaften ist der Schwächung der Kluftfüllung und der Schmierwirkung der eingerungenen Stützflüssigkeit in Bezug auf die Kluft-Asperities geschuldet. Numerische Berechnungen sind ein Weg zur Untersuchung des Einflusses der Infiltration der Bohrlochstützflüssigkeit auf die Bohrlochstabilität in geklüfteten Gebirgsformationen. Eine Voraussetzung für numerische Modelle ist die Fähigkeit den Bereich der Infiltration der Stützflüssigkeit zu prognostizieren. Diese Publikation beschreibt ein numerisches Verfahren, um die Reichweite der Infiltration von Stützflüssigkeiten mittels fluid-mechanisch gekoppelter Simulationen im engständig geklüfteten Gebirge mit dem Programm UDEC zu modellieren. Verschiedene Faktoren, wie Kluftmuster, Gebirgsspannungszustand, Reduktion von Kluftreibungswinkel- und kohäsion, Viskosität der Stützflüssigkeit und Rissabdichtung wurden untersucht. Ergebnisse numerischer Simulationen werden präsentiert, um die Vorgehensweise zu illu

Jan 1, 2003

By Willem Le Roux

1.1 Section 47(1) of the Mine Health and Safety Act, 29 of 1996 (?the MHSA?) establishes a Mine Health and Safety Inspectorate which is administered by the Chief Inspector of Mines. The Mine Health and Safety Inspectorate is part of the Department of Mineral Resources. The Chief Inspector is appointed by the Minister of Mineral Resources (see section 48(1) of the MHSA). 1.2 The Chief Inspector must, amongst other things, ensure that the provisions of the MHSA are complied with and enforced, and that all the duties imposed upon the Chief Inspector and the other Inspectors of Mines in terms of the MHSA and any other law are performed. The Chief Inspector of Mines must appoint Principal Inspectors of Mines and Inspectors of Mines to assist him/her to discharge his/her duties (see section 49(1)(a) and (c) of the MHSA).

Jan 1, 2011

Phase equilibria have been determined experimentally for pseudo-ternary sections of the form ?MnO?-(CaO+MgO)-(SiO2+Al2O3) with a fixed Al2O3/SiO2 weight ratio of 0.17 and MgO/CaO weight ratios of 0.25 and 0.17 respectively for temperatures in the range 1473-1673 K. The primary phase fields present for the MgO/CaO weight ratio of 0.17 include manganosite (Mn,Mg,Ca)O; dicalcium silicate a-2(Ca,Mg,Mn)O?SiO2; merwinite 3CaO·(Mg,Mn)O·2SiO2; wollastonite [(Ca,Mg,Mn)O?SiO2]; diopside [(CaO,MgO,MnO,Al2O3)?SiO2]; tridymite (SiO2); tephroite [2(Mn,Mg)O?SiO2]; rhodonite [(Mn,Mg)O?SiO2] and melilite [2CaO?(MgO,MnO,Al2O3)?2(SiO2,Al2O3)]. For the section with MgO/CaO weight ratio of 0.25 the anorthite phase (CaO·Al2O3·2SiO2) is also present. The liquidus temperatures of ferro- and silico-manganese smelting slags have been determined. The liquidus temperatures at low MnO concentrations are shown to be principally dependent on the modified basicity weight ratio (CaO+MgO)/(SiO2+Al2O3).

Jan 1, 2004

The November General Meeting of the Branch was held at the S1. Helena Club on Friday, 15th November, 1968. Mr. J. G. Kirchner (Chairman of the O.F.S. Branch) was in the chair. There were also present: President: Mr R. C. J. Goode. Eighteen Members: Mr A. E. Gilfillan (Council Member), Messrs T. Zadkin, J. N. Saunders, N. A. Honnet, D. D. Waterman, C. R. Netscher, (Committee Members), Messrs G. Thorburn, Z. Lombard, H. V. Henwood, C. J. Isaac, S. L. S. Swart, J. D. McNamara, H. H. Schellhorn, J. W. Wilson, G. C. P. Labuschagne, L. J. Thorne, R. C. Espley-Jones, J. Handley. Seventeen Associate Members: Messrs H. J. Reeders, R. Campbell, P. A. Hoffman, D. E. Couperthwaite, M. D. de Lange, G. J. C. Young, G. W. Futcher, U. Visser, F. H. De Groot, E. Schmid, K. G. Pearce, D. A. Viljoen, H. W. M. Eschenburg, R. Still, W. B. Howe, A. H. Edwards, R. H. Drake. Three Graduates: Messrs T. R. Stromsoe, J. G. Cockburn, T. A. Ward. One Affiliate: Mr O. A. Huss. Twenty-three visitors. Total present: 64. Apologies were reseived from Messrs L. O. W. Leimer, V. C. Barnes and A. Louw. WELCOME TO VISITORS The Chairman declared the meeting open and extended a special welcome to the following: Mr R. C. J. Goode, President of the S.A. Institute of Mining and Metallurgy; Mr A. E. Gilfillan, Member of Council and Mr D. A. Viljoen, all from Johannesburg. Also to Mr J. D. McNamara, the guest speaker for the evening who had made the trip from Oranjekrag. MINUTES OF PREVIOUS GENERAL MEETINGS The minutes of two meetings, viz., the General Meeting held on 26th June, 1968 together with those of the Annual General Meeting held on 14th August, 1968 were taken as read and their adoption moved by Messrs T. Zadkin and D. D. Waterman. MATTERS ARISING FROM THE MINUTES There were no matters arising from the minutes. ADDRESS BY PRESIDENT OF COUNCIL, MR R. C. J. GOODE With regard to the 75th Anniversary of the Institute, the President called upon those present to bear the following two dates in mind, viz.: 21st March, 1969-Banquet at the Wanderers' Club, to which ladies are invited. 24th March, 1969-General Meeting at Kelvin House at 9.30 a.m., the speakers being the President of the Institute, the President of the Chamber of Mines and Dr H. J. van Eck.

By M. M. Makhofane

Anhydrous zirconium tetrafluoride can be used as a precursor for the manufacturing of nuclear-grade zirconium metal. This can be done by fluorinating plasma-dissociated zircon with ammonium bifluoride in a batch reactor. This paper describes the batch process. It was proved that anhydrous zirconium tetrafluoride can be manufactured by this route as confirmed by X-ray diffraction. The process shows potential for scaling up to the kilogram scale and possibly the tonnage scale.

Jan 1, 2012

By H. S. Sichel

"The valuation of diamond ferous deposits depends on (i) the density distribution, (ii) the size distribution of stones and (iii) the selling price structure prevailing at a particular time.In the density distribution the stochastic variable is defined as the Dumber of individual stones found per sample unit irrespective of the stone size. The density distribution is discrete and allows for barren sample units.As diamonds often occur in clusters, a Poisson mixture distribution is derived which is entirely new, as existing discrete distributions cannot represent the stone number frequencies found in nature.For the sizes of diamonds, which are measured by weight, a new compound logarithmic normal distribution is developed.Combination of (i), (H) and (iii) leads to a meaningful appraisal of diamond ferous ground expressed in monetary value per production unit of mining.Finally, confidence limits are calculated which allow for inference from sampling to recovery."

Jan 1, 2014