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By J. H. Schubert

Mintek has developed a level-control system, FloatStar, for use in flotation circuits. Instead of controlling levels separately in each unit, the controller monitors levels throughout the circuit. It can thus take account of the global effects of any control actions. A collaborative project between Mintek and Karee Platinum Mine has begun, looking at aspects of flotation control. Karee plant was chosen as the site for this work because of its good existing control infrastructure. As a first stage of the joint project FloatStar was installed. Analysis during installation and running of the FloatStar has illustrated how circuit design and measurement technology can affect process control. Severe interactions have been observed in the levels of adjacent banks. The effect of FloatStar on flotation performance was tested and an improvement in level control was observed. Similarly, a faster settling of the plant after start-ups was observed. Both the improved level control and faster start-ups lead to higher platinum recovery.

Jan 1, 1999

By J. C. M. De Souza

The Samarco pipeline, the longest in the world for iron ore slurry transportation, started operation in 1977 to transport concentrate from the Germano facilities, in the state of Minas Gerais, to the pelletizing plant, located 396 km away, in the state of Espirito Santo, on the south-east coast of Brazil. Designed for a nominal capacity of 12 million tons per year, the pipeline reached 15.5 million/year due to operational improvement and, in late 2005, it was resized to transport 16.5 million tons per year, with the installation of a booster station. In order to ensure the accurate performance of the system, a pipeline cleaning programme was carried out and, since it has been 29 years from the operation start-up, precise knowledge of the pipe condition would be fundamental to guarantee the success of the project. The cleaning programme demonstrated the potential of operational gains from this initiative, and its effect on the corrosion control and future measures, which should be permanently adopted to maintain the improved capacity. The intelligent pig runs provided essential data used to establish a pipeline integrity programme that allowed Samarco to develop a pipe repair plan based on the severity and significance of the features and to implement a future pipe replacement plan.

Jan 1, 2007

The above paper is an important contribution to the field of physicochemical studies in ferromanganese production. The authors are to be congratulated on the well planned and competently executed experimental work and on the interpretation of the data. Although the paper is essentially descriptive, the results lend themselves to thermodynamic interpretation (but in such a complex system as that studied this cannot be done rigorously), as well as to an examination of the probable reduction mechanisms that operate at various stages.

Jan 1, 1979

By P. N. Lategan

Mining companies are challenged with increased difficulty in delivering capital projects on schedule and within budget. In 2005, PricewaterhouseCoopers global review of major capital projects in the mining industry only 2.5% of projects could be defined as successful when assessed across the four critical dimensions of scope, cost, schedule and business benefits. Thus 97.5% of major mining capital projects were not successful according to the criteria PricewaterhouseCoopers used. Normally if a project fails on all these criteria it indicates scope creep. Scope creep refers to the change in a project's scope after the project work has started. As a result, the projects drift away from their original design, timeline, and budget, and as a consequence destroy business benefits. The major reasons for scope creep are poor change control and the lack of proper front end loading. Change control and front end loading are based on project processes in the planning and monitoring & control process group of the Project Management Body of Knowledge1 (PMBOK). This paper will focus on key factors to consider during project scheduling/planning with special reference to cost and schedule (using Microsoft Project as a tool although the principal is universal)

Jan 1, 2009

By P. N. Lategan

Mining companies are challenged with increased difficulty in delivering capital projects on schedule and within budget. In 2005, PricewaterhouseCoopers global review of major capital projects in the mining industry only 2.5% of projects could be defined as successful when assessed across the four critical dimensions of scope, cost, schedule and business benefits. Thus 97.5% of major mining capital projects were not successful according to the criteria PricewaterhouseCoopers used. Normally if a project fails on all these criteria it indicates scope creep. Scope creep refers to the change in a project's scope after the project work has started. As a result, the projects drift away from their original design, timeline, and budget, and as a consequence destroy business benefits. The major reasons for scope creep are poor change control and the lack of proper front end loading. Change control and front end loading are based on project processes in the planning and monitoring & control process group of the Project Management Body of Knowledge1 (PMBOK). This paper will focus on key factors to consider during project scheduling/planning with special reference to cost and schedule (using Microsoft Project as a tool although the principal is universal)

Jan 1, 2009

By S. P. Pereira

The mechanized mining cycle using loaders and shuttle cars had its peak in terms of usage in the mining industry during 1950 through 1960. In Brazil, this system is still used at underground coal mines in southern Santa Catarina coal basin. With the aim of investigating the benefits of a new mining scheme using the room and pillar method for these local mines, a computational simulator model was developed in order to investigate the mining cycle. This paper presents the methodology used to develop the simulator and the results that the simulation shows regarding impact of the proposed new scheme on mining productivity.

Jan 1, 2012

By S. P. Pereira

The mechanized mining cycle using loaders and shuttle cars had it speak in terms of usage in the mining industry during 1950 through 1960. In Brazil, this system is still used at underground coal mines in southern Santa Catarina coal basin. With the aim of investigating the benefits of a new mining scheme using the room and pillar method for these local mines, a computational simulator model was developed in order to investigate the mining cycle. This paper presents the methodology used to develop the simulator and the results that the simulation shows regarding impact of the proposed new scheme on mining productivity.

Jan 1, 2012

By C. A. Rawlins

Deep underground mines use refrigeration systems to provide a reasonably comfortable ambient environment to increase productivity and to maintain safety as a priority. Deep level gold mines maintain the environment at an acceptable temperature, i.e. 27°C. However, the increasing cost of doing so through refrigeration is becoming a significant factor in the economic viability of mines. This paper discusses of the important facet of energy losses in cooling reticulation systems, laying with the specific emphasis on the subject of chilled water transport pipe insulation and its thermo-dynamic relationships. Aspects relating to the deterioration of open cell-type insulation materials such as polyurethane/styrene foams and the use of Phenolic resins that have good fire retardation properties have been investigated. The thermal conductivities of these insulation media are good (meaning below 0.05 W/°C)However, they are known to be negatively influenced by water vapour ingress and vapour pressure differences that result in the ingress of water into the material by means of absorption, condensation, hygrospicity, permeability and capillary action, to name a few of many. The overall effect on mine cooling efficiency takes in the two forms: first by the loss of refrigeration or increased chill in the water temperature arriving in a given section and second, by a loss in transfer efficiency when the gap between the arriving water temperature and the actual air temperature decreases. Keywords: Conductivity, vapour, insulation, fluid, thermal, temperature, pressure, transport, refrigeration.

Jan 1, 2007

The October General Meeting of the Institute was held in Kelvin House, Johannesburg, on Wednesday, 21st October, 1970, at 4.30 p.m. V. C. Robinson (President) was in the chair. There were also present 25 Fellows, including J. K. E. Douglas, Prof D. D. Howat, D. G. Maxwell, Dr R. E. Robinson, P. A. von Wielligh (Council Members). D. Ayres, G. Burrow, E. H. D. Carman, D. L. Carson, M. E. E. Douglas, S. A. Finney, W. R. Flook, A. J. Freemantle, W. A. Gilbert, E. B. Gordon, B. W. Gray, J. M. Jacobs, P. H. Kitto, C. H. Kruger, Dr P. J. D. Lloyd, D. G. Malan, W. Pilkington, W. G. Pyne-Mercier, K. S. Rae, W. T. Ruhmer, D. J. Tutt and D. T. Watt. Seven Members, including E. J. Dominy, S. I. du Preez, L. V. Grobler, D. R. Lings, G. D. Louw, J. S. A. Oelofse and O. B. Prentis. Fifteen Visitors, including J. R. Coppin, Dr A. Faure, P. E. Franzl, G. P. Hart, D. van Heerden, A. W. Hunt, A. R. F. MacDonald, B. G. Meyburgh, P. H. Radcliffe, J. M. Shirley, T. H. Tunley, A. D. Vellema and R. E. Wheeler. Secretary, D. C. Visser. Total present: 49. OBITUARIES The President: "It is my sad duty to announce the death of the following: Sir George Arthur Davenport, Honorary Life Fellow, who joined the Institute in 1930 and passed away on 17th September, 1970. The late Sir George was also, for many years, our corresponding member for Rhodesia. Andrew Malcolm Carmichael, Associate, who joined the Institute in 1944 and passed away on 22nd August, 1970. Cyril John Douglas Veal, Life Fellow, who joined the Institute in 1929 and passed away on 27th August, 1970. As a mark of respect to the memory of the deceased and in sympathy with the bereaved I would ask you all to rise and observe a few moments' silence." CONFIRMATION OF MINUTES The President: "May we confirm the minutes of the Annual General Meeting held on 26th August, 1970, and the minutes of the monthly general meetings which were held on the 20th of May and the 17th of June, 1970, as published in the August Journal." Agreed. 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: Members: Nikolaos Lalakakis, Gordon Phillips Rundle. Associates: Henry du Preez, James Robert Forbes, Johannes Stephanus Albertus Oelofse, Casper Vorster van Heerden. Graduates: Michael Harold Crosbie, Graham Robert Wallis Walker, Gary Walker Braithwaite. Students: Mohammad Ali Kazemzadeh, Gerhardus Petrus Benade. APPLICATIONS FOR TRANSFER From Graduate to Member: James Wormald. From Student to Graduate: Peter John Cook, Pieter Willem Greeff. "I welcome the newly elected members to the Institute and congratulate the members who have been transferred to a higher grade." PAPER FOR PRESENTATION The President: "This paper is entitled 'The Design, Erection and Operation of a Purlex Plant at Buffelsfontein Gold Mining Company Limited'. It is presented to the Institute by Mr B. G. Meyburgh, a visitor to our Institute. He is a graduate of the University of the Orange Free State and is the Uranium Plant Superintendent at Buffelsfontein and he, therefore, is in a very strong position to describe this very excellent job which is being done as he has been associated with this plant from the inception." After the presentation of the paper the President said: "Gentlemen, the paper you've heard from Mr Meyburgh is a very concise and interesting account of an important piece of work, and I think the title is so completely descriptive of the subject, which is admirably set out in the paper which you have heard. You probably haven't all had the opportunity of reading it, but you very soon will. I found it interesting to note that the results predicted were surpassed in the operation of the plant to date. The actual results obtained are significantly good, I think. Any process which, in this country, increases production and decreases costs, is to be welcomed, particularly when it is so necessary for South Africa almost to bend over backwards to utilise every avenue available in order to increase the scope of the production for overseas' markets, of her metallurgical and mineral potential. In lighter vein-and there is no reason why we should always be so serious-I am glad to see that, in a scientific journal like this, such words as the American word 'crud' which I have been picked out about so often, because my grandchildren use it, is now given an aura of respectability. Thank you very much, Mr Meyburgh, for an interesting paper. We have a long list of contributors, and I am not going to waste any more time. I am going to call on Mr Tunley of the N.I.M. for the first contribution." T. H. Tunley, P. de Bruyn (read by A. D. Vellema), E. J. Dominy, E. H. D. Carman, A. R. F. MacDonald D. C. Streicher (read by P. H. Radcliff), Dr A. Faure and Dr P. J. D. Lloyd then contributed to the discussion. (This discussion will appear in a later issue of the Journal.) The President: "I wish to thank members and visitors for their attendance, and now declare the meeting closed." The meeting closed at 6.05 p.m.

By K. Sasaki, Y. Oriia, Shigeto Kuroiwa, H. Miki, Yuji Aoki, T. Hirajima, G. P. W. Suyantara

The effect of a sulfite reagent on the floatability of chalcopyrite and enargite was investigated in this paper. The flotation tests using single and mixed minerals were performed under various concentrations of sulfite. The flotation tests using a single mineral showed that the sulfite reagent depressed the natural floatability of both minerals at pH 9. Surprisingly, enargite was floated after the addition of potassium amyl xanthate (PAX) following the sulfite treatment, and the floatability of chalcopyrite depressed under a similar condition. X-ray photoelectron spectroscopy analysis results showed that the sulfate species increased after the sulfite treatment on both minerals. However, the addition of PAX removed this sulfate species and rendered the enargite surface hydrophobic. This phenomenon was not observed on the chalcopyrite surface. FTIR analysis and PAX adsorption studies were performed to support this finding. The flotation of a mixed mineral was in agreement with the flotation of a single mineral, indicating a possibility for selective flotation of chalcopyrite and enargite using the proposed method. Keywords: Flotation, chalcopyrite, enargite, sulfite, potassium amyl xanthate

Jan 1, 2020

This paper reports on recent field observations on the performance of support systems under different corrosion environments in Canadian underground mines. Phenomenological data are used to gain a better understanding of the main causes of corrosion in underground metal mines. Preliminary field data collected from five metal mines have been complemented by atmospheric and water sample analysis as well as fractography and metallographic studies. This has identified dominant factors that control the corrosion of support systems. The data are analysed in order to develop a support strategy for mines operating in corrosion environments.

Jan 1, 2008

By M. Dworzanowski

The physical beneficiation of iron ore that has a wide particle-size distribution is problematic, regardless of the process applied, whether dense medium separation, gravity concentration, magnetic separation, or flotation. The problem of particle size is further compounded when there is a significant -10 µm fraction. Generally the approach to a wide particle-size distribution is to split into narrower size ranges and treat each separately. More often than not the -10 µm fraction is not treated but discarded. This approach results in a more complicated and expensive flow sheet and the loss of any potential value in the -10 µm fraction. Wet high-intensity magnetic separation (WHIMS) bench-scale test work was conducted on a haematite-rich material with a particle size of -200 µm. What made this material different was that it contained a 60% -10 µm fraction, hence discarding the -10 µm material was not an option. The objective of the test work was to determine how to maximize the recovery of the haematite across the full particle size range. Given the unusual particle size distribution, it was concluded that WHIMS would be the only practical beneficiation route. The -200 +10 µm and -10 µm fractions were treated separately and together under varying WHIMS conditions. For a given concentrate grade, the mass yield obtained was greater when the total particle-size distribution was treated. The inferred optimum conditions, using the same material, were tested on a pilot-scale WHIMS and similar results were obtained.

Jan 1, 2014

Milling circuits are known to be difficult to control. In order to address these difficulties, it was decided to develop and test a model predictive controller (MPC) for a milling circuit. A milling simulator was written using Microsoft Visual C++ and used to design and test the MPC controller. Due to the large number of tuning parameters in a controller of this type, an optimizing algorithm was written that automatically tunes the controller. Good, robust control was obtained when the controller was tuned using this algorithm. Control was further improved by combining feedback and feed forward control and by using quadratic programming in the MPC algorithm. The movement of the manipulated variables was reduced by using a novel technique that allows the controlled variable to vary within a specified region around the set point. An optimiser controller was also successfully implemented to control the circuit at its maximum throughput.

Jan 1, 2000

A banquet, attended by 467 members and visitors, was held at the Wanderers Club, Johannesburg, at 8 p.m. on Friday, 21st March, 1969, to celebrate the 75th Anniversary of the founding of the Institute. Introduction of Dr Carel de Wet R. C. J. Goode (President) Dames en here: Ons het 'n aantal vooraanstaande gaste in ons midde vanaand en mnr Maxwell sal u later meer van hulle vertel. Dit is my aangename plig om u voor te stel aan sy Edele, die Minister van Mynwese, van Beplanning, en van Gesondheid, Dr de Wet en sy gade, mev de Wet. Sy Edele Dr de Wet het geen bekendstelling nodig nie-alhoewel hy ons minister vir slegs die afgelope twee jaar is, het hy reeds talle funksies van ons Mynbedryf bygewoon en het baie vriende gemaak onder ons. Hy het homself baie bemind onder ons gemaak toe hy Wes-Driefontein onlangs besoek het om hulle ondersteuning en aanmoediging aan te bied in hulle uur van nood. The Honourable Dr de Wet was born in the Free State. He is a grandson of that very famous general Christiaan de Wet, who caused so much pain to the British forces and for so many months so successfully eluded them in the Transvaal and Orange Free State. He was educated at both the Pretoria and Witwatersrand Universities. He first practised medicine at Boksburg and then moved to Vanderbijlpark, so you see he has an early association with gold mining on the Witwatersrand, and in moving to the Vereeniging-Vanderbijlpark district he became closely involved in our coal mining and metallurgical industries. South Africa's first steel was poured from a l0-ton open hearth furnace belonging to the Union Steel Corporation in Vereeniging in 1913. Dr de Wet has been mayor of Vanderbijlpark and for several years has been their member of parliament. More recently, the Honourable Dr de Wet has filled with great honour that most important office of Ambassador for the Republic of South Africa in London. At present he wears two hats, in that he is Minister of Planning and of Health, but more important is his cloak, that of Minister of Mines, which I trust offers him the greatest comfort. To fulfill these three arduous tasks must demand of him a terrific devotion to duty, and in doing this he carries on that loyal tradition of service to his fatherland so evident in his grandfather. Dames en here, dit is vir my 'n groot genoeë om Sy Edele Dr de Wette vra om 'n heildronk in te stel op die Instituut vir Mynwese en Metallurgie. Toast to the Institute of Mining and Metallurgy Dr the Honourable C. de Wet (Minister of Mines): Mr President, ladies and gentlemen, Mr President you have introduced me gracefully to this distinguished company and I am appreciative of your remarks. I am fully conscious of the responsibilities that devolve upon me as Minister of Mines in a country where mining makes so vital a contribution to economic progress and development and has, in fact, laid much of the foundation on which our present proud edifice is built. The achievements of the mining and metallurgical industry in its diversified activities arouse feelings equivalent to paternal pride, but let me speedily add that in considering any family relationship that may exist, the Minister of Mines should not be regarded in the role either of a fairy godmother or an indulgent father.

By D. Harbottle, D. Rhodes, T. F. Jones, S. R. Biggs

Multiphase process design and optimization often depends upon the rheological properties of sludges and slurries. In practice the task of determining these important properties is usually carried out by removing small samples from a process line or process unit and performing tests with proprietary bench-top analysers near to site or at a remote laboratory. Sampling will remain an important procedure in industrial processes, but there is also a strong case for augmenting the routine information obtained using an in situ sensor, as suggested below. ?Sampling protocols can result in extensive turnaround periods from sample collection to the generation of results. The delay can have an effect on a variety of factors such as product quality, process operability and efficiency. ?Sampling of toxic or radioactive material can prove an even greater challenge to minimize human involvement. ?Removal often changes the rheology of a specimen, and might lead to incorrect conclusions being drawn about the condition of a sludge. ?Sludge and slurry in a containment suffers a gravitational gradient, so that a removed sample should be paired with its location, particularly in the vertical dimension.

Jan 1, 2007

Common practice in mineral resource estimation consists of partitioning the orebody into several domains defined by grade intervals, prior to the geostatistical modelling and estimation/simulation at unsampled locations. This paper shows the pitfalls of grade domaining through a case study in which we compare the performance of several estimation schemes and demonstrate that the use of domains defined by grade cut-offs implies a deterioration of the resource estimates, mainly in what refers to precision and conditional bias. Then, several conceptual limitations of the grade domaining approach are stressed, in particular the fact that it does not account for the spatial dependency between adjacent domains and for the uncertainty in the domain boundaries. Also, this approach is shown to be sensitive to the cut-offs that define the domains, to provoke artifacts in the kriging maps, histograms and scatter grams between true and estimated grades, and to lower the kriging variance, a feature that may impact the mineral resource classification. An alternative approach is finally proposed to overcome these limitations, based on a stochastic modelling of the grade domains and a co-kriging of the grades using information from all the domains. Keywords: geostatistics, kriging, conditional bias, geological control, grade zoning.

Jan 1, 2005

By A. Chuma, K. J. Nyembwe, H. Simonsen, J. H. Potgieter

Different concentration techniques were evaluated for preconcentration of a mineral ore at a coarser size to avoid energy and resource wastage. Specifically, the aim was to reduce milling costs and energy required in the beneficiation of tin. In this study, cassiterite (0.17% Sn) was the mineral of interest in a pegmatite ore body associated with quartz (SiO₂ > 60%) and alumina (Al₂O3 > 20%). Three concentration techniques, namely dense media, shaking table, and flotation, coupled with characterization analysis, were used to assess the concentration response. The results confirmed that particle size and mineral liberation impact the separation process. High recovery and grade were obtained with gravity concentration methods (dense media and shaking table) for coarser (+300 to +212 μm) and intermediate (+150 to +53 μm) particle sizes. Lower recovery and grade were identified for much finer sizes (−53 to −38 μm). Flotation produced a high-grade product at a relatively low recovery and appeared to be only applicable to finer grains. Separation efficiency based on Schulz’s equation measured a segregation performance of 74.8% for dense medium separation and 60.7% for the shaking table for the coarse and intermediate particle sizes. Flotation only achieved a separation of 30%–40%. The results suggest that use of dense media separation as a rough preconcentration method prior to further grinding, and the utilization of a more advanced concentration technique for mineral recovery and upgrade, constitute a successful approach to improve process economics.

Apr 14, 2024

By M. J. Sapko

The Pittsburgh Research Laboratory (PRL) of the National Institute for Occupational Safety and Health (NIOSH) recently conducted full-scale explosion experiments; these experiments evaluated the strength characteristics of various seal designs used for safely isolating worked-out areas in underground coal mines. Large-scale explosion tests were conducted within the multiple entry section of PRL's Lake Lynn Experimental Mine (LLEM) employing the only currently accepted test method endorsed by the Mine Safety and Health Administration (MSHA) for seal design in American mines. These explosion tests are labor-intensive, expensive to conduct, and can interfere with other critical underground safety and health research programs conducted by NIOSH. Therefore, the PRL has developed an alternative seal evaluation method, based on a hydrostatic pressure loading concept, that can facilitate the in-situ testing of seals in an operating mine. Two chambers within LLEM and one within the Safety Research Coal Mine (SRCM) were used for hydrostatic pressure loading various seal designs. The results from tests in these chambers compare favorably with those from the large-scale explosion tests in the multiple entries. Preliminary size-scaling relationships for predicting the strength of standard seal designs as a function of entry size is also presented. In addition to testing seal designs at the required 20 psi static pressure level, the new facilities also allow for the determination of the seal's ultimate failure pressure. This new approach shows promise as an alternative evaluation method for improving mine sealing technologies which, in turn, will enhance the safety of the underground personnel.

Jan 1, 2003

The theory of geostatistics covers a branch of .applied statistics aimed at a mathematical description and analysis of geological observations. Geostatistics can be used in pure geology (for example, for the analysis of trace elements in a metamorphic rock), in mineral exploration (for example, for the analysis of geochemical exploration data), as well as in mine valuation. This book is intended to provide a practical introduction to the theory of geostatistical methods of mineral evaluation. Over the years, various mathematical models have been developed to represent the distribution of values in mineral deposits. The simpler models are based on the assumption that the values are randomly distributed. Classical statistical methods, based on this assumption of the random distribution of values, are used to analyse mineral deposits to which these models apply or are assumed to apply. In all mineral deposits, however, one recognizes the presence of areas where the values are higher or lower than elsewhere. Also, the values of two samples in a mineral deposit are more likely to be similar if the samples are taken close together than if they are taken far apart. This indicates that there exists a degree of correlation between sample values, and that this correlation is a function of the distance between the samples. Models have been developed which take this correlation into consideration, with the degree of correlation between sample values being usually measured by the semivariogram function. In these models the fact that two samples taken next to each other will most probably not have the same value, must also be considered; even for very short distances the correlations are usually not perfect and a purely random component is present in the value distribution. The mathematical models will therefore assume the presence of two sources of variability in the values: a correlated component and a random component. Finally, one must consider the particular and very common case of mineral deposits in which the values present a systematic variation in space. This variation is usually referred to as a drift, or a trend. For example, the grade of an ore body may increase with depth of the ore, or it may decrease when one moves away from a central volcanic pipe. The earlier models did not give a satisfactory representation of drifts, and more complex models have been developed, in which three sources of variation are represented. These models are made up of: a deterministic component, a correlated component, and a random component. The deterministic component is used as a model of the drift. The correlated component explains regular changes in values which are not represented by the drift. The random component represents variations which cannot be explained by any of the above factors. The simpler models, based on the assumption of a single random component, will be described first (Chapter 2). The models based on the hypothesis of the superimposition of a correlated component on a random component, will then be analysed in detail. These models are most commonly used in the analysis of mineral deposits (Chapters 3-1 I). Finally, how to deal with the presence of a drift will be briefly described (Chapter 12). This book has been written essentially for students in mining engineering and for mining engineers who are interested in the background to the theory of geostatistics as well as its practical applications. The assumption is made that the reader has an elementary knowledge of statistics. Some knowledge of linear algebra is useful in part of Chapter 9, and is necessary to read Chapter 12. A proof is given of all the equations related to geostatistics, and which are not usually found in elementary textbooks on statistics. Understanding of these proofs is not necessary for practical application of the theory, and the reader may wish to skip them on a first reading, concentrating attention on the numerous simple practical examples given. Although the theoretical geostatistician will not find much new material in this publication, it is anticipated that he will develop some interest in the practical approach chosen to prove the various geostatistical equations. Many people and institutions contributed to the preparation and completion of this work. I am much indebted to Dr D. G. Krige and the Anglo Transvaal Consolidated In- vestment Company Limited, who gave me the opportunity to spend a considerable amount of time working on geostatistical problems, both theoretical and practical, during the time that I was in their employment. Dr Krige contributed greatly in developing my interest in studying both the theory and practice of geostatistics, always insisting that a correct balance be kept between theory and practice. I am grateful to Professor H. M. Wells and the Mining Department of the University of the Witwatersrand for inviting me to give lectures in a post- graduate course on geostatistics. The notes 1 prepared for that course became the foundation of the present work. I am also indebted to the Centre de Geostatistique of the École des Mines de Paris, where I received my first formal education in geostatistics during a summer course given by Charles Huijbregts, after many years of my lonely plodding through the published literature. Many graphs in the present volume are reproduced with the permission of the Centre de Geostatistique. The Department of Metallurgical and Mineral Engineering of the University of Wisconsin-Madison has also contributed in making this work possible, by allowing me to spend a considerable amount of time and resources in the writing, typing, and correcting of successive drafts. I am thankful to Lynn D. Kendall, who typed the entire manuscript under constant pressure.

Jan 1, 1978

By Hornsey R., P. van der Merwe

The Two Rivers Project is a feasibility study to evaluate the UG2 chromitite layer on Dwarsrivier372KT, Mpumalanga Province, South Africa. The project, which commenced in August 2001, is expected to receive go-ahead early in 2003. The project sponsors (AVMIN 55%, Implats 45%)required project delivery within a short timeframe requiring optimization of the geological and geostatistical programme. Geological modelling was carried out in parallel to the drilling programme, and significant up-front geostatistical preparatory work was done. The time saving was approximately 4 – 6 months on project delivery. The cost saving to the project (excluding NPV considerations) is estimated at R20–30 million. Keywords; Two Rivers Platinum, Dwarsrivier 372KT, UG2 chromitite layer.

Jan 1, 2003