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[The following notations will be used: O an ore body. W a sample of size w located in O; the size of this sample. W a block or a sample, of size W, located in O; the size of this block or sample. z' a point in W. W' a block or a sample, of size W' greater than or equal to W, located in O; the size of this block or sample. z" a point in W'. y (h) point semivariogram in O. s (h) point covariogram in O. In the previous chapter, we saw that the point semivariogram y (h) usually cannot be estimated directly from the data available. Rather, the values of samples of size w are available in O, and from these a regularized semivariogram y w (h) can be estimated. The following relationship has been proved (5.8): Y w(h) = Y (w;w+h) - Y (w;w). y (w;w+h) is the average value of y (z' z") when z' takes all possible positions in a sample w and z" all possible positions in a sample w+h of the same size, h being the distance between w and w+h. y (w;w) is the value of y (w;w+h) for h = 0, i.e. the average value of y (z' z") when z' and z" take all possible positions in w. We also saw that the regularized covariogram aw(h) is related to the point covariogram a (h) as follows (5.9): w(h) Gr In the following chapters, it will be shown that calculation of the average value y of y, or -a of a, in the general case relating to samples or blocks W and W' which need not be of the same size, plays a very important part in all the practical applications of geostatistical theory. The purpose of this chapter is to introduce various methods of calculating y and a-. Furthermore, mathematical equations and graphs are provided which can be used when the point semivariogram can be represented by one of the more common equations, and when the blocks W and W' are of simple shape. By definition (Fig. 6.1): [ ] Y (W;W) = WW f dz' f y (z' z") dz" (6.1) in W z" in W']

Jan 1, 1978

By A. Vogelzang

The paper describes how the level of the water-table was reduced as a result of increased pumping of water from the mine. Because such a condition in an area where there is compactable material above solid dolomite results In surface movement, steps were taken to restore the water-table to its former level. These included the return of water underground via a sinkhole and boreholes, and the piping of water from another mine.

Jan 1, 1978

By J. Meintjes

The measures taken by Rand Carbide Limited from the 1950s to 1976 to control dust emission from the electric furnaces at its Witbank factory are described. A new design of furnace for calcium carbide followed by a dry-fabric filtration plant for the furnace gases was not successful in arresting the dust. A 131 m chimney commissioned in 1968 effectively dispersed the dust-laden gases from both carbide and ferrosilicon production and so brought considerable alleviation. In 1974 a bag-filter dust-collecting plant was successfully commissioned on a 6 MV.A carbide furnace, and this was followed in 1976 by a bag-filter plant on a 46,5 MV.A ferrosilicon furnace. The company has spent considerable effort and money over two decades in trying to combat dust emission, but eventual success had to await technological development.

Jan 1, 1978

Council and Standing Committees, 1976-1977 President: Dr M. D. G. Salamon. Vice-Presidents: P. A. von Wielligh and Dr M. G. Atmore. Honorary Treasurer: J. K. E. Douglas. Immediate Past President: Dr R. E. Robinson. Members of Council: J. D. Austin, E. Collier, C. T. Fenton, J. A. Holmes, Dr P. R. Jochens, Prof. R. P. King, Dr D. G. Krige, Prof. F. Q. P. Leiding, D. G. Malan, C. T. Shaw, D. A. Viljoen, R. A. von Maltitz. Chairman, Witbank-Middelburg Branch: E. J. Jackson. Chairman, Orange Free StatelKlerksdorp Branch: A. N. Shand. B. Past Presidents Serving on Council: R. J. Adamson, H. Britten, J. K. E. Douglas, R. C. J. Goode, Prof. D. D. Howat, Dr J. P. Hugo, D. G. Maxwell, Prof. R. P. Plewman, V. C. Robinson, P. W. J. van Rensburg. Ten Council meetings were held during the year, and the standing and sub-committees held seventy-one meetings. Standing Committee Chairmen: Membership, Dr M. G. Atmore; Technical Programme - Metallurgy, J. A. Holmes ; Technical Programme - Mining, C. T. Shaw; Vacation School - Metallurgy, Prof. R. P. King ; Vacation School - Mining, Dr D. G. Krige ; Awards, Dr R. E. Robinson; Excursions, C. T. Fenton; Adjudi¬cation, Dr R. E. Robinson; Constitution, Rules and Policy, Dr R. E. Robinson; Mines and Works, C. T. Shaw; Education, Dr R. E. Robinson; Pyrometallurgical Discussion Group (Convenor), Dr J. B. See; Phoenix National Committee, Dr R. E. Robinson.

Jan 1, 1978

By D. W. Boydell, E. B. Viljoen

A flowsheet incorporating rotary-drum filtration for the solid-liquid separation step, followed by solvent extraction for uranium purification, is used as a standard against which four flowsheets are compared. These flowsheets employ either counter current decantation or belt filtration for solid-liquid separation, and either solvent extraction or continuous ion exchange plus solvent extraction for the purification step. Sales revenue, taxation, capital expenditure, and operating costs are estimated. These factors are taken into account in the calculation of an incremental net present value for each circuit by the discounting of cash flows at 25 per cent per year over a projected life of 15 years. For the material used in these examples, the highest net present value results from the circuit that employs belt filtration followed by continuous ion exchange and solvent extraction.

Jan 1, 1978

By E. Barnea

This paper simplifies and provides a strict mathematical proof for an equation developed by R. J. Woody for the c alculation of solute recoveries in countercurrent decantation. The equation offers a convenient method for the optimization of flowsheets involving a simple countercurrent-decantation circuit.

Jan 1, 1978

By R. G. Jurd

This paper considers the introduction of large-scale longwall mining into South African coal mining, instead of the conventional mechanized bord-and-plllar mining that is widely practised at present. The two methods are compared, and longwall mining is found to have the advantage in several respects in some seams. The most cogent reasons for the introduction of the longwall method In some seams are associated with safety strata control and increased labour costs.

Jan 1, 1978

By M. E. E. Douglas, A. K. Haines, D. I. Nicol, C. M. Olëm, W. M. Craig, G. D. Louw

A description is given of the design of the continuous ion-exchange demonstration plant at Blyvooruitzicht Gold Mine, including details of the process design, the column construction, and the control system. The operating and process results gathered over a period of seventeen months are summarized, and development work and modifications to the process are discussed. It is concluded that the system comprising continuous loading and continuous elution is technically feasible and can be scaled up with confidence.

Jan 1, 1978

By F. L. D. Cloete

The following discussion relates to the paper by G. S. Hansford, C. D. Levy, and J. W. de Kock that appeared in the March 1976 issue of the Journal (vol. 76, no. 8, pp. 363-369) Competition for student members Each year the South African Institute of Mining and Metallurgy offers a prize (or prizes should the entries warrant it) of up to RI00 for the best paper or dissertation on a topic appropriate to the interests of the Institute. Engineering in South West Africa The SW A Engineering Profession Steering Committee was established on 4th April, 1977, its purpose being to formulate an Act covering the engineering profession in South West Africa.

Jan 1, 1978

By D. Duncanson, R. J. Davidson, C. G. S. Schmidt, G. A. Brown, J. D. Taylor, N. W. Hanf

The development of a cyanidation route for the treatment of gold-plant gravity concentrates is described. This work was carried out as a natural consequence of earlier improvements to the recovery of gold in the gravity sections of existing gold plants. Concern about the environmental aspects of the conventional amalgamation process was further motivation in the development of an alternative procedure. It was found that the partial pressure of oxygen in solution was the most critical reactionrate determining factor. The rate of gold dissolution was shown to be controlled by the reaction rate below approximately 25°C and by diffusion above that temperature. Thus, the efficiency of pulp agitation and oxygen partial pressure permitted a high degree of control over the rate of gold dissolution. The use of oxygen rather than air significantly increased the dissolution rate of both gold and silver. The solubilities of sodium, calcium, and potassium aurocyanide complexes under simulated reaction conditions were studied, and it was established that the values for the sodium and calcium complexes were limited, requiring the use of lower pulp densities and higher reaction temperatures for the treatment of very high-grade concentrates. The presence of excessive amounts of tramp iron in such concentrates of up to 25 per cent by mass was found to result in poor gold dissolution owing to the cementation of gold under certain reaction conditions. The maintenance of high oxygen partial pressures, together with high cyanide concentrations, high pH levels, and the presence of calcium in the system, all aided in passivating the tramp iron. Copper, gold, and iron were shown to be the main cyanide-consuming elements. Optimum gold dissolution was obtained in a closed bench-scale reactor incorporating a flotation-machine type of agitator for effective pulp agitation and oxygenation, the oxygen being recirculated. The reactor was designed to operate under a very small positive pressure. After reaction times of 2 to 6 hours at temperatures in the region of 30°C, both the gold and the silver dissolution averaged 99,S per cent. In the case of very high-grade concentrates, it was shown that gold could be floated in the same reactor by drawing off the flotation concentrate through a port in the reactor. A flotation recovery of 87,4 per cent of the gold in 3,9 per cent by mass was obtained. The recovery of osmiridium from cyanide-leach residues and the electrowinning of gold from the pregnant liquors were also considered as processing aspects in the treatment of gold-plant belt concentrates. Final table tailings with a gold concentration of 10to 12 gft were obtained. The results of the investigation strongly suggested that an alternative cyanidation route for the treatment of gold-plant concentrates was technically feasible, provided the system included effective agitation and oxygenation. In the case of lower-grade concentrates, cyanidation followed by the electrowinning of gold appears to be the simplest route, while, for high-grade concentrates, flotation and smelting of the concentrate followed by cyanidation of the flotation tailings are suggested. The use of oxygen rather than air for sparging the pulp would depend largely on the grade of material to be treated. A preliminary comparison of the costs related to the amalgamation and cyanidation processes for the recovery of gold from such concentrates indicated very similar capital and operating costs. It was concluded that other considerations, e.g. toxicity, safety, and lower labour requirements, were more important than such small cost differences. Furthermore, the 'opening' of the gold-plant gravity circuit, which would be made possible by a cyanidation route, would further reduce the operating costs because of the subsequent decrease in the tonnage to be treated.

Jan 1, 1978

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

Jan 1, 1978

By N. Boegman

The meteorological conditions in South Africa are not conducive to the effective dispersion of air pollutants. In the light of this, and because of the magnitude, concentration, and future growth potential of the metallurgical industry, control of air pollution is essential. Methods of abatement are discussed for each branch of the metallurgical Industry, as well as for open-cast mining and bulk ore storage. Some recommendations are made regarding potentially rewarding research and development.

Jan 1, 1978

To determine the characteristics of a mineral deposit, the usual practice is to take samples, analyse the properties of those samples and infer the characteristics of the deposit from these properties. This analysis can be done using statistical methods. In the present work we are concerned with two types of statistical approaches, classical statistics and spatial statistics. If one uses classical statistics to represent the properties of the sample values, the assumption is made that the values are realizations of a random variable. The relative positions of the samples are ignored, and it is assumed that all sample values in the mineral deposit have an equal probability of being selected. The likely presence of trends, zones of enrichment, or pay shoots in the mineralization, is ignored. The fact that two samples taken close to each other are more likely to have similar values than if taken far apart is also not taken into consideration. In contrast, spatial statistics will be used if one chooses to consider that the sample values are realizations of random functions. On this hypothesis, the value of a sample is a function of its position in the mineralization of the deposit, and the relative position of the samples is taken into consideration. The similarity between sample values is quantified as a function of the distance between samples and this relationship represents the foundation of spatial statistics. There are few situations where classical statistics can be used. The assumption that all sample values in the mineral deposit have an equal likelihood of being represented will be satisfied only if the sample values are randomly distributed, or if the sample positions are random. Sample values are in fact never randomly distributed within a mineral deposit. Further- more, geologists usually avoid taking samples at random (random sampling), as it is correctly accepted that samples located on a regular grid, or approximately on a regular grid, give more information than randomly located samples. In practice, classical statistics should be used only in the early stages of exploration, when the number of samples available is relatively small and the distances between samples are large. In these circumstances, and whenever the information available is not sufficient to permit the use of spatial statistics, application of the methods described in this chapter is justified.

Jan 1, 1978

By C. L. de Jongh

Fracturing of the rock caused considerable difficulties during the boring of a deep-level tunnel in hard rock. A pilot bore was suggested as a possible means of reducing the effect of the fracturing, and this possibility was investigated theoretically by means of a three-dimensional elastic stress analysis. Failure criteria were applied to the results of this analysis, and it was found that fractures predicted by the use of a simple criterion of limiting tensile macrostrain criterion agreed remarkably well with in situ observation. It was concluded that fracture could not be avoided and that a pilot bore was likely to aggravate tunnelling conditions.

Jan 1, 1978

By S. Stone

Because of problems encountered with conventional timber supports, a system of concrete sausageshaped support pillars was tested. The pillars are 3 m long, 0,6 m wide, and between 70 and 80 cm high (the height of the stoping width). They consist of bags filled with a grout of cement (slagment and sand in the ratio of I :2, and are installed in a staggered pattern 6 m apart on dip and 2 m apart on strike. These support packs have proved successful, and, although they cost more than the timber supports formerly used (R4,63 per cent are supported as against R2,26 for the conventional timber pack), their use is felt to be justified when account is taken of the costs of lost production and low productivity due to the bad hangingwall conditions that occurred with the conventional system.

Jan 1, 1978

By N. C. Joughin

Progress during the last two years in the Chamber of Mines programme for the development of mechanized stoping methods is reviewed, and advances in the basic technology are outlined. Specifically. advances in the understanding of rock fracture around stope faces. in rockbreaking techniques, in rockhandling techniques, and in engineering are described. The state of development reached with mining systems based on cutting, impacting. and blasting is also described.

Jan 1, 1978

By F. L. D. Cloete

he above article by E. Barnea, which appeared in the January 1978 issue of the Journal (vol. 78, no. 6, pp. 143-145), calls for comment in view of the author's claims for the novelty of his proof. He states in his article that its main purpose is to give a mathematically acceptable proof by induction of the 'recently proposed' equation

Jan 1, 1978

By G. E. Blight

The load-compression characteristics of mine supports are usually evaluated by means of relatively rapid tests, whereas in the mine they are subjected to much slower strain-controlled compression. The effects of slow strain rates on the load-bearing properties of mine supports were explored by means of straincontrolled tests on model timber packs and timber-filled steel telescopic props. It is shown that the load-compression characteristics of these supports are considerably influenced by the rate at which they are compressed. The species of timber influences the behaviour, but to a relatively minor extent. Preloaded supports are shown to lose a significant proportion of their preload by relaxation.

Jan 1, 1978

By R. C. O’Ferrall, W. G. Goulding

This paper describes the performance of a Robbins 52R Boxhole Borer from its introduction into the mine in July 1975 until late in 1977. As indicated by the costs involved, the performance has increased considerably and is expected to be even better once further envisaged modifications have been made. The average cost for the first half of 1977 was R275 per metre bored as against an average of R628 for 1975.

Jan 1, 1978

The following comment has been received from Mr A. D. Osche* on the above paper, which was published in the Journal in October 1977 (vol. 78, no. 3, pp. 51-62). Obituary: T. K. Prentice The Institute records with deep regret the death on 30th January of its senior surviving Past President, Mr Thomas Kennedy Prentice, at the age of 83. Book reviews R. A. Rich, H. D. Holland, and U. Petersen. Hydrothermal uranium deposits. (Developments in Economic Geology, vol. 6). Amsterdam, Elsevier Scientific Publishing Co., 264 pp. with 77 illustrations and diagrams, 30 tables. U.S. $34,75. M. David. Geostatistical ore reserve estimation. Amsterdam, Elsevier Publishing Company, 1977. 364 pp. World mineral industry The Australasian Institute of Mining and Metallurgy is celebrating its sesquicentenary in 1979. A conference will be held in Perth from 13th to 18th August, 1979, as part of the celebrations, the theme being 'Australia's Role in the World Mineral Industry'. Engineering teaching staff UNESCO has extended its technical assistance to the Venezuelan government in the training of engineers to suit the rapidly developing economy of the country. UNESCO vacancy Vacancy for a post of expert under the UNDP. (1) Title of post: Expert in metallurgical engineering. (2) Duty station: Instituto Universitario Politecnico of Ciudad Guyana (Venezuela). Shell Design Awards The annual Shell Design Awards, organized by the Design Institute and sponsored by Shell South Africa (Pty) Ltd, focus attention on achievements in South African design.

Jan 1, 1978