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By Z. Bibak and S. Banisi

Granular systems, i.e. particles with realistic shapes, are commonly encountered in nature and industry. While the discrete element method (DEM) is a tool for the simulation of granular flow, in most of the DEM simulation particles are assumed to be spherical. It is questionable whether results drawn from a spherical particle could be easily transferred to a non-spherical particle. Thus, obtaining a fundamental understanding of the underlying physics of granular flows is not only of academic interest, but is also highly related to industrial applications. An in-house developed DEM software called KMPCDEM ©, which was coded to handle non-spherical particles, was used to simulate the particle behaviour. In this paper, the effect of particle shape on the dynamics of particles of non-spherical and spherical shape, including algorithms for the determination of the particle orientation, the moment of inertia, shape representation, and computation time was described. The assumption of a spherical shape has been justified by the complexity of simulation and significantly higher computation time if a realistic shape for particles was used. Dynamics differences showed that findings obtained from spherical particle systems could not be readily extrapolated to non-spherical particle systems. Consequently, particle shape is an important, if not even the most important parameter to be considered in DEM simulations, and therefore has to be captured accurately if DEM is to be used as a predictive tool. Keywords: Discrete element method (DEM), granular systems, non-spherical particles

Jan 1, 2020

By N. C. Joughin, H. Wagner

Research is a business activity, and is as different from other business activities as banking is from mining. attempting to use research to solve their problems, managers do not always recognize its unique features, are frequently disillusioned with the outcome. With a view to enabling managers to use research more effectively, an outline is given of the features of research as applied to mining. Types of research are distinguished, and stages in the research-and-development process are identified. The time-scales and resource requirements of the various types and phases of research are explained. Examples of research that have reached implementation in gold mining are given to illustrate the features mentioned. Practical and economic considerations are discussed, and pitfals and recommendations in the use of research are highlighted.

Jan 1, 1989

By H. E. Cross

Metallurgical considerations in the automation of gold-recovery plants By H. E. CROSS. Pr. Eng., B.Sc. (Eng.) Hons. (Fellow) The advantages of the automation of gold-recovery plants are examined. The various sections of a gold-recovery plant are analysed, and the extent to which instrumentation can usefully be employed is described. INTRODUCTION The scope of this paper is restricted to the ore-treatment and recovery plants on Witwatersrand gold mines. To extend the field to plants that process base metals and industrial minerals would result in a paper that would be too lengthy. However, the subject matter of this paper is applicable to most mineraldressing and recovery plants and will, it is hoped, be a foundation on which to build somewhat more sophisticated control systems required in the base-metals field.

In order to test the applicability of elastodynamic codes in the modeling of mining related problems, comparisons are made between seismic data and numerical analyses. The dynamic finite difference program WA VE is used for the modeling of a horizontal stope in a deep mine. The slip along a vertical fault situated within the positive excess shear stress lobe of the stope initiates seismic waves. The stope-fault geometry is modeled in both two and three dimensions. The three dimensional non-slip weakening WAVE analyses correlate well with Brune's analytical model. For accurate modeling of the peak particle velocities predicted by McGarr's empirical relationship, it is recommended that a three-dimensional stope -fault model is used, with the amount of slip weakening dependent on the magnitude of the event.

Jan 1, 1995

By A. V. L. Narasimham

The practice of refractory lining in Fe Cr furnaces is purely based on the behavior of various refractories used in different parts of the Furnace at elevated temperatures. The choice of the pattern of lining is mostly done on traditionally based concepts. Refractory Lining of a furnace is the most crucial enabler for operational excellence for Ferro Alloys production. During the last few years, no major technological change has taken place in ?Refractory Lining Management?, only freeze lining concept is becoming popular. Many ferro chrome furnaces today, have the refractory lining problems especially at tap holes, resulting in shutdowns and production losses. The author with his experiences for the last 37 years in furnaces of all sizes tried to attempt to investigate into the reasons for premature failure of lining.

Jan 1, 2007

By D. J. Bosman

Rapid fouling of condenser tubes in underground refrigeration plants is a frequent occurrence. It leads to low heat transfer efficiencies, with consequent serious reduction in capacity and increase in the horse-power requirement of the units. High pressures develop in the condensers, and frequent cleaning of the tube bundles is required. The cleaning operation takes up to 8 hours and in some cases results in significant loss of production. One of the possible causes of fouling is deposition of scale, but this can be readily overcome by controlling the concentration of the water. When water evaporates, the dissolved solids remain behind; thus evaporation increases the amount of dissolved solids per unit volume. If half the original volume evaporates, the concentration of the dissolved solids is doubled and the water is said to have a 'concentration' of two. Concentration may be controlled by regulating the amount of water allowed to bleed from the system. The actual concentration value required is a function of the chemical analysis of the circulating cooling water. In one instance, where the problem of scale formation had been eliminated, fouling still persisted, and the possibility of excessive quantities of dust in the re-circulating water was investigated. A dispersing reagent was added to the condenser cooling water as a means of preventing sludge deposition in the condenser tubes. As shown by curve A in Fig. 1 the reagent addition did not decrease the rate of fouling.

By L. A. Vermeulen, D. D. Howat

The use of pebbles as the medium in the grinding of quartz gravel in a laboratory mil provided experimental data that were used to quantify the relationships between the feed rate of ore to the mil, the fineness of grind of the product, and the wear rate and consumption of the grinding medium. Fineness of grind is expressed as the inverse of the harmonic mean size, a quantity that is calculated from data obtained by sieve analyses. The commonly used criterion for fineness of grind (the percentage of material smaller than 75 µm in the mil product) is shown to corelate approximately linearly with the inverse of the harmonic mean size. An increase in the feed rate was found to cause the harmonic mean size of the product to increase linearly, Le. the relationship previously found for metalic grinding media is applicable to al grinding media, irespective of shape or composition. Simple expressions for the consumption and wear rate of pebbles are derived from the experimental data, and are shown to be functions of the feed rate. The expression for wear rate is a monotonicaly increasing function, while that for consumption is a hyperbolicaly decreasing function of the feed rate. In contrast, a linear relationship was found between the rate of wear of the grinding medium and the rate production of fines. The expressions that were previously developed in relation to the use of metalic grinding media are shown to be equally applicable to pebble milling.

Jan 1, 1988

By M. Mabuza

Two Rivers Platinum Mine (TRP) is a 55:45 joint venture between African Rainbow Minerals and Impala Platinum, respectively. TRP is situated on the farm Dwarsrivier 372KT, in the southernsector of the eastern limb of the Bushveld Complex. Dwarsrivier is underlain by rock formations of the Critical Zone (Winterveld norite-anorthosite) and the Main Zone (Winnarshoek norite-anorthosite). Two economically significant PGE-bearing layers namely the Merensky Reef and the UG2chromitite are found within the upper Critical Zone. These are approximately 140 m vertically apart, separated by a series of barren norites and anorthosites. At Two Rivers Platinum, only theUG2 chromitite layer is currently being mined for PGEs. The UG2 sub-outcrops north/south along the Klein Dwarsrivier river valley with a very gentle dip to the west of 7º?10º. At Two Rivers the UG2 averages about 120 cm in thickness, overlain by a waste pyroxenite parting about 20 cm thick, above which is a leader seam about 20 cm in thickness. The mineable cut consists of the leader seam, the waste pyroxenite parting, the UG2chromitite layer including 25 cm of pegmatoidal pyroxenite footwall, below the UG2 reef to a minimum of 185 cm trackless mining cut. The mining method is a mechanized bord and pillar layout, which will yield a total of 185 000tons at full run of mine production from the underground UG2 mine.

Jan 1, 2006

By J. L. Gaigher

A simple mineralogical regression model is described, which was devised in order to help the flotation plant cope with rapidly changing headgrades and feed mineralogy. Minerals in the feed were determined by means of quantitative X-ray diffraction and compared with plant performance parameters and flotation reagent consumption rates, using regression analysis. A mineralogical regression model for predicting recovery served to motivate flotation plant personnel and also set standards whereby flotation performance could be measured. The reagent consumption model indicated in which direction any or all of five flotation consumption rates should be altered. All practically measurable parameters, even those showing poor or no correlation, were included in the model, provision being made for the continuous update of a batch of data of 30 lines. Compared with the method of multiple linear regressions, the r2 is poorer at 0,41 (versus 0,50), but the mean standard error of estimate for both methods is identical at ± 6,6 units. The regression model is simpler than the method of multiple linear regressions, and although the accuracy of prediction is not high (41%), the mineralogical regression model proved to be successful in practice. Flotation efficiency, as measured by the mean ratio of head to tails grade, for the 9 month period after the mineralogical regression model was implemented on an hourly basis, improved from 2,8 to 3,2, which is equivalent to an improvement in average flotation recovery of 5% relative.

Jan 1, 1987

By S. A. Ziebold

There is often a need to increase capacity through existing mist eliminator installations without significant tower modifications. Often there is not enough extra space outside existing vessels unless more expensive changes can be justified. Also, plant downtime must be considered. The challenge in retrofitting is to overcome velocity limitations inherent in the design while at the same time extend performance capability. The solution most often is to create new ways to add extra filter area while remaining constrained to the existing space. This strategy, however, can dangerously backfire if basic design principles are not followed. Mist eliminator design is a complex integration of many conflicting performance parameters. Often the objective is to increase scrubbing capacity while maximizing collection efficiency and service life and minimizing operating pressure drop (energy cost), particle regeneration (re-entrainment) and overall maintenance costs. Results of plant retrofitting using mesh pads, impaction fibre beds and diffusion fibre beds are presented based on actual plant projects. Often the retrofit project can be more effective by increasing the scope and combining other new plant equipment with the upgrade such as new tower components. In some cases, the type of mist eliminators can be upgraded from impaction type (velocity dependent) to Brownian diffusion type (velocity independent) if additional downstream protection or reduced emissions are desirable, especially at turndown rates. Trade-offs between different fibre bed types and styles are discussed as they relate to performance and maintenance.

Jan 1, 2007

By A. M. Starfield

Discussion J. de V. Lambrechts (Fellow): The author's paper is a brilliant follow-up of an earlier paper by Starfield and Dickson.1 I have no quarrel with Dr Starfield's computerization of a complex problem, but I do not believe that he is getting quite the right answers from his programme. My impression is that his predictions about wet bulb temperature increases in very deep mines are over optimistic; in other words, that it will be hotter than Dr Starfield predicts. This is putting my views in a nutshell. This is not the occasion on which to indulge in lengthy argument about the original paper by Starfield and Dickson, but the present paper is, after all, based directly on that earlier paper and if the one fails, the other cannot succeed. I did level certain criticisms at the first paper and cannot say that the authors' replies were very convincing. I do not think it is a sin to admit that I belong to the old school which believes in thorough field experimentation and practical trials and no amount of mathematical manipulation or physical theorizing, no matter how excellent, can make up for inadequate practical confirmation. This, as I see it, is still the crux of the matter. The original paper by Starfield and Dickson still rests on somewhat scanty practical evidence and I would be much happier if Dr Starfield's computer programme, based on the Starfield-Dickson model, had been checked against a large mass of observations in the practical mining situation. This is what both Wiles2 and myself3 had tried to do previously. What we lacked in mathematics and/or computer aids, I think the present paper by Dr Starfield lacks in practical substantiation. This is no condemnation of the author's paper which, taken by itself, is excellent but I think the final stage is still lacking, namely the bringing together of theory and empiricism in a manner acceptable to all. This may be wishful thinking on my part but I hope, within the next year or so, to come up with a modified Starfield-Dickson model in such a way that the computer answers will agree in the majority of cases with the few hundred field observations which are already on record. It might be a case of applying the proverbial 'Cook's Law' to the Starfield-Dickson model! REFERENCES 1. STARFIELD, A. M., and DICKSON,A. J. 'A study of heat transfer and moisture pick-up in mine airways.' J. S. Air. Inst. Min. Metall., 68, (5), 1967. 2. WILES, G. G. 'Wet bulb temperature gradients in horizontal airways.' J. S. Air. Inst. Min. Metall., 59, (7), 1959, p. 339. 3. LAMBRECHTS, J. DE V. 'Prediction of wet bulb temperature gradients in mine airways.' J. S. Air. Inst. Min. Metall., 67, (11), 1967, p. 595. R. Hemp (Visitor): Dr Starfield's paper has very effectively rounded off one particular aspect of the general problem of heat flow in mines. The ease with which this computer programme can be used to calculate temperature increases in horizontal airways must lead to its wider use in ventilation planning and, in developing this rapid method, Dr Starfield has indeed rendered a valuable service to the mining industry. One could consider further instances of heat flow in airways in which the availability of a rapid computer method would be desirable, e.g. the flow of air down a shaft, where there is an increase in temperature due to adiabatic compression, as well as an increase in virgin rock temperature as the depth increases. However, this particular case would not present any new problems and would merely require an extension of the exisitng work. I should like in this contribution to talk about an aspect of environmental control in mines which, I think, will become more important in the future. It is well known that wet bulb temperatures are subject to fluctuations underground. In some instances, particularly in stopes, the fluctuations, both with time and position, can be considerable. The theoretical work which has been carried out on temperature increases has been aimed at the prediction of mean temperatures, and no account has been taken of fluctuations around this mean. It is questionable whether this approach will, on its own, be sufficient, particularly when temperature increases in stopes are considered. The fluctuations in air temperatures underground arise from two causes. The first of these would be the fluctuations in surface conditions, and here one could list random, diurnal and seasonal fluctuations. The second cause is the multitude of things which vary in a mine and here one could list variations in air flow quantity, sources of evaporation, heat transfer from pump and compressed air columns and, particularly in the stope, variations in air flow patterns. Fluctuations arising from surface temperature variations should be amenable to calculation, and here one envisages figures relating the decay of temperature variation with distance to factors such as air flow quantity. Fluctuations resulting from changes in the mine are perhaps more difficult to tackle theoretically and the best approach could well be to analyse underground observations. In this connection, there is a good case to be made for the increased use of statistical methods in the analysis of underground temperature measurements, and it might be of value to look at current air-conditioning practice. When carrying out cooling load calculations for a particular location it is customary to use design wet bulb

Jan 11, 1969

In the investigation described here, it was found that the main effect of temperature is on the rate of flotation, and that adsorption of the reagent is not rate controlling. Above 10°C, the flotation rate of pyrite and gangue increases almost exponentially with a rise in temperature. Below that temperature, the flotation rate of pyrite shows a sudden marked decrease, that of gangue increases, and the sulphur grades are significantly poorer. In the flotation of pyrite, the mass transfer of the pyrite from the pulp to the troth is thought to be the ratecontrolling step, whereas the flotation of gangue is controlled by the combined effect of the stability and velocity of the froth and the viscosity of the elutriating medium. The latter is probably the controlling effect at temperatures below 10°C. Little difference was noted in the recoveries (provided no time limit was set) with changes in temperature; hence adequate recoveries can be obtained at Iow temperatures by the introduction of longer residence times for the pulp. The adverse effects of Iow temperatures on grades can be overcome only by additional cleaning or by heating of the pulp.

Jan 1, 1984

By N. B. Strydom, H. H. E. Schroder, A. van der Linde

This paper describes a study of the destination of the mercury that is present in the ore during the recovery of gold. It was found that over 96 per cent of the mercury passed through the process untouched. A small amount finds its way into cyanide solution, and is concentrated with gold in Zinc dust as Merrill precipitate. When the precipitate is calcined, the mercury is driven off and finds its way into the atmosphere. However, dilution of the stack gas in the atmosphere appears to be sufficient to prevent hazardous concentrations arising at ground level. No other significant concentrations of mercury were found at any stage of the process. The amount of mercury lost to the atmosphere by this mechanism appears to be less than 200 kg per year throughout the gold-mining industry in South Africa. Virtually no mercury vapour could be detected in the air in the smelt-house. Slight increases in mercury concentrations above background level were observed in soils around the reduction plants and in the discharge or return waters, but no environmental stress is anticipated from these increases.

Jan 1, 1982

By P. M. Swash

A mineralogical investigation of the main causes of refractoriness of some metalurgicaly complex gold ores in South Africa is reported. It is shown that this refractoriness is related to the presence of submicroscopic gold, carbonaceous material, pyrhotite, and base-metal sulphides. Gold ores can be classified according to their content of these components. Electron-microprobe analysis shows that gold occurs in arsenopyrite and pyrite, the gold contents of which can be up to 2700 gft. The gold and arsenic contents of these minerals are closely corelated. Furthermore, within zoned arsenopyrite grains, the concentration of gold closely folows that of arsenic. Mossbauer spectroscopy caried out on samples of concentrate from the Barberton area indicates that the submicroscopic gold within the sulphides is in a non-metalic form. The mineralogical examination of beneficiation products is important, since it sheds light on some fundamental aspects of the behaviour of the ore and gangue components during milling and flotation. Such basic information will lead ultimately to a better understanding of the problems in the beneficiation of these ores. Investigations have shown that the overmiling of the auriferous arsenopyrite and the disseminated nature of the sulphide mineralization are the main problems during beneficiation.

Jan 1, 1988

By A. García-Gutiérrez, A. Aragón-Jerónimo, R. Salazar-Mendoza

A theoretical analysis of a two-region solid-liquid flow system in horizontal pipes is presented, which considers a stationary bed of drill cuttings as a porous medium (-region) below of a two-phase dispersed flow (-region).The method of volume averaging was applied in this study to derive a rigorous mathematical model in which each variable is precisely defined. This model includes the volume-averaged transport equations for both the two-phase dispersed flow and the porous medium regions and terms from a macroscopic forces balance. The solution of the two-region model allowed evaluation of the behaviour of pressure gradient as a function of velocity, total volume fraction of cuttings and the relationship of the height of the stationary bed and pipe diameter. The solution is based on a backward finite difference explicit scheme. The simulated physical system is a pipe of 4.135 m in horizontal length and 0.0508 m in diameter. A one-dimensional, mesh-centred grid, consisting of 100 nodes, is used. The numerical results were compared with experimental data on slurry flows and a good agreement was found. Keywords: two-phase, cuttings transport, solid-liquid flow, drilling modelling, volume averaging.

Jan 1, 2007

By D. A. Vetter

A novel mathematical model is presented which describes the behaviour of beds of particles, of uniform size and shape but different densities, during autogenous separations. The approach used in the formulation of the dispersion model is a phenomenological one based on a statistical view, which leads to a diffusion-like representation of the autogenous-separation process. Although the model currently considers only density-related phenomena, it accounts quantitatively not only for the density-segregation aspects of the process but for the interactions between the particles. Quantitative predictions of the dispersion model are compared with the results obtained in tests using a specially constructed experimental batch jig, and it is shown that the model provides an adequate quantitative description of the process for particles of uniform size and shape. It is pointed out that, for the description of more complicated autogenous separations, a more rigorous formulation of the particle drag and density-segregation terms will have to be incorporated into the dispersion model. Nonetheless it is concluded that the model as presented in this paper provides not only a novel insight into the mechanisms of autogenous separations but a means by which to analyse similar systems.

Jan 1, 1987

By S. Konetschnik, E. Dreyer, A. Filzwieser

"More intense furnace operations require effective cooling in order to achieve low refractory wear and good furnace lifetimes, making cooling technology an important aspect of furnace operations. However, the use of water - today’s standard cooling medium - has some disadvantages, as it can cause problems both during furnace start-up and operation, namely hydration problems, corrosion, and explosions. Apart from these aspects, the energy that is removed by extensive cooling cannot be recovered and is normally lost in the cooling towers.With METTOP’s new patented cooling technology it is possible to overcome the disadvantages of water by using an alternative cooling medium, namely ionic liquids (ILs). The main advantage of ILs is the fact that there is no risk of explosion should this liquid come in contact with molten metal. Furthermore, ILs can be used at higher temperatures than water - up to 200°C. This relatively high cooling medium temperature avoids hydration and corrosion problems and allows recovery of the energy by combining the ILTEC system and the organic Rankine Cycle (ORC) technology, for example.Due to the removal of the explosion risk, much higher safety standards can be achieved, particularly in critical areas such as tap-holes"

Jan 1, 2014

By D. Vogt

"Rock has been cut in the process of mining since before the invention of explosives. Today, we seek to return to cutting to reap the benefits of continuous operations for South African underground hard-rock mines, to improve speed of access to the orebody, and to improve the efficiency of mining operations.Development of new technology fits within a framework of engineering knowledge. By understanding the characteristics of the rock, the tools we use to cut it with, and the history of mining and rock cutting, we can see the genesis of the road-header, the longwall, and the continuous miner, all drag bit cutters. They have emerged as the solutions of choice for underground mining of softer materials such as coal and potash. In hard rock, the challenges are the forces required to break the rock, and the wear of the tools caused by the rock’s abrasiveness. Only disc cutters currently handle the challenges, and even then, often not economically. New materials like thermally stable diamond composite will help, as will combinations of mechanical cutters and other methods such as high-pressure water or high temperatures.It is not clear what will emerge as the consensus technique for hardrock cutting. Experience teaches that development is expensive and the market is small. Will mining companies partner with equipment developers to make the technological leap? Or will the solution come from a systems approach, not considered here?IntroductionBlasting is the dominant method of breaking rock for the purposes of mining. When used underground, blasting is part of a batch process. If rock can be cut rather than blasted, mining can become continuous, leading to process and efficiency improvements.Coal produced from underground mines is now predominantly excavated using mechanical means, but underground hard rock is still broken primarily by explosives.This paper traces the history of rock cutting, reviews the main physical processes that are or could be used, and comments on the future. It is written from the perspective of narrow-stope hard-rock mining typical of South African gold and platinum mines."

Jan 1, 2016

By A. S. Macfarlane

"SynopsisMetal accounting and reconciliation is an increasingly important governance issue in all mining operations, in that it is required, from a risk management perspective, that the company is in control of its product throughout the whole mining value chain. Reconciliation is a grossly misunderstood term. It means different things to different people, and therefore one of the purposes of this paper is to ensure a holistic and integrated understanding of ‘reconciliation’.Previously, where reconciliation was done, it was often for internal control purposes and loosely applied, sometimes with a low degree of confidence and understanding of the underlying parameters and their natural variability.In most mining operations, issues such as dilution, stope performance, and recovery are critical to profitability and long-term value, and thus understanding and control of these key value drivers is essential, not only from the governance perspective, but also from the perspective of maximizing shareholder returns. In order to implement a system for metal accounting and reconciliation, it is important that the cause and effect of these value drivers is understood, and that a systematic control system be established.While a number of off-the-shelf solutions exist for this work, it is the contention of this paper that a full understanding of the metal flow, its variability, its underlying loss potential, and its control points is necessary before a systematic approach to reconciliation can be undertaken.The paper also advocates that this approach should ensure that the reconciliation system clearly addresses the reconciliation needs, within a consistent framework. Such a framework has been developed by AMIRA, in terms of a metal accounting code. However, up until now, this code has been aimed at plant processes, whereas this paper shows how the concept can be extended to cover the full reconciliation requirements for a base metal mine.IntroductionReconciliation is defined as ‘the process of finding a way to make two different ideas, facts, etc., exist or be true at the same time’. In terms of a mining process, this refers to the comparison of measures and estimates along the value chain, and at different points in time, in order to track and optimize metal recovery. This leads to the notion of having a system in place for accounting for the metal. The University of Cape Town defines metal accounting as ‘… the estimation of (saleable) metal in a mine and subsequent process streams over a defined time period. Comparisons of estimates, from different sources over a specific time period, are called reconciliation.’Traditionally, metal accounting has consisted of geological reconciliations of mineral resource to mineral reserve conversion, mine planning reconciliation related to the reconciliation of long-term plans to short-term plans, grade control reconciliation of head grades to sampled or block grades, and mine survey reconciliation of tonnage discrepancies and mine call factors. In addition, metallurgical reconciliation has tended to be based on metal balancing, followed by some commercial metal accounting that links dispatched product to sales quality, quantities, and revenues. Miners disparagingly refer to this plant process as ‘millmatics’."

Jan 1, 2015

The term geostatistics was introduced by Matheron (1960) to cover the development and application of mathematical and statistical models which take specific account of the spatial structure of a 'regionalised' variable. In ore valuation the relative positions of available ore values within an ore body or portion thereof, can only be ignored in the unlikely case where there is no significant pattern of association or correlation between them - that is, if they do not disclose any significant spatial structure. A structure might not be evident in the available data, e.g. where the spacing of the available values is relatively wide such as in surface drilling on a new deep gold mine. However, practical selective mining considerations could dictate the need for eventual underground valuation on a scale much smaller than that represented by this spacing and the possibility of a significant structure on such a smaller scale cannot then be ignored. Some spatial structure must be present wherever the average variability among the values of check ore samples from the same, adjacent or nearby grooves or of borehole cores from the deflections in the same borehole, is lower than the overall variability for ore values within the whole ore body. Another practical check on the presence of a spatial structure is where it is evident that there is or will be a significant variation in the ore grades for individual ore blocks. Any correlation between peripheral and follow-up internal ore block values also provides evidence of a spatial structure, and hence the regression techniques covered in §1.16-1.2 1 can be accepted as the first application of the geostatistical procedures. The spatial structure of a regionalised variable can be studied and measured by the pattern, usually a decreasing function, in the level of correlation or of the covariance between pairs of values as the distance or lag between the values increases, that is, by the correlogram or covariogram (Krige, 1968, 1969, 1976; and Fig. 18). In geostatistics, for various practical and theoretical reasons (Matheron, 1960, 1971), the measure most commonly used is the semivario- gram, which increases as the lag increases. The semivariogram and covariance values are interrelated and for the lognormal- de Wijsian pattern used extensively for gold ore valuation both measures as well as their relationship can be defined on a fairly straightforward basis. Provided the underlying as- sumptions are realistic, the choice of measure - correlogram, covariogram or semivariogram - will be dictated mainly by convenience. Paragraph 2.2 will cover some general geostatistical terms and $2.3-2.12 will deal mainly with the theoretical side of the lognormal-de Wijsian model for spatial structures. Wherever the relevant variable lends itself to normalisation via the 3-parameter lognormal distribution (see 51.9) the de Wijsian semivariogram model is also likely to be suitable and will provide substantial advantages in application. Various practical applications will be covered in Section 3. Although confined to the lognormal-de Wijsian model, much of the theory covered and the general approach is applicable to all spatial structures. [ ]

Jan 1, 1981