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By C. Kelley

For years urethane screen surfaces have been used in a wide range of wet screening applications where openings as fine as 75 microns and coarser have been used. In dry screening operations these same urethane screen surfaces have been relegated to only the coarser separation ranging from 1.0 mm and larger. The purpose of this paper is to expose the reader to new developments in both screen surface and screening equipment technologies, which allow an end user to consider urethane screen surfaces for dry screening operations where separations as fine as 75 microns are required. These technologies allow an end user to realize the inherent advantages of urethane in wear resistance while also realizing the benefits that a high open area urethane screen surface can bring. These benefits include non-blinding characteristics and feed capacities, which rival that of traditional stainless-steel woven wire mesh screen surfaces. The paper will highlight the features of this patented urethane screen surface technology and the screening machines in conjunction with which they are used. There will also be a presentation of several case studies of commercial installations where these technologies are utilized. These case studies are from the mineral sands industry; therefore relevance to the conference is direct and not inferred. Included in the paper will also be constraints, which must be taken into account when considering urethane screen surfaces such as temperature and chemical attack. This paper will expose potential end users to a possibility of using screens to achieve extremely accurate size separations in applications where screens were previously not considered. The paper will explain and demonstrate that prior concerns of screen surface blinding, high screen surface consumption rates and large screen surface area requirements can be eliminated by proper utilization of high open area urethane screen surfaces.

Jan 1, 2007

The statistical methods described in the previous chapter permit the estimation of the average value p of a deposit, and the calculation of confidence limits for this value. They are based on the assumption of independence of sample values. As soon as a reasonable number of samples has been obtained from a deposit, local valuation, or estimation of blocks of ore within the mineral deposit, becomes necessary. The assumption of independence of values must then be rejected. Local valuation is possible only if there is a relationship between the value of a sample and the value of the surrounding ore, provided this relationship is a function of the position of the sample with respect to the blocks of ore to be valued. Whichever method is used for the valuation of a block of ore, the following assumptions are always made: ? The values of samples located near or inside the block are related to the value of the block. ? The values of the samples located closest to the block are most closely related to the value of the block. These assumptions will hold true only if the following assumption can also be made: ? There exists a relationship between sample values which is a function of the distance between samples. We are saying that the value x (z) of a sample centred at a point z has properties which are functions of this point. A certain spatial structure exists in the sample distribution. We are therefore dealing with a regionalized phenomenon, and we must treat x (z) as a regionalized variable. This can be done statistically by means of a model chosen to represent the spatial structure of the phenomenon. We shall see that the relationship between block values and sample values can be deduced from the relationship between sample values, and all local valuation problems can be solved using the statistical model obtained from the analysis of the sample values. It is important to realize that this statistical model is obtained by analysing the properties of known sample values, and will be used for the estimation of unknown block values. Such a statistical inference is valid only if the model developed represents the properties of both the sampled section of the ore body and the section to be valued: some stationarity conditions must be satisfied, and the model with the least restrictive conditions is preferred. In the following chapters, the most important models used in spatial geostatistics are presented. The models which can be used when there is no significant drift (trends) in values are described in Chapters 3-1 1. These models can also be used to solve some specific valuation problems when a linear drift is present. A general study of the more difficult problem of analysis of an ore body whose values present a drift is described in Chapter 12. Note that the area considered for local valuation of a block of ore is often small enough for any drift which might be present to be ignored.

Jan 1, 1978

By J. H. Zietsman, W. J. Leipoldt

"To be able to responsibly develop a multiphysics model of the steel belt sintering (SBS) process used to sinter chromite fines, it is important to have a comprehensive understanding of the process. This understanding was gained through a site visit, observation of the process in operation, and interaction with the operators. Material characterization will also reveal much about the process that is not yet fully understood. A well-defined and representative mass and energy balance will also give valuable insight into the process. The plan for the multiphysics model aims to combine a computational fluid dynamics (CFD) model with a discrete element method (DEM) model.To obtain a more accurate mass and energy balance representation of the SBS process, it was decided to develop a dynamic distributed parameter model of the mass and energy balance. This model will be used to gain better understanding of the SBS process so that a more complicated multiphysics model can be developed later. The reason for this is because the SBS process is very dynamic, with a large temperature distribution throughout the length of the process. In its current state, the mass and energy balance model is capable of handling solid and gas material packages and exchanging heat between these packages where they are mixed, and is able to model the heating of the gas by burning CO gas. The next step in the development of the model will involve enabling it to handle evaporatoin of liquid water, burning of solid carbon in the pellets, reduction of iron oxide in the pellets with the CO gas formed from carbon combustion, and then oxidation of the reduced iron in the oxygen-rich cooling zones."

Jan 1, 2014

By B. Gamble

Solid Energy's project evaluation process utilises a standard staged gate approach, with five levels leading ultimately to project execution (level 6). For a project to progress through each level, specific financial criteria need to be satisfied. Solid Energy primarily use value based (discounted cash flow) metrics to support investment decisions. Within this approach Solid Energy utilise a number risk-based techniques to quantify project uncertainty. This includes the use of risk-based probabilistic analysis using Monte Carlo simulation and probability-based scenario analysis. Figure 1 shows the net present value (NPV) cumulative probability. Project risks are identified through comprehensive risk workshops. The output of these workshops (list of key risks, ranges of uncertainty and probability of occurrence), is quantified within the financial models. Incorporating this risk information on a probabilistic basis allows an investment decision to be made with a robust knowledge of the range of possible project outcomes along with the likelihood (probability) of those outcomes occurring, for example 80 per cent confidence that the project value will be greater than NZ$10 M, 50 per cent confident it will be greater than NZ$50 M and ten per cent confident it will be greater than NZ$70 M. Incorporating risk implicitly into the financial analysis allows the business to easily evaluate/measure projects with different risk profiles. The detailed risk analysis does away with the complexity of arbitrary risk-based hurdle (discount) rates, as projects can be evaluated based on their specific risk characteristics. Whether a project will progress to the next level of investment and ultimately into implementation depends firstly on the value assessment in comparison with the associated risk/uncertainty, and secondly matching this with the businesses appetite for risk. At Solid Energy standard criteria are used for specific project evaluations, but in addition projects are considered on a portfolio or strategic basis also. Solid Energy attempts to maintain a mix of low risk (low value) projects with some high risk (high value) opportunities. The mix of projects must remain in line with the shareholders' risk appetite. One of the keys to a successful investment decision is ensuring that the appropriate information is available to decision-makers so that they may proceed with a comprehensive understanding of the risks and impacts associated with the decision.

Jan 1, 2007

By L. G. Snyman

"South Africa is well endowed with a plethora of valuable minerals, as well as being of world renown for its significant ecological and cultural resources. The unfortunate reality is that these two important attributes often come into collision when developmental decisions are made. Robust environmental planning tools are required to guide such development in areas of heightened sensitivity. Environmental management frameworks are one of the tools that can attempt to achieve the desired developmental and ecological balance by utilizing early identification and mapping of sensitive ecosystems and resources to assist in pre-empting potential future land use conflicts. This paper unpacks the characteristics of environmental management frameworks and further investigates their potential, as well as its current design and implementation challenges. The findings show that environmental management frameworks have the potential to provide meaningful resource information to decision-makers on the opportunities and risks of developments in sensitive areas. They further provide a platform and process through which local stakeholders can voice their opinions and collectively drive the developmental priorities of the identified area.IntroductionAt the core of a harmonious and prosperous society is the balancing of a broad spectrum of needs, rights, and imperatives. As South Africa’s resource and energy needs expand, it becomes increasingly important to safeguard environmental rights and ensure sustainable development through creative measures. The State’s drive for accelerated development to meet the targets in the National Development Plan 2030 is contributing to the growth of invasive developments in previously undeveloped areas. The unfortunate reality is that the heightened tensions between rapid economic growth and environmental sustainability are threatening sensitive areas."

Jan 1, 2017

By A. H. Swart, M. F. Handley

Unplanned stope panel collapses occur on most near-surface and shallow mines in South Africa. Although these incidents often occur during blasting, they pose a major threat to the safety of underground workers and the economic extraction of orebodies. Most stope panel collapses occur due to excessive panel lengths that are not designed according to a systematic design procedure or methodology. Instead, panel lengths are often dictated by the equipment in use and by previous experience under similar conditions. Hence, a rock engineering design methodology for the design of stable stope panels between pillars is of vital importance for optimum safety and production in shallow mining operations. Using the proposed design methodology described in this paper, rock mechanics practitioners and mine planners should be able to identify and quantify the critical factors influencing the stability of stope panels. The critical factors should then be used as input to the design of stable stope panels that will provide the necessary safe environment for underground personnel working in stopes. The proposed design methodology is an iterative process, which includes aspects such as rock mass characterization, estimation of rock mass properties, identification of potential failure modes, consideration of appropriate stability analyses and other elements of the rock engineering design process. This process continues after implementation. During monitoring, new data should be included in the database and the design process repeated on a regular basis. Design approaches included in the proposed design methodology include empirical methods such as different rock mass classification methods, analytical methods such as elastic and Voussoir beam analyses, kinematic analyses, probabilistic analyses, and numerical analyses. Keywords: stability, stope panels, design methodology, hard rock mines, shallow mining operations

Jan 1, 2004

Gold Fields is the world?s fourth largest gold producer with operations in South Africa, Australia, Ghana and South America. All of Gold Fields? South African Operations are located in the Witwatersrand Basin and are intermediate to deep level underground mines exploiting gold bearing, shallow dipping tabular orebodies, which have collectively produced over 50 kt (1,608 Moz) of gold over a period of more than 100 years. Although the use of Monte Carlo as a business tool was introduced in 1964, it has only been in the last 30 years that it has gained increasing acceptance within the mining industry. However, the application thereof has been mostly limited to determination of risk in project areas. This paper however, considers the possibility of using Monte Carlo simulations to asses the underlying ?Root Cause? criteria critical to the operations management of existing mining operations. Currently, working operations have a distinct advantage over project areas as they have a wealth of historical information at hand. This, in turn, can be utilized to model distributions and relationships that can be used in Monte Carlo simulations, the results of which can be analysed to determine areas of concern. Projects can then be set up to ameliorate the effects of these and in turn reduce the risk of not achieving the operational targets. It is here that it must be stated emphatically that it should be the ?root causes? and the associated relationships that need to be emplaced within the model in order to achieve results that reflect the true causal relationship. The paper outlines possible sources of ?root cause? relationships and considers the outcomes of these in a case study on a large South African Gold Mine.

Jan 1, 2009

By C. A. Preece

Finsch Diamond Mine, part of De Beers Consolidated Mines (DBCM), is situated between Kimberley and Postmasburg in the Northern Cape, South Africa. The kimberlite pipe was discovered in 1960 and De Beers assumed full mining rights three years later. Production commenced in 1966 from an opencast mine, and the operation moved underground in 1990 by developing and implementing a new mining method of blast hole open stoping. A mechanized block cave was brought into production in 2005. While block caving was not new to DBCM, with productive caves having operated in Kimberley and Cullinan, from the outset, the Finsch caving operation was designed as the most advanced with a semi-automated ground handling system. The extraction level was laid out as a single sided herringbone system due to the very poor ground conditions on the south side of the pipe. These factors combined to create a unique environment, which necessitated a completely new approach to draw control. The required system was developed by a team consisting of DBCM personnel from head office and Finsch, GEMCOM and Sandvik-Tamrock, the equipment manufacturers. It was essential that the system could be run quickly, provide daily updates and issue calls directly to the LHDs. It was also important that the base data were obtained from the resource model, which was to be depleted on a monthly basis, thus forming a close link between mine planning and draw control. A further requirement of the system was that it would form a central database for the extraction operation where all data pertaining to delays and changes in conditions, be they production or ground condition related, could be recorded and analysed. The design brought together empirical rules and tables developed at Cullinan plus concepts from programming developed for the front cave at Koffiefontein so that the new system was based on sound practical experience. These facets were incorporated into PCBC (GEMCOM) and CMS and PCS (Sandvik-Tamrock programmes). The system has now been operational for just under a year and while modifications have had to be made, it has proved itself as a practical and reliable tool with which to manage the draw control at Finsch. The system is unforgiving and has forced the production team to focus on the specified drawpoints. Problems have been encountered but most of these have been related to re-educating a workforce, familiar with a flexible mining method, to the strict discipline required for a modern block cave.

Jan 1, 2007

Bougainville Copper Limited (BCL) operates a 50 Mtpy copper/gold/silver mine and concentrator on Bougainville Island, Papua New Guinea. BCL has installed an in-house developed data logging and supervisory process control system using a DEC PDP 11/73 mini-computer in the mill and has recently installed a similar system in the crushing plant. Together with the central DEC VAX 11/780 computer, they form part of a high speed, fibre optic, local area network in the concentrator. The in-house developed software, known as BIAS (Bougainville Copper Information and Automation System), was developed as a low cost option to interface to a number of different existing plant input/output systems while providing the capability to make maximum use of computer networking facilities. The package includes the more usual control system colour displays and data logging features, but also makes provision for two novel features: (a) Any user connected to the computer network can access the system displays. This allows metallurgists and management to monitor (but not control) plant operation from their offices. (b) Specialized application programs for performing advisory and supervisory control, dynamic simulation, and data analysis are easily incorporated into the system. The mill process system currently runs rougher/scavenger flotation stabilizing control and general data logging. The crushing plant system currently performs data logging only; however it will soon be augmented with the facility to run dynamic crushing plant simulations. Future developments will concentrate on making greater use of the detailed information available from the mine's fully automatic truck dispatch system which runs on a VAX 11/780 computer. Milling process control will be expanded to examine possible economic control of the operation of regrind and cleaner flotation circuits. An advisory water management system to optimize water supply within powerhouse generating capacity constraint will also be investigated.

Jan 1, 1987

A large body of work exists discussing the impact of grinding media on mineral flotation. Generally, the work indicates that a change to a less electrochemically active grinding environment has positive benefits on downstream processing. There is a fear, however, that these benefits may not be realized when treating low sulphide containing ores, typified by UG2 style deposits. A series of experiments was developed to test the flotation response of UG2 ores using the Magotteaux Mill® to determine if measurable differences in the pulp chemistry could be discerned using a range of grinding media types. Further, the flotation responses of the contained sulphides (chalcopyrite, pentlandite and pyrrhotite) were determined. The data collected provided strong evidence that the grinding environment can significantly influence the pulp chemistry and flotation characteristics of all sulphide minerals, even when the ore contains less than 0.5 per cent total sulphide. The results show that the change to an inert media type produced a substantial improvement in the flotation rate of all sulphide minerals, as well as the PGMs.

Jan 1, 2009

By C. Nangolo

Mineral commodity prices comprise one of the key criteria in the selection of mining stocks. We contend that of the three principal elements of mineral commodity prices, spot price, forward price and long-term price, one has a greater impact on the share valuation processes used by investors. This research paper examines the extent to which each of these elements influences the valuation process. The intention is to provide investors in mining stocks with a greater understanding of how fluctuations of commodity prices over time affect the prices of the mining stocks they hold, or intend to sell or buy. Three mineral commodities, gold, silver, and copper, were used as case studies, since market data on these commodities is readily available in the public domain. Nine market indices covering all three mineral commodities were selected. These are based on clearly defined criteria with the intention of eliminating ambiguity and to test for correlation with the three sets of mineral commodity prices. Nine mining companies, which were not the primary drivers of the relevant indices employed in the study, were used to validate the results obtained from the indices in order to avoid duplication of the same correlation during cross-checking. Each commodity price was adjusted for operating costs. For each market index, an average operating cost was calculated from the companies comprising its basket, while each company?s annual operating costs were used for the stocks of the individual companies examined. The data was collected for the period January 2004 to October 2010. This period was further split up into three sub-periods to account for the Global Financial Crisis (GFC) period that started in mid-2008. We conclude that mining stock prices are correlated with mineral commodity prices, but with spot and forward prices exhibiting stronger correlations than long-term price. This finding should be useful for evaluation purposes. Where cash flow methodologies such as discounted cash flow or earnings per share are used to value ordinary shares and commodity prices are required to estimate future cash flows, the findings suggest that spot prices should be used as opposed to long-term prices. The work reported in this paper is part of a current MSc research study at the University of the Witwatersrand.

Jan 1, 2011

By H. E. Bartlett

This paper deals with the sampling and mass measurement for ore delivered from a shaft to a processing plant and the contribution of the data from these measurements to the metal balances from shaft deliveries to final metal production. Accurate measurement of the grade and tonnage of run-of-mine ore is important for four main reasons; ? It enables the measurement of the production from different profit centres to within statistically determined confidence limits for daily, monthly, or annual averages. The profit centres could be individual shafts within a mining complex or ore treated on a toll basis ? The monthly production at shaft head is compared to the grades and tonnage determined from underground sampling and mass measurement in terms of a shaft call factor ? The sum of the production from the shafts is the input to concentrators. This input is a major part of the total input into a complex with concentrators, smelters, and refineries. In terms of the Codes of Practice for Metal Accounting the inputs are compared to outputs and inventory changes to assess the efficiencies and unaccounted losses or gains at the various stages in the flow of metal from source to market ? On a daily or daily moving average basis, the grades and tons from shafts are monitored and compared against these quantities from underground measurements. This acts as a control on off-reef mining, dilution, and other factors underground. Accurate measurement of grade of ore at the shaft head has been a challenge because of the large particle size. The conventional wisdom has been that ore can be sampled accurately only after it has been milled to give a slurry that is sampled as feed to a flotation process. However, when the ore fed to a flotation plant comes from multiple sources each source has to be sampled separately. So, relying on the grades determined using the sampling of concentrator input with cross-stream slurry samplers is not an option for determining the grade from an individual shaft. Impala has developed a system for sampling and weighing run-of-mine ore from multiple shafts. The system involves sampling the inputs to the plants using cross-belt (hammer) samplers and weighing the deliveries using in-motion railway weighing systems. Many samples are taken. Individually they have a high variance but, as a consequence of the averaging effect of large numbers and as shown by statistical analysis, the mean results are fit for the purposes of daily grade control for shafts and for monthly accounting of production from individual shafts. In the metal accounting systems at Impala, the measurement of input, including ore and toll-treated material is compared to the output in the form of final metal and tailings losses, as well as any inventory change that takes place, in order to determine a final metal balance from mill feed to product. The calculated inventory is compared to that measured, and the difference, or unaccounted- for metal, is then reported as a percentage of input. The balances obtained over several years yields balances for platinum that are below 1% imbalanced. Keywords metal balancing, platinum mines, AMIRA codes of practice, metal accounting, sampling, run-of-mine ore, statistical analysis.

Jan 1, 2014

By M. Timusk

"The working environment for ground support installation in mines has improved during the last 20–30 years, with more mechanized equipment for installation of ground support elements such as bolts, cable bolts, and screens. Ground support installation productivity has, however, not followed the same development curve, remaining more or less constant. In some cases, for example the mechanized installation of bolts, productivity has even dropped. One reason for this is that modern mechanized bolt rigs are complex. In this paper we evaluate manual and mechanized ground support systems, propose a way to measure the productivity of bolt rigs, and make relevant comparisons between different mines and equipment. Some productivity measures for rock reinforcement are suggested, using productivity results from eight case study mines.IntroductionTo improve safety for operators and equipment underground, ground support systems (bolts, screens, etc.) are installed in mines to stabilize the rock mass (Hoek, Kaiser, and Bawden, 1995). Important questions to ask when selecting a ground support system include where ground stability problems are located, why they have occurred, how problems should be addressed, and when and how the ground support system should be installed (Hadjigeorgiou and Potvin, 2011). The performance of bolting and screening operations in underground mines is important for both safety and productivity reasons. With greater mine depths and an increasing focus on safety, ground support has become a significant bottleneck in the production process of many mines.Many factors play a role in establishing safe and stable underground structures. Equally, there are several factors to consider in productivity, including the mining method, organization, logistics, mechanization level, and procedures. Today, most mines in Scandinavia have changed from manual to mechanized bolting, as this improves operator safety and arguably boosts net capacity. Internationally, however, manual installation of bolts remains common, with some claiming that manual installation is more productive (Bawden, 2011)."

Jan 1, 2016

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

By D. F. Caicedo, I. A. Brum, L. A. Betancourt

Ferricyanide ()()*is one of the most stable cyanometallic complexes present in the gold mining effluents. This cyanocomplex is hard to degrade by natural attenuation and generates a negative impact on aquatic environments. Although free cyanide (CN-) can be obtained by acidifying the solution, the CN- is lethal for all forms of life. The oxidation of ()()* in a typical photocatalitic system was evaluated with the addition of H2O2. To verify the degradation, chemical parameters, such as free cyanide, the formation of ammonia, nitrate, and total iron were analysed at the end of the process. The degradations obtained were up to 70% in a heterogeneous photocatalysis system with TiO2, and a low rate of dissociation was observed by photolysis. The best result was achieved with the H2O2 and TiO2 photocatalytic system, and the stoichiometric concentration was about 2.5 times less than the peroxide used in the real gold mining industry, reaching 83% degradation. The photocatalytic process obtained less toxic byproducts than the original synthetic ferricyanide used as mining wastewater. Keywords: Cyanide, heterogeneous photocatalysis, titanium dioxide, UV radiation, gold wastewater

Jan 1, 2020

By O. S. Lubbe, G. Annandale, J. W. van Wyk

This paper deals with the development and evolution of room and pillar mining in the South African chromitite and platinum mining industry over the past sixteen years. The paper describes the need for cheaper, more effective and safer mining methods in hard rock mining. It also describes how a mining method traditionally only applied in coal mining in South Africa evolved into a method ideally suited to conditions in chromitite and platinum mines. The paper also touches on joint efforts from mining houses, mine management and equipment manufacturers to design and build mechanized equipment custom designed and unique to South Africa in order to overcome challenges presented by the harsh operating conditions encountered in the mines in the Bushveld Complex.

Sep 1, 2001

By L. G. Austin

The paper summarizes the current state of development of simulation models for SAG and FAG mills, and gives the results of recent investigations of the physical processes occurring in autogenous grinding. The breakage process is treated as the sum of three regions of breakage actions: normal breakage caused by nipping of particles between media (steel balls or pebbles); abnormal breakage caused by media when the particle or lump is too big in relation to the media to be readily nipped; and self-breakage resulting from the chip¬ping fracture and abrasion of the tumbling action of rock lumps. Each region of breakage action has associated specific rates of breakage and primary progeny fragment distributions. A simplified form of the model was used to predict the performance of an 8 m diameter SAG mill with L/D = 0.5 grinding a copper ore, and predicted maximum capacity and minimum kWh/ton at about 6% ball load at 25% total filling. Two FAG mills of L/D = 2 were necessary to give the same capacity, and the simulations indicated a lower kWh/ton for these mills. For this ore, both systems were technically feasible.

Jan 1, 1987

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

Jan 1, 1978

The mathematical models of semivariograms can be classified according to whether or not they correspond to situations where the second order stationarity conditions are satisfied (§ 3.3.4). If second order stationarity exists, the a priori variance s2 of x (z) also exists and is finite. For large distances h such that x (z) and x (z + h) are not correlated, the semi- variogram ? (h) will reach a value equal to s2 [this is a consequence of (3.27) above]. This limiting value is called the sill C of the semivariogram, and the distance at which ? (h) reaches the sill is called the range. The range of the semi- variogram obtained from a given type of sample corresponds to the distance of influence of these samples. If only the intrinsic hypothesis is satisfied, the sample variance is an increasing function of the size of the area or volume in which the samples are located, and the semivariogram ? (h) will be a continuously increasing function of h. Remark: It will be shown in Chapter 7 that the variance s2 of x (z) in the ore body O is equal to the average value of ? (h) in O. If ? (h) is a non-decreasing function with sill C, the average value of ? (h) in O will be less than C. s2 and C will be equal only if for some values of h in O, ? (h) exceeds C. In practice, if the range of the semivariogram is small with respect to the dimensions of the ore body, the difference between C and s2 will be negligible.

Jan 1, 1978

If an orebody has been drilled to achieve some level of regulatory compliance, then a number of associated geological databases will exist, representing 10 000 to 100 000 m plus of core intervals. The databases usually contain data about assays, lithology, mineralisation and geophysical attributes. They will also include location information such as collar positions and downhole surveys. Obviously this data is collected by geologists for, predominantly, geologists and mining engineers. However, from a process design viewpoint process engineers usually ignore the geology where possible and rely on a small number of metallurgical test samples. Typically these test samples are sourced from convenient and available cores or from a small number of specially drilled metallurgical holes. One of the worst instances known to the author was the design of a SAG mill using only two SAG specific test results (one for each of the major ore types) while, geologically, the orebody was defined by more than 30 000 m of drilling. This paper sets out a philosophy to maximise the use of the geological data, both for process design and in preparation for the commissioning phase of projects. Geological data is used in the identification of preferred locations for metallurgical test samples, for checking the metallurgical validity of the geological ore-type definitions, where necessary developing new ore-type definitions (geometallurgical domains) and developing mathematical relationships for the estimation of important metallurgical factors across the geological database. If the estimation of factors (for example ore competence) is considered reliable enough then there is also the possibility of feeding calculated data back into the block modelling process to allow the generation of metallurgically relevant outputs in the mine plans.

Jan 1, 2007