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By S. Blancher, A. Perroton, H Smith, T. Nzima, T. Wallmach, V. Dieudonné

Chromite beneficiation is generally performed by crushing and density separation using spirals. At the Dwarsrivier Chrome mine spiral efficiencies seam to vary, the reason for which is not evident. This sometimes results in the production of low-grade products, which are sold at relatively low prices. This paper represents a Qemscan® study that investigated mineralogical reasons for these variations. Variations in liberation of chromite particles as well as variations in chromite compositions were investigated. The results showed that the so-called low grade chromite product can be improved to become a high grade chromite product by means of a refinement in mineral processing. A detailed Qemscan® database (SIP file) was developed to account for variations in chromite chemistries. It can be shown that chemical variations with respect to Cr, Al, Mg and Fe in chromite particles reporting to the scavenger tails are larger than in the high grade product. A combination of these chemical variations together with a decrease in liberation of chromite particles in the scavenger tails can potentially help to recover more chromite particles from this specific process stream.

Sep 1, 2021

By Q. Zhang, X. C. Wang, X. Q. Ao

The flotation separation of apatite and calcium-bearing gangue minerals (dolomite and calcite) has always been a problem in phosphate ore mineral processing research. The crystal structure and surface properties of minerals have an important influence on their floatability. In this paper, the theoretical and comparative analysis of the crystal structure and surface electronic properties of apatite, dolomite and calcite were carried out using the first principle calculation based on density functional theory. As a supplement and validation, the surface wettability of three minerals under different flotation conditions were compared and analysed by contact angle test. The results theoretically revealed that the three calcium-bearing mineral surfaces have similar surface electronic properties and thus exhibit similar floatability. In the flotation process, the anion difference between apatite and carbonate gangue should be fully utilised, and the minerals can be separated only after surface modification by flotation reagent. The contact angle test shows that phosphate and carbonate can be separated by using anion flotation collector after surface modification with acid. It is expected that this research is of interest for understanding the surface structure and electronic properties of apatite and carbonate gangue minerals and providing the theoretical basis for surface interaction. Keywords: Apatite, dolomite, calcite, surface structure, electronic property, density functional theory

Jan 1, 2020

By M. Izadi Yazdan-Abadi, S. H. Amiri, M. Ramezanizadeh, M. Bazmandeh

Iron ore concentrate is used as the fresh feed of pelletising plants. The green pellet properties depend on iron concentrate characteristics such as particle size distribution (PSD), specific surface area (Blaine value), iron grade, moisture content and grinding methods. The grinding methods affects particle size distribution and Blaine value. To find out the effects of grinding methods on pelletising process, green pellets were produced with concentrates that were reground by means of HPGR (high pressure grinding rolls) and ball mill. The Blaine values of ground concentrates in both types of milling were approximately 1400, 1600 and 1800 cm2/gr. The results of green pelletising tests on a pilot plant scale showed that at the same Blaine values, drop numbers of green pellets produced by ground concentrate inside HPGR were higher than the green pellets produced by ground concentrate inside a ball mill. Also, reground concentrates by means of HPGR, in comparison with ball mill, caused the production of green pellets, at higher wet and dry compression strengths. As a result, it was found that preparing the pelletising feed by means of HPGR led to more positive effects on the properties of green pellets. Keywords: Ball mill, HPGR, green pellet, drop number, wet and dry compression strengths

Jan 1, 2020

By H. P. Kritzinger, T. C. Kingsley

Rotary kilns are used for a variety of mineral processing operations. Hatch makes use of a kiln model developed from first principles to evaluate designs for its clients. This tool has been applied to a variety of pyrometallurgical applications. This paper illustrates the application of numerical optimization techniques in combination with the kiln model in the interrogation of a generic iron-ore reduction process. The fundamental modelling concepts are explained, followed by a description of the optimization approach. The results show how the combination of the two methods, with modern computing power, can generate a large number of viable design and operating candidates.

Jan 1, 2014

By R. Van Deventer

The BIOX® process was developed for the biological pre-treatment of refractory gold ores and concentrates ahead of conventional cyanide leach gold recovery. Rights to the process are currently with BIOMIN Technologies SA, a subsidiary of Gold Fields Limited. There are currently eight operating installations worldwide employing the process on a commercial scale. EKATO is a company specializing in developing new or optimizing existing mixing applications. EKATO has acquired a vast amount of expertise in agitation over its 75 year history. In a joint research project the reactors of the BIOX® process were characterized from the aspect of their mixing performance. BIOMIN is constantly testing new mixing solutions and reviewing potential vendors to increase the efficiency of the BIOX® process. EKATO?s intention was to qualify as an approved vendor for supplying agitation equipment to the BIOX® process. A two step approach was planned: In phase one of the project EKATO would develop an alternative agitation solution to the established option, exhibiting at least similar performance levels. In phase two potential possibilities to improve the overall design would be developed. This paper focuses on phase one and addresses the systematic approach applied by EKATO in characterizing the mixing processes. Mixing tasks were assessed individually applying basic theory and scale-up and -down rules to the individual tasks. Testing with model systems was done at the EKATO technology center in Schopfheim, Germany, on scales of 50 liters and 1 m³. The results showed that the ISOJET-B impeller design showed promising performance under BIOX® reactor conditions. Scale-up with the ISOJET-B was done in order to apply it in the 21 m³ live volume test reactor at Fairview mine in South Africa. At Fairview tests were performed using model systems and eventually under real plant conditions with BIOX® slurries. The results were a success and confirmed that the scale-up factors determined during the testing at EKATO?s technology center could be substantiated in the ?model scale? 25 m³ reactor. Testing under the actual process conditions showed that all design parameters were within the desired range to be considered an excellent leaching performance. This successful joint development shows the importance of a close cooperation of technology licensors or end-users and equipment suppliers. It is vital for understanding all factors influencing the mixing performance of processes. Exercises such as this will provide equipment suppliers and plant operators more confidence in managing further scale ups at ever larger engineered plants.

Jan 1, 2009

By D. van der Westhuizen, H. Krieg, M. Kruger

In the field of Fischer-Tropsch synthesis catalysts, cobalt, platinum, and aluminium are the primary metal constituents of the conventionally used cobalt catalyst. While platinum recovery remains a focal point in this field, a recent endeavour by a South African company emerged, which aimed to recover cobalt and aluminium from spent Fischer-Tropsch synthesis catalysts for potential use in the agricultural sector. This study aimed to optimally separate cobalt and aluminium from spent Fischer-Tropsch synthesis catalyst for this purpose. It further leverages the OLI database to predict metal speciation during solvent extraction to aid with experimental planning. Shake-out tests were conducted to determine optimal separation. conditions, which were validated using three distinct methods: (i) evaluating the experimental error, (ii) comparing results with similar research, and (iii) validating results against the OLI database. The investigation revealed the pivotal role of the aqueous pH yielding effective separation at pH 3.13 ([H2SO4] = 2.5 × 10−4 M) when using 20 vol.% CYANEX 272 and 50 mol.% pre-neutralisation. Effective cobalt scrubbing was achieved with 50 g/L Al at pH 2.8, while successful stripping required 1 M H2SO4. Competitive interactions between complexing aluminium and cobalt species were observed when contacting with CYANEX 272 at a pH < 4. Equipment design analysis for a targeted separation efficiency of 87% dictated the necessity of two mixer stages and a settler measuring 1.5 m × 1.5 m × 6.0 m (height × width × length). This settler would ensure sufficient residence time for gravity separation at a flow rate of 10 m3/h.

May 27, 2025

By M. R. MacIver, M. Pawlik, S. Finora, H. Alizadeh

The dispersion of mature fine oil sands tailings (MFT) by the addition of sodium lignosulfonate was studied using contact angle measurements, optical scattering, and particle size measurements. Lignosulfonate caused the release of residual bitumen to the slurry surface and settlement of fines. Dynamic contact angle by captive bubble measurements were carried out on bitumen to determine the effect of the dispersant on the wettability of bitumen. Lignosulfonate caused a change in the aggregation state of the MFT and increased sedimentation of particles, as indicated by optical scattering measurements. Zeta potential measurements indicate that this change was caused by an increase in adsorption of lignosulfonate onto particles, which caused improved settling of the colloid. Ultraviolet Visible (UV) spectrophotometry and organic carbon content measurements showed that only a small amount of the reagent remains in the aqueous phase of the tailings, which is critical for decontamination of recycled water. Keywords: Oil sands tailings, bitumen recovery, dewatering, dispersion, surface chemistry

Jan 1, 2020

By F. Nakhaei, M. Le Roux, Q. P. Campbell, S. Botlhoko

The results of coal sink and float tests are plotted as washability curves. Analysis of these curves indicates the most effective method by which the coal can be cleaned. Sink and float experiments are samplingdependent, destructive, and use toxic chemicals. The present research introduces an alternative method based on a 3D imaging system called RhoVol, in which the density of individual particles is determined from mass and volume measurements. A quantitative error analysis was conducted on coal sample density measurements obtained by RhoVol, and the main factors influencing the errors identified and investigated. The results show that the drawback of this technique is related to its not being able to detect hidden concavities in the particle, resulting in an overestimation of particle volume. Furthermore, it is difficult to capture the impact of porosity and cracks on the volume of coal particles obtained from 3D silhouette images. This mismatch between the RhoVol data and sink and float test results has led to attempts to apply neural network (NN) and linear regression techniques to produce a fully reliable model for correction and estimation of coal density. The NN approach offers superior predictive capability over linear regression, and the estimated density distribution is in line with the sink and float analysis. The root mean square error in estimation of density using the NN model was less than 0.05 g/cm³.

Aug 2, 2022

By H. Ruthert

An understanding of wear in systems conveying solids is extremely important from the standpoints of design and economics. The lifetime of any bulk solids-handling system depends on the type of solids present and the operating parameters of the transportation system. The relationship between wear in backfill pipelines on South African gold mines and the transportation system&apos;s operating parameters is well understood. However, the effect of the transported solids on the pipe wear is less well understood, because of an inability to characterize particle sharpness. The sharpness of the particles, together with their size and hardness, is responsible for the aggressivity of particles, or their ability to cause damage and wear. This paper presents a novel method for the characterization of particle sharpness. The results presented rank particles according to the sharpness of their surfaces.

Jan 1, 1993

By S. Bradshaw, A. Mabentsela

"Physical and numerical modelling methods were followed to identify mechanism(s) for tundish slag entrainment in a bare tundish and one with a flow control device (FCD).The physical and numerical models made use of water and paraffin to model steel and slag respectively. Observations from the physical model showed that the steel-slag interface remains immobile in both cases. Entrained paraffin formed droplets approximately 1 mm in diameter. Results from both models (numerical and physical) showed that in both cases (bare and FCD case), areas of high entrained slag concentration exist near the inlet region. The entrained slag concentration decreases towards the tundish endwalls.Flow patterns and velocities tangential to the steel-slag interface from the numerical model showed that slag entrainment in both the bare tundish and tundish with a FCD possibly takes place via two mechanisms. First, the slag moves across the steel-slag interface via mass transfer; secondly small velocities tangential to the interface at depths greater than 10 mm below the interface carry the already ‘entrained’ slag into the bulk steel phase. These tangential flow patterns are dominant in the inlet region, hence the high concentration of entrained slag in this region. IntroductionThe tundish serves as the last metallurgical vessel through which steel passes before solidifying in the moulds. It is in the tundish that the last traces of non-metallic inclusions should be removed, otherwise the inclusions carry over to the moulds and cause defects in the steel product. In the tundish, the slag is less dense than the melt and thus resides on the top of the melt. The slag provides a sink into which the non-metallic inclusions float to and dissolve. The slag also protects the melt from air and heat loss. However, when slag is entrained in the melt as a result of increased turbulence or shearing at the steel-slag interface, slag can become a source of nonmetallic inclusions.Numerous studies on flow patterns in the tundish have been carried out since the introduction of the tundish. These studies were aimed at improving the flow characteristics in the tundish (Chattopadhyay, Isac, and Guthri, 2010; Cloete, 2014; Jha, Dash, and Kumar, 2001; Jha, Rao, and Dewan, 2008;"

Jan 1, 2017

By M. R. L. Blackwell

Over the period 1964 to 1969 Conzinc Riotinto of Australia undertook and completed an evaluation of a large low-grade copper orebody on Bougainville Island in the Territory of Papua and New Guinea. From the outset it was clear that the geographic, climatic and topographic characteristics of the area would necessitate a heavy capital outlay on production and support facilities. Both the physical problems and the magnitude of the investment amplified the need for a thorough and rigorous evaluation of the various strategies for exploiting the orebody. In view of the number of independent and inter-related variables and the flow of new data, a computer-based evaluation process extended the scope and depth of the analysis considerably. The system used permitted an iterative assessment and re-assessment of the various strategies with the results becoming increasingly refined with time. This process encompassed the modelling of the orebody, the simulation of alternative operating strategies and the determination of the financial profitability of the project,

Jan 1, 2014

By M. -A. de Ville d’Avray, J. Bosman, S. Brochot

Dense Medium Separation (DMS) technologies are used for light (coal, lithium) or heavy (chromite, iron ore, diamonds) minerals concentration, but also for ore pre-concentration (Pb/Zn) or waste (plastics). Dense media are mainly formed from a suspension of magnetite or ferrosilicon in water. Such DMS circuit design or optimisation requires a full and detailed material balance which can be obtained by the aid of modelling and simulation tools. This balance is not limited to ore and its valuable minerals, but also the recovery of the dense medium itself. If the density is the main property used for separation, the particle size plays a non-negligible role, and, more precisely, the liberation classes which can be associated to the washability curve. The paper presents how the modelling and simulation platform USIM PAC can answer this challenge with the set of models for DMS operating units such as drums or cyclones, and their associated screens (drainage, rinsing) and magnetic separators for medium recovery. Some examples for mineral concentration will illustrate this approach. Keywords: Process simulation, process modelling, dense medium separation, process optimisation

Jan 1, 2020

By G. van Aswegen

The geometry and morphology of a set of low-angle fractures around a stope in a deep Witwatersrand gold mine are explained in terms of extension fractures forming under variable conditions of stress. Primary extension fractures (E1) form some distance ahead of an advancing stope along the s1, s2 plane. With stope advance, a couple of these fractures end up in a stress regime conducive to transpressional shear and a secondary set of extension fractures(E2) is formed at a high angle to the primary fractures. i.e. at a low angle to the stope. As the E2 fractures are undermined, they migrate into a stress regime of transtensional shear and a third set of extension fractures (E3) may develop between E2 fractures. These have sigmoidal shapes, being parallel to the E2 fractures at the E2 discontinuity where s3 is negative, and curved through the unfractured rock between E2 fractures where s3 is positive at the instant of fracturing. The fractures all display fractographic features characteristic of dynamic extension failure with striae indicative of the direction of rupture propagation and the local, instantaneous orientation of s1.

Jan 1, 2012

By L. C. Woollacott, A. K. Tripathy, J. H. Potgieter

This paper presents the second of a two part study on density stratification in a laboratory batch jig. The first study, reported elsewhere, investigated the effect of operating conditions on the stratification profile achieved at equilibrium. The study reported in this paper investigated their effect on the kinetics of density stratification under 18 different sets of operating conditions - five for binary systems with different particle densities; and 13 for a ternary system with different configurations of the jig cycle. Although the study was academic in nature (it involved simple systems of 8 mm glass beads) it has a number of practical implications. It found that the most influential operating variables affecting stratification kinetics are the amplitude of water displacement, the pulsion hold time, and, to a lesser extent, the pulsion time. It also found that reasonable rates of stratification can be expected in systems with density differences as low as 237 kg/m3 but below this the kinetics deteriorate significantly. The two studies together suggest that, within a broad range of operating conditions, the equilibrium stratification profile is independent of control variables and it is the control of stratification kinetics that has the primary influence on the quality of density separations in a jig. Keywords: Jigging kinetics, stratification, equilibrium stratification, batch jig

Jan 1, 2020

By L. Ziyuan, S. Chunbao, K. Jue, H. Yang, S. Tichang

In this study, potassium ferrocyanide, a non-toxic cyanide precursor in dark and diffuse reflection environments, was applied as a reagent for the leaching of gold. The free cyanide ions were gradually released from the potassium ferrocyanide solution under the ultraviolet light. Orthogonal leaching experiments were performed in gold ore to analyse the effect of solution pH, potassium ferrocyanide dosage, and temperature in potassium ferrocyanide solution system under UV light. Response surface methodology (RSM) was applied to explore the role of potassium ferrocyanide in gold leaching, Optimised results showed that the gold recovery reached 67.74% in a high-alkaline environment at a 12.6 pH, 3.8 kg/t potassium ferrocyanide dosage, 62°C, and irradiance of 10mW/cm-2. The gold leaching kinetics was monitored by quartz crystal microbalance with dissipation (QCM-D) of potassium ferrocyanide solution. The results indicate that the gold extraction process consists of two processes: adsorption and leaching, and a rigid adsorption layer formed on the reaction surface. Furthermore, Xray photoelectron spectroscopy (XPS) analysis of the gold sensor surface after leaching reaction showed that -C≡N appears on the gold sensor surface, and the gold is oxidised to form AuCN complexes. Keywords: Gold leaching, potassium ferrocyanide, UV light, QCM-D, AuCN complexes

Jan 1, 2020

By L. Rojas Mendoza, F. J. Hrach, A. Gupta, K. P. Flynn

ST Equipment & Technology (STET)’s tribo-electrostatic belt separator technology allows for the beneficiation of fine mineral powders by means of an entirely water-free technology with high throughput and low energy consumption. The STET separator is suited for separation of very fine (<1 μm) to moderately coarse (500 μm) particles, in contrast to other electrostatic processes that are typically limited to particles >75 μm in size. STET has performed exploratory studies with several iron ores including tailings and experimental results to date have demonstrated that low-grade iron fines can be upgraded by means of STET tribo-electrostatic separator to commercial grades (58-65%Fe). Experimental results together with high-level economic evaluations indicate that scavenging processes involving low drying costs, DSO operations and tailings beneficiation offer a commercially viable processing method to recover fine iron that would otherwise be lost by traditional processing. Dry electrostatic processing of iron ore presents a clean, low-energy opportunity for iron producers to reduce costs and wet tailings generation associated with traditional gravimetric, flotation and wet magnetic separation circuits. Moreover, STET technology allows for mining waste utilisation and resource recovery from iron ore fines and tailings, therefore offering processors a novel method to recover fines that would otherwise be difficult to process to sellable grades with existing technologies. Keywords: Iron fines, industrial minerals, dry separation, calcium carbonate, talc, barite, quartz, tribo-electrostatic charging, belt separator, fly ash

Jan 1, 2020

By A. F. Silva, R. Dockendorff, J. M. Girao Sotomayor, V. F. Navarro Torres, C. Castro

This paper shows the importance of performing probabilistic analyses in open pits, especially for mine planning, which can lead to more efficient ore extraction and meeting the acceptability criteria for safety in mine slopes. Three-dimensional stability analyses were performed to evaluate the future geometry of a large open pit for iron ore extraction in Brazil. The strength parameters of the lithologies were calibrated using ruptures in the pit walls. After determining the factors of safety (FoSs) from the calibrated parameters, probabilistic analyses were performed using the total range of values of each parameter under different field conditions to verify the reliability of the initial analysis. In this sense, it was possible to plot the probability of failure (PoF) and the FoS on the graph of slope height versus slope interramp angle (IRA) for the future pit in each lithology. IRA recommendations are made for two scenarios: (1) the best scenario: dry without ubiquitous joints and (2) the worst scenario: the water table at 10 m depth with ubiquitous joints in the most unfavourable direction. The results show that probabilistic evaluation is an important tool for establishing alert mechanisms in slopes that can be termed stable.

Jul 2, 2022

By L. A. Cisternas, R. I. Jeldres, D. Calisaya

"Flotation of copper-molybdenum sulphide ores in seawater entails critical challenges such as selective recovery of molybdenite, effective pyrite depression, and reducing the lime addition required to reach highly alkaline conditions. It is essential that laboratory flotation tests aimed at solving these problems give reliable, reproducible results and indicate the correct approach for industrial operations. Rougher flotation of coppermolybdenum sulphide ores in seawater was investigated using two different cells: a modified Denver cell and a standard commercial cell. The effect of an organic reagent on the flotation performance was tested, and the fast/slow-floating model was used to describe the results. The modified Denver cell significantly improved the reproducibility of the flotation test results, due to technological enhancements such as the impeller being driven from below without a stator, which enables the whole froth surface to be scraped with a paddle at a constant depth and rate. Organic reagents are a promising alternative to inorganic reagents for depressing pyrite in seawater. However, further studies should be conducted to investigate their impact on molybdenite recovery, as well as to evaluate the possibility of depressing pyrite after molybdenite separation. The fast/slow-floating model was found to be appropriate for describing the flotation kinetics of the copper-molybdenum ores. The parameters are useful for comparing the performance at different conditions. IntroductionOwing to the increasing scarcity of fresh water, the use of seawater mining and mineral processing is becoming increasingly important (Cisternas and Moreno, 2014). Seawater can be desalinated by reverse osmosis, but this involves considerable costs, limiting it to the big mining companies (Akgul et al., 2008; Leidner et al., 2012; Ghaffour, Missimer, and Amy, 2013). Furthermore, desalination has environmental consequences (Lee, Arnot, and Mattia, 2011); for example, a desalination plant designed to process 2.5 m3/s requires an electrical energy supply of around 30 MJ/s. To supply this power demand, a thermoelectric plant burning bituminous/sub-bituminous coal mixtures at a thermal power generation efficiency of 35% might release around 1200– 1500 t of CO2 per day. Furthermore, the effluents from desalination plants are typically discharged into the sea, and their high temperature and ionic content inevitably modifies the marine environment, with unknown consequences. The direct use of seawater is, therefore, more attractive, but it also poses major challenges since seawater contains ions that adversely affect mineral recoveries. In particular, in the flotation of sulphide ores in seawater, the floatability of molybdenite is depressed (Castro, 2012; Laskowski, Castro, and Ramos, 2014)."

Jan 1, 2017

By C. Chapman, M. G. Reading, M. P. Amsden

Ecstall Mining Limited, a subsidiary of Texas Gulf Sulphur Company, operates the Kidd Creek Mine, a 10000 tons per day base metal producer, near Timmins, Ontario. Two different types of ore are mined and milled: copper-zinc and silver-lead-zinc. At the highly automated Ecstall concentrator the ores are processed by selective flotation in three individual circuits. One of the most important metallurgical tools for process control is a sample system incorporating continuous on-stream X-ray analysis. Recently this system was automated further by the addition of computer control of reagents for two copper-zinc flotation circuits. The computer programs, utilizing optimum seeking methods and smelter contract terms, have increased copper recovery by 1.1 per cent, zinc recovery by 1.4 per cent, and have reduced reagent costs by 16 per cent. Although not expected, copper and zinc concentrate grades were improved slightly as well.

Jan 1, 2014

[The following notations will be used: O an ore body. z a point in O. z&apos; another point in O. w0 (z) a point support of infinitely small dimensions w0 centred in z. w (z) a sample (or block) of finite dimensions kv centred in z. W (z) a block of size W greater than or equal to w. W&apos;(z) a block of size W&apos; greater than or equal to W. W" (z) a block of size W" greater than or equal to W&apos;. x (z) value of the regionalized variable x with support wO at point z. p (z) average value of x in w (z). pw WZ) = E[x(z&apos;)l zt in w(z) pw (z) average value of x in W (z). pwl (z) average value of x in W&apos; (z). pwU (z) average value of x in W" (z). Note that pW (z), pw (z), pwf (z) and pw,, (z) are (regular- ized) regionalized variables with support w, W, W&apos; and W" respectively. The relative sizes of wO, w, W&apos;, W" and O are represented schematically in Fig. 7.1. The variance of pw (z) when w (z) takes all possible positions in O is known as the dispersion variance of w in O and is denoted by a? (w in O) or a\: 0; = a2(w in a = Ew,z, inn {[p~ (z) - p121. (7.1) For convenience, the following simpler notation will be used: a> Ew in n [(p w - pl21. Consider now a large block W (z) in O with average value p~(z), and all the possible smaller blocks (or samples) w (z&apos;) of size w in W (z). We can calculate the variance of the blocks w (z&apos;) in the block W(z), which is the dispersion vaciance of w in W (z), from the relationship a2 [w in W(z)l = Ewcz,, in W(Z) {[PW (z&apos;) -pw (z)l21. (7.2) Provided the intrinsic hypothesis is satisfied (§3.4.4), this variance is a function only of the dimensions of the supports w and W, and is independent of the position z of the block W (z). We can therefore define the dispersion variance of w in W, as follows: u2 (win W) = Ew in w [(ptti - PW)~]. (7.3) In cases where the intrinsic hypothesis is not satisfied, the variance of samples w in blocks W may vary only slightly from block to block, so that the average dispersion variance of w in W (z) for all possible W (z) in O can be used: ayw in W) = Ew(,, ~n n {a2 [W in W (z)]}. (7.4) The following example will help to illustrate the importance of the variance of dispersion. Assume that we plan to develop a bedded coal deposit Q. We consider mining the ore body with only one giant dragline, which will extract each day a block of coal of size W&apos;. The total area mined in a year will have a size W". We want to know whether this scheme is acceptable, given that the daily variation in ash content must not exceed a given percentage specified in the sales contract, which is renewable on a yearly basis. On a given day, if we mine the block W&apos; (z), the ash content will average pwT (z). In a period of one year, the expected daily variation in ash content is measured by the expected variance of pwf (z) in W", i.e. by a2 (W&apos;in W"). An alternative mining method might be to use two smaller draglines, each one mining W&apos;/2 of ore per day, and Wn/2 per year. If the draglines are used to mine two distinct sections of the deposit, the expected daily variation in ash content will be u2 (W&apos;/2 in Wj1/2)/2 Other situations, where economic decisions cannot be made without knowledge of the dispersion variance, are illustrated in § 7.4 and 7.5 below. Remark: The notation a2 (w in W) is used in this publication because of its clarity. An alternative notation, which is increasingly accepted in the literature, is s2w/W. ]

Jan 1, 1978