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By Pandey H. D.

The paper describes a fluidised bed ion exchange method for simultaneous removal of phenols and cyanide from the effluent. Use of an eluant enables regeneration of the resin in the continuous operation mode. The breakthrough experiments conducted both on the laboratory scale and on a pilot plant scale have shown that while the level of phenol can be brought down from 462 ppm to about 6 ppm, the free cyanide is almost totally removed. An examination of data indicates that the method can serve the twin objectives of pollution control and phenolic compounds recovery.

Jan 1, 1992

By James P. Kimball

AMONG the curious results of the recent advance of prices in the iron trade of the United States, one of them at least is to be regarded as of great importance. I allude to the utilization of mill cinder as a cheap and almost costless substitute for high-priced iron ores in many blast furnaces, situated within easy reach of such raw material. It has been, with but few exceptions, the practice in this country, based upon tradition rather than upon authority or European precedents, to waste this material on 'account of its high proportion of silicic and phosphoric acids, although known to contain more iron than most ores, and although also known to be sometimes applied to the blast furnace in greater or less quantities without serious detriment to the iron for specific purposes. While in use to a limited extent in the Hocking Valley and Hanging Rock iron regions of Ohio for several years, its use in Western Pennsylvania has only become general of late, under the exigencies of high prices and a short supply of ore. Especially has mill cinder largely entered into the stock of furnaces attached to rolling mills in and about Pittsburgh. Under such circumstances the cinder pig has been paddled on the premises, and the malleable iron produced has been unexpectedly good. Cautiously as at first mill cinder has been applied, it is evident that the temptation to use it freely is a strong one whenever the commercial rates for high-class ores are out of proportion to the general conditions of the iron trade, as sometimes happens in this country, especially as the free use of it is apparently justified by the quality of the iron produced from this cheap and abundant material. Indeed the consumption of cinder pig has., not been wholly confined to mills using up the production of furnaces belonging to the same plant. One furnace at least on the Ohio, at Covington, for several' months has been making foundry pig from "all cinder." The iron has gone into the general trade. It is probable that malleable iron of good quality can he made from the poorest cinder pig, but with what degree of economy will

Jan 1, 1881

By Glenn Kosick, Roger Amelunxen, Glenn Dobby

"The variability in flotation response within an orebody is often a significant problem to address during the design phase of a flotation circuit. In addition, for existing operating plants, the reasons for such a variability need to be clearly understood and accounted for if plant performance is to be optimized. MinnovEX Technologies, in collaboration with major mining companies, is developing methodologies and tools to address the issue of variability in ore characteristics (such as ore hardness and flotation response). The tool is used for design and scale-up of flotation circuits from lab flotation data, and for prediction of recovery and final concentrate grades throughout the mine block model for any given circuit design.INTRODUCTIOTNH: EI SSUEB EINGA DDRESSEDThis paper describes the current development of a methodology and software tool for improved flotation plant design and enhanced prediction of froth flotation performance in an operating plant. The need for this tool is attributed to two primary factors: variability of flotation response properties throughout an orebody and related difficulties with scaleup from laboratory tests. Consider these in more detail.It is well recognized that separation performance via froth flotation will vary significantly within a single mineral deposit. This has been enhanced through the wide application of SAG milling. Throughput with SAG mills is more susceptible to ore hardness changes than is the case with crushing-rod-ball circuits; it is not uncommon to see SAG mill throughput to vary by up to 100% on a regular basis, e.g. 1000 tph to 2000 tph.The implication of this on laboratory testing for prediction of metallurgical performance is as follows: it is unlikely that either the plant grind (size distribution) feeding froth flotation or the flotation residence time will be known at the time of laboratory testing for a given block of ore. Hence, the grind used for the laboratory test is not likely to be that which actually occurs once the ore is processed, and the laboratory retention time may not represent the plant conditions."

Jan 1, 2002

By M. F. G. Bruce

Two backfill systems have been developed on West Driefontein, namely the centrifuge dewatered tailings system and the cyclone-classified tailings system. Modifications to the two systems since the publication of the original paper (Close and Klokow, 1985) are discussed in addition to the results obtained. Considerable experience has been gained from the operation of the centrifuge dewatering units as well as the placement of dewatered tailings in a difficult mine environment. The centrifuge dewatered tailings method has proved successful in the extraction of a highly stressed block of ground at No. 5A Sub-vertical Shaft. The utilization of backfill support in this area made it possible to dispose of a high-grade barrier pillar. This pillar was considered necessary prior to the introduction of backfill support. The recovery of the gold from this pillar made the use of dewatered tailings backfill cost- effective, despite high labour and maintenance costs. Current experience with the bagfilling method of placing cyclone- classified tailings indicates that it is viable and requires considerably less capital investment. Although expensive at present, it is envisaged that costs will decrease once cheaper bags and other forms of stope support are used. The placement of backfill in small-diameter sausage-type bags requires no change in mining cycle and allows the backfill to be placed close to the stope face. Both backfill systems are being expanded but preference is to be given to the cyclone-classified tailings system.

Jan 1, 1988

By M. J. Deats

INTRODUCTION To prepare the reader adequately, reference should be made to the paper 'The Pioneering of Fully Mechanized Longwall Coal Mining in South Africa' by R. T. Naude and M. J. Deats, published in the February, 1967, edition of the Journal. At the time mechanized longwalling had been proved operationally feasible with encouraging results since its inception in South Africa in mid 1965. Subsequently, further top seam panels were successfully extracted with improved productivity and with some modification to equipment. In 1968, after an overseas visit by mine officials, equipment specific to suit local conditions was acquired and lower seam trials commenced. Despite initial obstacles and difficulties the first panel was successfully mined. Modification and improvements to equipment and techniques resulted in the second lower seam panel being extracted economically during 1969-1970 and with productivity exceeding even that of top seam faces. During extraction of the second lower seam panel, gradual and complete surface subsidence occurred over the panel without affecting face operations. Rock mechanics investigations had originally indicated some uncertainty regarding adverse dolerite sill behaviour which could have caused longwall mining to be hazardous. All such doubts have now been removed. RESUMÉ AS AT FEBRUARY, 1967 Mechanized longwalling was introduced in 1965 on an experimental basis in an effort to improve productivity in the newer area of the mine and to increase the quality of the comparatively dirty run of mine feed to the washing plant. In addition advantages could be predicted in the long term by better utilizing reserves of straight coking coal and increasing the life of the mine. The top seam unit was obtained on a rental basis and by the beginning of 1967, two panels, the first having a face length of 215 m, a panel length of 345 m, seam section of 1 219 mm, and the second the same face length, a panel length of 453 m and a seam section of 1 067 mm had been successfully longwalled. At this stage a best month of 24 602 metric tons with an average of 17 364 metric tons per full working month could be reported. Results were sufficiently encouraging for the company to exercise its right to acquire the equipment as its own asset and from 1967 onward, the unit has operated on this basis. From the point of view of rock mechanics, the dolerite sill over the first two panels was known to have 'bridged', only the material below the base of the sill having truly 'goafed'. No adverse pressure effects had significantly affected face operations except for two 'bumps' towards the end of operations in each panel. Gate road maintenance presented no problem. The strong inflows of water experienced on the first face were now known to be associated with an isolated water bearing fault plane and were not experienced on the second face. TOP SEAM EXPERIENCE - MAY, 1966, TO DATE Panel 2 (February, 1966, to November, 1966) The operations in panel 2 (see Fig. 1 for location of panels) continued uneventfully until the final month in this panel. At this stage, the chocks behaved most inconsistently often lowering under the weight of the canopies alone. Roof trouble became so severe that the unit was unable to produce adequately and blasting of chocks became a daily occurrence. Finally 24 m short of the planned limit it was decided that a complete overhaul was the only solution and the extraction operations commenced. At this time, the only fatal accident associated with longwalling occurred when a Non-White inadvertently fell into the panzer conveyor transfer point at the main gate. Some gate road difficulties in this panel were overcome by bolting tapes to the roof as decking and allowing them to pass over the gate chocks and collapse into the goaf. Two cribbed roof falls were also negotiated by the gate chocks at the face ends without undue difficulties. It was decided in the light of maintenance problems encountered on this face that the best solution would be to appoint a foreman solely in charge of face maintenance crews. This step has to a large extent contributed to success achieved subsequently. Panel 2-face length 213 m panel length 456 m cutting height 1 092 mm average monthly output 16 443 t best month 19 130 t Panel 3 (December, 1966, to June, 1967) By the end of 1966 results were sufficiently encouraging for the company to exercise its right to acquire the equipment. This was negotiated and the unit has operated as such to the present date. Prior to installation in panel 3, all face equipment was thoroughly overhauled underground and the chocks boost-tested to yield-load. The costs of overhauling, including almost complete hose replacement, were much higher than anticipated. Advice had been received that complete hose replacement was common practice after +/- 18 months' operation. Shortly after commencement of operations in panel 3 the chocks again failed as they had towards the end of panel 2. At this stage, the suppliers advised that the valve gear should have been repaired during the overhaul as the needle and seat seals could no longer be relied upon. This operation was impossible to carry out on the face and would have been e1ttremely time consuming. Fortunately a new type of valve gear was then available from the suppliers, termed the capsule-type valve, and a complete change over could be made on the face. The encapsulated valve has a delrin pad sealing over a raised

By E. J. Maunders

This paper describes briefly a computerised model of the South African electricity system which has been developed jointly by the Atomic Energy Board and the Electricity Supply Commission. The results of an analysis of this system have been subjected to a fairly extensive sensitivity analysis which reveals that up to the year 1990 between 680 and 700 million tons of coal will be required for electric power generation, together with between 7 000 and 10 000 tons of uranium. This result is fairly insensitive to data variations, but the prediction of a cumulative requirement up to the year 2000, of between 1 300 and 1 800 million tons of coal and 25000 to 70000 tons of uranium, proves to be very data-sensitive.

By K, J. MAUNDERS

This paper briefly describes a computerised model of the South African electricity system which has been developed jointly by the Atomic Energy Board and the Electricity Supply Commission. The results of an analysis of this system have been subjected to a fairly extensive sensitivity analysis which reveals that up to the year 1990 between 680 and 700 million tons of coal will be required for electric power generation, together with between 7 000 and 10 000 tons of uranium. This result is fairly insensitive to data variations, but the prediction of a cumulative requirement up to the year 2000, of between 1 300 and 1 800 million tons of coal and 25 000 to 70 000 tons of uranium, proves to be very data-sensitive.

Jan 1, 2014

By Paul H. Earl

This paper discusses the evolution of a modeling methodology for explaining price behavior in the aluminum industry. Three generations are described, each utilizing as a foundation a microeconomic stages-of-processing approach. The second generation represents an improvement over the initial version, by incorporating more rigorous specifications of energy cost, and market strength (demand-supply balance) as well as endogenous treatment of market strength. International linkages across prices, costs, and markets, are the major extensions in the third generation. The discussion covers theoretical considerations, data problems and limitations, and model specifications. Simulation and forecasting properties of the models are also addressed.

Jan 1, 1979

Gold was discovered in the Bendigo area of Victoria in 1851 (Willman and Wilkinson, 1993), and all the early gold mining of any note involved washing (puddling) the gold out of the regolith or alluvium. The waste material from this process was a semi-fluid mixture of rock debris, soil and water, referred to as `sludge'. Puddling machines were gradually introduced to speed up the puddling process (Cole, 1994), and by 1855 an estimated 2000 machines were in the district (Anderson, 1978). In 1859 it was estimated that approximately 2 293 000 m3 of material was puddled annually by the machines on the eastern side of the goldfield, whose waste drained into Bendigo Creek and its tributary gullies. It was also estimated that after the gold was removed, approximately one-quarter of the residue/sludge consisted of the heavier, coarse-grained material which settled out fairly quickly, while the remainder, approximately 1 720 000 m3, was the fine-grained material which flowed downstream for some distance (VPP, 1859 - 60). From these figures it can be assumed that for the ten years during which this volume of puddling was maintained (1854 - 1864) over 5 700 000 m3 of gravels and sands and 17 200 000 m3 of fine-grained sludge had been discharged into and around Bendigo Creek. This was enough to cover an area of over 400 km2 to a depth of 5 cm. By 1859 the problems associated with the sheer volume of sludge being discharged were such that a Royal Commission was appointed to `Enquire into the Best Method of Removing the Sludge from the Gold Fields' (VPP, 1859 - 60). The goldfields referred to were those in the Bendigo area around the township of Sandhurst (now known as Bendigo). The Report of the Commission (VPP, 1859 - 60) stated that: `... inspection of the country bordering upon the course of the Bendigo Creek, to a distance of about fifty miles from Sandhurst . . . ' had revealed that the sludge had ' . . . filled up watercourses and flooded pasture lands . . . '. It also noted that ' . . . even on the plains, thirty or forty miles away from Sandhurst, where the sludge flows thin, and is relieved from its heavier particles, we found it baked into a perfect concrete, and in thicknesses varying up to two feet or more . . . '. The italics were used for emphasis in the original text. As it was considered unlikely that the physical evidence for such widespread inundation would have disappeared completely over the intervening 130 or so years, a project was initiated to locate any evidence of the inundation in the current landscape. If such evidence were to be found, then an estimate could be made of both its extent and its effects on the topography, drainage, and land-use of the inundated area. Extensive field work has determined that over 700 km2 to the north of Bendigo was inundated by the sludge. The area has not been uniformly covered, but has occasional `inliers' which have obviously escaped inundation by being slightly higher than the surrounding areas. Today the sludge is readily identified as a very fine-grained, hard-setting, concrete-like `capping' overlying a well-developed, well-structured, pedal horizon, or in some instances, the gravels and sands of a creek bed. The thickness of the sludge capping varies between a few centimetres and three metres (Peterson, 1996). The buried topography was gently undulating, in direct contrast with the almost unnatural flatness of

Jan 1, 1997

By Coates D. F, Neil T. J, O&apos

A proper economic analysis of pit slope design must reflect the trade-off between the benefits and the increased risks of slope fail- ure inherent in steeper slope angles. However, no formal framework for a proper analysis existed to date. This paper describes the results of the past four years' effort in which a formal eco- nomic analysis framework was developed and tested through a case study. This framework, in essence, consists of the availability of tested procedures and com- puter programs. The procedures as well as the programs are divided into two broad functional categories; (1) the first category related to assessing the economic benefits and costs associated with various pit slope angles and (2) the second category that determines the overall financial impact which the assessed benefits and costs exert to the mine operator's overall economic stature.

Jan 1, 1977

By B. Maybee, J. Venter, J. Wesseloo

The selection of open-pit slope angles involves high-value decisions with small changes in slope angle, often representing significant changes in net present value. The existing methods used to define design acceptance criteria have evolved from factor of safety to probability of failure (P[F]) to risk consequence to risk frontiers, which represents current state of the art. Current design acceptance measures are based on references to published tables representing the experience and judgement of their authors, who did not specify the purpose of the measures contained therein. As the purpose of the published design acceptance criteria is not specified (i.e., definite stability, marginal stability, optimization, etc.), such tables cannot be used to achieve optimum slope angles that maximize profitability. This paper develops a design acceptance criterion that maximizes profitability by defining a formulation for optimum risk that balances expected risk and reward. The model developed is titled the Mining Risk Model (MRM), and is applied to open-pit slope angle selection through an equation for optimum probability of downside (P[D]O) that balances the upside or opportunity, the P[F], and the downside impact. This formulation for optimum risk is unique, as many authors have presented objective functions for their risk models that can be optimized, but none of the sources reviewed contained a formulation for optimum risk. The MRM is sufficiently flexible to allow the design performance measure that drives P[F], and hence P[D]O, to be selected based on the intended goal. Furthermore, the essential information that must be known to quantify optimum risk is defined. This allows users to determine what information to collect for optimum risk decisions. A further benefit of the MRM is that slope angle decisions and pit shells can be ranked to select the best option, and a threshold is provided that separates acceptable from unacceptable decisions. Finally, the workflow and information required to determine optimum risk are presented.

Sep 9, 2024

Computer programs commonly used to simulate mining operations generally require a fair amount of data. The common data input methods have been by either creating an ASCII data file or answering numerous questions during the data input phase. Both methods of data entry are tedious, time consuming, and inflexible. A screen handling system has been developed to drive FORTRAN-77 application software for the MS-DOS environment. The system utilizes keyboard functions with an aid of extended ANSI codes. It also allows a multi-view input data entries.

Jan 1, 1990

By A R. Sale

This paper highlights two aspects of the mineral sands industry in Australia: the development of the industry from approximately 1870 through to 1980, and the author’s experience in the industry from 1966 to date.The first real heavy mineral (HM) mining in Australia started in 1870 with the mining of heavy mineral slicks on the beaches along the east coast of Australia. The real potential of Australian heavy minerals was however only realised in the 1920s with the first production of a heavy mineral concentrate that was shipped to Canada for processing. Post WW 11 and the Korean War, Australia was the largest producer of mineral sands products in the world as well as a significant developer of associated separation equipment and technology. The number of producing companies in the east coast peaked at 33 in 1957, was reduced to ten by 1965, and subsequently further reduced to five in 1980 as a result of potential mining areas being declared National Parks or Conservation Reserves. Today there is one company, Unimin Australia Pty Ltd (formally Consolidated Rutile Ltd) operating on the east coast. In contrast there were three companies on the west coast in 1965, four companies in 1980, and four companies today (albeit not the same companies).There have been considerable ups and downs for the industry in Australia, however world wide it was renowned in the past as being an industry that attracted numerous interesting and innovative characters that played a major role in developing it into the vibrant industry that it is today. This, given the current climate, is predicted to continue into the future.The author has been continuously involved in the industry for over 45 years from 1966, initially as an electrician at Consolidated Rutile Ltd culminating in the role of General Manager/President of Iluka Resources Limited USA, prior to his retirement in 2009. His exposure has been world wide and has covered all aspects of the industry but in the main focused on project development and operational areas. During this time there have been significant technological advances, yet to some extent the basic principles have not changed at all. Some of the most noteworthy advances include the development of the Wright Spiral in 1977, the development of the Reading High Intensity Wet Magnet (WHIMS), the rare earth magnets, the CRL floating thickener and the improvement of analytical techniques. From a safety, health and environmental perspective there has been significant advances that the industry has much to be proud of. These include wetland restoration both in Australia and in the US, the restoration of farmland in Virginia and Capel, and the re-establishment of native species, for example at Eneabba and Richards Bay to name but a few.

Oct 5, 2011

"Mining used to be a business primarily focused on the technical aspects of getting valuable ore out of the ground and extracting the minerals efficiently. Without denying the importance of these skills, a narrow focus on technical issues is no longer enough to guarantee success when it comes to exploiting rare earth element (REE) deposits. Molycorp failed to enter the global REE market in a successful manner, while none of the many REE exploration projects has turned into an active mine so far and none is expected to commence operations in the near future. Accordingly, the world of REE is far more complex compared to other commodities. This paper looks into the REE industry to identify the factors that can connect potential U.S. REE mines to the market. The ability to break free from past thinking and become future-focused is a key driver. Mining of REE is pointless without a corresponding value-adding chain, while developing a value chain without first establishing an uninterruptible source of REE is also senseless. The mining sector must be based on the REE value chain and vice versa, along with the establishment of a market channel for the REE products that come out of the mine. INTRODUCTION It has been seven years since rare earth elements became the subjects of front-page headlines. It was when the controversial Chinese export policy for these critical commodities was epitomised in a maritime border dispute with Japan in September 2010 that resulted in the big REE crisis and price spike of 2011 (Barakos et al, 2016c; Mancheri, 2015). The world was dismayed, especially in REE-importing countries, such as the United States that was and is still totally dependent on Chinese production and exports (Barakos et al, 2016c; Kennedy, 2015). The short-lived alarm initiated a treasure hunt by way of exploration for REE deposits all over the world. The continuously growing demand on the one hand and the Chinese sovereignty of the REE-market on the other, led the rest of the world to explore their own REE resources. In just a few years, more than 400 projects were initiated to explore REE deposits outside of China (ERECON, 2015; Goodenough, 2016). The prices of REE, however, dropped rapidly and at the moment of writing this paper are in 6-year lows, at the level of the price average before the 2011 crisis (Barakos, 2017). The viability of even major established producers is being challenged, not to mention the development prospects of potential REE-market entrants (Barakos et al, 2016b; Rollat et al, 2016). Production cutbacks and industry consolidation in China impel REE market experts to forecast that prices have already reached their lowest point and have nowhere to go but up (Adamas, 2015; Roskill 2015). Yet, expectations for increased REE prices are limited and drastic changes are unlikely to happen in the near future, as there is still excess supply in the overall REE market (Barakos, 2017). Nevertheless, the low prices of rare earths are not the only reason that potential producers are struggling to enter the global REE market. Among other parameters, the separation of the individual elements seems to be the most important factor, as it is technically challenging and expensive to build and to operate."

Jan 1, 2018

By Jens Gutzmer, Helmut Mischo, George Barakos

"It has been nearly eight years since rare-earth elements (REE) became the subject of frontpage headlines. It was when the controversial Chinese export policy for these critical commodities was epitomized in a maritime border dispute with Japan in September 2010 that resulted in the big REE crisis and price spike of 2011 (Barakos et al., 2016c; Mancheri, 2015).The world was dismayed, especially in REE-importing countries such as the United States that was, and still is, totally dependent on Chinese production and exports (Barakos et al, 2016c; Kennedy, 2015). The short-lived alarm initiated a treasure hunt by way of exploration for REE deposits all over the world. The continuously growing demand on the one hand, and the Chinese sovereignty of the REEmarket on the other, led the rest of the world to explore their own REE resources. In just a few years, more than 400 projects were initiated to explore REE deposits outside of China (ERECON, 2015; Goodenough, 2016).The prices of REE, however, dropped rapidly in late 2017 and were in six-year lows, before the 2011 crisis (Barakos, 2017). The viability of even major established producers is being challenged, not to mention the development prospects of potential REEmarket entrants (Barakos et al., 2016b; Rollat et al., 2016). Production cutbacks and industry consolidation in China have impelled REE market experts to forecast that prices have already reached their lowest point and have nowhere to go but up (Adamas, 2015; Roskill 2015). Yet, expectations for increased REE prices are limited and drastic changes are unlikely to happen in the near future, as there is still excess supply in the overall REE market (Barakos, 2017). Nevertheless, the low prices of rare earths are not the only reason that potential producers are struggling to enter the global REE market. Among other parameters, the separation process of the individual elements seems to be the most important factor, as it is technically challenging and expensive to build and to operate."

Jan 8, 2018

By S Saydam

Professional engineers need to be able to apply university learning to practice. In particular, they have to take responsibility for interactions between technical systems and the complex social environments in which they operate. The most effective way of building this competency is through active experiential learning. We have been developing an advanced educational integrated simulation system to provide mining engineering students with an interactive and immersive learning experience that is not otherwise possible. This will give students an authentic experience in working with industry software packages, while also contextualising the learning in terms of the broader and longer-term impact of technical decisions. We have been piloting the system, in undergraduate courses in order to establish its effectiveness in building systems thinking competencies for mining engineering. For postgraduate students and professionals, the same tools and methods can support studies of more challenging and complex scenarios where mining engineers have to place their decisions within complex global industry contexts.

Nov 22, 2011

By Wang Zhong Qian, Liu Hui

The paper proposed a fractal and damage model for rock-breaking by blasting, which assumed that the process of rock-breaking results from intrincent fractal development and the accumulation of damage. Remarkably, the process is of fracture character. Based on the model, a computer program is compiled to calculate the 3-dimension damage distribution in blasting crater. Trial results agree well with the predicted results, showing the model set up in the paper is sound.

Jan 1, 1997

By J A. M Luz, A T. Bernardes

HukkiÆs law is an empirical law, which does not take into account several events of energy loss during the fragmentation processes. Since experimental results are very difficult to obtain, for a large range of fragment sizes, the verification of the law is very difficult. The relation between fractures and fragmentation processes with fractal geometry was proposed some decades ago. Empirical laws known in this context show basic features of fractal geometry, mainly self-affinity and power law behaviour. Thus, in this work a model was developed to simulate the fragmentation process and to check the relation between energy consumption and fragment sizes. The model is represented on a regular lattice. Links can represent pathways for fracture processes. The events of fragmentation have energy given by a probability distribution function. In the model there is no mass loss. Propagation of fractures occurs as self-avoiding random walks on the regular lattice.

Sep 26, 2011

By M. J. Gagnon

The agglomeration of particulate materials is used in many mineral processes to enhance the settling of the fine particles, Depending upon many physical and chemical parameters, the aggregates demonstrate specific density-size distributions, In this study, a fractal model of the agglomeration process is introduced, Based on reliable experimental data and on physical calculation, the model presented helps to envisage the initial formation of the micro-flocs, and to interpret the subsequent interactions between the aggregates in terms of either coagulation or flocculation, Data from different sources, materials and different agglomeration processes are analysed and compared in the light of the proposed model.

Jan 1, 2005

The type of population encountered in the sampling of coal, ores and other products of natural phenomena is one in which the variance within a cluster of elements generally increases steadily as the size of the cluster increases. To enable estimation of variances of stratified random or systematic sampling for such populations one must model the serial correlation function or alternatively, the variogram function. The author has postulated a specific symmetry of the serial correlation function which leads to expressions with rich theoretical and practical implications. These expressions provide a spatial correlation function which explains power law relationships often observed in studies of dispersion variances. They also enable straightforward calculations of sampling variances. The importance of the role of finite population size in the equations leads one to examine previously held concepts of ælargeÆ and æsmallÆ sample populations. The model based on the symmetry postulate is a fractal model with the serial correlation function of a hypothetically infinite population being of the same form as that developed by Mandelbrot for discrete fractional noise. Techniques used in fractal mathematics apply, including box counting and fitting of a dimension function. The paper establishes a framework for the understanding of this fractal theory and demonstrates how to calculate sampling variances from the model variogram using simulated data fitting the model.

Jan 1, 2008