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By Carolina Achiardi, Álvaro Videla

"In pre-design a flotation plant copper sulphide is useful to apply a simplified methodology of economic analysis that relates the size of the grinding product (P80) with the throughput and their effect on copper grade and recovery of copper in the final concentrate of a flotation circuit. With this objective, this methodology covers the following analysis, perform by evaluation of five sizes grinding products (P80): 120, 150, 180, 210 and 240 microns. • Flotation testwork (rougher kinetic, open and closed cycle test) has been done to determinate the optimum operating conditions and to estimate the maximum recovery of copper in the concentrate, using Klimpell model • Flotation plant design assumes a conminution product obtained from a 25,000 HP ball mill • Metallurgical balance is performed for the circuit based on flotation testwork • Economic evaluation by calculating capital expenditure (CAPEX), operating expenditure (OPEX) and sales revenue, to determine NPV is performed and relates to the NPV. An optimum grind size is then obtained based on cash flow. The results shows a grinding product size that optimizes flotation and allows a higher NPV and INPV over other alternatives."

Jan 1, 2014

By Y. G. Sun

This paper mainly reported separation manganese silver oxidized ores process by amylum de-gradation reduction and its influencing factors. When dosage is given according to nMn : nH2SO4 : n(C6H10O5)n : nH2O=1:k21.8: k116.66:30, the amount of up to 95.93% Mn leach rate and less than 2% silver loss can be obtained. Cyanidation process was used to extracted silver from leaching Mn residues. Silver leach rate could reach 94.15% at consumed amount of 1kg/t NaCN for 1h. Silver leach recovery rate was more than 92.27% by leaching Mn and cyanidation two-step processes so manganese and silver were separated effectively.

Jan 1, 2014

By Paulo Braga, Carlos Junior, Silvia França

"Lithium is the lightest of the metals, with high reactivity and great electrochemical potential. It has a low thermal expansion coefficient and high caloric value, and it forms very light and resistant aluminium alloys. These properties make lithium an attractive element for use in battery manufacture and glass and ceramics production, in addition to its applications in the aeronautic industry. Today, two sources of raw material are economically viable for lithium production: pegmatite rocks and brine. The world production, in 2012, was approximately 150,000 tons of LCE (lithium carbonate equivalent), almost triple the production in 2000. The forecasted consumption for the current year, 2013, was approximately 162,000 tons of LCE, and for 2020, it could be as much as 280,000 tons of LCE, stimulated essentially by the growth of world production of electric (EV), hybrid (HEV) and hybrid plug-in vehicles (PHEV), the batteries of which are based on Li-ions. With the growth of world demand and increasing prices, lithium minerals such as spodumene, petalite and amblygonite, once considered uneconomical for the production of lithium carbonate, are regaining their economic value. New projects to produce lithium compounds based on mineral sources are being developed in many countries, aiming to produce battery-grade lithium carbonate (99.95% Li2CO3). Although Brazil has large lithium pegmatite reserves, the domestic production of lithium carbonate and hydroxide is very low, at approximately 600 tons of LCE, which represents 0.4% of the world production. The application of these products is mostly in the grease and ceramic industries. The national lithium market is under government protection due to its potential use for nuclear purposes. Thus, the industrialization activities and import and export of ores and lithium minerals, as well as organic and inorganic products, such as metallic lithium and lithium alloys, are controlled by the National Commission for Nuclear Energy (Comissão Nacional de Energia Nuclear - CNEN). The objectives of this work to quantify the real lithium demand in the Brazilian market, considering that a large amount of lithium is indirectly imported in the form of the Li-ion batteries used in equipment such as mobile phones, cameras, tablets, notebooks and e-bikes, and to compare this demand with the current national production of LCE. Finally, some technological alternatives will be discussed, with the aim of increasing the competitiveness of the lithium industry in Brazil."

Jan 1, 2014

By Fangming Liu

The key problems of current flowsheets and equipments are analyzed. A new steel slag's crushing flowsheet whose key equipments are the improved inertia cone crusher and inertia vibrating jaw crusher is proposed. An advanced two stage open-circuit crushing method is adopted in the flowsheet, with 90% of particle size crushing under 6mm. Using inertia vibrating technology and selective crushing principle the crushers can realize steel slag separating fully into steel and slag and with flexible transmission mechanism the crusher can be protected when iron lump is passing. The flowsheets can enhance the recovery of metal greatly, and expand the application range of tail slag and added value.

Sep 1, 2012

By E. Isokangas

The production of minerals for economic use is a two-stage process, involving mining to extract the mineral from the ground, and processing to convert the mineral into a marketable product. Generally, mining and processing have been viewed as self-contained entities. Both have separate objectives, separate cost centres and key performance indicators (KPIs) that do not reflect the customer/supplier relationships that inherently exist. However, mining and processing operations are inter-connected and therefore intimately inter-related with the performance of one operation affecting the performance of another. Optimizing each stage separately without considering the whole system often misses potential economic benefits and energy savings. During the past fifteen years, the authors have been involved in implementing a holistic methodology ?Mine to Mill Process Integration and Optimisation (Mine to Mill PIO)? to maximize the overall profitability of the operation rather than just optimizing any individual process in a mining operation. Metso Process Technology and Innovation (PTI), along with their project partners, have conducted several projects to significantly increase their production- generating typically 5% to 20% higher throughput and improve the overall mine and concentrator performance through PIO methodology. This proven methodology has applications ranging from greenfield projects to long-standing operations with AG/SAG, HPGR or conventional grinding circuits. This paper explains the Mine to Mill PIO methodology and discusses the benefits of such an approach on the energy consumption, the overall costs and benefits of mining operations. The paper also summarizes several case studies illustrating the use of PTI methodology in a variety of applications. Keywords: integration, optimization, simulation, modeling, mine-to-mill, comminution, blast, drill, crushing, grinding

Sep 1, 2012

By Z. H. Zhang

Shizhuyuan is a world-class WO3, Mo, Bi and CaF2 poly-metallic deposit; it has rich reservation, but great difficulty in ore?s processing; thereby, for many years, it has been the target problem of beneficiation technologies. This paper, while briefly reviews its main scientific and technological advancement, pays special attention to the complete set of new technology and technical index achieved in recent years, which is characterized by using full-floatation flow-sheet as the backbone flow-sheet, explores some key factors influencing tungsten floatation, and presents a brief introduction to such new equipment as flotation column and comprehensive utilization of fluorite.

Jan 1, 2014

By A. V. Yevdokimov, Ye. V. Bogorodsky

The paper presents the results of the research on the development of gravity concentrates processing technology (gold grade is from 50 g/t to 1 kg/t and over) using intensive cyanidation with gold recovery to pregnant solutions followed by precipitation of metals from them using various methods. Test work and pilot plant results confirm that a new developed hydrodynamic regime provides an efficient treatment of gravity concentrates of polydisperse composition without their grinding and preliminary desliming. The resulting pregnant and washing solutions are amenable to metals recovery using electrowinning, cementation onto zinc dust and CIS. Cone plants with a lower ball valve for cyanidation of unground gravity concentrates developed by IRGIREDMET JSC have been successfully tested at a number of Russian operations. Currently, a modular plant equipped with gold electric precipitation from pregnant solution unit is successfully operated at a Russian gold processing plant. Cyanidation of the resulting high-grade gravity concentrate is carried out at the concentration of 8-10 g/L NaCN and 10 g/L NaOH. Gold recovery to the solution is 97-98%. Electrowinning is carried out in flow cell GNC-40M. In this case, the residual gold concentration yield is 0.3-0.5 mg/L. Also, a modular plant for relatively low-grade middlings (50-100 g/t Au) of gravity concentration has been introduced. The concentration of NaCN and NaOH is 2-3 g/L and 1.5-2 g/L, respectively, during leaching. This plant is equipped with a unit for gold cementation from pregnant solution with zinc dust. This cementation unit is of original design. It is made in the form of a filtering device and is composed of several layers of carbon fiber which contacts with zinc powder. The residual gold concentration yield from a cementation unit is less than 0.1 mg/L. Gold recovery is 93-97%. In 2017-2018, the introduction of intensive cyanidation modular plants to gravity concentrates will be planned at new projects of Russia and the CIS.

Jan 1, 2018

By Alok Tripathy

A simulation code called SIMJIG and the user interfaces have been developed using discrete element method (DEM) and the .NET platform respectively for the jigging process. DEM platform is used for tracking of particles in the jigging operation. DEM uses the net force balance on the particles to track the trajectory of the particle. Simulation results are compared with experimental results obtained by jigging of low grade iron ore lumps. Two different iron ore samples one from Chatishgarh and one from Odisha were used for the experimental studies. The Alljig? stratification test rig meant for batch laboratory experimental studies has been used in the present work. The behavior of different sizes of material on jigging has been examined. Later, the particle size behavior during jigging at different layers of the jig bed has been studied. Further stratification profile across the jig bed has also been studied. It was observed that simulation results are matching quite nicely with the experimental results. The SIMJIG simulator developed in the present study could be used for predicting the performance of the jigging operation effectively. Keywords: DEM, gravity concentration, jigging, iron ore, simulation

Sep 1, 2012

"The JKMRC researchers have been redeveloping the suite of breakage testing techniques to more realistically align with the breakage environment in comminution equipment. Computational modelling, especially with the DEM, has highlighted the modes of impact and contact, along with the energies of these interactions in a wide range of equipment. This has driven the need to match these modes in laboratory ore characterisation tests. The objective has been to build a continuum of breakage tests and associated models that span the required range of breakage forces and environments. The ore sample is subjected to a sequence of tests covering: abrasion (surface breakage) of angular through to smoothed particles; single particle impact from high energy single impact breakage down to low energy; incremental breakage covering 60 mm down to 50 µm particles; particle strength distribution; and bed breakage over a range of compression and energy input. These tests are suited to multi-component ores with a distribution of strengths. A modelling technique is also being developed to utilise primary breakage for modelling breakage under different types of confinement. This paper draws together these techniques, previously published by the authors, into a coherent whole. The suite of tests is approaching the point where a fixed set of tests can be used to model the performance of a full range of equipment, removing the need to conduct repeat ore characterisation tests for each different piece of equipment incorporated in a circuit design. This path should open up the application of different circuit configurations and novel equipment in comminution circuit design.1 INTRODUCTION Comminution modelling utilizes a wide range of ore characterisation techniques and methods to deal with the range of comminution equipment available for production use. In general, the tests have been designed to correlate with specific pieces of equipment, using calibration factors to provide the link between the small-scale test and industrial-scale performance. The majority of tests focus on estimating the power requirement of process equipment to achieve a desired throughput and grind size. Overall, this approach has achieved acceptable outcomes in the past, but the reality is that equipment sizing suffers from considerable uncertainty, in excess of ±20% is not uncommon. This uncertainty is covered by safety margins and automatic scaling factors in equipment selection. In striving to improve reliability, the industry tends to add more adjustment factors to the tests, and design margin rather than question the basic validity of the testing process. As the tests are often correlated to production equipment via carefully guarded databases, they are also locked into historic operating inefficiency, not providing direction or revealing opportunities to improve production efficiency in comminution equipment or circuits. Safe in the knowledge that they are achieving the expected production based on test work predictions, a site is unlikely to set their sights on reducing specific energy consumption by 10%."

Jan 1, 2018

By F. Boylu

In this study, Ca-bentonite was subjected to a series of systematic hydrocyclone tests with the aim of developing separation procedures and in turn achieving optimum recoveries. In hydrocyclone tests, vortex and apex diameters and also feed pressures were investigated. In each hydrocyclone set, vortex diameter was kept constant while the other two parameters varied to produce bentonites con-centrates of various smectite contents. The separation efficiencies were evaluated based on the cation exchange capacity (CEC), particle size and swelling index. The detailed hydrocyclone tests showed that, upgrading of Ca-bentonites require procedures different from the bentonites reported in the literature. Sodium and mixed bentonites are easy- to-disperse and easy-to-separate whereas calcium types need to be scrubbed rigorously for disintegration. Scrubbing properties of ca-bentonite were investigated as a function of scrubbing time and percent solids by weight (PS). The scrubbing conditions at 700 rpm for 1.5 hours and percent solids of 30 % were found more effective for achieving a better quality bentonite. In addition to the parameters mentioned above, the effect of percent solids on hydrocyclone separation was also studied. Although Ca-bentonites permit studying at higher percent solids, increasing solids content of the pulp deteriorated the quality of the clean products. Application of an appropriate separation scheme enabled the development of a unique separation procedure involving stage wise scrubbing followed by hydrocycloning which yielded calcium bentonite concentrates with CEC of 90 meq/100 g and high swelling indexes of 12 mL from the original bentonite of 65 meq/100 g and 7.0 mL, respectively. These results indicate that upgraded bentonite products can be conveniently used in various diverse industrial applications including bleaching earth, desiccant, cat litter, paper etc.

Jan 1, 2014

By A. Lane

Africa is ripe with opportunity for the mining industry. The continent has large, and relatively unexplored mineral deposits, and recent high economic growth rates have meaningfully improved the political, economic, and infrastructural environments. However, these opportunities are accompanied by significant risks, including resource nationalism, uncertain regulation, corruption, and continuing political instability (up to and including war). Forward-looking companies actively manage these risks by creating a sense of shared purpose with the countries and communities that own the resources, using tools such as stakeholder analysis, local narratives, scenario planning, and constituency engagement. They also measure socio-economic impact to insure the creation and demonstration of shared value.

Sep 1, 2012

By Ana C. C. Pacheco, Maurício L. Torem

"The aim of this work was the study of the effect of the type (Fe3+, Al3+ and Fe3+ and Al3+ mixture) and of the coprecipitant concentration on As5+ removal by ACF. Removal of As5+ using Sodium Dodecylsulfate (SDS) as a collector was studied by Adsorbing Colloid Flotation (ACF) at laboratory scale. The morphology of the precipitate retained in the foam was analyzed by Scanning Electron Microscopy (SEM/EDS).By comparing the coprecipitant type and concentration studies it could be concluded that As5+ removal in the presence of Fe3+ (160 mg.L-1) alone, or a Fe3+ (80 mg.L-1) and Al3+ (40 mg.L-1) mixture, is equivalently effective (99,9%) and greater than in the presence of Al3+ (80 mg.L-1) alone (97,7%).Through SEM/EDS analyses, it was possible to observe that both morphology and composition of the precipitate produced in the solution and retained in the foam depend on the physico-chemical conditions of the system, that is, on the species present in the solution."

Jan 1, 2003

By Yuhua Wang, Haitao Zheng, Guangli Zhu, Yuehao Zhao, Fushun Yu, Dongfang Lu

"Spodumene, feldspar and quartz possess similar surface properties, which make the difficult to separate spodumene from other silicate minerals by flotation. The differences of crystal structure, surface property and floatability of three minerals were studied by various technical means. The results show that Li-O and Al-O bonds in spodumene structure are not strong and easy to be broken. However, Al-O and Si-O bonds in feldspar and Si-O bond in quartz are very strong and not easy to be broken. High contents of Al and Li on spodumene surface were found by XPS measurements, which is benefit for the adsorption of anionic collector. The surface energies of main cleavage planes of spodumene (110), feldspar (001) and quartz (001) are 1.88 J/m2, 2.97J/m2 and 2.68J/m2, respectively. Hence, the exposed surfaces of feldspar and quartz are not saturated and easy to adsorb OH- ions from solution and cause the lower IEP than spodumene. The contact angles of three minerals in water are lower than 16º, suggesting that the hydrophilicity of three minerals is high, and the order of hydrophilicity is quartz > feldspar >spodumene. Correspondingly, contact angles and flotation recoveries of spodumene are bigger than that of feldspar and quartz in presence of a combined anionic and cationic collector named YOA.INTRODUCTION Flotation technology plays most important role for the recovery of spodumene from pegmatite ore. Generally, spodumene with fresh surface is easy to be floated using soap and oleic acid as collector, and the best flotation pH range is 4.0 to 9.0. However, the flotability of spodumene will become worse when its surface was polluted by slime which produced by the weathering of spodumene and other silicates (Dresler et al. 1998; Moon and Fuerstenau 2003; Menéndez et al. 2004; Yu et al. 2015). In addition, the species of Ca2+, Fe3+, Mg2+ and other metal ions in pulp can not only activate the flotation of spodumene, but also the activation of gangue minerals, and then the flotation selectivity of spodumene from gangue minerals became wores (Wang and Yu 2007; Yu et al. 2014). In order to eliminate the negative effects of slime and metal ions on the flotation of spoddumene, the desliming and long time scrubbing with the addition of NaOH and Na2CO3 were adopted. Usually, NaOH shows the activation for spodumene flotation, and the recovery of spodumene increases with the increase of NaOH dosage. Na2CO3 can eliminate the non selective activation of Ca2+, Fe3+, Mg2+ ions in the pulp, and the concentrate grade of spodumene increases with the increase of Na2CO3 dosage. Anionic collectors such as chelants, hydroxamic acid, oxidized paraffin soap, naphthenic acid and oleic acid were widely used for the flotation of spodumene (Dresler et al. 1998; Moon and Fuerstenau 2003; Menéndez et al. 2004; Yu et al. 2015)."

Jan 1, 2018

By M. D. Kaizer

PETROBRAS started its Oil Shale process development in 1953, the PETROSIX process which was developed and tailored to Irati Oil Shale formation. Since 1991, the industrial plant called MI (Industrial Module) has been operating, producing more than 20 million barrels of oil. In order to continue the oil shale exploration, a new shale mine is been opening. This article reports the planed measures taking in order to limit the environmental impacts and to return the land as close as possible to the original condition, as well as with the disposition of the process waste and the city garbage. It shows that the remediation process starts during the mining activities and continues after the mine exploration. Another characteristic of the Petrosix process, the pyrolysis of tires will be focused.

Jan 1, 2014

By G. Aguilera

It is known that an addition of rigid particles into a fluid medium changes the flow field. Therefore, the rheological behavior of suspensions will be hardly Newtonian, such as their continuum phase. This phenomena was studied by Einstein in 1906 (Einstein, 1956) for the single case of spherical particles in a continuum liquid of a very dilute suspension. The final analysis applied for suspensions was derived from the evaluation of the behavior of ideal gases, finding a simple expression for the viscosity of the dispersion. All the following works about the hydrodynamics of suspensions at low and high solid contents was based in the Einstein´s model. For clay minerals suspensions where the physical and chemical properties of the particles are complex, it was found that the Einstein´s model is not a good approximation, even so for the most dilute dispersions. The present paper shows a new approximation that describes the non-Newtonian behavior of the suspensions of clays, and the attempt of understand how the different fine sizes, shapes and physico-chemical properties of clay particle surfaces give specific characteristics of plasticity, viscosity or visco elasticity to suspensions. Keywords: viscosity, clay minerals, einstein´s model, dilute suspensions

Sep 1, 2012

By B. Orberger

The fine fraction (< 2 mm) of the high grade Mn-ore from the world class Moanda deposit, Francevillan basin, in Gabon, contains up to 30 wt. % of manganese and about 0.4 wt. % phosphorous. A pilot study at laboratory scale integrating mineralogy and geochemistry before and after ultrasonic treatment was conducted on the fine fraction (< 2 mm) of oxidized Mn ore in order to reduce the phosphorous content and enrich this fraction in manganese. The fine fraction was dried, crushed at 2 cm and sieved at 2 mm. The two fractions (< 2 mm and 2 mm ? 2 cm) were investigated by X-ray diffraction and scanning electron microprobe ? electron dispersive spectroscopy analyses. Both fractions contain lithiophorite, cryptomelane and pyrolusite as Mn carrier, and goethite, muscovite, illite and quartz as contaminants. The Mn hydroxide nsutite was only found in the fraction 2mm ? 2 cm.The < 2 mm fraction is significantly richer in goethite, muscovite/illite, and quartz. Phosphorous carriers are mainly goethite (up to 2.8 wt. % P2O5), while the Mn minerals contain up to 0.8 wt. % P2O5. The Mn minerals are partly included in an agglomerate of goethite, muscovite/illite, and quartz. The < 2 mm fraction was treated by ultrasound for 30 s in normal water. Mineralogical and chemical analyses after ultrasound treatment showed that the Mn-minerals were largely liberated from the goethite-muscovite-illite agglomerate. Mass balance calculations show that after ultrasonic treatment the < 2 mm fraction was ? 50 % enriched in Mn and ?50 % impoverished in P.

Sep 1, 2012

By D. Endara, E. De la Torre, S. Echeverria

"The study was conducted with the sulfide mineral from the province of Zamora Chinchipe. It was characterized physical, chemical and mineralogical, obtaining between its main results a copper concentration of head ore of 0,58 %. The mineral was homogenized and taken to direct closed circuit: rollers mill - vibratory sieve (mesh # 16). Flotation was carried out in two stages: the collective and selective where in each one were performed 6 water recirculation as suggested by the technique used to relate information of a batch flotation to a continuous circuit called cyclic flotation tests (LCT). In the collective flotation (bulk) 2 Kg of mineral were grinded with 10 Kg of balls for 30 minutes and 62.5% of solids, the pulp was taken to the flotation process with solids percentages of 33.3% and pH 7, it was conditioned with 45 g / t of KAX 1%, 50 g/t of Aerofloat 208 and 20 g /t of Pine oil. The concentrate and tailings bulk obtained were filtered separately for the recovery of water and it was recirculated to the next grinding of 2kg mineral. In the selective flotation 1Kg of bulk concentrate was carried to regrind for 40 min, 62.5% percent of solids, 10 g of lime and 5 g of tannin FLOATAN T5, the pulp was taken to the roughing-collection-refining flotation circuit controlling the pH between 10.5 and 11 where conditioning (60 g/t of Aerofloat 208 and 30 g/t of Pine oil) and adding lime to the circuit and FLOATAN according to the procedure. The four fractions obtained from the circuit were filtered; the water was recirculated to the regrind process of the bulk concentrate. In the collective flotation process tends to stability in the fourth recirculating water to obtain a copper content of 4.5% and a recovery of 87%, recirculated water represents 69.8% of all water used in the 6 recycles. In the selective flotation circuit the fifth recirculating of water is the optimal where obtaining a copper content of 13% and a recovery of 72%, recirculated water in the selective flotation circuit represents 95% of the total water used in the 6 recycles."

Jan 1, 2018

By X. Q. Ma

The beneficiation test on low grade phosphate ore from a state of Russia is carried out. The rougher-cleaner ? re-cleaner system is used in the flotation process, The fineness of grind is 39.07% minus 200 mesh. The result indicates that concentrate containing 31.25% P2O5 can be obtained from the flotation feed assaying 6.18% P2O5, with 93.54% P2O5 recovery. The test result is also a guideline for further development of some currently operated phosphate beneficiation plants.

Jan 1, 2014

By G. Y. He

The large-scale 8.53m×3.96m (28?×13? F/F) SAG mills was first applied in Donggua Hill Copper Mine which processes 13,000 tons ore per day. The crushing and grinding circuit went into operation in the Donggua Hill plant in October 2004. However, at the beginning, the productivity of grinding only reached 58% of the capacity expected and some indexes of the crushing and milling circuit didn?t meet the requirements. Especially, the total load of the 8.53m×3.96m (28?×13? F/F) SAG mills was up to 34%~41% (25%~30% designed)and some hard rocks with the size of 25~70mm, which can?t be treated as a medium or even would be crushed and make larger ores or steal balls necessary, were seriously accumulated in the SAG mills. Consequently, they occupied the effective mill volume which in turn reduced the efficiency of the SAG mills and increase the energy consumption. In order to solve the problem of accumulation in the SAG mill and increase its productivity, some measures were taken, such as passing more hard pebble through the grate at mill dis-charging end, changing the type of steal balls and so on. And the results showed that these measures functioned well and had good effects, which is that the filling percentage of the SAG mills has been reduced to 26%~29% from 34%~41% with the composition of particle sizes improved a lot and the productivity increased by 77.4% reaching up to 13,380 tons per day.

Jan 1, 2014

By Rob D. Morrision, Paul W. Cleary

"The best accepted method for design of autogenous and semi-autogenous mills is to carry out pilot scale test work using a 1.8 m diameter by 0.6 m long pilot scale test mill. The load in such a mill typically contains 250,000-450,000 particles larger than 6 mm, allowing correct representation of more than 90% of the charge. This scale of DEM model is now within the practical range of standard workstations running an efficient DEM code.This paper describes various ways of extracting collision data from the DEM model and translating it into breakage and wear estimates. Account is taken of the different breakage mechanisms (impact and abrasion) and of the specific impact histories of the particles in order to assess the breakage rates for various size fractions in the mills. These impact histories have the potential to be directly related to breakage as they most resemble the single particle breakage tests which are used by the JKMRC to calibrate more traditional population balance models for variations in ore behaviour. However, the specific impact histories also show a background of many low energy collision events within the mill. This Background may constitute what is usually regarded as “abrasion” breakage. As might be expected, high impact events are concentrated in the toe of the charge and near to the mill shell where the forces associated with the load bearing on each particle is more concentrated."

Jan 1, 2003