A liberation model for comminution based on probability theory

Mineral processing plants use two main processes; these are comminution and separation. The objective of the comminution process is to break complex particles consisting of numerous minerals into smaller simpler particles where individual particles consist primarily of only one mineral. The process in which the mineral composition distribution in particles changes due to breakage is called 'liberation'. The purpose of separation is to separate particles consisting of valuable mineral from those containing nonvaluable mineral. The energy required to break particles to fine sizes is expensive, and therefore the mineral processing engineer must design the circuit so that the breakage of liberated particles is reduced in favour of breaking composite particles. In order to effectively optimize a circuit through simulation it is necessary to predict how the mineral composition distributions change due to comminution. Such a model is called a 'liberation model for comminution'. It was generally considered that such a model should incorporate information about the ore, such as the texture. However, the relationship between the feed and product particles can be estimated using a probability method, with the probability being defined as the probability that a feed particle of a particular composition and size will form a particular product particle of a particular size and composition. The model is based on maximizing the entropy of the probability subject to mass constraints and composition constraint. Not only does this methodology allow a liberation model to be developed for binary particles, but also for particles consisting of many minerals. Results from applying the model to real plant ore are presented. A laboratory ball mill was used to break particles. The results from this experiment were used to estimate the kernel which represents the relationship between parent and progeny particles. A second feed, consisting primarily of heavy particles subsampled from the main ore was then ground through the same mill. The results from the first experiment were used to predict the product of the second experiment. The agreement between the predicted results and the actual results are very good. It is therefore recommended that more extensive validation is needed to fully evaluate the substance of the method. (C) 2003 Elsevier Ltd. All rights reserved.

Comparison of grinding media - Cylpebs versus balls

Cylpebs are slightly tapered cylindrical grinding media with a ratio of length to diameter of unity. The manufactures have made conflicting claims regarding the milling performance of Cylpebs in comparison with balls. One major point of interest is which one grinds finer at the same operating conditions. The difficulty in comparison is due to the shape difference. The two grinding media have different surface area, bulk density and contact mechanisms in grinding action. Comparative tests were conducted using the two types of grinding media in a laboratory Bond ball mill at various conditions of equality such as media mass, size distribution, surface area and input specific energy. The laboratory results indicate that at the same specific energy input level the Cylpebs produce a product with slightly less oversize due to their greater surface area, but essentially the same sizing at the fine end as that produced with the balls. The reason may be that the advantage of greater surface area is balanced by the line contact and area contact grinding actions with the Cylpebs. A new ball mill scale-up procedure [Man, Y.T., 2001. Model-based procedure for scale-up of wet, overflow ball mills, Part 1: outline of the methodology. Minerals Engineering 14 (10), 1237-1246] was employed to predict grinding performance of an industrial mill from the laboratory test results. The predicted full scale operation was compared with the plant survey data. Some problems in the original scale-up procedures were identified. The scale-up procedure was therefore modified to allow the predicted ball mill performance to match the observed one. The calibrated scale-up procedure was used to predict the Cylpebs performance in the full scale industrial mill using the laboratory tests results. (C) 2004 Elsevier Ltd. All rights reserved.

Using DEM to model ore breakage within a pilot scale SAG mill

The best accepted method for design of autogenous and semi-autogenous (AG/SAG) 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 in Discrete Element Method (DEM) simulations. Most AG/SAG mills use discharge grate slots which are 15 mm or more in width. The mass in each size fraction usually decreases rapidly below grate size. This scale of DEM model is now within the possible range of standard workstations running an efficient DEM code. This paper describes various ways of extracting collision data front the DEM model and translating it into breakage 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. At some future time, the integration of smoothed particle hydrodynamics with DEM will allow for the inclusion of slurry within the pilot mill simulation. (C) 2004 Elsevier Ltd. All rights reserved.

Influence of charge size distribution on net-power draw of tumbling mill based on DEM modelling

Modelling and optimization of the power draw of large SAG/AG mills is important due to the large power draw which modern mills require (5-10 MW). The cost of grinding is the single biggest cost within the entire process of mineral extraction. Traditionally, modelling of the mill power draw has been done using empirical models. Although these models are reliable, they cannot model mills and operating conditions which are not within the model database boundaries. Also, due to its static nature, the impact of the changing conditions within the mill on the power draw cannot be determined using such models. Despite advances in computing power, discrete element method (DEM) modelling of large mills with many thousands of particles could be a time consuming task. The speed of computation is determined principally by two parameters: number of particles involved and material properties. The computational time step is determined by the size of the smallest particle present in the model and material properties (stiffness). In the case of small particles, the computational time step will be short, whilst in the case of large particles; the computation time step will be larger. Hence, from the point of view of time required for modelling (which usually corresponds to time required for 3-4 mill revolutions), it will be advantageous that the smallest particles in the model are not unnecessarily too small. The objective of this work is to compare the net power draw of the mill whose charge is characterised by different size distributions, while preserving the constant mass of the charge and mill speed. (C) 2004 Elsevier Ltd. All rights reserved.

Analysis of stirred mill performance using DEM simulation: Part 2 - Coherent flow structures, liner stress and wear, mixing and transport

Stirred Mills are becoming increasingly used for fine and ultra-fine grinding. This technology is still poorly understood when used in the mineral processing context. This makes process optimisation of such devices problematic. 3D DEM simulations of the flow of grinding media in pilot scale tower mills and pin mills are carried out in order to investigate the relative performance of these stirred mills. In the first part of this paper, media flow patterns and energy absorption rates and distributions were analysed to provide a good understanding of the media flow and the collisional environment in these mills. In this second part we analyse steady state coherent flow structures, liner stress and wear by impact and abrasion. We also examine mixing and transport efficiency. Together these provide a comprehensive understanding of all the key processes operating in these mills and a clear understanding of the relative performance issues. (C) 2006 Elsevier Ltd. All rights reserved.

Analysis of stirred mill performance using DEM simulation: Part 1 - Media motion, energy consumption and collisional environment

Stirred mills are becoming increasingly used for fine and ultra-fine grinding. This technology is still poorly understood when used in the mineral processing context. This makes process optimisation of such devices problematic. 3D DEM simulations of the flow of grinding media in pilot scale tower mills and pin mills are carried out in order to investigate the relative performance of these stirred mills. Media flow patterns and energy absorption rates and distributions are analysed here. In the second part of this paper, coherent flow structures, equipment wear and mixing and transport efficiency are analysed. (C) 2006 Published by Elsevier Ltd.

Anatomy of a hemiramphid pharyngeal mill with reference to arrhamphus sclerolepis krefftii (steindachner) (teleostei: hemiramphidae)

The structure and function of the pharyngeal jaw apparatus (PJA) and postpharyngeal alimentary tract of Arrhamphus sclerolepis krefftii, an herbivorous hemiramphid, were investigated by dissection, light and scanning electron microscopy, and X-ray analysis of live specimens. A simple model of PJA operation is proposed, consisting of an adductive power stroke of the third pharyngobranchial that draws it posteriorly while the fifth ceratobranchial is adducted, and a return stroke in which the third pharyngobranchial bone is drawn anteriorly during abduction of the fifth ceratobranchial. Teeth in the posteromedial region of the PJA are eroded into an occlusion zone where the teeth of the third pharyngobranchial are spatulate incisiform and face posteriorly in opposition to the rostrally oriented spatulate incisiform teeth in the wear zone of the fifth ceratobranchial. The shape of the teeth and their pedestals (bone of attachment) is consistent with the model and with the forces likely to operate on the elements of the PJA during mastication. The role of pharyngeal tooth replacement in maintaining the occlusal surfaces in the PJA during growth is described. The postpharyngeal alimentary tract of A. sclerolepis krefftii comprises a stomachless cylinder that attenuates gradually as it passes straight to the anus, interrupted only by a rectal valve. The ratio of gut length to standard length is about 0.5. Despite superficial similarities to the cichlid PJA (Stiassny and Jensen [1987] Bull Mus Comp Zool 151: 269-319), the hemiramphid PJA differs in the fusion of the third pharyngobranchial bones, teeth in the second pharyngobranchials and the fifth ceratobranchial face anteriorly, the presence of a slide-like diarthroses between the heads of the fourth epibranchials and the third pharyngobranchial, the occlusion zone of constantly wearing teeth, and the unusual form of the muscularis craniopharyngobranchialis. The functional relationship between these structures is explained and the consequence for the fish of a complex PJA and a simple gut is discussed. (C) 2002 Wiley-Liss, Inc.

Determination of lifter design, speed and filling effects in AG mills by 3D DEM

The power required to operate large gyratory mills often exceeds 10 MW. Hence, optimisation of the power consumption will have a significant impact on the overall economic performance and environmental impact of the mineral processing plant. In most of the published models of tumbling mills (e.g. [Morrell, S., 1996. Power draw of wet tumbling mills and its relationship to charge dynamics, Part 2: An empirical approach to modelling of mill power draw. Trans. Inst. Mining Metall. (Section C: Mineral Processing Ext. Metall.) 105, C54-C62. Austin, L.G., 1990. A mill power equation for SAG mills. Miner. Metall. Process. 57-62]), the effect of lifter design and its interaction with mill speed and filling are not incorporated. Recent experience suggests that there is an opportunity for improving grinding efficiency by choosing the appropriate combination of these variables. However, it is difficult to experimentally determine the interactions of these variables in a full scale mill. Although some work has recently been published using DEM simulations, it was basically. limited to 2D. The discrete element code, Particle Flow Code 3D (PFC3D), has been used in this work to model the effects of lifter height (525 cm) and mill speed (50-90% of critical) on the power draw and frequency distribution of specific energy (J/kg) of normal impacts in a 5 m diameter autogenous (AG) mill. It was found that the distribution of the impact energy is affected by the number of lifters, lifter height, mill speed and mill filling. Interactions of lifter design, mill speed and mill filling are demonstrated through three dimensional distinct element methods (3D DEM) modelling. The intensity of the induced stresses (shear and normal) on lifters, and hence the lifter wear, is also simulated. (C) 2004 Elsevier Ltd. All rights reserved.

Influence of explosive energy on the strength of the rock fragments and SAG mill throughput

Extensive in-situ testings has shown that blast fragmentation influences the performance of downstream processes in a mine, and as a consequence, the profit of the whole operation can be greatly improved through optimised fragmentation. Other unit operations like excavation, crushing and grinding can all be assisted by altering the blast-induced fragmentation. Experimental studies have indicated that a change in blasting practice would not only influence fragmentation but fragment strength as well. The strength of the fragments produced in a blast is clearly important to the performance of the crushing and grinding circuit as it affects the energy required to break the feed to a target product size. In order to validate the effect of blasting on fragment strength several lumps of granite were blasted, under controlled conditions, using three very different explosive products. The resulting fragments were subjected to standard comminution ore characterisation tests. Obtained comminution parameters were then used to simulate the performance of a SAG mill. Modelling results indicate that changes in post blast residual rock fragment strength significantly influences the performance of the SAG mill, producing up to a 20% increase in throughput. (c) 2004 Elsevier Ltd. All rights reserved.

The mirror-ball effect: Investigating channels, messages and participation levels

Journalists have always used equipment which has been generally available in the communities in which they worked. This has been a result both of economy and necessity, since they found they had to connect with their audiences using means that were available to the audience, not just to the sender. Newspapers sold on street corners in the very early media days; SMS and email have become the rule for the early 21st century. This development also admits the possibility of the roles of the communication professional and the community merging during the “public journalism” process, and has become most recently evident in the areas around the Bay of Bengal, struck by the tsunami on December 26, 2004, especially in the Indonesian province of Banda Aceh, and in the Andaman and Nicobar Islands, where tiny portable radios, featuring solar panels and hand-cranked dynamos, have suddenly become part of a vital news media channel. In this article participant-observation and personal interview techniques are used to record and compare many of the digital channels used by news and information senders up to 2005. It also investigates the level of genuine participation which these new technologies have brought to the communications process.

Hydrogen storage properties of MgH2/SWNT composite prepared by ball milling

A systematic investigation was performed on the hydrogen storage properties of mechano-chemically prepared MgH2/Single-walled carbon nanotube (SWNT) composites. It is found that the hydrogen absorption capacity and hydriding kinetics of the composites were dependent on the addition amount of SWNTs as well as milling time. A 5 wt.% addition of SVVNTs is optimum to facilitate the hydrogen absorption and desorption of MgH2. The composite MgH2/5 wt.% SWNTs milled for 10h can absorb 6.7 wt.% hydrogen within about 2 min at 573 K, and desorb 6 wt.% hydrogen in about 5 min at 623 K. Prolonging the milling time over 10 h leads to a serious degradation on hydrogen storage property of the MgH2/SWNT composite, and property/structure investigations suggest that the property degradation comes from the structure destruction of the SWNTs. (c) 2005 Elsevier B.V. All rights reserved.

Modelling comminution patterns within a pilot scale AG/SAG mill

The patterns of rock comminution within tumbling mills, as well as the nature of forces, are of significant practical importance. Discrete element modelling (DEM) has been used to analyse the pattern of specific energy applied to rock, in terms of spatial distribution within a pilot AG/SAG mill. We also analysed in some detail the nature of the forces, which may result in rock comminution. In order to examine the distribution of energy applied within the mill, the DEM models were compared with measured particle mass losses, in small scale AG and SAG mill experiments. The intensity of contact stresses was estimated using the Hertz theory of elastic contacts. The results indicate that in the case of the AG mill, the highest intensity stresses and strains are likely to occur deep within the charge, and close to the base. This effect is probably more pronounced for large AG mills. In the SAG mill case, the impacts of the steel balls on the surface of the charge are likely to be the most potent. In both cases, the spatial pattern of medium-to-high energy collisions is affected by the rotational speed of the mill. Based on an assumed damage threshold for rock, in terms of specific energy introduced per single collision, the spatial pattern of productive collisions within each charge was estimated and compared with rates of mass loss. We also investigated the nature of the comminution process within AG vs. SAG mill, in order to explain the observed differences in energy utilisation efficiency, between two types of milling. All experiments were performed using a laboratory scale mill of 1.19 m diameter and 0.31 m length, equipped with 14 square section lifters of height 40 mm. (C) 2006 Elsevier Ltd. All rights reserved.

Prediction of slurry transport in SAG mills using SPH fluid flow in a dynamic DEM based porous media

DEM modelling of the motion of coarse fractions of the charge inside SAG mills has now been well established for more than a decade. In these models the effect of slurry has broadly been ignored due to its complexity. Smoothed particle hydrodynamics (SPH) provides a particle based method for modelling complex free surface fluid flows and is well suited to modelling fluid flow in mills. Previous modelling has demonstrated the powerful ability of SPH to capture dynamic fluid flow effects such as lifters crashing into slurry pools, fluid draining from lifters, flow through grates and pulp lifter discharge. However, all these examples were limited by the ability to model only the slurry in the mill without the charge. In this paper, we represent the charge as a dynamic porous media through which the SPH fluid is then able to flow. The porous media properties (specifically the spatial distribution of porosity and velocity) are predicted by time averaging the mill charge predicted using a large scale DEM model. This allows prediction of transient and steady state slurry distributions in the mill and allows its variation with operating parameters, slurry viscosity and slurry volume, to be explored. (C) 2006 Published by Elsevier Ltd.