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By L. G. Austin, P. T. Luckie, R. R. Klimpel, R. S. C. Rogers

1. INTRODUCTION The Bond method(1.2) for sizing tumbling ball mills has been used successfully for many years. The primary purpose of the Bond calculation is to predict the mill size and mill power to give a desired capacity (Q tph) from a wet overflow ball mill in normal closed circuit operated with a circulation ratio of 2.5. The input to the calculation is the make-up feed size characterized by the 80%-passing size in micrometers (xG), the desired circuit product size characterized by the 80%-passing size (xQ), and an empirical grindability number (the standard Bond Work Index) determined by a standard test. A series of empirical correcting factors(2) are used to convert the results to open-circuit or dry grinding in grate discharge mills. The Bond method has two major engineering advantages: (i) it is very simple; (ii) experience has shown that it works for many circumstances, as a reasonable approximation, because it is based on direct conversion of test data to results measured on industrial mills. There are four main disadvantages of the Bond method. First, there will be a range of error for any specific mill and material and set of operating conditions because the method does not explicitly include several variables which are obviously important: (i) recycle ratio and classifier efficiency (ii) mixture of ball sizes in the mill (iii) variations of residence time distributions with mill geometry and slurry density (iv) lifter design (v) slurry rheology (vi) different underfilling or overfilling of the mill as flow rate is changed. Second, the Bond method explicitly assumes that specific grinding energy E is not a function of ball load, whereas industrial practice and laboratory tests(3) show that the specific grinding energy (to go from a specified feed to a specified product) is less for lower ball loadings than the ball loading for maximum mill capacity. Third, the method uses only the 80% passing size of circuit feed and product to characterize the size distributions, whereas mill capacity in general must depend on the shape of the feed size distribution and the product size distribution. The prime example of this is the use of the reverse closed circuit which removes some fraction of the make-up feed before it is

Jan 1, 1982

By Yusuf R

Many heap and dump leaching processes involve competitive, complementary and sequential reactions between multiple minerals and reagents. A comprehensive model has been developed to deal with these complex chemical interactions which is based on diffusion control of the reaction rates. All of the mineralogical and chemical data are obtained from representative samples of the ore or the chemical literature. These properties have been incorporated in a general way, making the model applicable to a range of ore-process systems. The simulation is used to predict the absolute reaction rates and can be used before any leach tests are carried out on the ore itself. The applicability of the model and some tests of its validity are presented.

Jan 1, 1984

By C. J. Barbee, P. J. Bethell, C. J. Wood

Heavy medium cyclones (HMCs) are commonly used to clean run-of-mine coal in the 50 x 0.5 mm size range. Unfortunately, field studies suggest that industrial HMC circuits are often poorly designed or improperly operated, resulting in significant losses of recoverable clean coal. To assist plant engineers in overcoming these problems, a spreadsheet-based simulation package has been developed to predict HMC performance based on mathematical expressions originally developed by Wood (1990). A case study is provided to illustrate the predictive capabilities of this simulation package for an industrial HMC.

Jan 1, 2004

By Ji Hoe Kwon

Hindered-settling column process has been used for the separation of mineral particles for many years. In this study, a model based on DEM (Discrete Element Method) was used to simulate the movements of particles in a settling column separation process. DEM model is capable of describing the motion of particles and calculating the impact forces between particle and particle, and particle and wall contact under various operating conditions. Drag force, rotation induced Magnus lift force, contact force and the gravitational force acting on individual particles were considered for establishing the mathematic models. The overall motion of the particles in water is satisfactorily simulated by the DEM, and the result shows good agreements with the result of lap-scale experiment.

Jan 1, 2014

By Harushige Kusumi, Yuzuru Ashida, Toshiki Watanabe, Toshifumi Matsuoka

ABSTRACT: The technique of various kinds of numerical analysis offered remarkable results to explication of many rock mechanical phenomena. These techniques regarded a rock stratum as a continuum body and solved the governing equation of continuum mechanics by using finite differ-ence method, finite element method and/or others. Using numerical analysis based on continuum mechanics, however, the simulations of destruction phenomena caused by elastic waves and on the other hand, the elastic wave propagation which generated by fracturing events are quite difficult. In this paper, we express a rock stratum by a granular body model and develop a simulation tech-nique can simulate both wave phenomena and destruction phenomena at once. The DEM (discrete element method) simulation results are compared with finite difference solutions of elastic wave equation. Furthermore, we simulate Hopkinson effect by this proposed method. Hopkinson effect is famous as a destruction phenomenon caused by elastic wave propagation. ABRISS: In dieser Studie drücken wird eine Felsschicht durch ein Granularkörpermodell aus und entwickeln eine Simulationstechnik, die sowohl Wellenphänomene als auch Zerstörungsphänomene simulieren kann. Die Ergebnisse der Simulation mit DEM (Diskrete-Elemente-Methode) werden mit denen der Finit-Differenz-Lösung von Gleichungen elastischer Wellen verglichen. Desweiteren simulierten wir den Hopkinson-Effekt mit dieser vorgeschlagenen Methode. Der Hopkinson-Effekt ist als Zerstörungsphänomen berühmt, verursacht durch Fortpflanzung elastischer Wellen. RESUME: Dans cette étude, nous exprimons un lit de roches par un modèle à corps granulaire et développons une technique, permettant de simuler d'un coup le phénomène des ondes et le phé-nomène de destruction. Les résultats de la simulation DEM (méthode d'éléments discrets) sont comparés aux solutions à différence finie de l'équation d'ondes élastiques. En outre, nous simulons l'effet d'Hopkinson par la méthode proposée. L'effet d'Hopkinson est connu comme phénomène de destruction, causé par la propagation d'ondes élastiques.

Jan 1, 2003

By Alexander Siefert, Steffen Pankoke

In the development of commercial vehicles as well as of passenger cars, the effects of vehicle vibrations on operating safety, health and comfort can only be predicted by numerical simulation when appropriate occupant models are available. Such models must be based on human anatomy and have dynamic properties of real humans in order to achieve realistic results. Since human dynamic behavior depend on posture and percentile, the occupant model needs to be adjustable to these parameters with respect to geometry and dynamic properties [1,2]. Dynamic Human Finite-Element-Model CASIMIR CASIMIR is a non-linear, dynamic finite-element-model of the human body. It consists of a dynamic model of the upper torso with head, neck, shoulders and arms as well as of a dynamic model of the lower extremity with pelvis and legs. The most important part is the lumbar area with dynamic non-linear models of the lumbar spine and of back and abdominal musculature. The frequency-dependent characteristics of the intervertebral discs and the effects of muscle activation and non-linear frequency-dependent muscle properties are included. In the latest stage of development, CASIMIR has been equipped with a compliant model of the body surface in the contact areas to the seat. This results in a very realistic transmission of static and vibrational forces into the human body, see fig. 1. Intense model verification and validation has been performed in all stages of model development, starting with validation of small components like intervertebral disc, ending with validation of whole-body-vibrations using measurements of the dynamic mass / mechanical impedance [4]. For an in-detail examination of stresses in the vertebral bodies and discs, a non-linear submodel of the lumbar spine with an increased number of degrees of freedom can be coupled to the whole-body-model, enabling the researcher to examine local effects of vibrations and single shocks on the lumbar materials. [ ] Since it is well known that human dynamic behavior is significantly affected by anthropometric data and posture, CASIMIR can be individualized to the anthropometric status of single individuals or to the mean values for specific percentile groups. Furthermore, posture can be adjusted to the seating conditions applicable to a specific vehicle. Posture modification capabilities include the variation of the lumbar lordosis [3].

Jan 6, 2006

By Kenji Matsuzaki

A mathematical simulation model of the Imperial Smelting Furnace operation has been developed for purpose of improving the furnace operation. The model consists of top, shaft and bottom regions, Analysis in the shaft region is based on differential heat and materials balances taking account of reaction kinetics and heat transfer rates, and those in the top and the bottom regions are based on heat and materials balances under a steady-state condition, Longitudinal distributions of process variables such as temperatures of gas, sinter and coke, gas composition and fractional conversion under a practical operating condition were calculated, With this model, the furnace performance under various operating conditions also can be shown reasonably predicted,

Jan 1, 2003

By Malsuzaki. Kenji

A mathematical simulation model of the Imperial Smelting Furnace operation has been developed for purpose of improving the furnace operation. The model consists of top, shaft and bottom regions. Analysis in the shaft region is based on differential heat and materials balances taking account of reaction kinetics and heat transfer rates, and those in the top and the bottom regions are based on heat and materials balances under a steady-state condition. Longitudinal distributions of process variables such as temperatures of gas, sinter and coke, gas composition and fractional conversion under a practical operating condition were calculated. With this model, the furnace performance under various operating conditions also can be shown reasonably predicted.

Jan 1, 2003

By M Phil Schwarz

"A CFD model for the gas-side of an impinging jet iron bath reactor has been developed to assist in the interpretation and design of oxidizing gas-melt reaction rate experiments. Heat transfer and reaction at the surface have been included. A free surface model, which solves for the liquid motion within the bath as well as the gas motion above the bath, has also been developed. This model also predicts extent and shape of the dimple formed on the liquid surface by the impinging jet. Both models have been run for conditions typical of jet impingement experiments using CO2 , H2O and O2• The main conclusions are• Results from the model for gas-side mass transport are in good agreement with the empirical correlation of Belton and Belton (1980)• Experimentally determined rates of decarburization by CO2 should be corrected for mass transfer because the experiments are often carried out under mixed rate control, eg for gas flow rate 10 L/min when the sulphur concentration is lower than 0.045• If the rate constant for oxygen reaction is greater than about 5 mol/m2.s.atm, it cannot be determined using a gas flow rate of 10 L/min or lower because of mass transfer control.• A cavity of depth 4.5 mm is predicted for a gas flow rate of 10 L/min and this substantially changes the flow field (and hence reaction rate) compared with a simulation in which the surface is assumed to be flat."

Jan 1, 1999

By E. Topuz, M. J. McPherson, I. M. Konduri

The research is carried out to investigate the flow mechanics and effectiveness of face ventilation using induction fans, as an effort to provide a more efficient alternative to conventional auxiliary duct or brattice ventilation systems. The induction effects and plume longevity of fluid jets are being studied with the help of a plexi-glass model, using water as the fluid medium and creating a system that is dynamically similar to the flow in mine headings. This scaled model represents a typical 1.5m x 6m x 25m heading connecting to a crosscut. Reynolds Number criteria are used to obtain dynamic similarity of the flow in the designed model to simulate real mining conditions. The role of various parameters such as nozzle position in three dimensions, airway roughness, nozzle geometry, and flow rate in the jet are studied. During the laboratory tests, flow visualization techniques, coupled with still and video photography, were employed to identify the flow patterns. The results indicate that in typical coal mine headings, jet fans can produce effective face ventilation for distance up to 30 meters.

Jan 1, 1995

By B. K. Mishra, R. K. Rajamani, A. D. Joshi

The liners are the most important part in the SAG mill operation. Hence, the liners and their design parameters are primarily studied to see its effect on SAG mill operations. Effective liner designs are directed to reduce downtimes, which is needed for the replacement of worn liners. There exists constant chance of improvement in the capacity of mill by studying the effect of liner design on the charge motion inside the mill. This need is satisfied by three-dimensional discrete element code "Millsoft", which uses Discrete Element Method (DEM) to analyze the motion of charge. This simulation of SAG mill keeps track of all the moving bodies like ball and rock and observes its interaction with liners and lifters. The recent work done on this software helps generating mill to more reality by putting conical wall at feed and discharge end, over the earlier flat walls. Millsoft is an effective tool to watch the change in the motion of the charge due to different types of lifter bars and different design parameters. It was concluded that by simply increasing chord length between the lifters and increasing the face angle of the lifters, capacity of the mill could be increased. On the other hand, this software can also be used to get power draft at the respective mill design.

Jan 1, 2002

The paper examines the design issues associated with the integration of mineral processing within underground mining systems. It demonstrates conceptual integrated system design options appropriate to a range of geological scenarios. Particular reference is then given to a case study of stoping in narrow base metal veins. The performance of such integrated systems in terms of productivity, economic and environmental criteria is demonstrated by means of simulation. Particular attention is given to the potential benefits to mine waste management. Processing technologies appear to offer genuine potential benefit, whilst underground mining methods may need to evolve further to facilitate full integration. This paper is based on industry supported research aimed at developing selective and clean underground mining systems.

Jan 1, 2003

By John ?gren, Martin Schwind, Henrik Larsson

"A new model for internal oxidation, as well as similar processes, has been implemented on computer. It is based upon a combination of random walk and cellular automata and is capable of treating 3-dimensional cases. To model diffusion, it utilises quantised units of matter. All steps of the process are included: nucleation, growth and coarsening. The effect of grain boundaries on diffusion as well as nucleation is taken into account. Further possible development is briefly discussed; especially the treatment of nucleation needs further consideration. IntroductionComplex diffusion-controlled processes may now be simulated on a routine basis when concentration varies along one co-ordinate only. One-dimensional simulations capture much of the information of interest but not all. For the case at hand, especially the spatial and the size distribution of precipitates, as well as the impact of grain boundaries, would be interesting information not accessible from 1-D simulationsSolving the full Fick-Onsager law in three dimensions does not seem feasible with the computers of today. In the model described in this article, random walk by quantised units of matter are considered. The model should be useful for a number of cases involving dispersed systems. With further development, it would indeed seem possible to simulate most types of phase transformations.Previous workWe have previously published two articles [1,2] on the new approach discussed in this work. In those articles we described the basic idea and showed, among other things, that very good agreement with an experimental concentration profile can be obtained, in a single-phase system, using independently assessed thermodynamic and kinetic data. Also, Schwind used the same random walk based concept to model coarsening [3]."

Jan 1, 2001

By J. R. Bredell, J. Branehog, C. Coetzee, J. J. van Tonder

A nutating grinding mill, exemplified by the commercial HICOM mill, achieves efficient particle size reduction through the accelerated motion of the material charge within the nutating chamber. This design, characterised by high particle velocities and rapid charge circulation, offers a compact solution compared to tumbling mills. There have been concerns regarding the mechanical reliability of kinetic joints for certain specialised mining applications. Recognising the need to model internal forces in such systems, this study focuses on the uncoupled simulation using multibody dynamics and the discrete element method. The investigation employed a small-scale experimental test mill, referred to as the NuMILL, featuring a cylindrical chamber (140 mm internal diameter, 245 mm height, 6° nutation angle). Instrumented with an array of sensors, the NuMILL provided internal load data for validating the simulations. Experiments were conducted with an empty chamber or filled with charge material. Charge materials included coarse sand or steel pellets with a charge-to-chamber mass ratio of 0.25. The mill speed ranged between 100 to 700 RPM. Multibody dynamics modelled resultant inertial and frictional loads within 5%, while the discrete element method simulated the internal material contact loads with accuracies ranging from 1% to 19%. The combined simulation approach predicted the resultant forces in the critical kinetic joint within a 20% margin. Representing the charge using rigid lumped mass elements was also studied. The presented simulation techniques, validated against experimental data, offer a robust foundation for analysing larger systems, including the industrial-scale HICOM.

Mar 5, 2025

By Guangyuan Li

A 3-D block-spring model (BSM) has been developed for simulating the behaviour of jointed rocks. The model uses a discontinuous formulation and an iterative procedure to solve the large displacements in jointed and faulted rock masses. The 3-D BSM has been used to simulate mining excavations in jointed rocks around an open pit and underground settings. The applications have demonstrated that it is a practical tool to solve complicated problems of rock mechanics in civil and mining engineering. This model has recently been modified to incorporate complex geological conditions, such as underground water flow (seepage), unstable blocks and the time-dependent behavior of backfill materials. To demonstrate the capability of the 3-D model this paper presents the fundamentals of the 3- D BSM and its application for open-pit mining. A complete computer package BSM3D has been developed based on the 3-D block-spring model. The package consists of a solving engine for numerical analysis and a Windows based processor for mesh generation and results display. The multi-functioned pre-processor provides tools and menus to help users setting up models easily and conveniently. The fully featured post-processor allows users to view the results in different windows and orientations. The graphical results include contours, vectors, animation of rock movement, and the failure state of the rock structures.

May 1, 2001

By J. T. Ryan, Wayne H. Griffin

Solutions to typical leaky ventilation circuits such as multiple entry headings and ventilation tube or brattice face ventilation are obtained using the discrete continuous simulation language SLAM II. While the continuous aspect of the language allows exact numerical solution of leaky systems, the particular discrete-continuous interface of this language is easily adapted to space varying geometry and flow parameters encountered in mine ventilation. The ease with which this simulation system is adapted to ventilation problems and the availability on personal computers encourage its wider application in the field.

Jan 1, 1987

By Yi Zheng

Under normal circumstances, methane released along a longwall face represents only 10%-20% of the total me- thane emitted from the entire longwall panel. However, there might be a sudden surge of methane at the face which may cause a potential problem because the friction from shearer cutting, support movement, and scraper conveyor dragging can be ready ignition sources. Therefore, to predict the distribution of methane will be critical to prevent possible explosions. In this paper, methane dispersion patterns along a lognwall face are simulated under normal and abnormal conditions. With the simulation of methane released from the face, around shearer drum, and from the broken coal on the conveyor, places with possible high methane content can be identified by different phases of working process and shearer positions. Local ventilation measures are evaluated so precautionary measures can be planned ahead.

Jan 1, 2012

By A. De1

Because of the extremely low utilization of strain energy in the breakage of solid particles, the energy efficiency prevalent in comminution technology is extremely poor. Schoenert considered that single-particle comminution under slow compression is the most energy-efficient mode of comminution and that energy efficiency should be compared to that. The usual method for grinding minerals and cement has been the ball mill, in which the hit-and-miss aspect of loose-bed comminution severely reduces energy efficiency. The fine grinding of minerals is a particularly energy-intensive process. Schoenert showed that the energy consumed in the comminution of particles in confined beds is second only to that of single-particle comminution under slow compression and developed the method of conducting particle-bed comminution continuously in a high-pressure roll mill. Since its first industrial installation in 1985, the high-pressure roll mill has established itself as the comminution device of choice for significantly improving the productivity and energy efficiency of size reduction from coarse size feeds down to products finer than 20 microns. The first of several hundred installations were in cement plants. The preliminary design and optimization of the industrial operation of high-pressure grinding roll (HPGR) systems, owing to the continuous nature of the device, cannot be efficiently done through laboratory experiments and needs to be achieved through proper system modeling. While the energetics of size reduction in high-pressure grinding rolls has been modeled very well, no model exists for the macroscopic variables in HPGR comminution. In high-pressure roll mill grinding, size reduction results from confined particle-bed comminution under compressive stresses such that the daughter particles produced are highly fractured, stressed, or otherwise weakened. This paper attempts to relate the comminution / compaction behavior for confined particle-bed under compression in a piston-die press with the macroscopic variables in HPGR comminution. A model describing the pressure-densification relationship is presented and used to accurately simulate the macroscopic variables in high-pressure grinding rolls, utilizing experimental data for particle-bed comminution with the piston-die press. The accuracy of the predictive simulations strongly suggests that, starting with a few batch-mode laboratory-scale experiments, it should be possible not only to identify the optimal operating conditions for existing operations but also to successfully design new industrial high- pressure grinding roll systems.

Sep 1, 2012

By Baicheng Liu, Houfa Shen, Wensheng Li

"In order to understand the formation of macrosegregation in steel ingots, a mixture model has been developed which accounts for coupled mass, momentum, species, and energy transport to describe the sedimentation of free equiaxed grains during solidification. In this model, the mushy zone is divided into the slurry and porous regimes according to a solid packing fraction. Settling velocity of equiaxed grains in the slurry regime is given by an explicit expression. The solidification of a binary steel ingot (Fe-0.36wt.%C) with a two-dimensional geometry is numerically simulated. It is demonstrated that the predicted macrosegregation patterns agree to some extent with classical experimental results. Further refinement of this model is still necessary for realistically simulating steel ingot solidification.IntroductionModeling macrosegregation in steel ingots is still a challenging study, mainly due to the length scale of the products and the complexity of global multiphase transport phenomena coupled with microscopic solidification kinetics [l]. The thermal-solutal convection and the motion of equiaxed grains are the two main mechanisms responsible for macrosegregation. But there are few models that deal with the motion of equiaxed grains, which is confirmed as the main phenomenon that explains the negative macrosegregation along the centerline of large steel ingots [2]. A model which takes into account melt convection and grain sedimentation was first proposed by Beckermann and co-workers ([3], and references therein). More recently, similar multiphase solidification models with advanced nature have been presented by Wu and Ludwig [1,4] and Combeau and co-workers [5,6]. It is known that the application of these sophisticated models to steel ingot casting is at its beginning.In this paper, a solidification model based on continuum mixture approach, using much less sophisticated relations to obtain the settling velocity of free equiaxed grains, has been proposed in order to predict the macrosegregation in steel ingots. The model is applied to simulate the solidification of a binary steel ingot with a two-dimensional geometry, and preliminary modeling results are presented."

Jan 1, 2011

By Alejandro Gutiérrez, David Ahues, Paola Merino, Felipe González

The semiautogenous grinding (SAG) mill is one of the most important pieces of equipment in the comminution of materials. Its objective is to reduce the size of the ore until the ore can be released and continue on its transformation process. Although it is a simple process that involves impact, abrasion and attrition, its energy consumption is extremely high and inefficient, with no more of 17 percent of the energy supplied going toward size reduction. This gives rise to an important challenge because any improvement generates great economic benefits.