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By Stein Tore Johansen

The flow of a liquid through a large grain filter has been considered. An improved form of the fluid dynamic equations describing flows through porous media is proposed. The theory is applicable to all Reynolds numbers. Particulate inclusions are described by passive scalar fields where only very simple mechanisms for particle removal are included. However, the deposition of particles are allowed to change the "porosity" of the filter. Hence, the flow pattern through the filter will change as the filter ages. The theory is employed to the filtration of aluminum in an industrial grain filter. The model shows that the filter is not effectively designed and there is room for considerable improvement. The dynamic "aging" process of the filter is shown to change the filtration from bed filtration to cake filtration. Finally, the predicted inclusion collection efficiencies are compared to efficiencies measured in an industrial filter. The predicted initial efficiencies are in very good agreement with experimental results.

Jan 1, 1990

By Rudolf E. Greuer, Xintan Chang

Mine fires have always been of great concern to mining engineers and their behavior has been studied for a long time. Although an abundance of observations exist, no satisfactory mathematical model for their interpretation and extrapolation has become known. The paper presented here tries to close this gap, making use of the laws of chemical kinetics, energy and momentum conservation. To overcome the mathematical difficulties, the fire zone is axially divided into segments and radially into sections, each one with an extension of only a few inches. Conditions in segments and sections are updated in time intervals of one second or less. To solve the large number of resulting equations, a numerical solution is performed. The model has so far been tried on timber fires. It confirms experimental observations on the ignition phases and equilibria of these fires.

Jan 1, 1987

By David G. Dixon

A mathematical model is derived in dimensionless form which simulates the effluent concentration response of reagents from spent heaps under both fresh and recycled water rinsing. The model is based on dispersion from isochoric pathways distributed in length and cross-section, oriented normal to convection channels in ideal plug flow. The effects of heap height, rinsate flow, and initial reagent concentration are examined. It is shown that the rinsing cycle undergoes a distinct shift between fast and slow rinsing at a certain time depending on the amount of stagnant solution in the heap, and the distribution of dispersion pathways. Results of preliminary column rinsing tests on both agglomerated and unagglomerated ores are presented which partially validate the model.

Jan 1, 1994

By E. F. Vegman, Ndabezinhle Dube

"In the practice of conventional sintering, production is always afflicted with the problem of being unable to get a uniform quality of produced sinter in the bed. Invariably the top layer of the sinter cake is composed of weak but highly sinter, while the bottom layer is over-fused, forming a sinter that is very strong but less reducible. These symptoms point to a variable distribution of the heat balance in the process of sintering which results in a deficit of heat in the top layers of the sinter bed and an excess of heat in the bottom layers, due to an increasing input of regenerated heat in the heat balance down the bed. This causes losses in the productivities of the sinter machine and the blast furnace.The current work was designed to improve on the solution to the above problem through the establishment of a more accurate combustion zone heat balance of the sintering process. This development is mostly on the method of determining the regenerated heat input in the overall heat balance. Previous methods were based on the assumption that the width and the velocity of the combustion zone remain constant through out its whole life, which is not the case since tests have shown that both its width and velocity increase as the combustion zone moves down the bed. In this work, these factors have been taken into account. Tests and calculations using the model were carried out for haematite and limonitic ores. The high sensitivity of the model to changes in the sinter mix composition and sintering conditions was demonstrated.The results present the following prospects:• The minimum theoretically possible coke breeze consumption during the sintering of any type of iron ore fines, under any sintering conditions, can be established.• The model can be used to control the metallurgical quality of the sinter in any point in the sinter bed since calculation data includes desired basicity, combustion zone temperature and FeO content in the sinter produced."

Jan 1, 2001

By H. W. Gao

During the last decade, the feasibility of applying the in situ leaching technology to the recovery of copper from deeply buried deposits containing chalcopyrite has received much attention.(1-4) The major incentive for using this technology is that under certain circumstances, copper in deep underground deposits, which cannot be mined economically by conventional means, can be recovered economically. Basically, this technology involves rubblization of the deeply buried copper ore body followed by in-place leaching of the rubblized copper ores. Rubblization of the ore can be achieved by some suitable method such as the use of block caving mining. The rubblized chimney is then filled with water until the original water level is reached. Leaching occurs when the eater saturated with oxygen is introduced into the chimney- and flows through the fractured rock masses and within pores of rocks. As the dissolved oxygen oxidizes the primary sulfides, heat is generated. Because of low conductivity of the surrounding rocks, the generated heat is able to raise the temperature of the chimney. The increase in the temperature of the chimney and the relatively high content of dissolved oxygen in the leach solution under high hydrostatic pressure will result in an enhanced dissolution of the primary sulfide minerals. To ensure a successful application of the in situ leaching technology, a complete understanding of the effects of the ore particle size distribution, ore grade mineralogy, temperature, pressure, lixiviant concentration, pH, etc. on the rate of copper recovery is necessary so that copper can be recovered efficiently and the amount of copper extracted can be predicted. These can be achieved through mathematical modeling of the in situ leaching process and conducting laboratory tests. In this paper we will present a mathematical model that simulates the in situ leaching process as depicted in Figure 1. To model this process properly, not only the 'kinetic and thermodynamic aspects of leaching chemistry must be known, but the effects of heat generation, the physical aspect of fluid flow and other related multicomponent transport phenomena must be considered. Furthermore, since most factors involved in the leaching process change with time, a leaching system must be described using unsteady state equations.

Jan 1, 1981

By J. E. Sepulveda, R. Morrow

"In full scale mineral grinding operations, the steel balls normally utilized as auxiliary grinding media get to be consumed at different specific rates, as determined by 3 basic mechanisms: abrasion/corrosion (wear), impact ball breakage and impact surface spalling, the latter relating to the removal of rather small pieces of steel coming off the exposed surface of the balls due to repetitive impact with other balls in the charge or the surrounding mill liners. In conventional ball milling applications, the clearly predominant mechanism is gradual wear by abrasion/corrosion. In the case of SAG mills, where the make-up balls may be as large as 6”f diameter, breakage and spalling mechanisms are significant contributors to total ball consumption, although not to the extent of overriding wear mechanisms.Ball wear has been well characterized by the Linear Wear Theory, as presented at the last CMP 2014. Impact breakage has been customarily monitored, at the ball manufacturing site, via Drop Ball Tests (DBT) consisting of repeatedly dropping balls from a standard height and accounting for the number of broken balls and the weight loss (spalling) of the remaining unbroken balls. When properly conducted, DBT’s should provide meaningful indications of the breakage and spalling resistance of large diameter balls. The current publication is focused on the interpretation and projection of DBT results to full industrial scale, taking into account all 3 mechanisms of grinding media consumption in SAG mills.INTRODUCTIONA thorough, quantitative understanding of the independent contribution of all active grinding media consumption mechanisms is of the highest practical relevance, particularly in semiautogenous (SAG) milling operations where ball breakage and spalling can not be ignored or neglected, as it has been normally acceptable for conventional ball milling processes. The high severity impact conditions currently imposed in typical SAG mill environments create serious challenges to the manufacturers and suppliers of large diameter (5”–6”) SAG balls, whose products must be capable of surviving such harsh operational conditions with minimum breakage or spalling."

Jan 1, 2015

By Zhou Jiemin

In order to fully understand the behavior of the rectangular six- electrode electric smelting furnace and improve its design and operation, a three-dimensional mathematical model has been developed which incorporates the electrical and thermal flows into numerical solutions, assuming a steady state regime. The model has been used to simulate the performance of the 16500 kVA nickel matte smelter at Jinchuan in China, and various factors have been investigated. The results of computation are in agreement with the measured data obtained from this furnace and its physical model. Application of this model is described and the calculation on the Jinchuan smelter shows that the operation expenses can be reduced by optimizing the furnace geometry and some operating parameters.

Jan 1, 1991

By I. Fedotov

One of the most effective methods of metal surface heat treatment is through laser hardening. In most cases, laser parameters are determined experimentally, which is expensive and time-consuming. A mathematical model for the surface heat treatment process will allow a significant decrease in costs, and reduce the time required for optimization. In the present work, the authors present a mathematical model for laser heat treatment with forced cooling which can be applied to medium carbon steel. The model is based on a three-dimensional heat transfer equation using Green?s function. The model allows one to calculate the temperature of the treated steel at different depths below the surface with and without cooling, for set values of the laser power and travelling speed, when the heat transfer coefficient is a known constant. It also takes variations in the radiation adsorption coefficient on the metal surface and laser beam spot size into account. The model was illustrated by comparing calculated and experimental temperature profiles of mild carbon steel with 0.5% C with and without cooling. A reasonably good agreement was achieved between experimental and predicted values to ensure that a high enough austenizing temperature with short enough cooling time was reached for direct martensite formation. It also predicted the depth of treatment accurately. The incorporation of cooling in the model substantially improves previous models based on heat transfer only. It delivers a tool that can with a reasonable accuracy predict the depth of surface heat treatment and cooling time required from operational parameters, such as laser power, speed of motion, and distance between laser and cooling source, that can be controlled in the work set-up. This can eliminate trial and error efforts and result insignificant time and cost savings. Keywords Laser, surface treatment, martensite transformation, carbon steel, heat treatment.

Jan 1, 2011

By L. R. Plitt

A series of experiments were carried out in an effort to develop a universally applicable mathematical model of the hydrocyclone classifier. The design and operating variables studied were: cyclone diameter and height, the inlet, vortex finder and apex diameters, the feed pressure and the solids content of the feed slurry. The model consists of four basic equations which express the cut size ( dso), volumetric split between overflow and underflow, volumetric throughput, and sharpness of separation in terms of the operating and design variables. Although empirical, the model is nevertheless in general agreement with fundamentally derived models. The model clearly 1•eveals the effect of the major variables on the operation of a hydrocyclone. Because of its broad data base and the inclusion of all the major variables, the model may be used without experimental data to predict the operation of cyclones over a wide range of different operating conditions. With operating data, the equations may be modified to serve as an operational model.

Jan 1, 1976

By A. H. Castillejos E., F. A. Acosta G.

Filtration is widely used as a terminal refining step for metals, particularly for the casting of aluminum alloys, but still more knowledge is required to understand how several factors affect the efficiency of removal of inclusions. In this study, both, initial and long term filtration efficiencies of a ceramic foam filter have been obtained from the computed trajectories of solid particles suspended in molten aluminum. The complex structure of the foam filters is represented by a unit cell which is formed by a pair of pores with average dimensions. The fluid flow field was determined from the numerical solution of the Navier-Stokes equation, and periodic fully developed flow was assumed at the inlet of the calculation domain, as a boundary condition. This flow field corresponds to laminar flow as that found in ceramic filters operating under normal conditions. Computed initial filtration efficiencies showed that filtration efficiency decreases sharply with fluid velocity for particles larger than 30 µm, but smaller particles are better trapped at higher fluid velocities. Finally, it was found that long term filtration efficiency for particles of 8 µm decreased with time, in spite that perfect particle-wall attachment was assumed. Filter aging was considered in this study, and it was found that the distorted flow field, around the already trapped small inclusions prevented further collection.

Jan 1, 1999

By B. Yu, M-H. Cao, C. Zhou, X-Z. Zhang

The transient infiltration and lubrication behaviour of slag during continuous casting of steel is important for billet quality. A two-dimensional coupled mathematical mould model was developed to investigate these phenomena. The accuracy of the model was verified by comparing the calculated slag consumption with measurements by the plant. The results show that the liquid slag is consumed from the middle and late period of positive strip time to the next early period of positive strip time, including the entire negative strip time. The maximum downward infiltration velocity and positive pressure in the slag channel is at the middle of the negative strip time. Increasing the positive pressure of the slag channel is conducive to lubrication. The shear stresses acting on the shell surface and at the mould side were determined by the lubrication slag consumption and total slag consumption, respectively, and gradually decreased with increasing slag consumption. The negative strip time was lengthened to increase the slag consumption and prolong the time near the maximum downward shear stress, so as to be conducive to the demould.

Apr 16, 2024

By David F. Gibson

This paper presents an outline of several models that have been developed to aid surface mine planners evaluate alternative mining methods and dragline sizes. The models presented belong to a larger group of models that are incorporated in the SEAMPLAN computerized mine and reclamation planning system. SEAMPLAN was developed in the College of Engineering at Montana State University. Initial funding for the development was derived from the USDA Forest Ser- vice and EPA. Enhancements to SEAMPLAN are currently being funded by DOE (Contract DE-AC22-80ET-14173). SEAMPLAN is a comprehensive surface mine and reclamation planning tool that contains a number of major modules: Data Entry and Review, Production Analysis, Reclamation Analysis, and Impact Analysis. The Production Analysis Module contains programs that enable the user to evaluate alternative methods of removing overburden in a surface coal mine and then to assess auxiliary activities required to support the overburden removal operation. A set of these programs addresses the use of draglines for removing overburden. Six basic dragline mining techniques have been modeled. For one-pass dragline operations four methods can be analyzed: (i) simple side cast, (ii) side bench, (iii) extended bench, and (iv) extended bench with side bench. Two methods of two-pass operations are modeled: (i) single dragline, and (ii) tandem draglines.

Jan 1, 1982

In this paper, a mixed integer linear programming (MILP) model for the short-term scheduling of open pit mines is formulated. The proposed model aims at sequencing the blocks extraction over multiple short-term periods. The model takes into account multiple processes, waste dumps, and multiple stockpiles. The short-term scheduler makes a decision on the period, destination, and route that ore and waste are supposed to take to minimize costs while meeting all the mining and processing constraints. The destinations of the extracted materials are also controlled by their rock types. A monthly short-term production scheduling case study of an iron ore deposit is carried out over a year to validate the model.

Jan 1, 2011

By Raúl Carretero de la Hoz, Leonardo Soares Chaves, João Paulo Soares Toneli, Francisco Felipe da Silva Dantas, Marcos Peres Lopes, Marcus Vinicius da Silva Gonçalves

The mining activity results in environmental impact and thus requires the adoption of techniques to minimize its effects. The rock blasting process is required to break up and move the rock enabling the haulage of the material, however, it might also cause undesirable effects such as flyrock, overbreak, excessive ground vibration or air-blast at the neighboring communities and damage to civil or geological structures located nearby. The Serra Sul mine, commonly referred to as S11D project, has obligations to preserve two natural tropical montane lakes and several maximum relevance natural cavities whose legal preservation radius represents constraints to the mine development and operation. Controlling measures are undertaken to ensure preservation of the cavities, especially during rock blasting stage, with limitations of the maximum instantaneous charge (MIC) and ground vibration control. The demand for high productivity and the large areas with hundreds of blastholes to charge are challenging factors to the charge control. This work presents the development and field application of a map for limiting explosive charges in the rock blasting process at the Serra Sul mine, used for the definition of maximum charges according to the blast location, ensuring the preservation and compliance with the defined ground vibration limits for each cavity. The map is applied at the mine for every blast and when there is a charge constraint, the map helps to define the areas with different charging profiles in the field contributing to higher charging productivity.

Jan 21, 2025

By Gregory P. Cole, Peter G. Kovalchika, Rudy J. Matetic, Adam K. Smith

Previous studies conducted by the National Institute for Occupational Safety and Health (NIOSH) have shown that approximately 90% of coal miners and 49% of metal/nonmetal miners had a hearing impairment by age 501. Mine workers are exposed to additional noise levels underground due to the reflection of machine generated noise that would otherwise dissipate in an above ground setting. Determining the sound absorption coefficients is essential in modeling the sound field in an underground mining environment. Sound absorption is a measure of the amount of acoustic energy that strikes a surface and is absorbed, rather than reflected. The acoustic environment that mining machines operate in is a critical factor affecting the sound pressure level exposure for mining machine operators. Impedance tube testing is an inappropriate method for determining underground absorption coefficients due to the brittle composition of some of the materials such as coal and slate. Classic absorption coefficient estimation using T60 measurements will not work well in an underground environment because the theory assumes: a finite room, a diffuse field, and relatively uniform absorption. None of these assumptions are true in an open-ended mine entry. This paper will present a method using a ray-tracing technique to determine absorption coefficients for underground mines. Absorption coefficients are determined and presented for octave bands from 63 Hz to 8 kHz. The absorption coefficients will be essential for determining and predicting potential overexposure to machine operators in different mine environments.

By M. Ashraf Mahtab

In Louisiana salt mines a sudden erruption or outburst of salt and gas occurs when the heading face approaches a pressure pocket (altered salt with high pressure gas). The resulting cavity is semi-ellipsoidal, reaching lengths of 50m or more. Potential risks from the outbursts include loss of life and equipment. A gas outburst is initiated by "disking" of the salt in biaxial compression and propagates by spalling of the cavity walls and further disking. The outburst is terminated by a combination of dilatancy hardening, increase in stress along the cavity axis, and enlargement to boundaries of the pressure pocket.

Jan 1, 1982

By William H. Dresher

A study has been made of the reaction mechanisms occurring during the salt-roast process to form water-soluble sodium vanadate compounds from the vanadium oxide compounds present in vanadium-bearing ores and concentrates. Two reactions have been identified, either of which lead to water-soluble compounds--oxidation of sodium chloride by water vapor and. oxidation of sodium chloride by oxygen. The former reaction has been found to be predominant in the salt-roast process. A kinetic treatment of the data has shown that for the formation of sodium metavanadate the rate-controlling step in the reaction, in which sodium chloride is oxidized by water vapor is the decomposition of a species containing water and sodiumm chloride, on the surface at the gas-solid interface. For the formation of sodium pyrovanadate, the rate-controlling step is the decomposition of a species containing water and sodium metavaradate on the surface. The transportation of water through the system, perhaps as a sodium chloride-water complex or a sodium metavanadate-water complex, and the actual chemical reaction are relatively fast compared to the initial surface decomposition step. A similar treatment on the data for the oxidation, of sodium chloride by oxygen has shown that the rate-controlling step, is the actual transportation of oxygen from the gas-solid interface to the reactive site. This transportation is by a sequence of two diffusion processes. Transportation during the early stages of the reaction is by the diffusion of oxygen through a continuous layer of reaction product. After, the first few minutes of reaction time a second diffusion process begins and is continuous for the remainder of the reaction. This second diffusion process involves the diffusion of oxygen, through a layer of reaction product that has developed voids around which the oxygen must diffuse. The hindering, nature of this latter process causes the rate of transportation of oxygen to the reaction site to be considerably slower than by the simple diffusion mechanism initially followed. A thermodynamic treatment of the data has shown that the energy of activation for the decomposition of the water-sodium chloride species on the surface is -12.1 Kcal. per mole. For the decomposition of the water-sodium metavanadate species on the surface' the energy of activation is -15.1 Kcal. per mole. The results of this study indicate the limiting mechanisms of the basic reactions occurring during the salt-roast process. These results suggest what variables should be examined in applying this information to actual plant operations.

Jan 1, 1961

By P. Condori

In spite of the importance of the slurry transport and discharge in autogenous and semiautogen-ous (AG/SAG) mills, it is evident that a more comprehensive and useful model is still required. Semi-empirical models used up to now have many limitations and cannot be used beyond the ranges in which they were developed. The breakage of particles as they are transported along a mill com-plicates the experimental analysis and the modelling of the transport process within the mill. The interaction of the grate discharge and the pulp lifters, with the added issue of backflow from the pulp chamber into the mill, makes the discharge modelling process difficult. In order to overcome these difficulties, a mechanistic approach has been applied. The general transport and discharge model was subdivided into four independent models: Flow through the charge, flow through the grate, flow in the pulp lifter, and flow-back. This paper gives an overall description of the modelling approach and discusses in particular the modelling of transport of fluids through the charge. In order to evaluate and calibrate the model, experimental work was carried out. To evaluate the gradient pressure under different conditions of charge packing and flow rate, a specialised experimental rig with a highly sensitive pressure gauge was used. Preliminary results identify the differences of the charge and grate on the restriction of flow. The existence of a dynamic voidage in our particular system was more evident and as a result, a semi-empirical correlation for the voidage was developed. In general, results show that the me-chanistic model derived from Ergun?s equation for flow through a packed bed can be satisfactorily adapted.

Jan 1, 2014

By Elbasher M. E. Ahmed, Indresan Govender

"A mechanistic model of axial charge segregation in rotating drums is presented. We show that granular material composed of different frictional properties diffuse into axial bands as a consequence of concentration fluctuations in the free surface layer that is caused by friction-limited mobility. A Bagnoldian stress assumption ensures an asymmetric free surface profile thereby providing the essential ingredients for the evolution of axial bands and the subsequent band coarsening observed in the literature. The formulation is sensitive to the boundary conditions of tumbling mills, including particle size and density, mill speed, inter-particle bulk friction, end wall friction and drum geometry (length and diameter).INTRODUCTIONA mechanism to fully describe the axial segregation of charge in a rotating drum remains elusive to the mineral processing industry. With regard to low aspect ratio mills (like ball mills), current thinking favours the use of closed circuit mills with correspondingly low residence times to offset the completely random contact probabilities between particles and balls (Wills & Napier-Munn, 2006). Conical end caps are argued to exploit the centrifugal force to achieve a regular gradation of ball size along the mill with larger sizes at the feed end and smaller ones closer to the discharge. However; segregation along the length has been observed in the absence of conical end caps (Oyama, 1939; Levine, 1999): In these investigations, sufficient differences in the particle’s mechanical properties (particle size, density, shape, surface roughness) was enough to successfully achieve axial segregation. Figure 1 shows the segregation of a bimodal distribution (by size) into bands of larger (darker colour) and smaller (lighter colour) particles."

Jan 1, 2016

A Mechanistic Model of Batch Grinding in Ball Mills

Sep 13, 2010