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By S. Esfahani, M. Barati, Y. Kauwachi

"Heat recovery from slag has gained attention due to its high potential in lowering energy intensity of metal extraction processes. A direct method to recover the thermal energy of slag is to use countercurrent air flow that extracts the heat from falling droplets. Often, the solidified slag is aimed to be used as a substitute for Portland cement, thus high cooling rates are required to form an amorphous slag with sufficiently strong hydaulicity. Rapid cooling however involves using large gas flow rates that in turn lower the thermal efficiency of the process. This article presents a mathematical model that was developed to determine the optimum conditions in the heat recovery process and to investigate the effect of the air flow and granule diameter on the cooling rate of the droplets as well as the thermal efficiency of the heat recovery system. INTRODUCTIONMetallurgical slags are the largest by-product of high temperature materials refining and extraction processes. The total amount of metallurgical slag produced in the year 2008 has been estimated at up to 422 million tonnes containing up to 222 TWh/y (Barati and Esfahani, 2011) of thermal energy. Over the past four decades attempts have been made to recover this substantial amount of energy as heat, electricity, or fuel, while none of the proposed method has been commercialized yet.During slow cooling the slag tends to crystallize the constituents (CaO, SiO2, Al2O3, etc.) into a hard, heavy solid. In the past, over 90% (Bengt, 1983) of the molten waste was discharged onto heaps and allowed to cool slowly, then crushed and used in road construction or land filling or as coarse aggregate for concrete. However, later it was found if cooled rapidly, the slag can be used as a substitute for Portland cement. As a result, processes such as wet granulation were created in which molten slag is fragmented with water, forming amorphous (glassy) phases. Despite its effectiveness in producing a suitable material, heat would not be recovered through this process. Thus, dry granulation was introduced in 1930’s and was developed further in 1970 – 1980’s."

Jan 1, 2012

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 William Y. Mo

The OPEC oil embargo and the subsequent higher prices for oil have drawn public attention to the critical problems associated with security of supply of oil and other key industrial materials, especially nonfuel minerals. This concern has stimulated the interest of decisionmakers in analyzing policy options to cope with the emergency situations resulting from a sudden foreign- induced supply interruption or a cartel price increase. Several policy options are available to counteract foreign-initiated embargoes or cartel price actions. The type of response will differ depending on the commodity action intiated. A mathematical model that measures the impact of foreign-induced commodity actions on the domestic economy is formulated. The paper also presents a computer method that can be used to determine the optimum policy response to counteract such actions.

Jan 1, 1977

By G. A. Irons, G. S. Hanumanth

A three-dimensional mathematical model for the electric furnace of Cominco's Kivcet process was developed to compute the electric field intensity, power dissipation, temperature and velocity distributions in the furnace. A number of simulations of the electric furnace operation were carried out for various electrode immersion depths and electrode currents. The results showed that the current penetrated the bullion layer, generating high current densities in a layer approximately 0.3 m thick located in the slag/bullion interface region. An increase in the electrode immersion depth increased the furnace power as well as slag temperatures, and generated more vigorous bubble stirring and thermal homogeneity in the slag. For a given applied current, the computed power was in reasonable accord with the measured power input. The calculated temperatures were in rough agreement with the tapping temperatures of slag and bullion.

Jan 1, 2000

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 A. C. Scott

A detailed fundamental model of a zinc electrowinning cell has been developed and validated for both steady state and dynamic simulations. This model was used to investigate the effects of a range of operating variables and to find their optimum values. As well as providing useful design information for a planned upgrading of the EZ refinery, more generally it demonstrates the potential benefits to the minerals industry of the applications of modern CAD flowsheeting techniques. The SPEEDUP equation oriented CAD package was found most suitable for this task as the user can easily generate models specific to his site with any number of components and mixture properties.

Jan 1, 1987

By Julian Szekely

Through the simultaneous statement of Maxwell's equations. the turbulent Navier-Stokes equations and the differential thermal energy balance equation, a mathematical representation has been developed for heat transfer and fluid flow in electric arc furnaces. In broad outline the theoretical predictions appear to be consistent with experimental measurements. A discussion is presented of the general arc furnace control and optimization problem, together with the potential for the incorporation of the mathematical model given in the paper, into future control and optimization schemes. ELECTRIC ARC FURNACE STEELMAKING accounts for about 24% of the total steel produced in the U.S., consuming about 550kw-hr/ton of steel which amounts to about 1.4x1010 kw-hr annually. The percentage of steel produced by the electric arc furnace route has doubled since 1960 and is expected to increase further in the foreseeable future, particularly with the more extensive use of direct reduction technology. Table I shows, in terms of percentages, the principal items that contribute to the cost of running an electric arc furnace. It is seen that in addition to the fixed costs (labor, depreciation, taxes etc.) electrode costs and power consumption are the dominant inputs, and it follows that process changes that would ultimately reduce any of these cost components would have a significant impact on the efficiency of the operation. There are three main areas where progress in arc furnace design and operation must be directed in the next decade (Committee on Technology, 1981). 1. Increased furnace productivity 2. Reduction in processing cost 3. Improvement in the thermal efficiency of the furnace An estimate of the current operating efficiency of the electric arc furnaces may be obtained by comparing the theoretical minimum energy consumption per ton of steel with those achieved in operational practice. Theoretically 330-360 kw-hrs of electricity are required to melt one ton of cold scrap. For superheating, 8-12 kWh per 100°F are required. The actual energy requirements are given in Table II. It is seen that furnaces currently operate at 70-80% efficiency, with the major heat loss from the furnace resulting from the waste gases (Committee on Technology, 1981). While it is apparent that operational experience has produced a technology that is reasonably energy efficient this has been achieved in the almost complete absence of any detailed knowledge concerning the fundamental heat transfer mechanisms occuring in the furnace. The purpose of the present paper is to present a case for the usefulness of mathematical models in increasing the thermal efficiency of furnaces by investigating these heat transfer mechanisms and then combining this knowledge with existing electrode regulator mechanisms to produce truly efficient power cycles for melting and refining. In particular, existing mathematical models describing convection, radiation, and electro-magnetism in the furnace should be employed, and the development of optimization models which balance the cost of electrodes and energy against the thermal efficience of the furnace should be undertaken. Recent work in this laboratory (Szekely, McKelliget, 1981, 1982, 1983; Szekely, McKelliget, Choudhary, 1983) has made a useful start towards solving the problem of heat transfer within the electric arc furnace but the work still needs to be directly related to existing furnace power cycles and tested against plant scale measurements.

Jan 1, 1984

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 Jin C, Shu H

The effect of operating parameters of a shaking table on the separation of mixed quartz-magnetite artificial feed has been experimentally investigated by use of laboratory-scale shaking table. Based on a great number of experimental data collected, the multi-variate non-linear model of shaking table has been developed. The model allows for the calculation of the product grade and recovery. A computer model has been programmed, for inclusion in a software package for the simulation and optimisation of shaking table if the feed characteristics and the concentrate grade are given.

Jan 1, 1993

By Denholm WT

A mathematical model has been developed for intense pneumatic smelting processes, such as the Sirosmelt group of processes, to assist in establishing optimum process conditions and to permit operator training. The model first solicits input operating conditions from disk files and from the operator. During operation, the feed, fuel, and air (or oxygen) rates are automatically adjusted to maintain the desired process targets. Alternatively, these parameters, as with all other inputs, may be manually controlled by the operator. Selected process parameters are displayed to the terminal in a regularly updated diagram of the process,. Outputs of detailed information including heat and mass balances are available for immediate inspection or for use by ancillary plotting packages. Development of a robust free energy minimization routine has led to a flexible and time efficent model capable of handling a range of pyrometallurical systems. Modelling of tin smelting, lead smelting, copper smelting, matte fuming, and pneumatic steel-making has been sucessfully carried out. Typical outputs from the model are given and discussed in terms of their internal consistency and relationship to the operation of the relevant Sirosmelt process. `

Jan 1, 1984

By F. A. G. M. Camisani-Calzolari

The uranium production forecasting program described in this paper projects production from Reasonably Assured, Estimated Additional and Speculative Resources in the cost categories of less than $130/kg U. Originally designed to handle South African production, it has been expanded and redimensioned using available published information to forecast production for countries of the Western World. The program forecasts production from up to 400 plants over a period of fifty years and has built-in production models derived from documented historical data of the more important uranium provinces. It is particularly suitable to assess production cavabilities on a national and global scale where variations in outputs for the individual plants tend to even out. The program is aimed at putting the uranium potential of any one country into a realistic perspective, and it could thus be useful for planning purposes and marketing strategies.

Jan 1, 1987

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