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An efficient and portable mathematical model has been developed for simulating heat transfer in six-in-line slag-resistance-heating electric furnaces for smelting sulphide ores to produce base metals and platinum group metals. This model is a steady-state one relating furnace conditions and performances to various control and input parameters. Some transient effects occurring in electric furnaces are neglected for computation efficiency. This article describes the model development and modelling results. The present model is capable of predicting: (i) temperatures at various locations in a six-in-line furnace, such as slag bath, matte bath, solid charge, freeboard space, freeze lining, cooling water, and air gaps between solid material components, etc. (ii) freeze lining thickness, (iii)smelting rate, and (iv) heat loss rate, etc. A typical feature of the model is that it is easily portable to different application platforms and sufficiently efficient with execution times less than a few seconds. Therefore, it is possible to apply the model for online prediction and control of heat transfer and freeze lining thickness in industrial electric furnaces.

Jan 1, 2011

By M. I. Kalashnikova, Y. M. Shneerson, E. E. Zhmarin, Y. V. Degtiarev, E. M. Vigdorchik

Separation of a magnetic fraction from nickel concentrate following matte flotation, and its treatment in a separate circuit enable reduces precious metals losses. The magnetic fraction is treated in two stages of oxidative leaching: atmospheric and pressure leaching. A study of the atmospheric stage, using mathematical modelling, is described in this paper. The mathematical model and experimental data were used to carry out industrial process calculations. The model enabled extrapolation of the results of batch laboratory test to industrial-scale continuous processing and the selection of optimal process conditions and large-scale equipment. In December 2004, commercial oxidative leaching tests were performed on the magnetic fraction at the Severonickel Plant (Monchegorsk, Russia). A comparative analysis of the mathematical modelling results and the actual process parameters is presented.

Jan 1, 2005

By Lynton Gormely

Oxygen transfer in a stirred tank bioreactor has been modelled mathematically to determine the trends in transfer efficiency (kg transferred per kWh) with transfer rate, tank depth, superficial velocity, and mixer power.

Jan 1, 1990

By K. Kabezya

A study on slag dispersion in a model of bottom-blown bath smelting converter was undertaken at room temperature. The aim was to investigate the behaviour of the dispersed slag phase at various operating conditions with very high gas flow rates in low slag volume (10%) systems. For simulation purposes water, paraffin-oil, and air were used to represent the bulk steel, molten slag, and gases respectively in a one-fifth cold model of the commercial 100 t Creusot-Loire-Uddeholm (CLU) converter used in the manufacture of stainless steel in South Africa. Dimensional analysis was done to correlate mathematically the dispersed phase holdup with the operating conditions and the modified Froude number. The overall expression of the holdup revealed that the dispersed slag phase decreased with the vertical distance from the original interface between the liquid phases. The dispersed phase also decreased with the radial distance in the water plume zone toward the sidewall. The holdup was apparently much higher on the side of the reactor where there were no tuyeres. The modified Froude number ensured the correlation between the model and the prototype.

Jan 1, 2014

By Gillies A. D S, Just G. D

The advancement of computer applications in the coal industry is focusing interest on the presentation of washability data by mathematical functions.The normal method of presenting washability data is in the form of five curves, usually filled by eye or by cubic spline functions. It has been shown that coal washability can be characterised by two basic relations: the instantaneous ash vs relative density relationship and the instantaneous yield vs relative density relationship. In a new approach to the mathematical modelling of the instantaneous ash vs relative density relationship, theapplication of the algorithm to a data set from a mine in central Queensland was successful.

Jan 1, 1991

By Pattinaja MA

Mathematical modelling was carried out to determine the probable convergence and vertical stress patterns around a retreating longwall panel in an underground coal mine in New South Wales. An 'Electrical Resistance Analogue' and a program called 'THREED' based on the displacement discontinuity method were used for the modelling. Parts of the obtained results are presented here and compared with some measurements of convergence at the site. The modelled and measured data agree better qualitatively, than quantitatively.

Jan 1, 1986

By J. M. Czaplicki

The problems connected with deep mine hoisting and the increasing complexity of this process can be analysed through the application of such mathematical tools as stochastic modelling to study the effectiveness, reliability or safety of hoist methods. To relate these theoretical investigations to real practice, knowledge about components, their stochastic nature and stochastic order of appearance is necessary. This paper presents results obtained during the ten-year (1976-85) period of research undertaken in the Polish mining industry by the Mining Mechanisation Institute of the Silesian Technical University, Gliwice, Poland.

Jan 1, 1987

By P. A. Bahri, D. G. Dixon, T. M. Woodward

A comprehensive mathematical model of the Sherritt-Gordon ammoniacal pressure leaching process at K winana Nickel Refinery has been constructed. The process is comprised of six autoclaves functioning as a three-stage leach circuit, operating over the temperature and pressure ranges of 85-95°C and 750-1000 kPa, respectively. The process chemistry forms a complex series-parallel reaction network, characterised by: (1) the gas-liquid mass transfer and reduction of oxygen, (2) the oxidation of eight distinct minerals, (3) the oxidation of sulphur, and successive reactions involving various intermediately oxidised sulphur species, and (4) the oxidation of Fe(II) to Fe(III), and subsequent precipitation as a hydrated ferric oxide. Material balances were developed for species in all three phases, and an energy balance to account for all reactions and phase conversions. The multiple convolution integral (MCI) statistical reactor model was employed for the scale-up of particle kinetics. The model has been validated against plant data, and simulation results are in agreement with plant performance.

Jan 1, 2005

By Vladimir Panjkovic, Ostrovski. Oieg, Campbell Cripps Clark, John Truelove

"Effects of properties of raw materials and blast on the performance of an iron bath reactor have been examined by a mathematical model. The model consists of three modules: 1) chemical reactions in the gas phase and heat transfer from gas to droplets ejected from the bath; 2) heat losses from the vessel and radiative heat transfer from the freeboard to the bath; and 3) heat and mass balances for the bath. The following parameters of the process are calculated: coal, ore, flux and oxygen consumption, post-combustion ratio and heat-transfer efficiency, temperature and composition of the off-gas, and slag and metal chemistry.IntroductionOne of the anticipated advantages of smelting reduction over conventional ironmaking is the use of lower-grade raw materials. In this work, the effect of-properties of raw materials on the performance of an iron-bath reactor is examined with a numerical model. The model is also used to assess the effect of properties of the blast (flowrate, temperature and oxygen enrichment) and ejected droplets (generation rate, size and ratio of total weights of slag and iron droplets) on the key parameters of the process. In the process coal, oxygen, ore (which may be partly prereduced) and fluxes for specified slag composition are charged to the bath. Slag and iron droplets are ejected from the bath into the gas phase, where they are heated before returning to the bath. Iron droplets undergo decarburisation and reoxidation with CO2 and H2O. Dust is also generated from the bath, and oxygen or preheated air for post combustion is injected from the top of the vessel.The model consists of three modules: 1) reactions in the gas phase and heat transfer from gas to droplets ejected from the bath; 2) heat losses from the vessel and radiative heat transfer from the freeboard to the bath; and 3) heat and mass balances for the bath. The structure of the model and the data exchange between the modules are shown in Fig. 1. The following parameters of the process are calculated: coal, ore, flux and oxygen consumption, postcombustion ratio (PCR), heat transfer efficiency (HTE), off-gas temperature and composition, slag and metal chemistry, and rates of decarburisation and reoxidation of the iron droplets."

Jan 1, 1996

By Isobe K, Muchi I, Hsieh YS

Theoretical and experimental studies have been made-to clarify the physical and chemical behavior of the tuyere combustion zone of blast furnace. Gas streamlines around this zone were visualized by the use of the two-dimensional equip- ment. Close agreement between the observed stream- lines and the calculated ones is found. The three- dimensional experimental studies have revealed that there exists a so-called dry zone in the neighbor- hood of the raceway and the trickling liquid be- haves approximately like a continuum. A kinetic model is develdped to describe the behavior of coke combustion in the tuyere zone. The model is based on the reaction kinetics, the differential balances of heat and mass, and the mechanics of gas flows. Regarding-the-axial distribution of gas composition in the tuyere zone, good agreement is obtained be- tween the model prediction and the data observed in a working furnace by the other investigators. Cal- culated results-show that the maximum consumption of coke occurs at the intermediate region of the raceway. For the blowing of oxygen-enriched or high -humidity blast, the position at which the maximum consumption of coke occurs is shifted toward the tuyere nose. Similar effect is found when the par- ticle diameter of coke in the tuyere zone is de- creased. The solid flow pattern around the tuyere combustion zone was visualized by the use of the two-dimensional equipment in which the sublimation of dry ice particles in front of the tuyere was

Jan 1, 1981

By Bruno Alves Resende, Antonio Adel dos Santos

Temperature, microstructure and dimensions are the main material parameters to be controlled during hot rolling of steel. Although thermal mathematical models have long been developed and applied for hot strip rolling, each Hot Strip Mill (HSM) must have its own model adapted to its facilities. Thus, a mathematical model for temperature evolution during rough rolling has been developed for the Usiminas HSM at Ipatinga Plant. The model achieved a high level of accuracy, which was assessed by comparing measured values of temperature at the hot strip mill entry with the calculated ones, the difference ranging from 9°C to 17°C. Application examples have shown that the slab can be occasionally stopped before start of rolling for as long as a couple of minutes without compromising its further processing. On the other hand, if the transfer bar stops after rough rolling even for short time, further processing in the HSM can be hindered, due to excessive temperature drop. In case of such abnormal line stop, the model can be used as a tool for decision-making to either continuing the planned rolling schedule or to changing the route, thus improving the overall rolling process.

Oct 1, 2019

By Pramod C. Thakur

Tunnels are defined as underground passages made without removing the overlying materials. From time immemorial men have driven tunnels for mining purposes. Even today tunnels are the building blocks for underground mines. The total length of such a network of tunnels in a mine may add up to 10-100 miles! In addition to this, rapid development of vehicular traffic, needs for air raid protection and metropolitan traffic problems have given a great impetus to underground tunnel construction. But for the successful drivage of any tunnel an adequate air environment has always been and remains an essential prerequisite. This is particularly true for tunnels in mines which are driven in gas bearing strata often at a substantial depth from the surface. An adequate air environment is designed to promote the health, safety and comfort of workers which results in greater productivity and efficiency. Its legal definition varies from country to country but, in general, it means the provision of sufficient circulating air, often at specified velocities, to maintain: (i) at least 19% oxygen in the working areas (ii) Concentration of pollutants, e.g., methane, carbon monoxide, respirable dust, etc. below specified limits. Table 1 shows the maximum allowable concentrations for some of these pollutants.1 (iii) Temperature and relative humidity below specified limits. Ventilation of tunnels in mines assumes ever. greater importance today because of increased mechanization and concentration of output which leads to higher rate of production of inflammable gases and respirable dust. Efficient management of the tunnel air environment, however, depends heavily on a thorough knowledge of how

Jan 1, 1974

By Samyguin VD, Filippov LO

The aim of this paper is to emphasise the importance of knowing of the rate of the elementary flotation acts (EFA) - attachment and detachment. By studying the simplest linear model notion of the column flotation, the results of the nonlinear simulaton of flotation separation in the column with lengthwise upward mixing show two principal different types of separative mass-transfer in the column. The first is, the case of a small EFA intensity, almost without the detachment. The second is, the case of a big EFA rate, when the process is close to a local attachment-detachment equilibrium. There is also an attempt to estimate the EFA rate for three different kinds of quartz particles, floated by cation collector in the laboratory column apparatus.

Jan 1, 1993

By Shuyu Qin, Shujiang Sun, Jingfu Zhao

The three key parameters of mine fires are local airflow velocity, temperature and oxygen concentration. According to the theories of seepage in porous media, heat transfer and heat dispersion, mathematical models were constructed based on the three parameters. The models can be used for early prediction of mine fires and for estimation of the level of spontaneous combustion. Proper use of the models can assist in preventing and controlling mine fires. KEY WORDS: airflow velocity, temperature, oxygen concentration, numerical modelling, mine fire prediction.

Jan 1, 1993

By A. L. Mular

Some specific cases of the collection of data from industrial grinding and classifying operations, and the development of models from the data so obtained, will be described. The problems encountered, the effort involved, and the value of the derived models in improving the plant efficiencies will be discussed and documented where possible.

Jan 1, 1971

By Dan G. Cojocariu, E. Ene-Danalache, I. Huber-Panu

A general model which represents not only batch but also continuous flotation in multi-cell machines is presented. This model considers both the size distribution and the distribution of flotabilities in a size class for valuable mineral particles in the pulp. The general expression is shown to reduce to several previously reported models. In addition, a number of new models are found to arise for different specific assumptions concerning the flotability distribution and/or the size distribution of the particles undergoing flotation. Several of these new models are tested experimentally using laboratory-scale batch and pilot-scale continuous data. Model parameters are estimated from this data and a comparison of calculated recoveries and those experimentally determined are presented. Finally, the influence of the feed rate, aeration rate and valuable mineral content of the feed on the recovery is examined.

Jan 1, 1976

By J. Herbst, I. Heber-Panu, Dan G. Cojocariu, E. Ene-Danalache, G. Poling

A general model which represents not only batch but also continuous flotation in multi-cell machines is presented. This model considers both the size distribution and the distribution of flotabilities in a size class for valuable mineral particles in the pulp. The general expression is shown to reduce to several previously reported models. In addition, a number of new models are found to arise for different specific assumptions concerning the flotability distribution and/or the size distribution of the particles undergoing flotation. Several of these new models are tested experimentally using laboratory-scale batch and pilot-scale continuous data. Model parameters are estimated from this data and a comparison of calculated recoveries and those experimentally determined are presented. Finally, the influence of the feed rate, aeration rate and valuable mineral content of the feed on the recovery is examined.

Jan 1, 1976

By A. G. Royle

The reasons for constructing a model of an orebody for which both the parent population and the sampling distribution are known are discussed and details of the model are given. A brief summary of Matheron's theory of regionalized variables is included, with particular reference to his kriging estimators and their variances. Using the model, a comparison is then made between these kriging estimators and other commonly-used estimators. These are compared to find the one with the minimum variance, and an analysis is included to investigate whether any of the estimators is biased. Also included is a comparison between theoretical and experimental variances for some of the estimators.

Jan 1, 2014

By D. N. Madge

A survey is given of production scheduling systems currently in use or contemplated for future use in Cominco operations. Emphasis in this presentation is made on the chain of decisions that are made with the help of mathematical programming models. Some attention is devoted to the structural properties of the models.

Jan 1, 1966

By R. Venkataramani

Crushed stone operations have become more difficult due to rising costs of labor and equipment, with the consequent reduction in profit margins. Competition from other operators and the encroachment of vertically integrated companies place severe restrictions on available markets. The seasonal demand for stone precludes any definite production level, and changes in productivity have to be accommodated. These influence profitability, and therefore production plans must be continuously adjusted to keep pace with rapidly changing conditions. The basic problem of stone companies seeking to maximize profits is one of balancing stone production costs, costs of inventory holding and stock-piling, marketing costs and any other charges accruing over time against the selling price of stone. Because of high peak demands, slack period production must be stored and then distributed to supplement peak period production. For a multi-plant operation, there is a need to evaluate at the same time the interaction between the plants and the various marketing sectors. In a multi-plant operation with different production capacities and production costs, stone producers are interested in the answers to the following questions: 1. How much stone should be produced at each plant in each time period? 2. What should be the optimum stone shipment from each plant to each market? 3. What are the effects on net returns and shipping plans, if production capacities are altered at the plants? These questions have many different answers that, will satisfy demands. From the point of production scheduling, the minimum production cost may be the objective. From the inventory standpoint, the best solution will be to synchronize production with sales. However, when the transportation of stone is also considered, the desired end is to achieve that delivered cost which maximizes the company f s net return. Besides, only an extremely naive analysis ,wouId attempt to

Jan 1, 1971