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By Eren H

For a hydrocyclone of fIXed geometry, DC, Di, DO and ? are constants, the variable parameters affecting the performance are Qi, Fi, Du and H. (See Appendix 2 for definition of symbols).The relationship between d50c, Qi, Fi, Du and H gives models which can effectively be used for performance predictions. Such models have already been established by Lynch et al and by Plitt.These models have been tried in a limited manner under continuous operating conditions for on-line cowol. For on-line control effective and accurate instrumentation is required for which a new set up is proposed. Using this set up, a new model was established. A feature in this model is that deviations from the norm of operational parameters affecting d50c were considered. It is shown that these deviations generated by the disturbance of one or more of variations in the parameters, can be monitored by a computer and suitable signals generated to control servo mechanisms for restoring the required d50c value.The logic followed in developing the computer software is described and the application of the model is indicated.

Jan 1, 1990

By Batterham RJ

A 'research model' can be used to investigate cause and effect relations and generally improve the understanding of extractive metallurgical processes. As such, it is a useful research technique which complements the traditional methods of laboratory and plant measurement. The procedure of model development is iterative and involves observation of the process, hypothesis of phenomena, prediction using mathematical descriptions of the phenomena and comparison of predictions with real-world measurements. Lack of agreement of predictions with real-world measurements usually indicates an inadequacy in the hypotheses and necessitates revision. Experimentation has an integral role in the process of model development but its emphasis is different from that when experimentation alone is used to study processes. Since a process as a whole is investigated by using a model, experimentation is restricted to the study of specific phenomena to aid the description of these in the model, to the characterisation of the raw materials (for initial values of the model parameters) and to the measurement of physical and chemical constants required in the model equations. Similarly, plant measurements are made for the purpose of comparison with the model predictions not to establish cause and effect relations. This makes plant experimentation much simpler and cheaper'since most measurements-can be taken during normal operation.

Jan 1, 1984

By Gemei Yang, Pierre Mousset-Jones, Felipe Calizaya, Malcolm J. McPherson

Laboratory tests on controlled airflow recirculation have shown the development of transient states in response to changes in system prevailing conditions such as those generated by a sudden start-up and stoppage of fans. Researchers in many European countries have developed various models to explain these phenomena. However, these models failed to consider some important factors such as diffusion and dispersion of gas in turbulent flows. For both in-line and cross-cut recirculation, tests have shown that after the start- up of a booster fan, the gas concentration in the system fluctuates, reaching high levels at the initial states and slowly dying out with time. These fluctuations cannot be represented adequately by simple step-wise functions but rather by smooth, albeit complex equations. In this paper, the phenomena are explained by the convection-dispersion theory, and represented by a mathematical model. Based on a few simplifications and applying Fourier's Transform Method to the differential equations of the flow recirculation model, an integral form of gas concentration function was derived. The Simpson Integration Method was used to compute numerical results for two laboratory tests. The paper also discusses the range of the dispersion coefficient to improve the accuracy of the model.

Jan 1, 1989

By M. Moys

The use of temperature measurements for unusual applications in the analysis and control of column flotation and milling is discussed. This is followed by a review of some of the authors current research in the application of the discrete element method to the modelling of particulate processes, specifically milling, fluidized beds and chute flow.

Jan 1, 2005

By Y. Y. Sheng

Plume flows created by gas injection into liquid metals have been studied extensively, however the dynamics of bubbles within the plume have not received adequate attention, particularly for large, irregular bubbles, characteristic of the processing of liquid metals. The present model uses a combined Eulerian-Lagrangian approach in which an estimated void fraction distribution is used to calculate the liquid flow field with a conventional Eulerian scheme. The trajectories of bubbles are then computed in a Lagrangian manner using the estimated flow field, and experimentally measured information on bubble drag coefficients', lateral migration due to lateral lift forces and interaction with turbulent eddies, and variation in bubble size due to break-up. Turbulence in the two-phase zone is modeled with a modified k-e model with extra source terms to account for the second phase which have been recently determined by the present authors. The computed void fraction and turbulent liquid flow field distributions are in good agreement with experimental measurements.

Jan 1, 1993

By J. Zou

With the increasing applications of the Chinese metal magnetic liners, the requirement for their technical specifications has become stricter and stricter. It is necessary to deeply analyse the metal magnetic liners in order to improve their reliability and economics. The key issue of metal magnetic liners is magnetic forces: their attractions to mill shell and protection layer. Mathematical models were developed using finite-element analysis software and systematic simulation analyses of the two most critical indexes of magnetic liners were performed to find out the most important parameters and their effect on the liner?s characteristics. The relationships between magnetic forces and installation gaps, thickness of permanent magnets and thickness of protection layer may be used to guide the design of metal magnetic liners for ball mills in order to achieve good economic indexes.

Jan 1, 2014

The paper presents an algorithm for calculating the natural air distribution in a ventilation network (sub-network) on the basis of following data: - for each network branch: labels of starting and ending nodes, label of the branch, resistance and natural depression; - for each fan: the characteristic in the form of a second order equation and initial flow.

Jan 1, 1977

By Saikat Chatterjee, Xintong (Brett) Liu, Kinnor Chattopadhyay

Magnesia carbon bricks are commonly used in BOFs and are generally pre-heated before the BOF goes into service. Owing to very stringent emission regulations, the BOF pre-heating process need to be controlled and optimized so that, the emission standards are met. One of the major concerns in organic emissions are its stringent limits on emission rates and total volatile emissions. In the present work, an attempt has been made to integrate CFD and Thermodynamic models to predict the emission rate of volatile organics during the pre-heating process. A one dimensional heat transfer model was developed using visual basic and then integrated with thermodynamics calculations using FactSage 6.4. The parameters that affected organic emissions were the pre heating procedure, gas composition of the burner, heating rate and type of the burner. Typical composition of MgO-C bricks and binder materials were obtained from literature and vendor data sheets. Chemical reactions between organic materials, refractory and burner gasses were considered. The model predictions indicated that certain burner conditions could destroy all organics before it exits the vessel while other conditions needed the use of an after burner at the mouth of the vessel. The model was also able to predict the organic emission rates based on the chosen pre-heating profile. This kind of predictive model will be very useful for the steel industry and enable them to justify permit limit applications and stick to the limits by fine tuning their pre-heating process.

Jan 1, 2015

By V. P. Kolosyuk, A. M. Bryukhanov

Occurrences of hazardous events (explosions of methane or coal dust, fires, outbursts) have been investigated and presented as a flow of events in time. It has been shown that flows of hazardous events in a long time span are homogeneous, stationary and no-after effect flows and can be considered as stationary Poisson flows. A flow of CH4/coal dust explosions that had happened for the last 27 years in Ukraine was analyzed. The explosions have been statistically processed. Practicability of agreement of statistical and theoretical data on mathematical expectation and mean square deviation of time interval between explosion and the explosion intensity has been stated. Probability of an emergency event in time is expressed through an exponential function, while mathematical expectation of an accident and mean square deviation of time interval between successive explosions are in inverse proportion to the accident intensity. Accident probability for practical purposes can be determined as a product of accident intensity by calculated time interval.

Jan 1, 2003

By Taylor R. N

Flow simulations have been performed on the flash-smelting burners currently used at KNS. This paper presents studies of the heat transfer between gas and particles at the burner exit. Gas and particle temperatures, velocity and concentration profiles of the two-phase flow are calculated by the mathematical model. The predicted gas temperatures have been favourably compared against values measured by thermocouples placed near the burners in the flash furnace. The predicted particle temperatures are also reasonable when compared with the measured temperatures.

Jan 1, 1992

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