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By Q. G. Reynolds

The problem of direct-current plasma arc behaviour, interaction, and dynamics is considered in the context of metallurgical DC arc furnace applications. Particular attention is paid to the transient flow behaviour of arc systems. A mathematical formulation of the physics used to describe the arc system is presented, and includes the spatial and temporal evolution of fluid flow, heat transfer, and electromagnetism. Based on this formulation, a numerical model is developed using a finite difference approach on a regular cartesian grid in both two and three dimensions, with a special focus on robust stability, high resolution modelling, and high performance. A collection of results produced using the numerical model to study pilot plant-scale furnaces is then presented. These address a range of process and design variables and their effect on the numerical model?s results. Where possible, the qualitative behaviour of the model is compared to available experimental data. A number of novel effects and phenomena are seen in the dynamic behaviour of the DC plasma arc model for both single and multiple arc systems, which may lead to improved understanding, control, and manipulation of such systems where they occur in industrial applications. Keywords Pyrometallurgy, direct-current furnace, plasma arc, modelling.

Jan 1, 2010

By J. W. Evans

Mathematical modeling has now become a standard technique in the development of new technology and the improvement of existing technology in the processing industries. Physical modeling has a longer history but a smaller following at present. The paper reviews some examples of the application of both types of modeling in non-ferrous metal extraction, particularly within the copper and aluminum industries. The objective is to show that well founded models can lead to results that have practical consequence in scaleup, design and operation.

Jan 1, 1993

By Y Li, D J. Williams, E Topal

A mine waste rock dump does not have any intrinsic value, yet is an inevitable structure in surface mining operations. Since the purpose of mining is to maximise profit, possible expenditure reduction in hauling waste rock to the dump, which can represent up to 50 per cent of the total operating cost, is highly desirable. Apart from cost, potential acid mine drainage (AMD), due to seepage from surface waste rock dumps containing reactive waste rock, could threaten the ecological balance, drinking water supplies and irrigation systems downstream from a mine site. In order to minimise these potential risks, selective placement of benign and reactive waste rock, and the encapsulation of reactive waste rock by benign waste rock, need to be carried out during the construction of the rock dump.In this paper, a new methodology, based on mixed integer programming (MIP) is developed to manage waste rock dumping. The model aims to minimise waste rock haulage costs by locating the optimum destination(s) for each waste rock block, while at the same time controlling the placement of reactive waste rock to minimise the potential for AMD. Tests on small-scale virtual data demonstrated that the model is capable of dealing with selective placement of different waste rock types, encapsulating reactive, potentially acid forming (PAF) waste rock, and stockpiling benign waste rock for encapsulation and rehabilitation purposes. The solution time for the MIP model is far less than the traditional manual approach, and the resulting schedule is up to 46 per cent more cost effective.CITATION:Li, Y, Topal, E and Williams, D J, 2012. Mathematical approach for better mine waste rock dumping management, in Proceedings Life-of-Mine 2012 , pp 207-214 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jul 10, 2012

By H. H. Kellogg

The thermochemical properties of molten solutions in the binaries Cu-Bi, Cu-Sb and Bi-Sb, as well as the ternary Cu-Bi-Sb, have been correlated and described in mathematical form by use of the associated species concept combined with the three-suffix Margules equations to account for the non-idea 1 behavior of the solution species. Agreement of the correlations with experimental data is excellent (relative deviation of less than 2.5% in the values of the activity coefficients) in most cases. The correlations are applicable over the entire composition range of each system, and in the temperature range 700°-1250°C.

Jan 1, 1985

By W. G. Davenport

The remainder of this book develops and uses mass and heat balances to describe steady"state flash smelting. Its objectives are to: a) describe the many ways a flash furnace operator can produce specified products, e,g. 65% eu matte, 35% SiOz slag, 1500 K (b) determine the oxygen, air, flux and hydrocarbon fuel requirements of each method (c) show how the flash furnace can be controlled to give specified products with varying feed compositions (d) suggest how the flash furnace operator can maximize profitability while producing specified products. This chapter develops the basiC heat and mass balance equations of steady-state ?flash smelting. It then adapts the equations to industrial feed materials .and products. Lastly it determines the amounts of oxygen and flux needed to produce molten matte and 35% SiOz slag from chalcopyrite concentrate in an Inco oxygen flash furnace,

Jan 1, 2001

Mathematical economic models for assess ment of technological progress in the mining industry in the USSR are discussed. The models are based on a simple index, TT which approxi- mates the rate of growth of the people's living standards. However, for application in the mining industry it is necessary to incorporate various parameters to account for the dynamic charges in the geological, mining and other technological conditions. Derivations of the models are shown and examples of results are Included.

Jan 1, 1977

By Jing Zhong, Yugang Li, Chen Yan, Shaoda Zhang, Qian Wang

Online surface quenching technology has been developed for the hot charging process to prevent the surface cracks in high strength low-alloy steel slabs. In this paper, a two-dimensional heat transfer model of surface quenching process was presented. This finite element model includes nonlinear thermodynamic properties, by which the slab temperature distributions were computed. The model predicted temperatures show reasonable agreement with the measurements. The effects of the water flow rate and slab movement velocity on temperature variation during the quenching and subsequent tempering process were investigated. The result shows that the temperature drop increases but the tempering temperature changes slightly with increasing water flow rate and decreasing slab velocity. Keeping the slab movement velocity at 1.2-2.1m/min and the water flow rate at 55-70m3/h, the slab surface experiences a temperature drop of 400-600 firstly, then recovers above 650, the quenching and energy-saving effect are remarkable.

Jan 1, 2015

By G. Babut

The restructuring of mining operations in Valea Jiului coal basin imposed by the transation to the market economy calls for an increased coal production. Under the circumstances, the role of drainage networks grows ever more important. The paper describes an original mathematical model and software developed on its basis, with enables the ventilation engineer to assess the configurations of different systems, as well as to test their reliability and prognose their future performance before conceiving another methane drainage system or changing the existing one. The paper also includes the underlying principles of an optimization program for methane drainage networks, which will enable the detection of the optimal methane drainage system, both from a technical and an economic point of view.

Jan 1, 1996

By G. T. Brookman, P. B. Katz, D. K. Martin, J. A. Ripp

With the increasing emphasis on using American fossil fuel resources, more facilities are evaluating coal conversion. In addition, those facilities now using coal are considering better coal storage procedures to minimize negative environmental impacts. For example, rainfall and snowmelt on a coal pile produce a drainage stream high in acidity, suspended and dissolved solids, iron, sulfate, and trace metals. Usually, the characteristics of the runoff stream do not allow for direct discharge to streams and lakes. Detention in a holding pond and pH adjustment are traditional methods of treating coal pile runoff before discharge. Historically, this treatment methodology has been performed inefficiently without a good data base to assess how much runoff treatment is needed to meet effluent guidelines. A model was developed to simulate runoff volume and pollutant loadings under different rainfall conditions. This model will be used to size and design treatment works for coal pile drainage. The Ohio State University (OSU) version of the Stanford watershed model was selected as the base model. The OSU model simulates overland runoff in a rural area. It includes factors such as soil moisture, depression storage, infiltration, and flow to a ground water reservoir. TRC also used the OSU co-model for acid production in coal refuse piles as the basis for qualitative modeling work. A number of modifications were made to the OSU models to make them applicable to coal storage piles. The physical/chemical reactions included in the models are described in more detail in the project report. In addition, the models were altered so that a standard NOAA magnetic tape of historical meteorological data can be used as data input instead of requiring the user to create a data file. The resulting TRC coal pile drainage model is actually two models - a quantitative model, termed H2OTRC, and a qualitative model, TRCCOAL.

Jan 1, 1984

By Shklyar FP, Babushkin NM, Bokovikov BA, Fedotov PB

A mathematical model for gas flow dynamics and heat and mass transfer processes occuring in the tuyere raceways and in the zone of the final for- mation and heating of pig iron and slag has been developed and simulated on a digital computer. It takes into account the formation and size of the raceway zones, combustion of coke and its substit- utes, oxidation of the metal, radiation from the gases to the raceway boundaries, physical heat losses and the direct reduction of the pig iron elements below the raceway zones. To evaluate the distribution of heat produced by the oxidation of metal between gases and prod- ucts of smelting, the problem of heating the mat- erials in the raceways with the sources of heat in the materials under conditions of intensive gas circulation in the raceways is solved. To determine the amount of heat transferred by radiation from the gas to the boundaries of the raceways, the problem of radiant heat transfer be- tween two grey bodies forming a closed system is solved. Using the structural parameters of the furn- ace, the inlet parameters of the combination blast and exit parameters of the melt, the model permits the calculation of the temperatures of materials entering and leaving the raceways and also the res- idual temperature of the gases, which qualitatively differs from the theoretical combustion temperature. Analysis of the operation of several different blast furnaces has shown that the overall picture of the interaction between gas flow dynamics, mass and heat transfer processes occuring in the race- ways and in the zone of final product formation, obtained with the aid of the model, now permits us to approach from a different position the deter- mination of the limiting factors in furnace operat- ion. It also allows us to explain certain phenom- ena observed in blast furnace practice and to dis- cover new relationships which may be used in analy- sis and control of the smelting process.

Jan 1, 1981

By G. T. Lapidus, J. Trejo-Gallardo

A phenomenological model is presented for leaching silver from silver sulfide contained in mineral particles with ammoniacal thiosulfate solutions of copper in stirred reactors. Experimental results were used to adjust the kinetic parameters of the model, such as the reaction order and velocity. The incorporation of the cuprous sulfide-silver sulfide equilibrium at the reaction interface allowed the prediction of the conversion limits for different reagent concentrations. The information obtained from the reactor model was later integrated into a heap leaching simulation, whose results adequately describe tendencies observed in column tests, with respect to variations in copper and thiosulfate concentrations. Comp

Jan 1, 2005

By T. Fabritius, L. Hekkala, J. Härkki

The Outokumpu steel belt sintering technology is used for manufacturing chromite pellets that are charged into smelting furnace for ferrochromium production. Hot air is blown through the moving bed of raw pellets. Direct temperature and flow measurements are difficult to do in the bed of a real scale belt sintering process. Therefore, a tested and reliable mathematical model would be a valuable help for optimising operational parameters of the process and designing new constructional improvements. The aim of this work is to present a mathematical model that calculates the gas flow and temperature distribution in the bed of pellets and the atmosphere. Computational fluid dynamics program FLUENT is used to calculate the gas flow, composition and temperature of the gas in the sintering bed during processing. Energy equation for the bed, containing the effects of evaporation of water and oxidation of carbon and iron oxide, will be added to the model to obtain the temperature of the pellets. The porous media model used for pressure drop calculations in the bed is shortly discussed. A comparison between CFD-calculations and experiments with a pilot scale batch-sintering reactor are also presented. The final model can be used as an engineering tool when developing the process and the equipment further. Different designs can be easily tested with the model and the effects of the changes to the flow pattern and temperature distribution can be studied.

Jan 1, 2004

By Karel SPIRKO

The one-dimensional mathematical model of unsteady-state heat conduction through semi-infinite homogeneous and isotropic airway walls with convective heat and moisture transfer between their wet or dry naked surfaces and mine air with time variable temperature and humidity has been developed on the basis of introduction of acceptable simplifications of description of heat and moisture transfer between rock mass and mine air. The analytical solutions for computation of the temperature distribution and surface temperature of the airway walls and floor and for calculation of water vapour pressure near the wet surfaces at given time are obtained by means of the model presented. The presented solutions are derived for general conditions and they could be easily adapted to the actual ones. Results of the model represent basis for balancing heat and moisture transfer between mine air and its surrounding in deep mines under time variable temperature and humidity of the air and enable us to solve complicated dynamic changes of mine air temperature and humidity in an airway system by relatively simple mathematical tools. INTRODUCTION The importance of unfavourable influences and the costs of condition arrangements increases with mine depth. Precision demands on the methods which predict the environmental condition changes and by which it is possible to optimize condition arragements are still increasing. Environmental conditions in deep mines are determined especially by flow velocity, barometric pressure, temperature, and humidity of mine air. Therefore new and more exact mathematical models of mine air flow through airway system and those of heat and moisture transfer between mine air and individual important sources of heat and moisture are developed. The paper presented deals with description and solution of problems of heat and moisture transfer between mine air and airway walls as the rock mass is one of the important heat and moisture sources in deep mines. There are several different approaches to the problem. In some models the moisture transfer between mine air and airway walls is not considered at all. In other models the moisture transfer is described only by certain empirical coefficients. Simultaneous heat and moisture transfer is described seldom. This paper tries to describe in a simple way simultaneous convective heat- and mass-transfer processes taking place on wet naked surface of airway walls by means of corresponding

Jan 1, 1993

By H. Saint-Raymond, F. Gruy, P. Gardin, M. Cournil

"The control of inclusion elimination is getting more and more important to obtain clean steel. This paper presents a methodology under development for predicting cluster growth and elimination in ladle - RH system. The first key point is to express the collision efficiency, which is very specific for alumina cluster due to the non-wetting fluid. Second, a description of the two-phase flow in the system is necessary. In our calculations with Fluent CFD package and Lagrangian approach for bubbles, bubble growth is implemented, which improves the predictions. Using global reactor decomposition makes possible the prediction of the time evolution of cluster distribution. Important effect of fractal dimension is demonstrated.IntroductionElaboration of new steel grades requires not only to have a high purity in terms of C, O and N content but also to eliminate particles such as alumina or slag droplets. Flow optimisation making easier inclusion elimination is then a key figure to satisfy cleanliness requirements. Mathematical models of flow and inclusion behaviour are widely used for this purpose (1, 2). But having a predictive tool is still a challenge, because the number of phases is important in steelmaking industry: liquid steel, slag layer, bubbles and inclusions (with a large range of composition and rheology). The paper presents the methodology which is developed at IRSID to predict oxygen content evolution during RH degassing.The main mechanisms which have to be considered are :-inclusion growth by turbulent aggregation of elementary inclusions (keeping in mind that liquid steel is a non-wetting medium for inclusions); the difficulty is to express collision efficiency for alumina particles,-inclusion removal by flotation; the difficulty for alumina clusters stems from the complex morphology of particle; fortunately, the use of fractal concept makes it possible to cope with this problem.The paper describes the general modelling of inclusion removal taking into account the previous mechanisms. Hydrodynamic parameters are obtained by means of Fluent CFD package and a specific coding is developed for cluster growth."

Jan 1, 2001

By G. T. Lapidus, R. M. Luna-Sánchez

In the present study, a series of cyanidation experiments were performed on a bulk sulfide concentrate which contained silver in four distinct phases, to determine its extraction rate, varying the oxygen concentration. The results showed that three of the four phases were refractory, aguilarite (Ag,iSeS) being the only leachable phase, and that the effect of the oxidant concentration is minimal. Mathematical simulations were performed, adjusting only the Damkohler number to adequately fit the experimental data. This model, and the mechanism implied, was compared with that found for acanthite (Ag2S) in a previous study, and the differences between the two discussed.

Jan 1, 2005

By R. V. Ramani, V. T. Burgos, J. A. McClay

The systems contributing to the cost analysis, and the flow of data input and output related to these systems, are brought into focus in Figure 6. The various sub-systems of the Master Design Simulator provide the raw operating data basic to the cost model which, operating independently, accumulates the raw input, assigns costs to this data by standard or modified costing procedures, manipulates the costs into standard formats and outputs the data for managerial evaluation. Cost Modeling Direct costing methods are not complex in the sense that elemen¬tary arithmetic is employed using the same basic relations for each cost category. The basic cost model relations described above are illustrated in Figure 7. The greatest difficulty encountered in the transition from a dy¬namic systems simulation model to a costing model is the time frame of the input and output data. Dynamic simulation models utilize a small time increment, on the order of seconds or fractions of seconds, to analyze system operations and interactions. On the other hand, for cost computation and reporting, the smallest relevant time unit is the shift, with reporting periods expanding to days, weeks, months, and years. Complications arise in the accumulation of data for the various report periods due to the use of the Gregorian calendar by modern so¬ciety. The potential for simulation for the life of the mine, possibly in excess of 50 years, increases the complexity of the costing process

Jan 1, 1975

By Jianhua Xin, Min Chen, Lei Xu, Haohua Deng, Nan Wang

A mathematical model of converter slagging and steelmaking process by replacing part of lime with limestone is established. The rate equations of oxidation reactions and lime dissolution in converter under the limestone substitution proportion increasing from 25 to 50% can be obtained and the effects of limestone substitution proportion on the variations of the composition of hot metal, slag and converter gas during the steelmaking process are investigated. In the process of converter slagging and steelmaking by replacing part of lime with limestone, increasing the hot metal temperature and the lance height could be favor to increase the content of FeO in the slag and accelerate the limestone decomposition and dissolution. With the limestone substitution proportion increasing from 25 to 50%, the maximum of oxygen supply ratio increases from 10.7 to 19.7% and the temperature drop of converter bath is 8–60 °C.

Mar 1, 2018

By Pietro Navarra

Cooling of critical furnace equipment to produce freeze lining is of particular interest as many metallurgical processes are intensified while attempting to prolong campaign life. This idea was combined with high-capacity heat pipes in the design of a copper slag launder. The design methodology of the launder and heat pipe cooling system is examined in this paper. With reliable material properties and operating conditions, CFD was used to quantitatively predict the skull thickness and the corresponding heat load applied to the slag launder. The operational limitations of heat pipe technology were considered and an appropriate cooling system was incorporated into the model. Parametric modeling was used to simulate several launder and heat pipe configurations. The generated results were then used to optimize the design of the launder, which was built and tested in August of 2005. The experimental performance of the cooling system is evaluated and compared with the model results.

Jan 1, 2006

By Stavros A. Argyropoulos, Henry H. Hu

"The assimilation of exothermic additions in liquid metals exhibit an array of unique coupled heat, mass and momentum transport phenomena. These phenomena are further complicated by the presence of a moving boundary.This paper describes a) A mathematical model which simulates the complex phenomena, and b) An extensive verification of the mathematical model. The SIMPLER algorithm was employed to solve numerically the pertinent partial differential equations. The computational results indicated that the exothermic heat of mixing led to a rapid increase in temperature around the moving boundary, which produced an enhanced convective flow in the liquid phase. The intensification of fluid flow around the moving boundary resulted in an acceleration of the melting process.Verification of the model was carried out in two contexts. The first was, in a low temperature physical model consisting of ice immersion in different sulfuric acid solutions. In this physical model, both temperature and velocity measurements were carried out. The model results were compared with experimental measurements and they were found to be in excellent agreement. The second context employed high temperatures, involving the assimilation of silicon in high carbon liquid iron. The model was also applied to predict fluid flow, heat and mass transfer for these high temperature experiments and a good agreement was obtained.In addition new dimensionless heat transfer correlations that quantify these complex phenomena will be presented."

Jan 1, 2001

By W. E. Horst

In Part I of this paper we describe two techniques that were employed in the development of mathematical descriptions of the size reduction process which takes place in a ball mill. In Part II we show how the comminution model was imbedded in a process model to effect steady-state and dynamic simulation of a closed-circuit grinding operation. Increasing emphasis is being placed on development of approaches whereby the essential characteristics of a process can be succinctly represented in terms of a mathematical description of the relationships that exist among important process variables. This activity, commonly known as mathematical modeling, predates modern electronic computers: however, these computers with their tremendous computational capability have given new impetus to the whole field. Although the computer is quite helpful in the development of mathematical models, the real value to the engineer lies in the fact that computers represent such a powerful tool for simulating systems described by mathematical models. As a consequence, engineers may simulate and thereby study the behavior of complex. interacting, systems over a broad range of process variables and configurations once appropriate process models have been developed for the sequence of steps comprising the process.

Jan 1, 1970