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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 Pinczewski WV, Nowak LP, Tanzil WBU, Jenkins DR, McCarthy MJ

An experimental and theoretical study has been made of the drainage behaviour of two-dimensional packed beds drained from an outlet in the sidewall of the bed in order to identify the fundamental me- chanisms involved. Under these conditions a grad- ient develops in the air-liquid interface in the direction of flow with the interface tilting towards the outlet. This results in a significant volume of liquid being retained in the packing on completion of draining when the interface first reaches the bed outlet. Residual liquid volume and the shape of the air-liquid interface as a function of time were det- ermined experimentally in a two-dimensional packed bed where the packing consisted of glass spheres ranging in size from 0.6 to 10 mm dia. and the bed was drained at superficial liquid velocities rang- ing from 0.007 to 0.32cm/s. The test liquids used were water, glycerine/water solutions and kerosene resulting in a viscosity range of 1 to 10 mPa.s and a surface tension range of 0.0243 to 0.072 N/m. Assuming laminar flow within the bed, a compu- tational model was developed to predict both the liquid residual ratio and the temporal evolution of the drainage profile within the bed. The computed results were in good agreement with the experimental data over the entire range of conditions invest- igated. the computational model was used to estimate the relative importance of the effects of changes in hearth conditions on residual slag volume for typ- ical blast furnace operating conditions. On the basis of the computed results it is concluded that coke quality is a major parameter affecting hearth drainage performance.

Jan 1, 1981

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 Marius B. Wechsler

There are considered deep piles which are fixed in blocks of rotating machinery foundations. A mathematical background is developed for determining the behavior of this kind of piles for motions caused by horizontal and vertical oscillations, as well as by roc-king and twisting. It is assumed that the piles come across a top soil layer of depth c, not capable of lateral support, and penetrate over a length b, in a bottom firm soil layer, or in a bottom soft soil layer in which vibrations can produce voids around the piles. With respect to b and c, as well as to the elastic properties of piles and soils, the analysis leads to the maximum bending moments and shear forces subjecting the piles, to the maximum lateral bearing on the bottom soil layer, as well as to the deflection of the pile and the displacement of the foundation block. The results of the performed analysis can be applied to seismic loads too, and they are illustrated by a numerical example.

Jan 1, 1987

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

As a bubble travels through the pulp region of a flotation cell, it will collect the most hydrophobic particles of an intermediate particle size range, this being the primary source of true flotation selectivity. Despite its role on bubble-particle attachment, however, particle hydrophobicity is still missing a mathematical definition that can be used for plant simulation. In this paper, particle hydrophobicity is defined in terms of the induction time necessary for attachment and then linked to the mass of collector adsorbed per particle. This allows particle hydrophobicity to be written as a function of density of collector adsorption as well as particle size and mineralogy. The model is calibrated from the experimental measurement of the flotation rate constant. Liberation data from an industrial flotation rougher is used for model validation. It is demonstrated that the model can describe a broad experimental dataset by means of a minimal number of parameters. Main industrial application is in simulating the effect of the chemical environment upon plant metallurgical performance.

Jan 1, 2006

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

By Pascal Gardin

The purpose of the paper is the mathematical modelling of flows inside steel continuous casting mould. For CFD validation of flow oscillation prediction, unsteady calculations with a realizable k- model were performed in a billet caster with rectangular section. Self sustained and regular oscillations were obtained. Calculated flapping frequency is very close to what is mentioned in literature. For slab caster configuration, flow oscillation is influenced both by lower roll, which creates very small frequency oscillation (0.012 Hz for our water model), and upper roll, which creates slightly higher frequency oscillation (0.05 Hz). The two rolls interact and it is possible to detect both frequencies in the nozzle jet region. Numerical results are in good agreement with measurements for fluctuating velocity spectra and provide explanation for interaction of rolls. To improve flow stability inside the mould, it is established that gas injection in the nozzle has a very positive effect.

Jan 1, 2006

By Charles Larkey

NUMEROUS papers have been published on the use of graphic methods to determine the best curve to be used in estimating the production decline of oil wells but, as far as the writer has been able to ascertain, nothing has been published dealing directly with the subject as to how curves may be worked out mathematically, which will conform most closely to the production data under consideration in any given instance; hence the writer has endeavored to show by means of a few concrete examples just how such appli-cation can be made. Among valuation engineers, two types of curves are in current use for the representation of the decline in production of oil wells. One may be represented by the equation, y = krx, sometimes known as a percentage curve, for the reason that the production for any period is multiplied by a constant rate or percentage to obtain the production for the succeeding period. This curve appears as a straight line on semi-logarithmic cross-section paper. The other curve may be represented by the equation, y = kxn, and is shown as a straight line on logarithmic cross-section paper. In each of these equations, y represents the number of barrels produced over a given period of time, and x the successive periods of time. The other letters are constants to be determined for each well or group of wells considered in arriving at the most probable curve to represent the rate of production for a given property; from which the underground reserves may be estimated by extrapolation, or the extending of the curve beyond the last known period of production to show the most probable production values for the future.

Jan 7, 1923

By J. Versluys

WHEN a well strikes an oil-bearing layer, the oil has a pressure which is generally sufficient to enable it to rise to near the surface (sometimes above the surface). As soon as a well begins to produce, however, the liquid moves through the pores of the reservoir bed and the pressure in the well becomes much lower than the pressure originally prevailing there. At some distance from the well, however, the pressure in the reservoir bed remains unaltered; thus the pressure of the oil has not only to lift the oil, but also to overcome the friction resistance in the pores. The fact that so many oil wells are gushers is a consequence of the energy accumulated in the gas. In gushing the well acts as a gas-lift. A mixture of liquid and gas (the latter partly dissolved in the former) rises vertically from the oil¬bearing layer through a cylindrical casing to the surface. In time conditions alter and the well ceases to gush regularly, then the gushing can be further promoted by inserting a narrower tube in the well and connecting the top of the oil string to the tubing. If the action in time becomes irregular, the gushing can be kept up for a further period by forcing gas between the two tubes. In the oil fields the term "gas-lift" is used actually only where extraneous gas is applied, as in the last of the stages mentioned. The action, however, is just the same whether the gas exclusively originates from the formation, or is partly applied artificially. Thus by gas-lift we simply mean a vertical tube in which the energy of gas under pressure, and of dissolved gas, is utilized for raising a liquid. In gushing oil wells the pressure is frequently very high and the absorption coefficient 0.4 (expressed in vol. ratio) of the coexisting gas is not particularly high, so that in reality it should be assumed that a considerable portion of the gas, at any rate at the bottom of the gas-lift, is dissolved in the oil. For water-producing wells this is not usually of such importance.

Jan 1, 1929

Economic mathematical methods have been developed and applied in the design, planning, development and managing stages in the mining industry. Economic and technological efficiency is achieved with the aid of a large range of probability models, which are used to enable decisions to be made progressively during the different stages. The entire operation is considered as a total system made up of sub- systems and the models representing these are consecutively interrelated with each other. Algorithms and programmes representing the economic mathematical models for all the stages involved were tested and were found to be applicable to the various important mines in the Donetsk basin. Currently, these models are accepted and widely used.

Jan 1, 1977

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 Reichman J, Chapman G

The features of seam gas drainage from the point of view of mathematical modelling are outlined and discussed: 1. The use of conventional single phase gas reservoir simulator for very simplified modelling. 2 Alteration of a conventional petroleum reservoir simulator into a specialised simulator for seam gas drainage. 3. Application. of a conventional petroleum reservoir simulator for modelling of seam gas drainage by the way of pseudo-functions and sacrifying one dimension.

Jan 1, 1982

By Manuel Pérez-Tello

A mathematical model to represent the expansion and fragmentation of copper matte particles oxidized under flash converting conditions is presented. The model assumes the particles to be initially nonporous, have a constant mass prior to fragmentation, and travel at a constant velocity throughout the reaction chamber. The model requires the specification of five parameters: the particle expansion rate, a fragmentation diameter factor, a fragmentation size distribution parameter, and the fractions of the finest and the coarsest particles in the feed that undergo fragmentation. The model predictions show good agreement with experimental data collected in a laboratory flash converting furnace over a wide range of experimental conditions. The evolution of the size distribution of the particles along the reactor length was computed, and the model parameters were correlated with the experimental operating variables. Model predictions indicate that particle residence time is an important factor in the generation of dust. The presence of two maxima in the particle density function may be attributed to turbulent conditions prevailing in the furnace, which cause particles to follow very different trajectories within the furnace even if they are injected at the same location.

Jan 1, 2006

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 Gennady I. Gulyayev

A mathematical model of plastic deformation occurring in cold plug drawing of mother tubes with initial cross-sectional wall thickness variations (CSWTV) has been developed. The main provision of the model is that eccentricity em is of such value that projection of all forces acting upon the plug in the deformation zone along the axis perpendicular to the drawing axis equals to zero. Calculations have proven that with other conditions being equal increase in the die cone angle and the deformation cycle number reduces CSWTV. Theoretical findings were confirmed by practical results. Keywords: cold, drawing, plug, die cone, plastic deformation.

Jan 1, 2003