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By R. V. Ramani, A. S. C. Owili-eger

The quantity of methane emitted into the mine atmosphere and the movement of gas through solid coal and the adjoining country rock are dependent on the physical properties of the medium, boundary con¬ditions, the initial gas pressure distribution, and the combination of natural and mining factors. Functional relationships between these factors are not yet known. Consequently, the development of rigorous mathematical models to predict methane flow into the mine air is difficult and to date no model has been reported which is capable of such a function. Thus far, empirical formulas available for the calculation of gas quantity released from underground sources require too much his¬torical data, not currently available. Again, these estimations are at best only crudely approximate. The numerical methods available have not been made practical enough for industry wide application. Therefore, the development of a relationship amenable to numerical analysis and practical enough for use in the industry would provide the flexibility lacking in analytical approaches. The mathematical models given in equations (7) and (8) are further attempts in presenting practical models for predicting the quantity of methane emission into the mine environment. Equation (7) is the steady state model and equation (8) is the unsteady state model.

Jan 1, 1974

By R. K. Mehta

An electrochemical coal oxidation model involving heterogeneous kinetics is presented. This model was tested by collecting current transient data on three coals assaying different ash content under varying operating conditions such as particle size, temperature, and % solids. In all cases, the model fitted the data very satisfactorily. Three intrinsic rate constants, namely mass transfer coefficient of Fe(II) Ions diffusing from solution to the anode (kma), mass transfer coefficient of Fe(II) Ions diffusing from solution to the coal surface (kmc), and chemical rate constant for coal oxidation with respect to Fe(III) at coal surface (k), were calculated. It was interesting to note that in this system, the mass transfer at anode was as important as the chemical reaction at the coal surface. The validity of this model was further demonstrated through a comparison of the activation energy of coal oxidation: firstly, by utilizing calculated chemical rate constant and assuming Arrhenius' type of relationship: secondly, by utilizing conventional approach using limiting current values. The comparison revealed that agreement was quite close. This kinetic analysis is useful because such a model can be used in predicting the intrinsic rate constants so that the relative importance of mass transport can be rationally analyzed.

Jan 1, 1991

By Daniel Augusto Godinho de Carvalho

Since the beginning of BOF process, slag formation has been subjected to extensive development. During the initial stages of the blow, fast slag formation is primordial for the process performance. This is mainly to allow oxidizing reactions, and also to protect the refractory. A modeling of BOF process for the purpose of process optimization requires precise knowledge concerning the dissolution of CaO and MgO based materials. Using this knowledge, the optimal process conditions can be ensured by a controlling of the slag formation during the converter steelmaking process. Taking into account an application of large amount of different raw materials, as well as location-specific process conditions, the characterization of the dissolution behavior of different additives is an important key to improve the technological process. Thereby, in the frames of this project, an appropriate model for slag formation is established and compared to operational results for a 330t BOF, operating at ThyssenKrupp CSA, Santa Cruz, Brazil.

Aug 16, 2017

By Frank F. Aplan, Edward C. Jr. Dowling, Richard R. Klimpel

Thirteen kinetic models that mathematically describe the flotation process have been statistically evaluated for the flotation of copper, lead and zinc ores. Comparisons have been made for a variety of circuits involving roughing, cleaning, scavenging and regrind followed by cleaning. Variations in collectors, frothers, depressants and activators have been considered. Based on the statistical criteria used for the evaluation, and the reagent, circuit and ore variations studied, the most reliable flotation models have been identified and subsequently used to characterize the metallurgical results.

Jan 1, 1986

By Edward C. Dowling

Froth flotation has been used industrially for many years to separate valuable minerals from their associated gangue constituents. Notwithstanding the significance of this process to the mineral industry, many of the engineering tools needed for the evaluation of the flotation process are still in a developmental stage. Traditionally, the evaluation of a flotation test on both the laboratory and industrial scale has been based largely on a rougher recovery value achieved at a sufficiently long time to give a "final" or "equilibrium" recovery value. The assumption of a time equivalency for a given recovery value between various flotation tests or between laboratory tests and industrial operation underlies this method of evaluation. Such an assumption implies that flotation is an "equilibrium engineering process" and that the time-rate recovery of material from the flotation cell is not affected by changes in the flotation system. It has been shown by Bushell (1) and by Klimpel (2) that the assumption of time equivalency between various flotation tests is unjustified. Consequently, better tools are needed for evaluating flotation test results, Because mathematical flotation models which incorporate both a recovery and a rate function can completely describe flotation time-recovery profiles, they can provide an excellent tool to evaluate flotation tests.

Jan 1, 1984

By H. Y. Sohn, M. K. McCarter, Bradley C. Paul

"A computer model was constructed for bacterial leaching of the major sulfides found in porphyry deposits, including bornite, chalcocite, chalcopyrite, covellite, cubanite, enargite, native copper, pyrite, and pyrrhotite. The model incorporates equations for the sulfide minerals dispersed in the rock matrix. Leaching occurs by reactions with ferric ion diffusing into the rock fragment: Ferrous ion is resenerated to ferric with oxygen by bacteria at a temperature dependent rate. The model keeps track of the net acid generated, oxygen consumed by the bacterial oxidation of ferrous ion, heat generated, jarosite and hematite precipitated, and copper leached. The model was used to predict the rate of copper recovery, heat generation and oxygen demand for a variety of run-of-mine sized porphyry ores. These results were used in the design of a ventilation system and the economic analysis of a modified in situ extraction method that may be cost competitive with conventional copper production involving open pit mining.IntroductionA study was undertaken at the University of Utah to evaluate the technological and economic feasibility of mining copper by a method referred to as Flood Drain Leach Cell (FDLC) mining. Cells 60 by 75 meters in plan and 70 meters in height are created throughout the ore body by a modified Vertical Retreat Mining technique that includes the removal of 25% swell material. The swell material is leached in finger dumps on the surface while the cells underground are bulkheaded, flooded, drained, and artificially aerated to promote bacterial ferric sulfate leaching. Solutions are cycled through several cells to reach pregnant grade of 1 gram copper per liter of solution. These solutions are then fed to an underground solvent extraction plant and then a surface electrowinning tankhouse."

Jan 1, 1988

By C. Isaac Garcia, Sihai Jiao, Anthony J. DeArdo

"A practical model based on the Hill analysis has been developed to calculate the Lankford value of interstitial free (IF) steels and its distribution in different rolling directions, by considering only a few selected texture components. The Texture Intensity Ratio (TIR), i.e. (111 ) /(100), was used in the model to describe texture. By using the new TIR parameter, the texture-based prediction models can be used more easily to predict the Lankford value in a rather straightforward way.IntroductionThe deep drawing capacity of sheet steels is generally indicated by the Lankford value, which is mainly determined by the texture in steels1. Traditionally, various models derived from the Taylor model are employed to calculate the Lankford value from the texture2-4. In such models, the plastic deformation of steel is assumed to be the result of the slip of dislocations in certain slip systems, i.e., by either pencil glide or restraint glide. The slip direction is the <111> direction. In the case of pencil glide, the slip is thought to be possible in all crystal planes with the <111> crystal direction. Assuming the material is elongated in the X1-direction by d n and compressed in the X2 and x3-direction by qd n and (l-q)d n, respectively, corresponding to a deformation tensor"

Jan 1, 2001

By S. Simukanga, J. Masinja, P. A. Bepswa, A. N. Mwale

Screening is an important operation in dry and wet closed circuit mineral processing applications. Most of the operations have seen the benefits of using fine wet screens in primary grinding sections where the product is relatively coarse, and screens can handle the tonnage. Although many models are available, most of them are confined to dry and wet coarse screening applications. Most models do not give good predictions for wet fine screening. To facilitate model development, pilot plant tests were performed using a single deck Derrick Screen at aperture sizes of 45µm, 75µm, 106µm, and 150µm. Experimental data for a range of feed solids concentrations and flowrates was collected and used to calibrate the performance of the screen under the different operating conditions. The results showed that the performance of the screen deteriorated with an increase in feed solids concentration, and, similarly with an increasing feed flow rate. The percentage of fines carryover also increased with the reduction aperture size. The carryover was even more pronounced at higher feed rates and solids concentrations. A model was developed for predicting the performance of fine wet screening. Data from the test work was used to compare the actual and predicted results, and to calibrate the model. Additional independent data was used to validate the model and assess its limitations. This model will give an expected screen performance based on the initial feed conditions. It incorporates screen design parameters that allow for an estimation of a suitable screen size for a desired performance based on given feed conditions. This paper discusses; the results from the test work performed, the model development and its limitations.

Jan 1, 2016

By H. J. McQueen

Friction stir welding (FSW) generates complex microstructures in the nugget and thermomechamically affected zones (TMAZ) that have led to diverse explanations. However, consideration as an extension of microstructure development in piercing/extrusion can lead to a better understanding of flow patterns and microstructures during FSW. Furthermore, the intense strains in the nugget/TMAZ can be interpreted by comparison with ultra-high strains in torsion that exhibit dynamic recovery as extending into regions with high angle boundaries strongly serrated with spacing near the subgrain size defined by the high temperature. The subgrain diameter and extrusion pressure have been shown to be dependent on the Zener-Hollomon parameter Z (=t exp(Q/RT), Q activation energy, R gas constant) combining temperature T and strain rate E in the same mariner as for torsion and compression. Moreover, such tests exhibited steady state stress os above a certain strain Es (rising as Z increases) in which T, , subgrain diameter and dislocation spacing remain constant. Due to the subgrain boundaries (SGB, low angle <5°, i.e.,LAB), continually rearranging by migration, decomposition and reformation, the subgrains remain equiaxed in elongating grains, whose boundaries (GB) become serrated as they migrate to absorb SGB. As confirmed by straining in torsion at constant T and Z. , more subgrains bordering the greater GB area have several high-angle facets (HAB) ; these small cellular regions with a mixture of HAB and LAB facets are designated HAB-subgrains. As serrations in neighboring grain boundaries impinge, the grains pinch off becoming shorter; this occurs at higher strains as subgrain size decreases with rising Z. The pinching-off makes the neighbors thicker so the grains never become thinner than about two subgrain diameters. In conjunction with such geometric dynamic recrystallization (gDRX), GB&apos;s undergo a net migration into grains with denser substructure, enlarging those with larger subgrains. Consequently a better name has been proposed: grain dimensioning dynamic recovery (gDRV).

Jan 1, 2007

By Viswanathan N. Nurni

In metallurgical processes, more and more usage of hydrocarbons is encouragedto bring down the carbon emissions. In this regard, numerous investigations onreduction of oxides by C-O-H-N gas mixture have been reported. Attempts to simulatethese reduction processes using shrinking core model, one of the commonmodels used for such studies, have under predicted the reduction rates. This maybe owing to the fact that the homogeneous reaction in the gas phase is not being considered. If the reaction temperatures are above 1000K, generally so for manyreduction processes, the homogeneous gas reaction rates are expected to be sohigh that one can assume local equilibrium in the gas phase. In the present study,reduction of wustite in a C-O-H-N gas mixture has been modeled using shrinkingcore model considering the water gas shift equilibrium in the gas while it diffusesthrough the product layer.

Sep 1, 2012

By Young-Sool Jin, Heung Nam Han, Hong Joon Kim, Jae Kon Lee

A mathematical model was developed considering non-symmetric cooling' and stress distribution in both thickness and width direction of strip on a run-out table of hot strip mill. In order to solve a transient heat transfer equation including the heat evolved from phase transformation, a finite element method coupled with thermodynamic and kinetic analyses was applied. The heat capacity of each phase and heat evolution due to phase transformation were obtained from the thermodynamic analysis of the Fe-C-Mn-Si system based on a sub lattice model. The phase transformation kinetics of the steels was derived by using an inverse additivity technique with continuous cooling experiments. Heat transfer coefficients of strips on the run-out table were, by applying an inverse method, determined from the actual mill data under various cooling conditions. As for the stress analysis, the density change of strip due to cooling and phase transformation, and the transformation superplasticity were considered. A 90nstitutive equation for the transformation superplasticity, which is related to the phase transformation kinetics and the internal stress due to the density change of strip, was applied. A finite element method was adopted to calculate the deformation behaviour of strip on a run-out table of hot strip mill. Using the models, the temperature-phase-deformation history and distribution of a strip on the run-outtable was calculated.

Jan 1, 2001

By R. P. King

"A model of the flotation process can be used effectively for design and control. For design purposes it can be used to predict the performance of a large plant from laboratory and pilot plant data. It can be used for control purposes to assess the utility of any proposed operating modification to an existing plant, and it can also be used to determine optimal control settings for best operating performance.A model has been developed that will allow for variations in feed properties and for variations in fineness of grind. The model can be used to assess the effects of reagent addition rate, aeration rate and pulp level on plant performance and these are the control variables that are used individually or together in all operating flotation plants. The model provides for a distribution in the values for flotation rate constants, particle size and mineral fraction, and, because of its complexity, requires a large computer when it is to be applied to a typical plant configuration. The computational method that is used to apply this model to such configurations is described in this paper, and particular attention is paid to the problem of allowing for feedback of tailings from cleaners and recleaners."

Jan 1, 2014

By M. 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 that the particles are 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 the following 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 the experimental data collected in a laboratory 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 different trajectories within the furnace even if they are injected at the same location.

Jan 1, 2008

A mathematical model of a decision is represented by the table in Figure 4. The numbers in the matrix are a measure of the effectiveness of each alternate for an objective. In this case, it is the per cent of desired profit that is satisfied by each alternate for each objective. By adding all of the values in a row, we have a measure of which alternative is best for both objectives. However, if you think that alternate 1 is necessarily better than alternate 2, you are wrong. Why? Because the weight of the objectives may not be equal. It could just be that this plant can sell more than it can produce, so that the loss in profit represented by increased sales is more than twice as important as reductions in costs. (See Figure 5). In that case, let us weigh objective 1 as 30 per cent and objective 2 as 70 per cent. It must also be obvious that the sum of all the "objective weights" must equal 100 per cent. Now, by evaluating our alternates according to their weights. we find that alternate 2 is better than alternate

Jan 1, 1964

By Masahiro Hirasawa

"As a fundamental study on pyrometallurgical process that involves recycling steel-making dusts, of which major components are oxides of Zn and Fe, and waste polyvinyl chloride simultaneously ·at. a temperature below 1273 K, the reactions between the mixture of ZnO + Fe20 3 and PVC or the compound ZnFez04 and PVC are investigated in a series of thermogravimetric and small scale reactor experiments under inert atmosphere at below 1273 K. The reaction mechanisms are discussed· on the .basis of the thermogravimetric data. From the results of reactor experiments, it is shown that the chlorination of Zn in the oxides by Cl in PVC, the vaporization of ZnC12, the reduction of iron oxide to metal Fe by C and H in PVC, and, thereby, the separation of Zn and Fe in the oxides take place simultaneously at the temperature ~= 1200 K.IntroductionSteelmaking dusts are metallurgical wastes consisting mainly of oxides of Zn and Fe with smaller amounts of other heavy metal elements, such as Pb. In the recent investigation, [1] the present authors have investigated the fundamental aspects of a potential pyrometallurgical process· of recycling steel-making dust with polyvinyl chloride (PVC) at temperature T < 1273 K under Ar atmosphere. The performance of a similar process, in which HCl in the combustion gas of PVC is used to chlorinate Zn in the EAF dust under oxidizing atmosphere, has been investigated by Tailoka and Fray [2] with fundamental experiments. Figure 1 shows an example of the potential ·diagram of Zrt-Cl-0 and Fe-Cl-0 systems. In the figure, we can find two regions where ZnCl2(g) can be separated from Fe containing compounds. One is ZnCiz-Fe20 3 coexistence region at higher oxygen and chlorine potentials and the other is ZnCl2-Fe coexistence region at lower oxygen and chlorine potentials. The process adopted by Fray and coworkers is aimed mainly at the performance of Zn/Fe separation in the higher oxygen potential region. In the present study, the lower oxygen potential region is focused on."

Jan 1, 2000

By J. Dubinski

Underground mining of copper ore in the Legnicko-Glogowski Copper District basin generates a number of seismic events, whose energy often exceeds 108 J (Butra, 2010). The number of tremors and their location shows that the area of rock mass involved in the deformation and failure processes significantly exceeds the area of mining operations. Locations of seismic foci of high energy tremors, as well as the aftershocks that accompany them, extend hundreds of metres, confirming that processes to restore the energy balance of rock mass occur in a short amount of time and over a wide area. Thus, an area of similar size should be considered in predictive analyses of the tremor?s position. It should be emphasized that a large portion of the rock mass still has a level of freedom resulting from the way the rock mass is held together and its geometric continuity. This level of freedom is dependent on the scale and duration of mining, the number and size of natural structures, and rock mass pressure, including gravitational pressure constricting individual fragments of rock mass in the area (Burtan, 2012). It can therefore be assumed that in real conditions, areas where mechanical strength of the layers has been exceeded may be located a considerable distance from each other and do not necessarily need to coincide with the working area location. In this sense, a rock mass influenced by mining exploitation is essentially a rock mass in which numerous fragments with concentrated energy exist simultaneously. Energy will be released within these rock mass areas each time rock mass strengths are exceeded by the induced stress changes related to mining operations. This paper presents a discussion on how to predict the location of seismic activity areas based on a change of position of seismic energy equivalents. This parameter is calculated for a given set of seismic tremors with defined foci coordinates. For a given set of seismic tremors, the location of seismic energy equivalents may be used for predicting the location of high-energy seismic events.

Aug 1, 2013

By A. G. Pentland

MODELS of mines may be classified under three headings: (a) sheet models, (b) solid models, and (c) skeleton models. Sheet Models are made of sheets of glass, celluloid, or a transparent plastic material. The sheets are mounted in a frame which holds them in a parallel position, either horizontally or vertically. Mine plans are traced on the horizontal sheets; sections on the vertical sheets. The model may be illuminated by electric lights which are separated from the sheets by an opalescent screen. It is viewed from above or from the side in such a way that the plans or sections are superimposed. Sheet models are very useful for the illustration of mines with narrow, steep-dipping veins, but they do not give a satisfactory representation of a large mine with a flat-dipping vein. Large sheets of glass are difficult to handle and to support in a frame.? It is difficult to see through a considerable number of them. Solid Models are made of plaster, concrete, wood, or other material usually in the form of slabs in which the mine workings are indicated by properly dimensioned cavities in the model. The slabs are coloured to show the veins, country rock, faults, etc. The model is divided along selected sections in order to give access to the interior by the temporary removal of parts. Solid models may be used to illustrate large orebodies of the Sullivan type, but they are cumbersome because parts must be removed to study details of structure. Skeleton Models are ones in which the underground cavities are represented by metal, wood, plaster, or wax proportionately shaped and held in place by a frame. They illustrate the work which has been done but do not show the position of the veins, dykes, faults, etc., in the unworked parts. It is necessary to project by eye between workings in order to determine the location of these features. The essential difference between the skeleton model and the solid model is that the skeleton model represents the mine workings by solid forms and does not show the unworked parts of the vein, whereas the solid model shows the vein as a solid and the mine workings as cavities in it. The skeleton model lends itself well to the representation of a large mine with large stopes.

Jan 1, 1944

By D. G. Almond

Nkomati Nickel Mine in South Africa processes one of the world?s hardest ores in a 375k TPM autogenous grinding circuit. The plant employs an unconventional processing circuit, comprising a primary autogenous mill (AG or FAG) and pebble crushing circuit followed by a secondary hybrid pebble/ball mill and classification cyclone cluster. Advanced Process Control (APC) or Expert Control is now generally accepted as an advantage in most modern high capacity concentrator grinding circuits. This paper reviews the installation of model predictive control at Nkomati and examines the results and benefits of installation in an autogenous mill during plant ramp-up. The paper also demonstrates how predefining process control objectives together with good plant and supplier cooperation can achieve a robust and reliable APC implementation on a very short site program. The results conclusively demonstrate operational and economic benefits during circuit operation with the advanced process control system ON. Production performance and circuit stability were significantly better than during manual control.

Jan 1, 2012

By K. Becerra, D. G. Almond, T. D. Maru

"Nkomati Nickel Mine in South Africa processes one of the world’s hardest ores in a 375k TPM autogenous grinding circuit. The plant employs an unconventional processing circuit, comprising a primary autogenous mill (AG or FAG) and pebble crushing circuit followed by a secondary hybrid pebble/ball mill and classification cyclone cluster.Advanced Process Control (APC) or Expert Control is now generally accepted as an advantage in most modern high capacity concentrator grinding circuits. This paper reviews the installation of model predictive control at Nkomati and examines the results and benefits of installation in an autogenous mill during plant ramp-up. The paper also demonstrates how predefining process control objectives together with good plant and supplier cooperation can achieve a robust and reliable APC implementation on a very short site program.The results conclusively demonstrate operational and economic benefits during circuit operation with the advanced process control system ON. Production performance and circuit stability were significantly better than during manual control."

Jan 1, 2012

By Vincent C. Smith, Agit Singh, Bernard Muller

The control of minerals processing plants is by no means trivial. In order to address some of the difficulties, it was decided to develop and test a model predictive controller (MPC) for a milling circuit. A milling simulator was written to test the MPC controller. Due to the large number of tuning parameters in a controller of this type, an optimising algorithm was written that automatically tunes the controller. Good, robust control was obtained when the controller was tuned using this algorithm. The controller was tested for various scenarios that are often encountered in the minerals processing industry. When problems were encountered, the MPC algorithm was specially adapted to accommodate for these difficulties. Control was further improved by using feedforward control as well as quadratic programming. The movement of the manipulated variables was reduced by using a region of uncertainty that allows the controlled variable to vary within a specified region around the setpoint. Integrators were handled by adapting the algorithm slightly and adding an optional integral error portion in the MPC controller. The performance of the enhanced MPC controller was compared to PI controllers on both the simulator and a commercial plant. The MPC controller showed faster responses with less interaction in both cases.

Jan 1, 2003