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By Roberto Galery, Priscila Esteves, Braz Cardoso, Marcelo Stopa

"It was developed in this work a computational tool to aid in anomaly detection present in the operation of ball mills. The tool uses a torque estimator that is based on measurements taken exclusively in the drive motor. The ball mill equipment widely used in the mining industry has, inherent to its principle of operation, high energy consumption and low efficiency. These characteristics are accentuated when the mill operates outside the ideal conditions of velocity and loading. Direct measurement of these variables is extremely difficult because it requires the installation of sensors in moving parts of the mill. Thus, systems that can help monitoring the operating conditions and predict anomalies are useful because they contribute to improving the performance of the process, help to reduce the energetic consumption, wear on the mill surface and frequency of maintenance shutdowns. The detection strategy implemented in this work is based on the fact that operational anomalies such as an inadequate percentage of balls and incorrect angular velocity manifest itself as a change in spectral components of the torque signal in the mill driven by an electric motor. The mill torque was estimated by processing motor variables measured by sensors commonly used for control purpose and installed exclusively in the motor. The mill was operated at various fault operating conditions and signals from electric motor and vibration on the mill shaft were measured. The spectral components present in the estimated torque signal were then compared with signals from a vibration sensor in order to establishing a correlation with anomalous operation condition of the mill. The experimental results showed that the signals obtained has an excellent correlation with other variables obtained by direct measurement and have potential to be used to construct a system for automatic fault detection in the operation of ball mills."

Jan 1, 2014

By U. M. J. Boin, E. V. Verhoef

Pyrometallurgical reactors constitute a key processing component in the total primary and industrial/recycling resource cycle, being involved both in primary smelting, converting and extraction, as well as the reprocessing of scrap, from aluminium cans to end-of-life automobiles. Therefore the pyrometallurgical reactor?s role in achieving sustainability is the central theme discussed in this paper since optimising their operation minimises waste, residue and offgas (NOx, dioxin, CO2) and maximises product quality and therefore efficiency. To effectively control the overall resource cycle, one needs to take a systems modelling approach of the whole cycle, seeking to also understand the dynamic process behaviour of the individual components of the cycle, and then especially the part that contributes most to the chemical conversion, namely the pyrometallurgical reactor. This paper highlights the role of pyrometallurgical thermodynamics in the whole resource cycle and specifically places equilibrium thermochemistry in the context of process dynamics where large, variable inventories are recycled or maintained within the system. This paper will therefore review the semi-empirical dynamic modelling tools, which are used to model complex systems with the specific goal of developing dynamic predictive models, which also include slag-alloy chemistry, towards controlling the recycling in a feed forward manner. To illustrate the primary production of metals, high carbon ferrochrome and Ni-Cu-matte smelting will be presented as a brief case study. Also fundamental studies in blast furnace and waste incineration kilns will be given. It also will show how the distributed nature of the chemistry of melts in the case of primary extraction, and industrial (recycling) materials such as recycled end-of-life vehicles, have a significant impact on the process outcomes and model predictions. It is therefore argued that the fundamental thermodynamics and kinetics in metallurgical reactors play a final crucial role in modelling the closed material cycle, but only when it is used in conjunction with process systems theory based on reconciled data for parameter estimation and model calibration. System models for aluminium and car recycling will be given as well as a dynamical system model that describes the interconnected material flows for Ag, Au, Bi, Cu, Fe, Ni, Pb, PGM, Sn and Zn for a study on lead-free solder.

Jan 1, 2003

By M. Karamoozian

Modelling and optimisation of the power draw of large SAG mills are important due to the large power draw which modern mills require (5~10 MW). The cost of grinding is the single biggest cost within the entire process of mineral processing. Traditionally, modelling of the mill power draw has been done using empirical models. Although these models are reliable, they cannot model mills and operating conditions, which are not within the model database boundaries. Also, due to their static nature, the impact of the changing conditions on the power draw, within the mill, cannot be deter-mined using such models. Despite advances in computing power, on-line modelling of large plant scale mills could be a time consuming task. On the other hand, using on-line parameters for model-ling, result in more reliable control of SAG mill without performing any more costly tests. In this paper, SAG mill power draw is modelled using neural network approach. Six inputs, namely: solid percent, two bearing pressures, noise, recycle and feed rate were used to model the power draw. The produced model shows an acceptable correlation coefficient, R2 =0.9623.

Jan 1, 2014

By Moris Fresko, Julia Sun, Charles C. Golembewski, Vytas Svalbonas

"A history of mill strain gaging at Metso is presented. The output of these strain-gaging programs is compared with calculated stress ranges from different finite element solutions. These comparisons expose the amount of approximation that exists in the analytical solutions, starting from geometry, and material properties, and ending with different forms of internal load models. The influence of strain gaging results on mill design and analysis practices is also discussed. While these instrumentation programs are valuable in identifying areas of high stress in mills, and locations of stress concentration factors, they are by no means extensive or comprehensive enough to verify general internal load models. The vast majority of the programs were aimed at getting additional data about potential failure points, rather than describing overall mill stress behavior. This is especially true since the more recent gaging programs have not included the difficult task of gaging the mill rotating structure interior. This paper tries to avoid the novice path of leaping to general conclusions on the basis of insufficient data."

Jan 1, 2014

By A. Shibayama

Soil contamination by organic compounds is one of the most concerned issues on polluted soil. It is well known that there are limited methods to remediate the contaminated soil on site. Especially, the in-situ method for contaminated soil is too difficult to de-contaminate the organic pollutant. In this study, the fundamental ability of soil remediation, which aimed to decrease oil concentration in, in-situ process, have been researched by using a high pressure gas generated from ?crush composition? on artificially oil contaminated soil. The n-hexadecane (n-C16H34) and other organic compounds were selected as soil oil contaminators, gravimetric analysis by soxhlet extraction and GC-MS were used as qualitative and quantitative analysing methods. For the experimental examination, the influences on the difference in the concentration of n-hexadecane (and other organics), the tamping amount, position and repetition of crush composition in soil, and scale (size) of experimental model were investigated. The n-hexadecane concentration reduced by the explosive effect of crush composition showed a reasonable decrease of about 30 wt%~60 wt% compared to the initial n-hexadecane. The removed amount of n-hexadecane and distance from explosion point of the crush composition was related in scale and model of contaminated soil.

Jan 1, 2014

By J. D. Miller, C. L. Lin

In general, x-ray computed tomographic (CT) techniques are able to provide 3D images of the internal structure of opaque materials in a nondestructive manner. The unique cone beam geometry allows acquisition of all 2D projections with only one rotation of the sample thus providing for fast data acquisition and better x-ray utilization, as a complete 2-D detector array receives the cone-shaped flux of rays. Thus, an isotropic 3D volume can be reconstructed without the mechanical translation and the stacking of sequential slices as is the case for more conventional CT scanners. In this regard, a state-of-theart, custom designed x-ray microtomography facility to provide very detailed 3D spatial analysis of multiphase particles has been installed and is in operation at the University of Utah. The reconstructed 3D tomographic volume allows for an adjustable spatial resolution from 5 to 20 microns for sample dimensions from 10 to 40 mm in diameter, respectively. For example, a packed bed of coal particles is shown below in which different crystalline froms of pyrite are distinguished in 3D.

Jan 1, 2003

By J. B. Yianatos

A practical an interactive model to describe the operation of a flotation bank of mechanical cells was developed based on the hydrodynamic and metallurgical characterization of large industrial flotation cells. Thus, the mineral grade and recovery, as well as the stream properties along the flotation bank can be described in terms of the operating variables. The model was built considering the flotation bank as a distributed system, so the solution for the water and solids mass balances, per size classes, for each single cell, are sequentially solved. Also, each cell was described by two distinct zones, the collection zone characterized by the flotation rate constant and the froth zone characterized by the froth recovery. The mineral feed was described in terms of the mineral species and particle size classes, using a rectangular flotation rate constant distribution. Also, the effect of changing the actual operating variables (air flowrate, pulp level, pulp density, pulp flowrate, etc.) on the mineral collection process, in the collection (pulp) zone, was considered downstream along the bank. The froth recovery of floatable mineral has been estimated by measuring the mass flowrate of particles entering the froth by true flotation together with the concentrate mass flowrate (ton/h). The mass flowrate of collected particles at the pulp/froth interface level was calculated from direct measurement of bubble load (ton/m3) and gas flowrate (m3/h). Flotation recovery is mainly related to the froth depth and air flowrate. All parameters considered in the model have been adjusted from direct measurements in plant site. Also, the effects of other operating variables such as reagents dosage, top of froth grade, or froth discharge velocity are presently under study. This procedure has been tested using data from industrial rougher operations consisting of flotation banks with 5 cells to 9 cells in series, and different cell sizes, such as 45m3, 130m3, 160m3 and 250m3. Thus, it has been shown that the model approach is a powerful tool for flotation cells diagnosis, operation and development of new control strategies, as well as, to evaluate the effect that de-sign and operating variables have upon the collection and froth zones performance in large flotation cells.

Jan 1, 2014

By S. M. Viduka

This paper presents a numerical investigation of solid separation in jigging device, which is a gravity separation method widely used in ore processing. Separation is recognized as being heavily dependent on fluid motion in the jig. This study explores the effects of the inlet time dependent velocity profile on jigging performance. Modelling of the liquid-solid system is performed through a combination of computational fluid dynamics (CFD) to simulate liquid flow and discrete element method (DEM) to resolve particle motion. The initial packing conditions consist of a binary-density particle system of 1130 particles each 1 cm in diameter. A variety of jigging profiles are implemented in jigging. The saw tooth pulsation profile is selected with three variations in both amplitude and frequency. The performance of each profile variant is compared in terms of solid flow patterns, separation kinetics, energy, and mean particle position. These quantitative comparisons demonstrate significant differences in the segregation rate, energy, and solid phenomena, helping find an alternative optimum operating setting for the system.

Sep 1, 2012

By M. M. Moghaddam

Charge motion is of prime importance in the efficiency of comminution in tumbling mills. Since direct observation of charge shape and its motion in industrial mill are not possible, a combination of analytical and physical studies was used to determine charge trajectory. Software packages, which predict charge motion such as the GMT (Grinding Media Trajectory) only consider the outermost layer of charge (single ball) and ignore the interactions of grinding elements. In this research, the measured charge trajectory in a 1m-diameter mill with the transparent end, called model mill, was compared with that of the GMT. Four types of polyurethane rings were accurately machined to scale down the liners arrangements at two industrial mills. To explore various charge shapes and trajectories, the model mill was operated at 55, 70 and 85% of critical speed for five levels of mill filling (10, 15, 20, 25 and 30% by volume). The angular displacement of the toe, toe departure, shoulder and charge impact point were determined from the photographs taken from the model mill. New relationships to predict charge shape and charge impact points were introduced to modify the GMT results. The relationships were validated by the model mill using the new liner of the Sarcheshmeh copper complex SAG mill. The relative error of prediction was found to be 1.1%. The results indicated that when the lifter face angle increased from 7 to 30º, the distance between the charge impact point and the toe decreased from 52 to 31º for 25% filling. This meant increasing the probability of charge impacting the toe not the liner which favoured more efficient comminution practice. After converting AG mills to SAG mills on account of liner profile change, 31% increase in throughput (from 419 to 548 t/h) in addition to 4% decrease in the product size (from 516 to 496 µm) were realized which was a significant contribution in the plant performance improvement.

Sep 1, 2012

By Silvia França, Hudson Couto, Renata Barbosa

"The flotation process, largely used for mineral concentration processes, which is based on air bubble adhesion to the dispersed solid phase, is also being used for wastewater treatment purposes. Dissolved air flotation (DAF) is based on the separation of the solid-liquid phases with the aid of small air bubbles (10-100 µm), with high values of interfacial contact area, improving the process efficiency. In the process, the air bubbles and particles or flocs form aggregates, which rise to the surface of the flotation cell to be collected. The advantage of producing small bubbles is directly related to the fact that smaller bubbles result in greater bubble-particle interaction. Wastewater produced in alumina refinery - from the red mud filtration step - has a red colored aspect due to the presence of very fine particles of red mud and also dissolved matter that still remain in the filtrate. This wastewater might be treated, aiming to reuse the water in the refinery or discharge it properly in the environment. The aim of this study was to evaluate the DAF process efficiency for the treatment of red mud wastewater in order to decrease suspended particles and dissolved solids contents, in addition to mitigate the high causticity of this wastewater. The process efficiency was evaluated by comparing turbidity removal and total solids concentration in the treated wastewater to the feed. The influence of important variables of the DAF process as type and concentration of coagulant and flocculant were evaluated. It was possible to obtain good turbidity removal efficiencies (up to 90%) using low concentrations of coagulant (50 mg/L) and flocculant (0.5 -1.0 mg/L). In addition, for most of the experiments, the specification for effluent diposal, according to the Brazilian environmental regulation 430 (Conama, 2011): pH range 5 to 9 and turbidity < 40 NTU, was attained. These results emphasize the possibility of using the DAF as an alternative technique to settling and filtration process, that are traditionally used, for treating wastewater from the alumina industry, allowing the reuse of water in the plant or adequate discharge with less environmental impact."

Jan 1, 2014

By Fatemeh Saeidi, Malcolm S. Powell, Mohsen Yahyaei

In order to deal with the problems of existing comminution models a new approach towards the development of mechanistic models has been made so as to better understand the physics of milling processes and environments. Despite enormous improvement in this field a comprehensive study of rock breakage characterisation, appropriate for use in these types of models, is still scarce. This paper reviews the existing models of comminution according to ore characterisation techniques and parameters. The authors have looked into the existing testing methods and their applied mechanisms of breakage, using standard test results available at the JKMRC. The study includes classifying testing devices such as the drop weight tester, rotary breakage tester, slow compression, and piston and die based on the few major fundamental mechanisms of breakage that are experienced by rocks in the breakage process. The paper compares the range of particle size and energy utilisation, applied strain rates and loading mechanisms for the equipment. The product size distributions from the various equipment is compared for equivalent input energies, various loading rates but the same level of energy intensity, a broad range of energy including low energy utilisation and fines generation rate for equivalent specific energy input. The results clearly show that the outcomes and conclusions on competence and energy for breakage are a function of the test method that is applied. In ongoing work, it is proposed to investigate common tests that can be applied to characterising ores in a manner suited to modelling a range of comminution devices.

Jan 1, 2014

By T. Sun, J. Kou, C. Sun, D. Gong

"HPGRs (high pressure grinding rollers) have demonstrated higher energy efficiency than conventional comminution equipment due to their application of particle-bed breakage mechanism. In the past decades, a large number of studies have been conducted to understand the characteristics of particle-bed breakage, however, few of them concerned the difference between single-particle and particle-bed breakage in compression comminution. This comparison is able to demonstrate possible advantages of particle-bed against single-particle in a breakage event due to the isolation of the effect of force loading mechanism. The present study investigated progeny fragment size and energy efficiency of these two breakage methods at variable energy inputs and particle sizes. The results show that at low energy inputs of around 0.25 kWh/t, the numbers of fines resulting from the two breakage methods are very similar. However, at higher energy inputs of around 1.0 or 2.0 kWh/t, particle-bed breakage generated significantly more fines. From the perspective of newly generated surface energy, particle-bed breakage is obviously more energy efficient than single-particle breakage at energy inputs between 1.0 and 2.0 kWh/t. It was also found that HPGRs demonstrate high energy utilization rate in generating new surface energy within their typical range of specific energy input. INTRODUCTION Rock comminution is an important and energy-intensive process in mining operations. Nowadays, decreasing head grade and mineral liberation size of ore deposits greatly increase the energy cost of comminution process. HPGRs have been successfully applied in the mining industry to improve the energy performance of comminution circuits. Typically, 10 to 30% of energy saving can be achieved due to the application of HPGR (Wang et al., 2013; Casteel, 2005; Günter et al., 1996)."

Jan 1, 2018

By X. Q. Cui

The surficial collapse pits of the mining areas are continuously spreading in Beiminghe iron mine of Hebei Province as a result of the exploitation, which has done a lot of damage to the circumjacent ecological environment of the mine. It is a new path to handle the mine tailings at the present time that the thickened tailings are used to backfill the collapse pits, in which way the problems of the surficial collapse and the nowhere discharge of the tailings are both solved, and the rational utilization of the mine tailings and the clean production of the mine enterprise are realized. The?200 mesh content of the tailings of Beiminghe iron mine is 76.87%, and?325 mesh content is 63.50%. Semi-industrial dehydration experiments to the tailings have been done using the hydro-cyclone classified thickening process. The results show that when FX125 hydrocyclone is adopted, the concentration of underflow can achieve 73.31%, and the yield ratio is 61.78%; when FX150 hydrocyclone is adopted, the concentration of underflow is 70.57%, and the yield ratio is 54.31%, which indicate that the minor diameter hydrocyclone is propitious to improve the yield ratio of the underflow. The semi-industrial dehydration system of hydrocyclone classified thickening process is com-posed of FX125 hydrocyclone, D3600 high-efficient thickener and D2000 thickening bucket. The capacity to tailings disposal can achieve 3.07t/h and the tailings can be thickened from 28.86% to 62.45%. Compared with the traditional thickening-filtrating process and the total tailings directly filtrating process, the hydrocyclone classified thickening process has the merits of simple flow and high thickening efficiency, so it is easy to be realized in the mine.

Jan 1, 2014

The ball level and pulp load play a key role in the operation of industrial scale ball mills. These two operating variables have a significant influence on the performance of the ball mill and any attempts to optimize these devices require manipulating either one or both of these variables. There are several models that can be employed to perform simulations to optimize the performance of industrial ball mills. However, most of these models require ball load and pulp load measurements as inputs to calibrate the model. The changes suggested by the simulator also provide operating regimes that involve moving either the ball level or pulp load and sometimes both of these variables. A ball mill model coded in JKSimMet was used in conjunction with the Sensomag to optimize the secondary ball mill at Waterval concentrator in South Africa. The results show that the perfect mixing ball mill model can be used in conjunction with the Sensomag to optimize the performance of the secondary ball mill.

Sep 1, 2012

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

By Richard K. Komarek, Antonios Zavaliangos, Roman T. Dec

Roller presses are widely utilized in mineral industry for fine milling and compaction. Recently used models are providing only limited information about the material behavior in the roll bite. This paper introduces a 2-dimensional finite element model for analyzing those two basic processes. A pressure-dependent plasticity model with linear elasticity was used as a constitutive model for the particular material. Coulomb friction law was used to describe phenomena on the material/roller surface interface. Two basic roller geometries are considered: smooth (used for milling and compaction) and with cavities, commonly used for briquetting. Comparison of the results obtained from the model with experiment indicates that they are following the general trends of experimental values recorded with laboratory roller presses. It is shown, that the model is suitable to analyze material behavior through all stages of the rolling process: feeding zone, nip region, neutral plane and release section. It can predict pressure, shear stress, slip of the material over the roller surface, material velocity field, failure of the compact during release and the course of other important process variables. This allows the process engineer to gain an improved understanding, leading to a better process and equipment design and control.

Jan 1, 2003

By L. O. Filipov, N. E. Menad, A. Geneyton

"Zeta potential of synthetic monazites presenting various compositions were measured to investigate the effect of the main lanthanides substitutions on electrophoretic mobility and resulting IEP. The measurements are performed in a CO2 depleted and enriched solutions showing both reduced influence of monazite chemistry and strong influence of ions resulting from the solubilization and dissociation of CO2. The influence of oleic acid on the electrophoretic mobility of those monazites was also investigated. The influence of pH on oleate adsorption was studied using a bubble/particle adhesion system. Adhesion strength measurements were performed on pure synthetic monazite-(Ce) and monazite-(La). An extensive thermodynamic model of monazite in water was developed to highlight correlations between lanthanides hydroxides/carbonates species concentrations in the bulk solution and oleate adsorption. Based on electrophoretic measurements, advanced thermodynamic consideration and adhesion measurements, further details of the oleate adsorption model on monazite surface were proposed.INTRODUCTION Electrophoretic and potentiometric data on monazite and, a fortiori, other rare earth semi-soluble salts such as bastnaesite are extremely erratic (Chelgani et al. 2015). The isoelectric points measured with electrophoretic mobility methods range from 4.7 to 6.5 although sporadic data indicates an IEP (isoelectric point) far from that range. Different explanations are proposed in the literature to explain the IEP variability notably the numerous chemical substitutions that frequently occurred within monazite crystal lattice (Chelgani et al. 2015). Based on lanthanides speciation diagram, several authors highlighted the influence of specific lanthanide species on the flotation performance of rare earth semi-soluble salts when carboxylate or hydroxamate collectors are used. Although lanthanides ions have a great affinity for carbonates groups (Kragten et Decnop-Weever 1987), lanthanide (hydrogen) carbonates were not implemented in speciation diagrams. In this work, an advanced thermodynamic model is proposed to highlight correlation between flotation performance and lanthanide species predominance but also concentrations. Qualitative measurement of the monazite surface hydrophobicity are performed through tests of adhesion of coarse monazite particles onto bubbles. Since flotation and microflotation technics are highly influenced by hydrodynamic parameters, this method was investigated to obtain a sharp contrast between appropriate and inappropriate pH conditions. This paper is to investigate 1) the effect of lanthanides substitution on monazite surface properties through zeta potential measurements, 2) the mechanism of adsorption of carboxylates on monazite surfaces and 3) the effect of CO2 on monazite surface properties and carboxylates adsorption."

Jan 1, 2018

By H. Deng

Oxidized zinc ores are the main source of zinc metal except sulfides. To have a better understanding about the performance of smithsonite and the main gangue, quartz, in flotation, the aggregation behaviors of smithsonite and quartz in water were confirmed by different techniques (sedimentation tests and optical microscopy). The experimental results show that smithsonite and quartz particles aggregate in the pH range 7.5-11. The results of zeta potential suggest that the aggregation does not correlate with the DLVO theory, when the iso-electric point of smithsonite and quartz is 8.0 and 2 respectively. When the solution pH is less than 8.0, smithsonite has an opposite charge to the quartz particles. Electrostatic adsorption makes effort on these two kinds of particles according to DLVO theory. Whereas, solution chemistry calculation shows the pH range 8-11 corresponds to hydroxide formation, suggesting that this is the species responsible for aggregation. And their concentrations are much higher in sodium hydroxide system than that in sodium carbonate system. Aggregation of smithsonite and quartz due to the flocculation action of zinc hydroxide is proposed.

Sep 1, 2012

By M. M. Yahyaei

The Sarcheshmeh new concentration plant uses a 32 ft×16 ft constant speed (10.5 RPM) SAG mill with two 5500 hp motors which could rotate in two directions. The mill liners are chrome-molybdenum steel casting type with a Brinnell hardness between 325 and 375 with the lifter face angle of 14° and lifter height of 152 mm. The shell liner consists of 120 (two 60 rows) pieces with a High-High configuration in a rail design. A specially designed liner wear profile measuring device enabled fast and accurate measurements inside the mill during the mill shut-down periods. The measurements indicated that the liner wear profile along the liner length is non-uniform and the highest wear occurs between 1.25m and 2.75m of the mill length. The average weight of liners at the time of removal was 47% of the original weight indicating a significant metal loss. The modification of liner shape was undertaken with the aim of having a uniform profile at the liner removal time. The proposed liner unlike the pervious type did not have a uniform shape with a lifter height of 187mm at the section where the wear rate was high. It was believed that this new profile could arrive at a uniform profile at the liner change out time. A study was also directed to the possible change of charge motion due to the liner profile modification. The dynamic behaviour of charge was investigated through the analysis of forces acting on a single ball using mill characteristics such as mill diameter, rotational speed, lifter height and release angle. The simulation of charge motion with this method and Milltraj TM software indicated that the impact position of charge will change only one degree due to the maximum increase of 35 mm in the lifter height. This assured that the installation of the modified liner would not have any adverse effect on the mill because of ball impacting the mill shell. It was predicated that the amount of scrap metal will reduce to 30% from the current value of 47% beside 1500 h increase in the liner life time.

Jan 1, 2014

By T. Tumidajski

The purpose of the separation processes in coal processing is obtaining products of certain ash contents. In the most of cases it is assumed that the separation process is described by one, selected parameter, which usually is grain size or material density. The separation may be described by means of statistical distributions of random variables, what allows forecasting the separation results of certain enrichment method. There are very well known the applications of approximations of Tromp separation curves or distribution functions of Erasmus, Meloy or Weibull. It is necessary to say that if the fitness of the approximation more suitable, then the characteristics of the process itself is also better. In purpose of obtaining more appropriate results, these methods were modified by application the mathematical functions, as i.e. hyperbolic tangens function. Furthermore, on the basis of empirical data, so-called interpolations may be performed in purpose of getting more appropriate results of approximation. One of the most known techniques of interpolation is Hughes method. This method for interpolating standard data involves breaking down each interval into a number of smaller sub-intervals. The results of such one-dimensional approach not always contain the full in-formation of the searched distribution. It happens because such interpretation of the problem is not completely correct. In practice, the separation process depends not only on the one parameter (i.e. grain size), but also on many other features characterizing certain material (i.e. its density). It seems then that in some cases the application of multidimensional grain characteristics distributions will be more appropriate. In this paper, the technique of joining the distributions of grain size and density by means of so-called Morgenstern distributions is shown. The general form of these distributions is as following:

Jan 1, 2014