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By Xiaodong Jia, Williams. Richard A.

This paper describes the recent developments, arising from research at Leeds, in the computer modelling of packing of complex shaped particles and prediction of physical properties of the structures represented by the packing. The computer model DigiPac, is capable of packing particles of any shapes and sizes in a container of arbitrary geometry. The ability to predict packing structure of real particle shapes and to compute directly some structure-dependent physical properties (such as liquid permeability, mechanical strength/ stability, compaction and sintering, dissolution and leaching, etc.) is obviously highly desirable and has significant potential in industrial applications. Examples are presented relating to the packing of granular materials.

Jan 1, 2003

By D. Vega, P. R. Brito-Parada

"Small diameter (10 mm) hydrocyclones have been applied successfully for the separation of particle suspensions in the micron size range. These hydrocyclones are attractive because they show a bypass fraction larger that the water recovery, resulting in a high particle recovery to the underflow as well as low water recovery. However, this is a disadvantage when the purpose of the hydrocyclone is classification because of the large amount of fine particles that are misplaced in the underflow. The aim of this study is to explore, experimentally and computationally, the influence of design parameters on the classification process. In this work, a full factorial experimental design was defined to carry out comprehensive experimental tests using glass beads (0-20 µm) as the particulate system. We show that the dimensions of spigot and vortex finder diameter can be effectively manipulated to change the separation performance of the system and the energy consumption. A CFD model was developed that is able to predict particle size distribution. The numerical results for the partition curves showed very good agreement with the experimental data. INTRODUCTION Small diameter hydrocyclones are a very attractive separation technology for fine particle suspensions. Since the hydrocyclone diameter is directly proportional to the cutsize that can be achieved, 10mm hydrocyclones have been shown to be very effective in collecting particles in the micron-size range. In addition, while in large hydrocyclones the bypass, i.e. the fraction of particles that report to the underflow without classification, is similar to the water recovery, in 10mm hydrocyclones the bypass fraction is considerably larger than the water recovery. Its high particle recovery and low water recovery makes small hydrocyclones ideal for ultrafine particle classification and dewatering applications in mineral processing. The separation of mineral suspensions achieved using small hydrocyclones has been the focus of various studies. Pasquier and Cilliers (2000) derived a general classification model from experimental data of fine silica concentration in 10mm hydrocyclones; the model was able to describe the fish-hook partition curve. The effect of operating conditions has also received some attention in the literature. Cilliers et al. (2004) showed that an increase in temperature positively effects the recovery of fine silica particles in small hydrocyclones, by increasing the bypass and decreasing the cutsize. Neese et al. (2015) showed that the cutsize in 10mm hydrocyclones can be further decreased by operating at higher pressure, which also trebled the throughput."

Jan 1, 2018

As a leading global company in the mining sector, we are committed to sustainable development. To this end, we invest in the responsible, integrated management of economic, environmental and social issues. Vale?s objective is for our businesses to produce local, regional and global prosperity, enabling the construction of a positive legacy throughout the lifecycle of our activities. This covers everything from talking with stakeholders and preventing failures to complying with legislation, paying constant attention to environmental issues and respecting ethics in business. Keywords: sustainable development

Sep 1, 2012

There are interactions between different minerals from the same ore, minerals and grinding media, and the electrochemical conditions present in the system. Grinding in steel rod and ball mills is a common practice in minerals processing. It is accepted, that the electrochemical interactions between the grinding media and minerals in a grinding mill, influence the corrosive wear of balls/rods and the surface properties of the ground minerals. A complex massive sulphide, Cu-Zn, TAKNAR, Iran, was used for all the experiments. The aim of this study was to investigate the effect of grinding media (dry or wet) on the pulp chemistry and recovery of Cu and Zn in bulk concentrate. 1100 g of ore samples were milled, and mill products with d80=85 and 75 micron in wet and dry grinding methods were produced. Rougher bulk flotation experiments were performed with 550g ore samples, at 30% solids. SIPX in conjunction with Aero238 in 1:2 ratio (48 g/t), was used as mixed collector system, and copper sulphate (200g/t) and MIBC (20 g/t) were employed as sphalerite activator and frother. Lime and High purity Oxygen gas were used for adjusting pH at 8.5 and aeration. The results showed that, more positive pulp potentials were measured when the feed had been ground in a dry environment, and the difference in pulp potentials between the dry and wet ground feed was approximately 250 mV after the grinding stage. In dry grinding method, the recovery of Cu and Zn increased approximately 5 and 10%, respectively. In addition, in dry ground samples, the volume of middling and coarse particles (+100 micron) were more and Dry ground flotation feed had better agreed with using a mixture of collectors. After using copper sulphate, pulp potential increased about 50 mV in dry and 75 mV in wet grinding methods. Keywords: grinding media, pulp potential, Cu-Zn massive sulphide, bulk flotation

Sep 1, 2012

By Hernán Menares, Diego Hernández

"Over the last few years, the copper mining industry has been facing a changing scenario with respect to both the market and society which has resulted in taking a closer look at the way in which mining is being done. The cycle of high metal commodity prices of the last decade left the industry with high costs. Together with increased environmental and social requirements, a decrease in ore body quality, scarcity of resources such as human capital, water and energy, has resulted in an ever-increasing challenge to make a profit out of new ore bodies but also to maintain the current operations in the longer term competitive. The major challenge is to create value for all stakeholders, exploiting ore bodies that nowadays are not considered economically attractive, which applies to both new ore bodies and existing operations, but in a sustainable way. In order to achieve this objective, it is necessary to approach the mining business differently in five main areas: (1) operational efficiency through better use of installed equipment and skilled labor force; (2) efficient use of energy; using opportunities for alternative energy sources and efficient design; (3) efficient use of water; diminishing losses and use of seawater as an alternative source; (4) minimizing environmental impact by eliminating effluents and controlling dust emission; and (5) a more closer, proactive and collaborative relationship with the communities allowing them to be an active player in the solution to assure a sustainable business in the long term. This presentation will show how Antofagasta Minerals is facing these challenges with a long term strategy that includes all of the above mentioned aspects and that is allowing the company to exploit its mineral properties in an efficient and successful way."

Jan 1, 2014

By S. S. Indi, D. Santhiya, S. Subramanian, K. A. Natarajan

"With the gradual depletion of the high-grade ores and finer dissemination of values in the leaner samples, it has become imperative to develop innovative approaches to process such complex ores. The beneficiation of complex sulphide ores containing copper, lead and zinc minerals, remains one of the most important challenges in base metals metallurgy. The advent of biotechnology in mineral processing has opened up immense possibilities to exploit such difficult-to-treat ores. Bioprocessing techniques thus hold promise as potential substitutes for the conventional technologies in vogue. Several types of autotrophic and heterotrophic bacteria, fungi, algae and yeasts are implicated in mineral beneficiation processes. Adopting a bioprocessing route to mineral beneficiation has attractive benefits, such as lower cost and energy requirements, environmental acceptability and operational flexibility.The interaction of sphalerite- and galena-adapted Bacillus polymyxa (B. polymyxa) cells with sphalerite and galena has been investigated through adsorption, electrokinetic and flotation studies. The amount of sphalerite-adapted cells adsorbed onto sphalerite and galena is found to decrease with increase in pH. On the other hand, the adsorption density of galena-adapted cells onto galena shows a feeble maximum around pH 8, and the amount adsorbed is marginally higher in the pH range of 8 – 11.5. In the case of sphalerite the amount adsorbed is higher in the pH range of 5 to 7. The adsorption density of both the adapted cells is higher for galena vis-à-vis sphalerite. Electrokinetic studies indicate significant surface chemical changes on the chosen sulphide minerals and the bacterial cells, consequent to microbemineral interactions. Selective flotation tests on a synthetic mixture of galena and sphalerite confirm that sphalerite could be preferentially floated from galena, using galena-adapted cells, but not with the sphalerite-adapted cells. The cells adapted to galena assay a higher polysaccharide content and are more hydrophilic, while the sphalerite-adapted cells have a higher protein content and possess greater hydrophobicity. Transmission electron microscopic studies have provided evidence in support of the differences between the cell surface characteristics of sphalerite- and galenaadapted cells (Figure 1). Possible mechanisms of interaction between the minerals and the bacterial cells are discussed."

Jan 1, 2003

By H. Koca, D. O. Aksoy, S. Koca

"In this work, modelling of galena flotation from a disseminated Pb-Zn ore containing 0,83 % Pb was investigated. In the flotation experiments, collector type and amount, frother type and amount, particle size, pH and flotation time were kept constant while solid ratio and depressant dosage were varied. The varied parameters are described with a mathematical model by using statistical design method. Central Composite Design method which is one of the principle response surface methodologies was used in statistical design and analysis of experimental results and process modelling. Two quadratic mathematical models were developed for Pb grade and Pb recovery. Analysis of variance showed that models obtained for Pb grade and Pb recovery were found to be statistically significant in 95 % confidence level. Predicted vs actual values of Pb grade and Pb recovery were also given in graphically. It was found that predicted values represent approximately 96 % and 94 % of actual Pb grade and Pb recovery, respectively. The high values of R-square (R2) indicate that the models developed for two response variables are powerful. INTRODUCTION Lead and zinc metals are widely used in electrical, mechanical, military, metallurgical, chemical, light and medical industries. Sulfide ores are the main resources for lead and zinc minerals (Luo et al., 2016). Froth flotation is the main beneficiation method to achieve lead and zinc sulfide minerals separation. There are two basic approaches to obtain lead and zinc separation by flotation. First, flotation of lead sulphide is carried out and zinc sulphide and gangue minerals are depressed by various depressants and second, the bulk flotation of lead and zinc sulphide is carried out to obtain a concentrate of lead and zinc, followed by the lead and zinc separation. (Yuan et al., 2012). Apart from concentration of lead and zinc by flotation, there are a few literature that reports concentrations of lead and zinc by gravity and hydrometallurgical methods with remarkable success (Goktepe, 2005; Yanbo et al., 2016)."

Jan 1, 2018

By Z. H. Wang

The internal parameters of ball mill are very important in the grinding process and have significant impact on the grinding results. Accurate measurement of the internal parameters of ball mill is crucial and indispensable for optimization and control of grinding process. In this paper, a novel tri-sensor measurement method was used to measure the external signals (i.e., bearing pressure, sound intensity and power consumption) of ball mill. Mathematical models, which link the external signals of ball mill with its internal parameters, were established to predict the internal parameters of ball mill. Experimental results showed that the mathematical models could directly predict the internal parameters of ball mill once the external signals were obtained. The tri-sensor measurement method and the mathematical models proposed in this paper provided a new way and solid basis for optimization and control of ball milling.

Jan 1, 2014

By Z. G. Song, C. Y. Sun, X. R. Zhang, Y. Yu

In skarn type scheelite deposit, there are calcium minerals with floatability similar to scheelite, such as calcite, fluorite, etc., which are difficult to separate. Heating cleaning method developed by Petrov has been widely applied in processing rough concentrate of scheelite for nearly half a century, but there exists a general lack of full understanding of the interaction between floatation reagent and mineral particles surfaces. The mechanism on separation of scheelite and calcium minerals in heating cleaning process was investigated by mineral flotation experiments, XPS analysis, as well as solution chemistry and crystal chemistry calculations. The results showed that the sequence of minerals floatability using sodium oleate as collector and a large amount of sodium silicate as modifier in heating flotation test was scheelite > calcite > fluorite, which was the same as solution chemistry calculations based on Gibbs free energy vs. pH and also the same as Ca-X intensity order by crystal chemistry analysis. There are two sides about the mechanism of heating cleaning method: one is that the adsorbed collector on calcium minerals surface is desorbed more easily than scheelite, and the other is selective dissolution of calcium ions from the mineral surface because of Ca-X intensity difference in heating and stirring process.

Jan 1, 2014

By M. L. Torem, R. H. Rojas, A. G. Merma

"Fine particle recovery by conventional flotation processes is very low mainly due to the low probability of bubble/particle collision and adhesion. In order to solve the problem of low particle recovery, several flotation technologies have been developed to increase bubble/particle collision efficiency. Among these technologies, the electroflotation process stands out. This process has advantages in the generation of microbubbles (<100 µm) and in the production of different amounts of hydrogen and oxygen microbubbles. These advantages favorably influence the fine particle floatability, due to the greater probability of particle/bubble collision and adhesion. The electroflotation tests were conducted for a hematite/sodium oleate system in a Partridge-Smith modified electroflotation binary cell of 0.38 L usable volume. The sodium oleate concentration, particle size, pH and current density were evaluated. Satisfactory results in the recovery of hematite were found at pH values of 7, reaching hematite floatability of 99% and 90% with hydrogen and oxygen bubbles, respectively.INTRODUCTIONThe flotation recovery of fine and ultrafine particles is normally very low and is caused by several factors, among them, the low probability of collision and adhesion bubble-particle, the difficulty to overcome the energy barrier (entrainment and entrapment), low selectivity, surface oxidation and mineralogical changes (Schulze et al., 1989; Waters et al., 2008; Shahbazi et al., 2010). This problem can be overcome by decreasing the bubble size or by increasing the apparent particle size. However, it is worth noting that the use of small bubbles or micro bubbles also involves some disadvantages such as their low momentum resulting in a slower process comparing with conventional flotation. Electroflotation is an attractive alternative for treating fine particles with small bubbles less than 100 µm, generated by the electrolysis of water. Electroflotation is one of the variants of the flotation process, where the gaseous phase is produced by electrolysis of an aqueous solution, generating oxygen and hydrogen bubbles (Sarkar, 2010; Gupta and Ali, 2012). These smaller size bubbles allow the recovery of fine particles by increasing the collision efficiency. This process is versatile and competitive in relation to other techniques such as dissolved air flotation and dispersed air flotation because the electroflotation units are smaller, more compact and require less maintenance and less operating cost than other flotation units (Zouboulis and Matis, 1995,). In addition, the electroflotation process is a clean technique and provides results in a short time, requiring only the investment in the electroflotation cell construction stage and the choice of the electrodes (Ketkar et al., 1991; Sarkar et al., 2010; Sun et al., 2011). In this sense, this study assesses the effect of pH, particle size and sodium oleate concentration on electroflotation of hematite fines."

Jan 1, 2018

By S. S. Indi, D. Santhiya, S. Subramanian, K. A. Natarajan

The interaction of sphalerite- and galena-adapted Bacillus polymyxa (B. polymyxa) cells with sphalerite and galena has been investigated through adsorption, electrokinetic and flotation studies. The amount of sphalerite-adapted cells adsorbed onto sphalerite and galena is found to decrease with increase in pH. On the other hand, the adsorption density of galena-adapted cells onto galena shows a feeble maximum around pH 8, and the amount adsorbed is marginally higher in the pH range of 8 . 11.5. In the case of sphalerite the amount adsorbed is higher in the pH range of 5 to 7. The adsorption density of both the adapted cells is higher for galena vis-à-vis sphalerite. Electrokinetic studies indicate significant surface chemical changes on the chosen sulphide minerals and the bacterial cells, consequent to microbe-mineral interactions. Selective flotation tests on a synthetic mixture of galena and sphalerite confirm that sphalerite could be preferentially floated from galena, using galena-adapted cells, but not with the sphalerite-adapted cells. The cells adapted to galena assay a higher polysaccharide content and are more hydrophilic, while the sphalerite-adapted cells have a higher protein content and possess greater hydrophobicity. Transmission electron microscopic studies have provided evidence in support of the differences between the cell surface characteristics of sphaleriteand galena-adapted cells. Possible mechanisms of interaction between the minerals and the bacterial cells are discussed.

Jan 1, 2003

By Jacek Kolacz

A new sensor based sorting system related to complex image analysis has been developed at Comex AS - Norway. It makes it possible to separate different mineral particles regarding their color, shape, texture, size, density and indirectly their composition. The sorting system has been successfully tested and applied for sorting minerals providing high separation efficiency in the range of 95-99.9 %. The main advantage of this system is connected with its universality where many material parameters are analyzed in the same processing unit by a single passage.

Sep 1, 2012

By Manisha Singh, Manikanchan Sarkar

"Presently the global steel production is mainly based on iron ore sourced from high grade hematite deposits. India has large deposits of good quality hematite ore but with the prevailing practice, such deposits are depleting fast and getting exhausted. However, apart from such high grade iron ores, India is also endowed with large reserves of low grade iron ore, such as BHQ (Banded Hematite Quartzite), BHJ (Banded Hematite Jasper), BMQ (Banded Magnetite Quartzite) and Magnetite. In the present situation, it has become necessary to focus attention on upgradation of these low grade ores to produce useable concentrate. It augurs well that already substantial investigation work has been carried out in this respect and a few plants have been set up in India and abroad. One important aspect in this regard is the process route options with optimum yield and grade. Some of these low grade ores, particularly magnetite, are found to contain high phosphorous level, removal of which poses a major challenge. Since the grade is low, substantial upgradation necessitates fine grinding for appropriate liberation. Fine grinding is energy intensive and needs attention to achieve economy in this regard. Large quantity of tailings is generated in the process, wet disposal of which gives rise to a lot of hassles and hence, possibility of dry disposal of the same needs to be explored. The experience of the authors, with regard to aforesaid aspects which has been gained in course of carrying out relevant assignments is presented in this paper."

Jan 1, 2014

By Braulio Fernández, Gonzalo Montes-Atenas

The mechanisms taking place during the leaching of chalcopyrite when it is in contact with other sulphide minerals, particularly pyrite, is still a matter not fully solved. The GalvanoxTM process has been suggested as a technical solution to extract copper from chalcopyrite at commercial level inhibiting passivation phenomena widely reported in the field of hydrometallurgy. Although there are some rules of thumb to implement the process in fully flooded stirred conditions such as the optimum pyrite/chalcopyrite mass ratio should range between 2 and 4, among others; not many research studies have been focused on studying the effect of the surface contact area between chalcopyrite and pyrite to reach best copper extraction conditions. The aim of this research work is to determine the effect of the mass and surface area ratio between the minerals and the surface area of each of the mineral species effectively exposed to the leaching solution. Different particle size distributions of pure pyrite and chalcopyrite were contacted in a small column and subjected to leach tests using sulphuric acid in concentrations close those used in industrial leaching processes. The mass and surface area ratios which optimize the extraction of copper were obtained. It was found the best leaching conditions were attained when reducing the particle size distribution of pyrite regardless the particle size distribution of chalcopyrite. Further analysis concerning the impact of this conclusions on large scale operations is presented and discussed.

Jan 1, 2014

By T. N. Alexandrova

Results of mineralogical-technological research of carbonaceous rocks of Kimkansky precious metal occurrence are presented, on their basis new typemorphic natural and technological microelement associations were revealed using mathematical statistics methods. Keywords: carbonaceous rocks, processing, microelements, flotation, statistical criteria

Sep 1, 2012

By A. Qaredaqi, M. Mohammadi

Wet High Intensity Magnetic Separators, for short, WHIMS are used for recovery of Iron ores with low magnetic susceptibility. A Jones patent WHIMS with "grooved plates" matrix is being used in Dry Tailing processing line in Hematite Recovery Plant at Golgohar mining & Industrial Co. for recovery of Hematite. In this kind of separators Matrices are used for increasing the Magnetic field intensity and providing high magnetic field gradient. The laboratory WHIMS in Golgohar Iron Ore and Steel research Institute is capable to provide a background magnetic field strength up to 0.85 Tesla and in presence of ‚expanded metal? matrix, magnetic field intensity could increase up to 0.9 Tesla. More than 50% of feed particles in this separator were finer than 36 micron and recovery of these particles needs more magnetic field intensity. Hence, ‚Grooved Plates? matrices with Js= 2 Tesla and 3.8 mm gap were constructed. Measurements indicated that magnetic field intensity around the matrix will increase to 1.25 Tesla. Graph of Magnetic field intensity around the matrix to background magnetic field intensity was plotted and a model with Rsquare= 0.9 was offered. In addition, magnetic field gradient and magnetic force were calculated. In WHIMS with feed top size of 150 micron, the main effective forces on separation process are the magnetic force and the hydrodynamic drag force. With assuming that the particles are smooth and spherical and the flow is laminar, Recovery of fine magnetic particles is problematic in this separator because of drag force. Considering these facts and mentioned model, finest particles that are recoverable in different magnetic field intensities were calculated. Computations illustrated that with magnetic field intensity more than 0.8 Tesla, particles as fine as 4 micron are theoretically separable but it should be noted that in practice a larger attractable particle size would be expected.

Jan 1, 2014

By C. Suazo, O. Alruiz, A. Hofmann, I. Fernandez, W. Kracht, N. Mora

"Compañía Minera Dona Inés de Collahuasi, CMDIC, has developed a methodology that allows estimating economic benefit taking into account the variability of the ore characteristics (geometallurgical models). Currently, the grinding model allows predicting the treatment capacity, specific power and balls consumption for short, mid and long term planning. An alternative impact test to estimate SAG grinding parameters is presented in order to bring the geometallurgical model from mid and long term to short term planning. The impact test uses either the production bench or geological drill holes. This allows Geologists increasing the density of grinding parameters within the block model improving the geostatistical estimation of the rest of the blocks. The test requires a small amount of sample to obtain the requires grinding parameters for the grinding model in comparison to the well known grinding test and also, it can be performed easily and quickly by the geology team of a mining company. The alternative grinding test is presented in this article. The grinding model using this short grinding test has been successfully used in mining planning and the accuracy of the model is demonstrated using monthly average instantaneous throughput from January 2013 to March 2014, showing an average relative error of 5% and an R2 value of 0.9. Also, 111 individual variability samples were divided into two each, in order to compare the estimated grinding parameters based on this alternative test to the grinding parameters obtained from the conventional grinding test. The comparison shows an average relative error of 4% and an R2 value of 0.9."

Jan 1, 2014

By Herman Mendoza, Luisa Ciriaco

An investigation of the seeding mechanism using heterocoagulation and the Derjaguin - Landau - Verwey - Overbeek (DLVO) theory of two pure minerals is the objective of this study. The seed was silica with modal diameters of 4.529 µm (fine particles) and 5.216 µm (coarse particles) and the test powder was hematite with a modal diameter of 0.883 µm. Parameters included variations in the concentration and particle size of silica. Both particles were first subjected to size determination and settling tests via Stoke’s Law. The silica-hematite system was then suspended in 0.001 M KNO3 electrolyte solutions where pH was adjusted. Afterward, the suspension was agitated and was allowed to settle at different time intervals while obtaining turbidity readings. Results through settling time and turbidity vs. pH graphs indicate that maximum heterocoagulation occurs from pH 2 to 5 while minimum heterocoagulation occurs from pH 6 to 7. At these pH levels the zeta potentials of silica and hematite are negative and positive, respectively. On the contrary, repulsive forces dominate the system from pH 8 to 11 due to the particles’ negative zeta potentials. Furthermore, the attachment of hematite to silica increases when the parameters become larger thereby increasing the effectivity of heterocoagulation at acidic to neutral pH levels.

Jan 1, 2014

By Liu Xiaodong, Jiang Meifen, Kou Xiaoyan, Lu Xianjun

"Two low grade calcium bentonite (Ca-bentonite) from Hejia (HJ) and Boteng (BT), Shandong, China, mainly contain montmorillonite and quartz, and slightly feldspar, calcite, and montmorillonite content are 32.37% and 55.90%, respectively. In order to examine the feasibility to produce activated clay to meet the standard of Chinese chemical industry (HG/T2569-2007), three types of industrial production process are proposed according to the screen test. The first process is grinding the raw bentonite to -200 mesh and then activating. The second is to activate the raw bentonite directly, and then classify the production to -200 mesh. The last one is to activate the raw bentonite after purification. Three parameters, which are sulphuric acid strength, ratio of liquid to solid and treatment time, are optimized via orthogonal test for every process. The preliminary test indicates that it is feasible to produce acid bentonite of difference quality. For the sample of HJ, milling the raw to -200 mesh first and activating afterwards, the parameter is at 9% acid strength, the ratio of liquid to solid 2, the time 4 hours, temperature 90°C, the products can meet the qualified grade for animal and vegetable oils refining. For the sample of BT, milling the raw to -200 mesh first and activating afterwards, the parameter is at 15% acid strength, the ratio of liquid to solid 2.5, the time 2 hours, temperature 90°C, the products can meet the qualified grade of high decolorization for petroleum products refining. For the sample of BT, adopting purification to -325 mesh by stirring and rubbing at first, and then activating at 9% acidity, under the conditions that the ratio of liquid to solid is 2, the time is 2 hours and the temperature is 90°C, the products can meet the first grade of high activation degree for petroleum products refining."

Jan 1, 2014

By E. D. Gálvez, L. A. Cisternas, R. Acosta-Flores, F. A. Lucay

The optimal design of flotation circuits is a complex task as the mathematical model is nonconvex and includes binary variables, making it difficult to obtain the global optimum solution. Furthermore, there are epistemic uncertainties in the evaluation of the performance of flotation and grinding units. This epistemic uncertainty is generated because semi-empirical models are used with parameters that are a function of the circuit design. Therefore, it is not possible to adjust these models based on experimental data as the experimental conditions are not known at the design stage. This paper analyzed the effect of the uncertainties in flotation units, grinding units, and both units simultaneously. As a result, this paper demonstrated that, for a specific mineral, few structures exist that are optimal for a wide range of values in flotation stage recoveries and liberation fractions in the grinding units. A remarkable aspect of this work is that it introduces grinding, one of the operations that most influences energy consumption in mining and has not been studied in depth in the design of flotation circuits. To demonstrate that there are few optimal structures for a specific mineral when there is high uncertainty in the process units, an a priori approach or first principles was used. Two methods of proof were used: proof by construction and proof by exhaustion. Proof by construction is the construction of a concrete example with a property to demonstrate that something having that property exists. In this work, two examples were considered in the proof by construction. In proof by exhaustion, the conclusion was established by dividing it into a finite number of cases and proving each one separately. Here, 30,000 cases were included for each example. This knowledge can be useful in circuit design including grinding, e.g., after selecting the circuit (or the most promising circuits), and the equipment design parameters and operating conditions can be defined based on simulation and laboratory tests.

Jan 1, 2018