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By Magnus Evertsson, Haijie Li, Erik Hulthen, Mats Lindqvist

"The static and dynamic models for autogenous (AG) and semi-autogenous (SAG) mills have been studied for decades. Though the effects of mixing soft and hard ores in a mill and their interactions are not widely investigated. To develop a general numerical model for AG/SAG mills, a dynamic model has been introduced, and its capability to simulate multi component ore breakage has been examined and compared with previous publications. The simulation results show that the dynamic model can cover a range of milling conditions and is able to simulate complex scenarios with soft and hard ores. The dynamic model discussed here could provide substantial potential for the controlling and optimization of the comminution circuits. INTRODUCTION In the last decades, efforts have been devoted to studying the comminution circuit due to their high energy consumption. The energy directly spent in minerals comminution was about 2% globally in the year 2000 (Maurice et al, 2003). As one important part of the comminution process, AG/SAG mills are widely used for primary grinding in minerals processing. AG/SAG mill models include static and dynamic models (Kojovic et al, 2012; Yu et al, 2014; Yu et al, 2017; Liu and Spencer, 2004; Salazar et al, 2009). Many static models have been well validated over the past decades, but they are all based on steady state assumptions. Even though plants experience a steady-state condition under certain circumstances, it can be inaccurate to simulate the system by static models under all circumstances (Asbjörnsson et al, 2013). The advantages of a dynamic model are apparent that it provides more information and insights both inside the mill and through interactions with other machines in terms of pebble crushers, conveyor belts, screens and so on. In many mines, the multi-component grinding is inevitable, and the ratio of hard and soft components in the mill strongly affects mills operation and performance. Bueno (Bueno et al, 2010; Bueno et al, 2013) studied the effects of blending hard and soft ores in AG/SAG mills and used them to update the JKSimMet toolkit which was a steady state plant simulation software. However, due to the complexity of the particle interactions such as multi-component breakage function, appearance function, in mill transportation, there has been no dynamic AG/SAG mill models developed yet for simulating multi-component."

Jan 1, 2018

By H. J. Cao

Valuable elements could be extracted by microorganism ferment fluid from bauxite, which mainly due to bacteria acid namely organic acid. And after leaching, reclaiming the remainder organic acid in leaching solution was an important procedure for bauxite leaching process. the re-searching status about organic acid reclaiming process from bauxite ore bioleaching solution was summarized. Common processes for recycling organic acid from bauxite bioleaching solution in this period and their advantages and disadvantages, research aspects which need being confirmed for the future were Indicated

Jan 1, 2014

By P. V. Malyarov

"This paper examines the grinding and wear processes in drum mills. A summary of the industry’s long-term experience with the proposed linings is presented. A method is proposed for assessing the efficiency of the grinding energy distribution between the successive stages. A case study is presented of grinding energy redistribution at Talnakh Concentrator by replacing spiral classifiers with a drum-type hydraulic screen. The problems of the kinetics of grinding processes in ball mills and semi-autogenous (SAG) mills are examined. It is demonstrated that in ball mills the feed particles are disintegrated by triaxial compression in the mill zones where discrete slippage of the charge occurs at major force interactions between the layers. Mechanism underlying increases in the specific energy consumption in grinding circuits based on SAG mills is shown.The problem of improving the throughput and reducing the specific energy consumption in mineral feed grinding is highly relevant because of the significant energy intensity. Up to 80% of the consumed energy is used to disintegrate ore fed into the drum mill. At all development stages of the drum mill grinding theory, the researchers have paid a great deal of attention to studying the patterns of the charge motion and the kinetics of the feed particles disintegration processes. In [1], it was shown that, due to the slippage between the charge layers being lifted, drum mills at concentrator plants operate in a mixed cascade and waterfall mode. A feature of the mixed mode is the toe zone, where the charge contacts the lining and the transition to a circular path takes place. Studies of the charge motion in the toe zone made it possible to develop a method for designing cross-sectional profiles of lining plates [2] for ball mill drums. The method is based on the principle of interaction between the balls and the lining, where the non-working rear surfaces follow the relative motion path of the balls before impacting the lining, while the working surfaces are orthogonal to the rear ones. Lining with the proposed profile provides contact with the charge and slippage-free transition to a circular path. This ensures an longer service life of the lining, a reduction in specific energy consumption, and an increase in the mill’s feed rate. The proposed method is applicable when designing lining plates of various materials. Steel liners with the proposed profile have been successfully operated [3] for more than 40 years at a number of projects in the industry."

Jan 1, 2018

By Bianca Foggiatto, Marcos Bueno, Rajiv Chandramohan, Eddie McLean, Greg Lane

"With the increasing depletion of high-grade ore deposits, smarter mineral processing solutions are required to achieve sustainable and economic methods for mining and processing low-grade deposits. In order to make the treatment of low-grade deposits economically viable, large quantities of rock need to be mined and processed. The associated infrastructure costs (power, water supply, accommodation and support services, waste storage) result in a substantial penalty on the project, from both capital and operating cost perspectives. As a consequence, the challenge for the mining industry is to overcome the associated rise in energy and water consumption as well as increased project complexity when processing large amounts of low grade ore. Ore sorting technologies have been used for many years, predominantly on small projects, enabling the upgrade of marginal ores. Several sorting methods based on characteristics including specific gravity, radiometry, colour, particle size, grade and other detectable physical characteristics have been employed. The challenge for large low-grade ore bodies is to crush and sort at coarser rock size in order to minimise specific energy consumption in comminution and to reduce waste disposal costs. For large projects, the understanding of the economic impact of ore sorting is limited. The economic drivers include plant head grade improvement; sorting infrastructure capital, operating and maintenance costs; waste material handling and other environmental costs related to waste disposal. This paper analyses the economic impact of ore sorting in a large mineral processing operation. The focus of the analysis is to compare NPVs for a circuit including screening and ore sorting stages. A project for processing an Australian copper sulphide ore is considered as an example for this study."

Jan 1, 2014

By Michel Brissette, Shaheer Sanuri, Veroljub Mihajlovic

"The main purpose of geometallurgy is to improve the mine planning by mapping hardness and throughput into the mine block model using geostatistics to eliminate the large production fluctuations caused by the ore hardness variability coming from different parts of the pit. However, not all grinding testwork available commercially can be applied to geometallurgy because of large amount of sample required and the associated cost per test. Geometallurgy is now being used in designing grinding mill but as the mining project progress, the accuracy of engineering must improve from 30-35% during the scoping study to 10-15% at the bankable feasibility stage and less than 5% for Engineering Procurement and Construction Management. For SAG milling, the SAG Variability Test (SVT) is an abbreviated version of the standard SAGDesign test developed for this geometallurgical need. The same amount of ore than the original test is ground for three cycles into an open batch SAG test and then the SAG pinion energy is predicted to the standard end point of 80% passing 1.7 mm. For ball milling, a Bond Variability Test (BVT) was also developed using the SAG ground ore from the SVT. The Bond ball mill grindability (Gpb), corresponding to the average of the net grams per revolution from the last three cycles of the Bond test, is also predicted from the third cycle. The relative error for both the predicted SAG ore hardness (WSVT) and Bond Work Index on SAG Variability ground ore (Sv-BVI), in kWh/t, averaged 5.5% and 3.8% respectively compared to the SAGDesign testwork values and are within 7% and 10% respectively from plant benchmark and within 7% from the samples sent to all partner laboratories. Both tests can be continued to measure the true hardness necessary for mill sizing. This article discusses the development of these two new tests, SVT and BVT, their potential use and accuracies in any geometallurgical program."

Jan 1, 2014

By R. Paturi

Mill liners play an important role in the operation of a mineral concentrator influencing the throughput, availability, power drawn and the efficiency of the mill in the plant. Liners protect the shell and transfer energy to the grinding charge. Metso Technology Development has conceptualized, developed and successfully implemented physics based 3D DEM simulation techniques to predict charge motion, power drawn, energy spectra and wear over the life of the liner. This paper will present a case study of shell liner optimization for a 34? SAG mill including the input data requirements, and shell liner optimization methodology using the 3D simulations that eliminates the need for the traditional expensive and lengthy proto-type testing. These simulations will cover ball and particle movement, liner wear and mill power draw, and do not cover particle breakage and slurry flow. Even the liner manufacturers lack the ability to provide this type of qualitative and quantitative information on their products. The data from these simulations provides the plant engineers a scientific basis for their decision making and thus eliminates guess work. Keywords: liner, optimization, multi-physics, 3D-DEM

Sep 1, 2012

By G. S. Zeng

The mechanism of cobalt removal from zinc sulfate solution with zinc dust is still not understood well. The experiments in this paper were carried out by zinc dust from zinc sulfate solution with high cobalt to study the mechanism of cobalt removal. Residues after the cementation process from zinc sulfate solution were analyzed by SEM and Electron probe micro-analysis (EPMA) to investigate the morphology of products. Different temperature will cause different structure of particles. With the increasement of temperature, cobalt removal can be improved considerably. The mechanism of cobalt removal by zinc dust is thought as follows: firstly, the cobalt ion forms Co-Zn alloy with zinc particles, and the reaction reaches equilibrium quickly; secondly, the Co-Zn alloy continues reacting to Co with Co2+, which is the control procedure of the whole reaction.

Jan 1, 2014

By Z. H. Xu

Flotation as a versatile multiphase separation technology has been practiced for more than 100 years in coal and mineral processing. Although effective over a wide particle size range, flotation for mineral separation has been largely understood as an art rather than a science, treating the flotation system as a black box. With rapid progresses in microscopic technologies coupled with high speed video recording and imaging analysis, ingénue design of visualization systems has made it possible to understand fundamentals of flotation by visualization. In this presentation, the state of the art where visualization plays a key role in advancing our fundamental knowledge of flotation will be reviewed. The areas to be covered include characterization of bubbles (shape, size, velocity and sol-ids loading) in a running flotation system, either column or mechanical cell, bubble-solid attachment, hydrodynamic cavitation in fine particle aggregation and flotation, froth imaging, particle-particle interactions by zeta potential distribution measurements, and heterogeneous gas nucleation by atomic force microscope imaging. With these capabilities, critical roles, good or bad, of ore proper-ties, solution chemistry, slurry hydrodynamics, and operation variables in flotation systems as applied to mineral, coal and oil sands processing were clearly elucidated.

Jan 1, 2014

By A. Buchanan, M. Mirnezami, A. L. Restrepo, J. A. Finch, M. S. Hashemi

Settling rate studies on slurries from Cu/Zn flotation plants occasionally revealed two aggregation maxima at pH 8-10 and 10-12. From measurements on sphalerite and silica suspensions the double maxima were replicated by Zn ions (pH 8-10) and Mg ions (pH 10-12) corresponding to the presence of zinc hydroxide and magnesium hydroxide, respectively. A combination of chemical and electrostatic bridging by the hydroxides is considered to be the aggregation mechanism.

Jan 1, 2003

By Marzio Piller, Girolamo Belardi, Jure Mencinger, Paolo Bozano, Gianni Schena

"The hydrodynamics of the Tri-Flo™, a two stage cylindrical cyclone used in dense media separation, is studied using Computational Fluid Dynamics. The flow field is simulated with an Euler-Euler Volume of Fluid two-phase approach and the Reynolds stress turbulence model.A unique feature of the device is that the separation medium suspension is pumped and introduced tangentially into the two cylindrical compartments while the raw feed is conveyed to the feed hopper and fed at the axial inlet. This feature allows to use less pumping energy and limits the unavoidable production of fines. The Tri-Flo™ complex flow pattern is little known but central to the efficiency of the separation.The velocity field is computed within the two compartments of the separator. The interface of the air-core that forms in the inner axial part of the cylindrical sections is identified and visualized. The numerical results for a reduced-size 100 mm ID Tri-Flo™ are compared against laser Doppler measurements on a transparent acrylic model (Chinè, 1995) operated with water. The robustness of the model and its prediction capability are verified.The possibility to accurately predict the velocity profiles within the vessel and their dependence on the main Tri-Flo™ operating and geometrical variables paves the way to a better understanding of the functioning of the separator, its design improvements and scale-up."

Jan 1, 2014

By A. N. Zagorodnyaya, Ye. G. Bochevskaya, E. A. Sargelova, Z. S. Abisheva, A. S. Sharipova

"In Kazakhstan, there is a unique sulphide copper deposit, in the ores containing the natural isotope of osmium-187 (more than 90 %). In the pyrometallurgical processing of concentrates for the target metal, osmium is mainly sublimated, with wet cleaning of metallurgical gases (dust and gas mixture) 40 % of it together with rhenium passes into washing solutions (wash acid). On the basis of this acid, the production of ammonium perrhenate was organized at the enterprise of the RSE ""Zhezkazganredmet"" and for the first time in the world practice - the isotope of osmium-187. However, the degree of its recovery from solutions does not exceed 8 % of the amount supplied with the charge or 25 % of the amount that was received for extraction. But the bulk of it (~ 75 %) remains in the raffinate, discharged to sewage treatment plants (wastewater). The studies presented in this work are aimed at solving the problem of osmium isotope-187 extracting from wastewater, which are a potential source of increasing metal production in Kazakhstan. The aim of this work is the development and scientific justification of osmium deposition regimes from wastewater using such reagents as thiosulfate and sodium sulphide. The influence of various physicochemical factors on the precipitation of the osmium was studied and optimal conditions for its maximum transition to sediment were chosen. An original method for obtaining osmium concentrate in the presence of sodium thiosulfate with the addition of potassium iodide from a new type of wastewater - man-made ammonia solutions has been developed. These solutions were combined mother liquors of solid-phase stripping operations and dissolution of pulp of crude ammonium perrhenate. On the basis of the obtained results, a settling technology for extraction of the osmium from man-made ammonia rhenium-containing solutions was introduced at RSE ""Zhezkazganredmet"". It should be noted that the degree of extraction of osmium, depending on its concentration in solutions entering on the settlement, and taking into account the addition of sulfuric acid, will vary from 60 to 90 %. The recovery of osmium during the test period was 58 %."

Jan 1, 2018

By Nani Pajunen, Kari Heiskanen

"Products filling our societal needs, like communication and transportation needs, are becoming more sophisticated and efficient. The cost has been an increased complexity of material combinations. The same trend is also seen in investment goods. As an example, different crusher types have almost doubled the power to weight ratio in a relatively short time while producing even higher crushing rations. This has been possible by high performance materials and advanced designs. Another example is new hybrid materials in prefabricated high-strength steel structures in construction with the aim to lighten the products and obtain energy savings in the use phase e.g. in transportation. This development in general has made the end of life phase obscure. Recycling is often understood as the first phase of the material cycle. This has been supported by the material centric point of view. When, say indium, has been collected and mechanically treated to a concentrated fraction, it is assumed as recycled. This is not the case. The same applies to special steel alloys where one tends to lose some of the alloying elements to slag or even into the gas phase in the melting and refining stage, not in the earlier steps of recycling. At present there is no clear understanding of recycling of hybrid materials and no clear willingness to create new functional recycling systems. As the EU directives and most of legislation worldwide are based on the material centric thinking and implemented even on total mass recovery basis there is neither legislative incentive nor very strong economic incentives to work out the problem. In our research, we focus on industrial design towards sustainability from a product centric point of view from product collection to final metallurgical steps. It is vital, in the design phase of product, to understand the effects of decisions on recyclability to a saleable raw material. Main goal of our work is to create the fortunate circumstances in supply chain - to pass the barriers and find the effective and fruitful drivers - for reasonable use of raw materials and recycling co-operation with industry. The boundary conditions in the work are extractive metallurgical performance and the economic viability of all the steps. It can be shown from our work that small design alterations may have a large impact on the recyclability. The earlier the decisions are made in the product life chain the more positive impact they will have. It can also be shown, that a strong processing and metallurgical industry is vital to any meaningful recycling of the modern EoL products. Finally, it is also question of the individuals and values: supply and demand. Are you ready to take up the gauntlet: demand recyclable products."

Jan 1, 2014

By Pengbo Chu, James Finch

Bubbles around 1 mm diameter provide the high interfacial area for capture and transport of hydrophobic particles in flotation. The formation of such fine bubbles is commonly achieved by addition of frothers that appear to simultaneously retard coalescence and promote break-up. High inorganic salt content in process water can substitute for frother. In this work we focus on the action of salt (sodium chloride) on formation of bubbles by break-up. An experimental setup that isolates break-up from coalescence was employed. A pocket of air is exposed to controlled mechanical turbulence to produce single bubbles by the induced deformation of the air and the events imaged. The presence of salt is shown to produce smaller bubbles than in water alone. Comparison with a similar study on frothers is made. The argument is advanced that the presence of frother and salt creates surface tension gradients at the air/water interface which add to the mechanical energy of the deformation and break-up process.

Jan 1, 2014

By Yuhe Tang

High Gradient Magnetic Separator with Horizontal Magnetic Line is a new type High Gradient Magnetic Separator product. It has many specific advantages, such as water-air joint discharging technique, double pulses pulp dispersion technique, multi-magnetic gradient for collecting matrix with different diameter rods, better discharging rate with the especial matrix dispose, high separating accuracy and wide applicability. In this paper, the author makes a description of High Gradient Magnetic Separator with Horizontal Magnetic Line, and puts its emphasis on analyzing industrial production data using high gradient magnetic separator with Horizontal Magnetic Line to separate weakly magnetic minerals. It is found that as the rougher for weakly magnetic minerals separation, High Gradient Magnetic Separator with Horizontal Magnetic Line has more stable metallurgical performance and cheaper running costs than other types of High Gradient Magnetic Separator when the properties of the ore change greatly and there is in the case of embedded fine particle size distribution. Keywords: high gradient magnetic separator, self cleaning technology, horizontal magnetic line, water air discharging technique

Sep 1, 2012

By J. Lampke

The superior characteristics of iron ore pellets compared with natural ore and sinter are well known. Due to the higher grade and bulk density they show improved transport and material handling properties. While charging blast furnaces with pellets an increased productivity is realized through pellet?s uniform structure and composition. The increased productivity is caused by a high permeable furnace burden with a decreased coke usage via fuel injection and oxygen enrichment. Therefore, a narrow pellet size distribution and a minimum content -6.3 mm are necessary (Meyer, 1980). The required pellet size distribution can be achieved on the one hand by screening the fired pellets after the induration furnace and recycle the undersized pellets. On the other hand it is possible to produce high quality iron ore pellets with a high degree of sphericity, the important narrow grain size distribution ranging between 9 to 16 mm with high green strength directly in the pelletizing device. To produce high quality green pellets, possibilities and knowledge about adjustments of the pelletizing device are necessary. The paper presents a classification of state of the art pelletizing systems in accordance with the advantages of the pelletizing disc and pelletizing drum in issues like adjustability, green pellet quality, the recycling rate and the space requirement. By a systematization of the influences on pelletizing the common reliance of objectives on influence like pelletizing moisture, disc inclination, rotational speed, mass flow and rim height are given. A variety of industry-proven examples are shown, too. Keywords: Pellet, iron ore, pelletizing, pelletizing disc

Sep 1, 2012

By N. N. Ngoepe

Positron Emission particle tracking (PEPT), which makes use of a radioactively labeled tracer particle, a positron camera and a tracking algorithm has been shown to be a viable method for studying flow properties in both the pulp and froth phases of flotation cells. Detailed velocity measurements of 300-400 µm glass beads were extracted to assess turbulence from velocity fluctuations in a micro flotation cell. The effects of particle speed and orientation at the instant of attachment events were studied. A minimum speed of 0.16 m/s was needed for a collision to lead to attachment. The most attachment events happen when the particle is directly in line with the inlet tube at 90o.

Sep 1, 2012

By I. V. Shadrunova

Annually it is formed more than 95 Mt of clinkers in iron and steel industry of Russia, including 79 Mt of clinkers in blast-furnace, steelmaking, foundry and ferroalloy productions. Complex development of clinkers will provide not only extraction of valuable components, but also preservation of ecosystems. Processing of solid slags is realized, as a rule, in a cold condition by mechanical methods only including stage-by-stage crushing of slag on devices, working on principles of compression and shift (jaw and roll crushers). However it doesn?t provide the complete extraction of metals from clinkers. The intensification of decomposition, in our opinion, can be provided under the use of the devices working on a principle of free kick. At such influence on a material, its destruction occurs on micro cracks, sides of cohesion that is there is a selective destruction of the components possessing various resistances to impact. Decomposition of a piece on the basis of free kick about a material or metal is realized in centrifugal-shock crushers and mills of research-and-production association ?Ural Center?. The share of the joints sharply lowering the efficiency of enrichment thus is minimal. The efficiency of application is proved by morph-metrical measurements with the help of system of image analysis ?SIAMS-600? and physical-mechanical tests of clinkers and their components (impact strength, micro hardness). The experience of application the devices of centrifugal-shock crushing for processing clinkers in blast-furnace, martin and converter productions of Open Society MMC, clinkers of rough-edged copper melt of Joint-Stock Company "Karabashmed" and aluminium clinkers of Joint-Stock Company « Samara plant of aluminium alloys » has allowed to confirm the efficiency of application these devices for selective decomposition of metallurgical clinkers and the opportunity of using clinkers as resource of ferrous and nonferrous metallurgy.

Jan 1, 2014

By Q. Zhang

This paper, by studying the surface properties of pure dolomite minerals separated from representative marine sedimentary rare earth-bearing phosphate ores in Zhijin, Guizhou, aims to study the effect of different anions on the ? potential of dolomite. The research findings showed that the dolomite mineral had a point of zero charge (PZC) at pH 6.5, and the PZC shifted towards lower pH values with addition of anion SiO32- and PO43-. However, addition of anion CO32- and F- resulted in higher PZC values. Keywords: dolomite, ? potential, PZC, anion

Sep 1, 2012

By Y. Rama Murthy

Around 90% of the chromite resources of India are concentrated in the Boula-Nuasahi Sukinda belt of Orissa state. In order to conserve these valuable ore resources strategically, several companies established chrome ore beneficiation plants in this region. The general beneficiation process in these plants consists of gravity unit operations such as Floatex density separator, spiral, wet shaking table etc. Most of these gravity circuits suffer huge losses of valuable minerals in the tailing. Any attempt towards decreasing these losses would not only increase the limited reserves in India but also make the economics of the operations more attractive. Apart from the liberation phenomena, in many of the operating plants considerable quantity of values are lost in the tailings, due to inconsistent feed quality, inappropriate selection of operating and design parameters. Mineral engineers in this regard have to play a proactive and continuous role to improve the performance of all separating units by modifying even small changes based on tests conducted in laboratory under controlled conditions followed by attempts to make necessary changes in the plant. For such improvements, accurate data collection and proper data interpretation followed by making necessary change which is implementable in an operating plant play a very critical role in performance of the circuit. Databank collected over a period of time under various conditions would also help in overcoming the future problems related to either variation in the feed characteristics or specific demand by metallurgical industries. The above concept was adopted in one of the operating chromite beneficiation plant at Sukinda. The approach adopted and practical problems encountered during the study were reported in this paper. The result of trial campaign has shown that, an overall product assaying 30.2% Cr2O3 from the feed (18% Cr2O3 ) can be produced to in single stage. The final discards of the process contain 12% Cr2O3. Keywords: chromite, chromite beneficiation, chromite losses, gravity concentration techniques, plant operating data bank

Sep 1, 2012

By S. V. Bogdanov, S. I. Grishaev

"The article presents the materials about the appropriateness of the use of rental indices to assess the effectiveness of the use of deposits of rare earth elements (REE). The authors suggest from the standpoint of rent payments to rate for the owner the possibility of using the anticipated rental income as the indicator for the analysis of preferences and economic significance of enrichment of extracted raw materials in the emerging field of rare earth metals (REE). Usually from ore mined at the fields, for flotation technology to produce concentrates with collective REE, then they are subjected to chemical-metallurgical processing of the received products are divided into pure oxides, chemical compounds or isolated from them pure metals and alloys. This commercial product is shipped to the buyer. REE were a non-renewable natural resources, so the calculations for determining differential and specific rent showed that during the development of the technologies of mineral processing of a specific field it is necessary to consider what the expected rental income depends on the magnitude of differential rent is related to the volume of production of REE for the whole planned period of exploitation of natural resources. This income is determined by the amount of stock field. For long-term exploitation of the deposit is observed in almost direct proportional dependence between the annual differential rent and the rental income. The decrease in rents in the long run is determined by the change in the composition of ores included in the extracted raw materials and the balance between light and heavy REE. The largest 70% reduction of the rent projected for ""cerium"" fields, while for ""yttrium"" these losses are considerably smaller. Tomtor, Chuktukon and Katuginskoye Russian deposits are characterized by a level of rent that is comparable to the mastered foreign sources of REE. Thus, the enrichment of minerals with REM in the domestic deposits is quite competitive at the world level. INTRODUCTION Deposits of rare earth metals (REE) are non-renewable resources that should be developed and used so that it would be possible to provide a reduction due to payment of appropriate resources for future generations. This compensation, due to the reduction of natural resources, can be carried out both in natural and in economic terms (1). When analyzing economic compensation options, particular attention should be paid to rental income in assessing the attractiveness of using different REE deposits. It is known that absolute and differential rents are summands when calculating the value of natural rents. The value of the absolute natural rent is proportional to the unit price of the product obtained from mineral raw materials and sold on the commodity market. Limitations, as well as the use in production processes and business, contribute to the gradual reduction of natural resources, which increases their consumer value and affects the price of commodity products from primary raw materials."

Jan 1, 2018