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Pre-concentration at crushing sizes for low-grade ores processing – Ore macro texture characterization and liberation assessment
Minerals Engineering 147 (2020) 106156
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Minerals Engineering journal homepage: www.elsevier.com/locate/mineng
Pre-concentration at crushing sizes for low-grade ores processing – Ore macro texture characterization and liberation assessment
T
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Rui Sousaa,b, , Aurora Futurob, António Fiúzab, Mário Machado Leitea a b
Laboratório Nacional de Energia e Geologia, Rua da Amieira, Apartado 1089, S. Mamede de Infesta, Portugal CERENA, Faculdade de Engenharia da Universidade do Porto, rua Dr Roberto Frias s/n, 4200-465 Porto, Portugal
A R T I C LE I N FO
A B S T R A C T
Keywords: Pre-concentration Mineral liberation Separation efficiency Ore sorting
Mineral processing of low-grade ores requires high processing flow rates. Pre-concentration is a clever technological solution for this challenge because the rejection of barren rock, in the early stages of the processing flowsheet, leads to increasing the head grade of the concentration plant and reducing the corresponding input flow rate. As pre-concentration at crushing sizes depends on the ore texture and consequently, it relies on the achieved mineral liberation degree, a straightforward methodology to assess quantitative mineralogical data of the ore macro-texture, based on image analysis, was developed. For the purpose, photos of hand samples collected at the mine site were converted into a digital image representative of the ore macro-texture. Then, a random comminution algorithm simulating a coarse crushing stage, to generate particles in size range 19.3/6.7 mm was applied. The surface grade of each particle was calculated by pixel counting, allowing for the computation of the Grade Histograms (wt%) and then for the construction of ultimate upgrading descriptors, which has been proved to be a useful tool to assess pre-concentration feasibility and the separation efficiency. This methodology was applied to a Li-Mica lepidolite ore from Alvarrões deposit (Portugal) by simulating several separation scenarios. The separation efficiency of an optical sorting separation was also assessed using the proposed methodology. Furthermore, the influence of mineral liberation at different size ranges on the global separation efficiency was predicted. This paper intends to underline the importance of quantitative mineralogical data in the study of the preconcentration process. Data acquisition must be improved, taking advantage of the more accurate and faster systems, such as the modern multispectral analytical devices and ore sorting technologies.
1. Introduction
(Bond, 1961; de Bakker, 2014; Lessard et al., 2014). If successful, preconcentration techniques applied in the crushing stage (50–5 mm), would reject a high-quantity of non-valuables, preventing the entrance of this uneconomical material in the grinding circuit. The increase of energy efficiency and unit metal productivity would lead to lower concentration plant capacity, and consequently for lower investment and operating costs, both on mineral processing and tailings disposal (Powel and Bye, 2009; Bearman, 2013; Bowman and Bearman, 2014; Lessard et al., 2014; Carrasco et al., 2015). Within the modern concept of low impact mining, pre-concentration at crushing sizes is an important contribution of mineral processing. Pre-concentration has found application in mines worldwide, being an important factor for the viability of many mining projects. Dense media separation, jigging with ragging, magnetic separation, scalping
One of the main challenges of the mining industry is the processing of low-grade ores. This type of ores obliges high processing plant throughput rates, which would result in increased energy consumption and operational costs (Wills, 1992; McGrath et al., 2018). It has been referred that, on average, 44% of the total electricity consumption is dedicated to crushing and milling stages (BCS, 2007). As it is well established, the energy required for comminution increases with the difference between the feed and the final product particle size distribution. When longer grinding stages are needed to attain a suitable degree of liberation of low-grade ores, frequently below 1% mass, a high amount of energy is wasted in the comminution of gangue material
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Corresponding author at: Laboratório Nacional de Energia e Geologia, Rua da Amieira, Apartado 1089, S. Mamede de Infesta, Portugal. E-mail address: [email protected] (R. Sousa).
https://doi.org/10.1016/j.mineng.2019.106156 Received 23 July 2019; Received in revised form 22 November 2019; Accepted 10 December 2019 0892-6875/ © 2019 Elsevier Ltd. All rights reserved.
Minerals Engineering 147 (2020) 106156
R. Sousa, et al.
macro-texture allows for computing the Grade Histograms (wt%) with which the ultimate upgrading curves are calculated (Finch and Gomez, 1989; Dryzmala, 2006, 2007, 2008; Leibner et al., 2016; Sousa et al., 2018b). The ultimate upgrading is fundamental to predict the preconcentration feasibility, but it also allows for assessing the separation efficiency, as it describes the mineralogical limit of the separation performance given by the degree of liberation. Examples of this approach were reported to compare the impact of different flotation conditions in the separation performance using the Grade and Recovery curve (Bradshaw, 2014). Mayer diagram has been used to distinguish the influence of technical inefficiency from the lack of liberation on the global separation process (Sousa et al., 2018b). In this work, a straightforward methodology is proposed to acquire quantitative mineralogical data from a macro-texture of a Li-mica ore, based on image analysis. Grade Histograms (wt%) generated by a random comminution algorithm are used to compute Henry and Mayer ultimate upgrading curves. As Henry curve is a function of cut-grade, it is well suited to select the most appropriate cut-point for the separation. Then, the Mayer Ultimate Upgrading Curve (UUC) was compared with experimental data of an optical sorting to assess its efficiency.
Table 1 Effect of ore texture in the liberation pattern. Liberation in an early crushing stage
Macro-texture
Coarse-grained texture – About 60% of particles are pure gangue; – 40% of mixed particles; rich middlings are dominant – Pre-concentration would be feasible due to the high-contrast between valuable and nonvaluable particles. Fine and dispersive texture – Only of about 20% gangue particles – Low-grade mixed particles are dominant – Pre-concentration would be not recommended. Fine and clustered texture – About 60% of particles are pure gangue – 40% of mixed particles; intermediate middlings are dominant – Pre-concentration would be feasible, but a stronger selectivity is required. Mix of Coarse and Fine texture – About 30% of particles are pure gangue – 70% of mixed particles; intermediate and low-grade middlings – Pre-concentration would be feasible, but a very stronger selectivity is required
2. Experimental 2.1. Materials and sample description The ore used in this work is a Li-mica lepidolite (LPD), carrying 7.7% Li2O, from Alvarrões deposit, located in Gonçalo, south of Guarda (Central Portugal), occurring in a granitic (porphyritic biotite granite) pegmatite body of the western extreme of the European Variscan Belt, inserted in the Central Iberian Zone. Pegmatite sills are hosted by the synorogenic Beiras/Guarda granite (Ramos, 2007). The ore has pegmatitic and aplitic components, with LPD, albite, Li-muscovite, quartz and K-feldspar as major minerals, and montebrasite, topaz, cassiterite, columbo-tantalite, beryl, and zircon as minor minerals. In the pegmatitic component, LPD occurs mainly as medium to coarse-grained (> 500 µm), whereas in the aplitic component it frequently forms aggregates and is fine-grained (60–250 µm) to very fine-grained (≤60 µm) (Sousa et al., 2018a; Sousa et al., 2019). A set of hand samples (200 kg) was collected at the mine site. A subsample of 20 kg was randomly selected and kept aside for the macrotexture assessment, and other sub-sample was crushed in a jaw crusher (single toggle 5″ × 6″, 4 kW, 325–375 rpm, Denver). A sub-sample of the crushed material was size classified and then chemically assayed by atomic absorption spectrometry (AAS) (UNICAM-M SERIES) for Li. Fig. 1 shows the cumulated particle size distribution and metal distribution and metal grade by size class. It is possible to observe that the average Li2O grade remains practically constant along with the size range, meaning that comminution at coarse sizes can be considered almost random. The average grade of this sample is 1.9 %Li2O. These data were fundamental for the application
selective screening and the modern ore sorting systems are the most typical methods of pre-concentration referred to in the technical bibliography (Taggart, 1945; Kelly and Spottiswood, 1982; Wills, 1992). Being pre-concentration at coarse sizes highly dependent on the pattern of gangue liberation, which relies on the ore texture, mineralogy studies play a very important role in the optimization of this process. Table 1 was developed based on some important findings of this work, showing the implication of the most typical mineral occurrences in the pre-concentration feasibility. Modern technical developments in image acquisition and analysis and pattern recognition would allow for an accurate description of the ore texture in a macroscopic scale and valuable mineral occurrence (Leigh, 2008; Wielen and Rollinson, 2016; Ueda et al., 2017; Guiral, 2018; Pérez-Barnuevo et al., 2018; Koch et al., 2019; Rezvani et al., 2019). When available, quantitative mineralogical data of the ore
Fig. 1. Cumulated particle size distribution (left) and metal grade (Li2O) and distribution by size class (right) – Coarse crushing of Alvarrões ore. 2
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fraction. UUC is generated by the simulation of perfect separation of particles accordingly to their specific grade. The UUC, such as any experimental upgrading curve, can be presented by traditional graphical representations. For the present purpose, the Henry Curve was used to assess the feasibility of a theoretical pre-concentration, based on the obtained Grade Histograms (wt%). As it is well established, the Henry Curve relates cut-grade and yield of a separation at different cut-grades, from which concentrates and tailings average grades are calculated and plotted together. In a second step, experimental data of real separation are plotted in the Mayer Diagram together with the UUC obtained as above described.
of the methodology presented in this work since they confirmed only a slight discrimination effect of the comminution (a slight increase of the average Li2O grade towards the coarse sizes – Fig. 1). 2.2. Mineralogical quantitative data of macro-textures The set of samples saved for the macro-texture assessment was sawn to produce flat surfaces and photographed using a conventional digital camera Nikon D3200, equipped with a DX AF-S Nikkor 18–55 mm lens. The camera was mounted on a tripod to guarantee the same distance to different samples, and photos were taken under stabilized illumination conditions (artificial light). Then, a MATLAB® algorithm was developed to generate a binary digital image, distinguishing LPD from non-LPD pixels (px). Firstly, the LPD colour was calibrated according to the RGB model. Each image pixel is defined by the three levels of the RGB colour scale, using a 3-D mathematical array. If the RGB values that characterize LPD were clearly defined, it would be possible to distinguish LPD px from gangue (no-LPD) px. Using a set of 25 LPD images as standards and applying machinelearning techniques (Młynarczuk et al., 2013; Disckson, 2017), the computer was able to establish the range on the RGB scale that identifies LPD. The range defined by the standards was the following: (i) red level between 48 and 134; (ii) green level between 42 and 122; (iii) blue level between 44 and 126. According to this, each px is classified as an LPD px if the three values of the RGB array meet the three previous intervals. Then, Eq. (1) can be applied to compute the average grade of the digital image, considering the LPD and gangue minerals specific gravity (ρ) – 2.8 kg/m3 in the case of LPD and 2.6 kg/m3 in the case of gangue minerals (mainly composed by quartz and feldspar).
No. ofLPDpx × ρLPD %LPD = No. ofLPDpx × ρLPD + No. ofganguepx × ρgangue
2.5. Experimental testwork In order to apply the above-described approach to assess the separation efficiency of a real pre-concentration process, an experimental separation of a sample of the Alvarrões Li ore was carried out on an optical sorter using the size fraction 19/6.3 mm. The separation was performed in two steps: in the first one the separator was calibrated to produce a richer LPD concentrate; in a second scavenger step, the sorter was adjusted to accept a middling LPD content product and to reject a tailings fraction composed by particles with almost no LPD content. The objective of the first step was to assess the possibility of producing a high-grade marketable product that can be directly sent to a Li conversion plant. The second step allowed for the rejection of gangue in an early stage of the processing flowsheet, i.e., at crushing sizes. All products were weighted and chemical assayed by AAS. 3. Results and discussion 3.1. Mineralogical quantitative data and random comminution algorithm
(1)
The procedure applied to generate the digital image was calibrated by introducing a parameter (L) to adjust its grade according to the ore average grade. In the developed approach, it was assumed that the surface grade is an acceptable approximation for the volume grade, such as what is done in optical microscope procedures for the determination of modal mineral composition.
The application of the image analysis algorithm proposed in this work allowed for mineralogical data acquisition of the Alvarrões ore macro-texture. A tentative of reconstruc a hypothetical drill core, shown in Fig. 3, was made assembling binary images of photos taken from sawing cuts of hand samples. The algorithm was calibrated taking into account the average grade of the size fractions 19.3/6.7 mm, which was determined in the size and grade analysis as 1.97% Li2O (corresponds to 25.6% of LPD). Table 2 shows the adjustment of the parameter L, above mentioned, which adjusts the interval of RGB values to obtain a texture grade close to the ore grade. Random comminution algorithm applied to macro-texture generated the Grade Histograms (wt%) of the size fractions between 19.3 and 6.7 mm, as can be observed in Fig. 4. The evolution of liberation is well assessed by the generated Grade Histograms (wt%) of narrow size fractions. A joint histogram of a broader size range 19.3/6.7 mm can be computed (Fig. 5), considering the size composition of a crushed sample of Alvarrões ore, presented in Fig. 1 (left). According to this, the joint histogram was computed based on Eq. (2) (Madureira, 1988; Machado Leite, 1992; King, 2001).
2.3. Generation of grade histograms (wt%) After the acquisition of the ore macro-texture images, a random comminution simulator was conceived by overlapping masks of different geometry and size upon the acquired digital macro-texture (in the case square masks were used to facilitate calculations). At each iteration, a particle is generated with a specific size, and its px information is collected and stored. Then, using the formula presented in the Eq. (1), the grade of each generated particle is calculated. The procedure is illustrated in Fig. 2. Square masks of sides 18, 15, 12, 10, 9 and 7 mm were applied to generate the Grade Histograms (wt%) by size classes 19.3/16, 16/13.5, 13.5/11.3, 11.3/9.5, 9.5/8, 8/6.7 mm (size factor = 4 2 ). After the generation of 5000 particles for each size, the Grade Histograms (wt%) of each size fraction was computed applying this procedure.
Gi (x ) =
∑ Ci,j (x , y) = ∑ [Bi,j (x|y) × Aj (y)] j
j
(2)
where Ci, j (x , y ) is the joint grade and size distribution, Bi, j (x|y ) is the conditional distribution of grade x given the size y (i.e., grade distribution of a narrow size fraction of size y ), Ai (y ) is the marginal size distribution and Gi (x ) is the marginal grade distribution. As above mentioned, Grade Histograms (wt%) give important information concerning mineral liberation: at the above-referred crushing size, Alvarrões ore shows a slight amount of sterile material (around 10% of mass in the 0% grade class); approximately 58% of mass can be considered low-grade mixed particles (in the range ]0, 2] %Li2O); and 16.6% of mass above 4 %Li2O, meaning that the coarse crushing is able to produce lepidolite high content particles.
2.4. Ultimate upgrading Grade Histogram (wt%) is the most appropriate tool to characterize the liberation level of the mineral at a given size. It allows for the computation of the ultimate upgrading, in the sense that it expresses the technical limit of the separation performance (based on a 2D analysis), which can be called Ultimate Upgrading Curve (UUC). Grade Histograms (wt%) define the liberation potential of the ore because it takes into consideration the metal content of particles in each grade 3
Minerals Engineering 147 (2020) 106156
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Fig. 2. Procedure to generate Grade Histograms (wt%).
3.2. Assessment of pre-concentration feasibility
Table 2 Report of the L parameter adjustment.
In this step, a Henry Curve was used to plot the UUC calculated by simulating perfect separations applied to the Grade Histograms (wt%), as referred. The Henry Curve allows for predicting the separation for the desired cut-grade. Fig. 6 shows the representation of Henry and auxiliary curves and the pathway to read in the plot the yield, recovery and concentrate and tailings grade for any desired cut-grade. Now, based on the Henry UUC it is possible to predict several scenarios for the pre-concentration of Alvarrões ore. Table 3 presents some simulations of pre-concentration for different cut-grades. Ultimate prediction of pre-concentration of Alvarrões ore at crushing size (as indicated) points out to (i) rejection of pure gangue not greater than 10%; (ii) accepting Li losses in the order of 4–5%, mass rejection would reach 28%; (iii) operating with a cut-grade at around 1% Li2O, it would be possible to reject almost 40% mass along with 7% Li losses, which would be the most desirable scenario. Moreover, it was also observed that using a cut-grade of 3 %Li2O a high-grade concentrate of about 4.5 %Li2O could be produced, which could be appropriate for metallurgical Li extraction. Nevertheless, it is fundamental to emphasize that these results were obtained simulating a perfect separator, and for this reason, the presented Henry curve is called as Ultimate Upgrading, so it should be expected that the performance of any real separation would be lower than that predicted by the UUC.
Parameter L
0 1 2 3 4
Colour level ranges Red
Green
Blue
48–134 49–133 50–132 51–131 52–130
42–122 43–121 44–120 45–119 46–118
44–126 45–125 46–124 47–123 48–122
% Lepidolite
%Li2O
29.3% 28.1% 27.2% 26.4% 25.6%
2.26 2.16 2.09 2.03 1.97
Then, in Fig. 8, the experimental curve, UUC and Ideal Upgrading Curve, representing the theoretical result of a perfect separation of a fully liberated ore, are plotted together (Dryzmala, 2006; Sousa et al., 2018b). This methodology was carefully described in a previous work (Sousa et al., 2018b), in which it is considered that the distance between the UUC and the Ideal Upgrading line represents the lack of liberation (Zone A) and the distance between the experimental curve and UUC points out to the lack of technical inefficiency (Zone B), as illustrated in Fig. 9. The non-negligible distance between the UUC and the Ideal Upgrading (zone A) indicates low liberation degree, which is likely due to the superimposition of pegmatitic and aplitic textures in the Alvarrões ore. The experimental curve is also far from the UUC (zone B), meaning that the optical sorting separation was not as efficient as expected. Furthermore, as can be seen in Fig. 10, the influence of technical inefficiency (B) is lower when a high cut-grade is applied, meaning that the optical sorting separator exhibited a better performance to recognize high-grade particles. On the other hand, for a low cut-grade, the influence of technical inefficiency (B) increases, meaning that the optical separator revealed the lower performance when color contrast decreases. Conversely, the influence of the lack of liberation (A) is lower for a low cut-grade, meaning that some gangue is liberated,
3.3. Analysis of separation efficiency At this point, the results of experimental separations carried out in an optical sorter were compared with UUC to assess its performance. Global process efficiency depends both on the degree of liberation and the technical performance of the separator. The present study aims at distinguishing between both. As already mentioned, the separation process was carried out in two stages. Results are plotted in a Mayer diagram, as seen in Fig. 7.
Fig. 3. Comparison between RGB and binary macro-texture of Alvarrões ore obtained from a hypothetical half drill core reconstruction. 4
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Fig. 4. Grade histograms (wt%) for different square masks: (a) 18 mm; (b) 15 mm; (c) 12 mm; (d) 10 mm; (e) 9 mm; (f) 7 mm – Alvarrões ore.
4. Conclusions Pre-concentration at crushing sizes is a fundamental separation process and a promising solution for the processing of low-grade ores. According to that, it is crucial to develop proper methodologies to assess quantitative mineralogical data of macro-textures and comminuted particles at coarse sizes. Having access to that quantitative mineralogical data, Grade Histograms (wt%) can be obtained and used to build the UUC, which has been proved to be a tool to assess mineral liberation. During this work, a methodology to acquire the desired quantitative mineralogical data was developed and applied to the case of a Li-mica lepidolite ore from Alvarrões deposit, Center of Portugal. Then, the representation of UUC using the Henry curve showed to be a fast and accurate tool to assess the feasibility of pre-concentration. This methodology can be easily applied to photos of drill cores to get information about ore types and textures. For the studied case, the most promising theoretical scenario for pre-concentration would be the rejection of 40% mass with 7% Li losses. However, as this result was predicted as a perfect separation scenario, it should be considered that any real separation would lead to lower performances. When the methodology was applied to a pre-
Fig. 5. Joint histogram of size range [19.3/6.7]mm.
while LPD is practically non-liberated. This methodology can also be used to optimize the sorter settings, trying to approximate the experimental curves to the UUC, which is the limit of the physical separation given by the level of liberation produced by the comminution of the ore.
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Fig. 6. Henry UUC (left) and the representation of the reading procedure to simulate a cut-grade of 0.5 %Li2O (right). Table 3 Assessment of Pre-concentration feasibility. Cut-grade
%Yield
Concentrate grade (%Li2O)
%Recovery
0.0 0.5 1.0 2.0 3.0
90 72 61 40 26
2.2 2.7 3.0 3.9 4.5
100 96 93 77 59
Fig. 9. Identification of the graphical zones that represent the lack of mineral liberation (zone A) and the technical inefficiency (zone B).
Fig. 7. Experimental upgrading curve fitted by a mathematical model.
Fig. 10. identification of the influence of lack of liberation and technical efficiency in the global efficiency of the separation. Fig. 8. Comparison of the experimental results with ultimate upgrading descriptors using the Mayer curve.
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concentration by optical sorting of a Lithium-Mica ore, Mayer plots of the upgrading curves discussed in this paper point out to the following: i) UUC corresponds to a pre-concentration at the crushing sizes, in which non-valuables are more liberated than lepidolite; ii) the distance between the experimental curve and UUC indicates that a better separation performance can be achieved, acting in the technical component of the efficiency; iii) the optical sorter was more efficient when dealing with high-grade particles.
Dryzmala, J., 2006. Atlas of upgrading curves used in separation and mineal science and technology. Physocochem. Problems Mineral Process. 40, 19–29. Dryzmala, J., 2007. Atlas of upgrading curves used in separation and mineral science and technology (Part II). Physocochem. Problems Mineral Process. 41, 27–35. Dryzmala, J., 2008. Atlas of upgrading curves used in separation and mineral science and technology (Part III). Physocochem. Problems Mineral Process. 42, 75–84. Finch, J.A., Gomez, C.O., 1989. Separability curves from image analysis data. Minerals Eng. 2, 565–568. Guiral, J., 2018. Textural and mineralogical characterization of Li-pegmatite deposit: Using microanalytical and image analysis to link micro and macro properties of Spodumene in drill cores Keliber Lithium Project, Finland. Kelly, E.G., Spottiswood, D.J., 1982. Introduction to Mineral Processing. Wiley. King, R.P., 2001. Modeling and Simulation of Mineral Processing Systems, Oxford. Koch, P.-H., Lund, C., Rosenkranz, J., 2019. Automated drill core mineralogical characterization method for texture classification and modal mineralogy estimation for geometallurgy. Minerals Eng. 136, 99–109. Leibner, T., Bachmann, K., Gutzmer, J., Peuker, U.A., 2016. MLA-base partition curves for magnetic separation. Minerals Eng. 94, 94–103. Leigh, G.M., 2008. Automatic ore texture analysis for process mineralogy. Australasian Institute of Mining and Metallurgy Publication Series. Lessard, J., Bakker, J., McHugh, L., 2014. Development of ore sorting and its impact on mineral processing economics. Minerals Eng. 65, 88–97. Machado Leite, M.R., 1992. Liberation by Size Reduction. Consequences and Improvements on Flotation Kinetics. Flotation Technology, pp. 149–170. Madureira, C.M.N., 1988. Size, Grade and Liberation: a stochastic approach to the fundamental problem of mineral processing, in: Publisher, E.S. (Ed.), XVI International Mineral Processing Congress, Stockholm. McGrath, T.D.H., Eksteen, J.J., Bode, P., 2018. Assessing the amenability of a free milling gold ore to coarse particle gangue rejection. Minerals Eng. 120, 110–117. Młynarczuk, M., Górszczyk, A., Ślipek, B., 2013. The application of pattern recognition in the automatic classification of microscopic rock images. Comput. Geosci. 60, 126–133. Pérez-Barnuevo, L., Lévesque, S., Bazin, C., 2018. Automated recognition of drill core textures: a geometallurgical tool for mineral processing prediction. Minerals Eng. 118, 87–96. Powel, M.S., Bye, A.R., 2009. Beyond Mine-to-Mill - Circuit design for energy efficient resource utilization. In: AusIMM Tenth Mill Operators' Conference, Adelaide, pp. 357–364. Ramos, J.M.F., 2007. Locality n°5: Seixo Amarelo-Gonçalo rare element aplite-pegmatite field. In: (Eds.)., A.L.a.E.R.R. (Ed.), Granitic Pegmatites: The state of the art- field trip guidebook. Memórias n°9. Departamento de Geologia da Faculdade de Ciências University of Porto. Rezvani, A., Khalesi, M.R., Mirzaei, Z.S., Albijanic, B., 2019. Image analysis of liberation spectrum of coarse particles. Adv. Powder Technol. 30, 1989–1993. Sousa, R., Ramos, V., Guedes, A., Botelho de Sousa, A., Noronha, F., Machado Leite, M., 2019. Flotation of lithium ores to obtain high-grade Li2O concentrates. Are there any mineralogical limitations? Int. J. Mining, Mater., Metall. Eng. 5, 7–18. Sousa, R., Ramos, V., Guedes, A., Noronha, F., Botelho de Sousa, A., Machado Leite, M.R., Seltmann, R., Dolgopolova, A., 2018a. The Alvarrões-Gonçalo Li project: An example of sustainable lithium mining. Adv. Geosci. 45. Sousa, R., Simons, B., Bru, K., de Sousa, A.B., Rollinson, G., Andersen, J., Martin, M., Machado Leite, M., 2018b. Use of mineral liberation quantitative data to assess separation efficiency in mineral processing – some case studies. Minerals Eng. 127, 134–142. Taggart, A.F., 1945. Hanbook of Mineral Dressing. Ueda, T., Oki, T., Koyanaka, S., 2017. Stereological correction method based on sectional texture analysis for the liberation distribution of binary particle systems. Adv. Powder Technol. 28. Wielen, K.P., Rollinson, G., 2016. Texture-based analysis of liberation behaviour using Voronoi tessellations. Minerals Eng. 89, 93–107. Wills, B.A., 1992. Minerals Processing Technology, fifth ed. Pergamon Press.
Author contributions The manuscript was written through the contributions of all authors. All authors have approved the final version of the manuscript. CRediT authorship contribution statement Rui Sousa: Writing - original draft, Methodology, Software. Aurora Futuro: Investigation, Writing - review & editing, Validation. António Fiúza: Resources, Visualization. Mário Machado Leite: Conceptualization, Supervision, Data curation, Formal analysis. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment R. Sousa acknowledges the “Fundação para a Ciência e Tecnologia” for the scholarship programme with the reference SFRH/BD/114764/ 2016. References BCS, I., 2007. Mining Industry Energy Bandwidth Study. In: Program, I.T. (Ed.). U.S. Department. Bearman, R.A., 2013. Step change in the context of comminution. Minerals Eng. 43–44. Bond, F.C., 1961. Crushing and Grinding Calculations. Allis-Chalmers Manufacturing Company, pp. 16. Bowman, D.J., Bearman, R.A., 2014. Coarse waste rejection through size based separation. Minerals Eng. 62, 102–110. Bradshaw, D., 2014. The role of 'process mineralogy' in improving the process performance of complex sulphide ores. Carrasco, C., Keeney, L., Walters, S.G., 2015. Development of a novel methodology to characterise preferential grade by size deportement and its operational conditions. Minerals Eng. 91, 100–107. de Bakker, J., 2014. Energy use of fine grinding in mineral processing. Metall. Mater. Tans. 8–19. Disckson, B., 2017. Exploiting machine learning in cybersecurity, https://techcrunch. com/2016/07/01/exploiting-machine-learning-in-cybersecurity/. Accessed in: April, 2019.
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Pre-concentration at crushing sizes for low-grade ores processing – Ore macro texture characterization and liberation assessment
T
⁎
Rui Sousaa,b, , Aurora Futurob, António Fiúzab, Mário Machado Leitea a b
Laboratório Nacional de Energia e Geologia, Rua da Amieira, Apartado 1089, S. Mamede de Infesta, Portugal CERENA, Faculdade de Engenharia da Universidade do Porto, rua Dr Roberto Frias s/n, 4200-465 Porto, Portugal
A R T I C LE I N FO
A B S T R A C T
Keywords: Pre-concentration Mineral liberation Separation efficiency Ore sorting
Mineral processing of low-grade ores requires high processing flow rates. Pre-concentration is a clever technological solution for this challenge because the rejection of barren rock, in the early stages of the processing flowsheet, leads to increasing the head grade of the concentration plant and reducing the corresponding input flow rate. As pre-concentration at crushing sizes depends on the ore texture and consequently, it relies on the achieved mineral liberation degree, a straightforward methodology to assess quantitative mineralogical data of the ore macro-texture, based on image analysis, was developed. For the purpose, photos of hand samples collected at the mine site were converted into a digital image representative of the ore macro-texture. Then, a random comminution algorithm simulating a coarse crushing stage, to generate particles in size range 19.3/6.7 mm was applied. The surface grade of each particle was calculated by pixel counting, allowing for the computation of the Grade Histograms (wt%) and then for the construction of ultimate upgrading descriptors, which has been proved to be a useful tool to assess pre-concentration feasibility and the separation efficiency. This methodology was applied to a Li-Mica lepidolite ore from Alvarrões deposit (Portugal) by simulating several separation scenarios. The separation efficiency of an optical sorting separation was also assessed using the proposed methodology. Furthermore, the influence of mineral liberation at different size ranges on the global separation efficiency was predicted. This paper intends to underline the importance of quantitative mineralogical data in the study of the preconcentration process. Data acquisition must be improved, taking advantage of the more accurate and faster systems, such as the modern multispectral analytical devices and ore sorting technologies.
1. Introduction
(Bond, 1961; de Bakker, 2014; Lessard et al., 2014). If successful, preconcentration techniques applied in the crushing stage (50–5 mm), would reject a high-quantity of non-valuables, preventing the entrance of this uneconomical material in the grinding circuit. The increase of energy efficiency and unit metal productivity would lead to lower concentration plant capacity, and consequently for lower investment and operating costs, both on mineral processing and tailings disposal (Powel and Bye, 2009; Bearman, 2013; Bowman and Bearman, 2014; Lessard et al., 2014; Carrasco et al., 2015). Within the modern concept of low impact mining, pre-concentration at crushing sizes is an important contribution of mineral processing. Pre-concentration has found application in mines worldwide, being an important factor for the viability of many mining projects. Dense media separation, jigging with ragging, magnetic separation, scalping
One of the main challenges of the mining industry is the processing of low-grade ores. This type of ores obliges high processing plant throughput rates, which would result in increased energy consumption and operational costs (Wills, 1992; McGrath et al., 2018). It has been referred that, on average, 44% of the total electricity consumption is dedicated to crushing and milling stages (BCS, 2007). As it is well established, the energy required for comminution increases with the difference between the feed and the final product particle size distribution. When longer grinding stages are needed to attain a suitable degree of liberation of low-grade ores, frequently below 1% mass, a high amount of energy is wasted in the comminution of gangue material
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Corresponding author at: Laboratório Nacional de Energia e Geologia, Rua da Amieira, Apartado 1089, S. Mamede de Infesta, Portugal. E-mail address: [email protected] (R. Sousa).
https://doi.org/10.1016/j.mineng.2019.106156 Received 23 July 2019; Received in revised form 22 November 2019; Accepted 10 December 2019 0892-6875/ © 2019 Elsevier Ltd. All rights reserved.
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macro-texture allows for computing the Grade Histograms (wt%) with which the ultimate upgrading curves are calculated (Finch and Gomez, 1989; Dryzmala, 2006, 2007, 2008; Leibner et al., 2016; Sousa et al., 2018b). The ultimate upgrading is fundamental to predict the preconcentration feasibility, but it also allows for assessing the separation efficiency, as it describes the mineralogical limit of the separation performance given by the degree of liberation. Examples of this approach were reported to compare the impact of different flotation conditions in the separation performance using the Grade and Recovery curve (Bradshaw, 2014). Mayer diagram has been used to distinguish the influence of technical inefficiency from the lack of liberation on the global separation process (Sousa et al., 2018b). In this work, a straightforward methodology is proposed to acquire quantitative mineralogical data from a macro-texture of a Li-mica ore, based on image analysis. Grade Histograms (wt%) generated by a random comminution algorithm are used to compute Henry and Mayer ultimate upgrading curves. As Henry curve is a function of cut-grade, it is well suited to select the most appropriate cut-point for the separation. Then, the Mayer Ultimate Upgrading Curve (UUC) was compared with experimental data of an optical sorting to assess its efficiency.
Table 1 Effect of ore texture in the liberation pattern. Liberation in an early crushing stage
Macro-texture
Coarse-grained texture – About 60% of particles are pure gangue; – 40% of mixed particles; rich middlings are dominant – Pre-concentration would be feasible due to the high-contrast between valuable and nonvaluable particles. Fine and dispersive texture – Only of about 20% gangue particles – Low-grade mixed particles are dominant – Pre-concentration would be not recommended. Fine and clustered texture – About 60% of particles are pure gangue – 40% of mixed particles; intermediate middlings are dominant – Pre-concentration would be feasible, but a stronger selectivity is required. Mix of Coarse and Fine texture – About 30% of particles are pure gangue – 70% of mixed particles; intermediate and low-grade middlings – Pre-concentration would be feasible, but a very stronger selectivity is required
2. Experimental 2.1. Materials and sample description The ore used in this work is a Li-mica lepidolite (LPD), carrying 7.7% Li2O, from Alvarrões deposit, located in Gonçalo, south of Guarda (Central Portugal), occurring in a granitic (porphyritic biotite granite) pegmatite body of the western extreme of the European Variscan Belt, inserted in the Central Iberian Zone. Pegmatite sills are hosted by the synorogenic Beiras/Guarda granite (Ramos, 2007). The ore has pegmatitic and aplitic components, with LPD, albite, Li-muscovite, quartz and K-feldspar as major minerals, and montebrasite, topaz, cassiterite, columbo-tantalite, beryl, and zircon as minor minerals. In the pegmatitic component, LPD occurs mainly as medium to coarse-grained (> 500 µm), whereas in the aplitic component it frequently forms aggregates and is fine-grained (60–250 µm) to very fine-grained (≤60 µm) (Sousa et al., 2018a; Sousa et al., 2019). A set of hand samples (200 kg) was collected at the mine site. A subsample of 20 kg was randomly selected and kept aside for the macrotexture assessment, and other sub-sample was crushed in a jaw crusher (single toggle 5″ × 6″, 4 kW, 325–375 rpm, Denver). A sub-sample of the crushed material was size classified and then chemically assayed by atomic absorption spectrometry (AAS) (UNICAM-M SERIES) for Li. Fig. 1 shows the cumulated particle size distribution and metal distribution and metal grade by size class. It is possible to observe that the average Li2O grade remains practically constant along with the size range, meaning that comminution at coarse sizes can be considered almost random. The average grade of this sample is 1.9 %Li2O. These data were fundamental for the application
selective screening and the modern ore sorting systems are the most typical methods of pre-concentration referred to in the technical bibliography (Taggart, 1945; Kelly and Spottiswood, 1982; Wills, 1992). Being pre-concentration at coarse sizes highly dependent on the pattern of gangue liberation, which relies on the ore texture, mineralogy studies play a very important role in the optimization of this process. Table 1 was developed based on some important findings of this work, showing the implication of the most typical mineral occurrences in the pre-concentration feasibility. Modern technical developments in image acquisition and analysis and pattern recognition would allow for an accurate description of the ore texture in a macroscopic scale and valuable mineral occurrence (Leigh, 2008; Wielen and Rollinson, 2016; Ueda et al., 2017; Guiral, 2018; Pérez-Barnuevo et al., 2018; Koch et al., 2019; Rezvani et al., 2019). When available, quantitative mineralogical data of the ore
Fig. 1. Cumulated particle size distribution (left) and metal grade (Li2O) and distribution by size class (right) – Coarse crushing of Alvarrões ore. 2
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fraction. UUC is generated by the simulation of perfect separation of particles accordingly to their specific grade. The UUC, such as any experimental upgrading curve, can be presented by traditional graphical representations. For the present purpose, the Henry Curve was used to assess the feasibility of a theoretical pre-concentration, based on the obtained Grade Histograms (wt%). As it is well established, the Henry Curve relates cut-grade and yield of a separation at different cut-grades, from which concentrates and tailings average grades are calculated and plotted together. In a second step, experimental data of real separation are plotted in the Mayer Diagram together with the UUC obtained as above described.
of the methodology presented in this work since they confirmed only a slight discrimination effect of the comminution (a slight increase of the average Li2O grade towards the coarse sizes – Fig. 1). 2.2. Mineralogical quantitative data of macro-textures The set of samples saved for the macro-texture assessment was sawn to produce flat surfaces and photographed using a conventional digital camera Nikon D3200, equipped with a DX AF-S Nikkor 18–55 mm lens. The camera was mounted on a tripod to guarantee the same distance to different samples, and photos were taken under stabilized illumination conditions (artificial light). Then, a MATLAB® algorithm was developed to generate a binary digital image, distinguishing LPD from non-LPD pixels (px). Firstly, the LPD colour was calibrated according to the RGB model. Each image pixel is defined by the three levels of the RGB colour scale, using a 3-D mathematical array. If the RGB values that characterize LPD were clearly defined, it would be possible to distinguish LPD px from gangue (no-LPD) px. Using a set of 25 LPD images as standards and applying machinelearning techniques (Młynarczuk et al., 2013; Disckson, 2017), the computer was able to establish the range on the RGB scale that identifies LPD. The range defined by the standards was the following: (i) red level between 48 and 134; (ii) green level between 42 and 122; (iii) blue level between 44 and 126. According to this, each px is classified as an LPD px if the three values of the RGB array meet the three previous intervals. Then, Eq. (1) can be applied to compute the average grade of the digital image, considering the LPD and gangue minerals specific gravity (ρ) – 2.8 kg/m3 in the case of LPD and 2.6 kg/m3 in the case of gangue minerals (mainly composed by quartz and feldspar).
No. ofLPDpx × ρLPD %LPD = No. ofLPDpx × ρLPD + No. ofganguepx × ρgangue
2.5. Experimental testwork In order to apply the above-described approach to assess the separation efficiency of a real pre-concentration process, an experimental separation of a sample of the Alvarrões Li ore was carried out on an optical sorter using the size fraction 19/6.3 mm. The separation was performed in two steps: in the first one the separator was calibrated to produce a richer LPD concentrate; in a second scavenger step, the sorter was adjusted to accept a middling LPD content product and to reject a tailings fraction composed by particles with almost no LPD content. The objective of the first step was to assess the possibility of producing a high-grade marketable product that can be directly sent to a Li conversion plant. The second step allowed for the rejection of gangue in an early stage of the processing flowsheet, i.e., at crushing sizes. All products were weighted and chemical assayed by AAS. 3. Results and discussion 3.1. Mineralogical quantitative data and random comminution algorithm
(1)
The procedure applied to generate the digital image was calibrated by introducing a parameter (L) to adjust its grade according to the ore average grade. In the developed approach, it was assumed that the surface grade is an acceptable approximation for the volume grade, such as what is done in optical microscope procedures for the determination of modal mineral composition.
The application of the image analysis algorithm proposed in this work allowed for mineralogical data acquisition of the Alvarrões ore macro-texture. A tentative of reconstruc a hypothetical drill core, shown in Fig. 3, was made assembling binary images of photos taken from sawing cuts of hand samples. The algorithm was calibrated taking into account the average grade of the size fractions 19.3/6.7 mm, which was determined in the size and grade analysis as 1.97% Li2O (corresponds to 25.6% of LPD). Table 2 shows the adjustment of the parameter L, above mentioned, which adjusts the interval of RGB values to obtain a texture grade close to the ore grade. Random comminution algorithm applied to macro-texture generated the Grade Histograms (wt%) of the size fractions between 19.3 and 6.7 mm, as can be observed in Fig. 4. The evolution of liberation is well assessed by the generated Grade Histograms (wt%) of narrow size fractions. A joint histogram of a broader size range 19.3/6.7 mm can be computed (Fig. 5), considering the size composition of a crushed sample of Alvarrões ore, presented in Fig. 1 (left). According to this, the joint histogram was computed based on Eq. (2) (Madureira, 1988; Machado Leite, 1992; King, 2001).
2.3. Generation of grade histograms (wt%) After the acquisition of the ore macro-texture images, a random comminution simulator was conceived by overlapping masks of different geometry and size upon the acquired digital macro-texture (in the case square masks were used to facilitate calculations). At each iteration, a particle is generated with a specific size, and its px information is collected and stored. Then, using the formula presented in the Eq. (1), the grade of each generated particle is calculated. The procedure is illustrated in Fig. 2. Square masks of sides 18, 15, 12, 10, 9 and 7 mm were applied to generate the Grade Histograms (wt%) by size classes 19.3/16, 16/13.5, 13.5/11.3, 11.3/9.5, 9.5/8, 8/6.7 mm (size factor = 4 2 ). After the generation of 5000 particles for each size, the Grade Histograms (wt%) of each size fraction was computed applying this procedure.
Gi (x ) =
∑ Ci,j (x , y) = ∑ [Bi,j (x|y) × Aj (y)] j
j
(2)
where Ci, j (x , y ) is the joint grade and size distribution, Bi, j (x|y ) is the conditional distribution of grade x given the size y (i.e., grade distribution of a narrow size fraction of size y ), Ai (y ) is the marginal size distribution and Gi (x ) is the marginal grade distribution. As above mentioned, Grade Histograms (wt%) give important information concerning mineral liberation: at the above-referred crushing size, Alvarrões ore shows a slight amount of sterile material (around 10% of mass in the 0% grade class); approximately 58% of mass can be considered low-grade mixed particles (in the range ]0, 2] %Li2O); and 16.6% of mass above 4 %Li2O, meaning that the coarse crushing is able to produce lepidolite high content particles.
2.4. Ultimate upgrading Grade Histogram (wt%) is the most appropriate tool to characterize the liberation level of the mineral at a given size. It allows for the computation of the ultimate upgrading, in the sense that it expresses the technical limit of the separation performance (based on a 2D analysis), which can be called Ultimate Upgrading Curve (UUC). Grade Histograms (wt%) define the liberation potential of the ore because it takes into consideration the metal content of particles in each grade 3
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Fig. 2. Procedure to generate Grade Histograms (wt%).
3.2. Assessment of pre-concentration feasibility
Table 2 Report of the L parameter adjustment.
In this step, a Henry Curve was used to plot the UUC calculated by simulating perfect separations applied to the Grade Histograms (wt%), as referred. The Henry Curve allows for predicting the separation for the desired cut-grade. Fig. 6 shows the representation of Henry and auxiliary curves and the pathway to read in the plot the yield, recovery and concentrate and tailings grade for any desired cut-grade. Now, based on the Henry UUC it is possible to predict several scenarios for the pre-concentration of Alvarrões ore. Table 3 presents some simulations of pre-concentration for different cut-grades. Ultimate prediction of pre-concentration of Alvarrões ore at crushing size (as indicated) points out to (i) rejection of pure gangue not greater than 10%; (ii) accepting Li losses in the order of 4–5%, mass rejection would reach 28%; (iii) operating with a cut-grade at around 1% Li2O, it would be possible to reject almost 40% mass along with 7% Li losses, which would be the most desirable scenario. Moreover, it was also observed that using a cut-grade of 3 %Li2O a high-grade concentrate of about 4.5 %Li2O could be produced, which could be appropriate for metallurgical Li extraction. Nevertheless, it is fundamental to emphasize that these results were obtained simulating a perfect separator, and for this reason, the presented Henry curve is called as Ultimate Upgrading, so it should be expected that the performance of any real separation would be lower than that predicted by the UUC.
Parameter L
0 1 2 3 4
Colour level ranges Red
Green
Blue
48–134 49–133 50–132 51–131 52–130
42–122 43–121 44–120 45–119 46–118
44–126 45–125 46–124 47–123 48–122
% Lepidolite
%Li2O
29.3% 28.1% 27.2% 26.4% 25.6%
2.26 2.16 2.09 2.03 1.97
Then, in Fig. 8, the experimental curve, UUC and Ideal Upgrading Curve, representing the theoretical result of a perfect separation of a fully liberated ore, are plotted together (Dryzmala, 2006; Sousa et al., 2018b). This methodology was carefully described in a previous work (Sousa et al., 2018b), in which it is considered that the distance between the UUC and the Ideal Upgrading line represents the lack of liberation (Zone A) and the distance between the experimental curve and UUC points out to the lack of technical inefficiency (Zone B), as illustrated in Fig. 9. The non-negligible distance between the UUC and the Ideal Upgrading (zone A) indicates low liberation degree, which is likely due to the superimposition of pegmatitic and aplitic textures in the Alvarrões ore. The experimental curve is also far from the UUC (zone B), meaning that the optical sorting separation was not as efficient as expected. Furthermore, as can be seen in Fig. 10, the influence of technical inefficiency (B) is lower when a high cut-grade is applied, meaning that the optical sorting separator exhibited a better performance to recognize high-grade particles. On the other hand, for a low cut-grade, the influence of technical inefficiency (B) increases, meaning that the optical separator revealed the lower performance when color contrast decreases. Conversely, the influence of the lack of liberation (A) is lower for a low cut-grade, meaning that some gangue is liberated,
3.3. Analysis of separation efficiency At this point, the results of experimental separations carried out in an optical sorter were compared with UUC to assess its performance. Global process efficiency depends both on the degree of liberation and the technical performance of the separator. The present study aims at distinguishing between both. As already mentioned, the separation process was carried out in two stages. Results are plotted in a Mayer diagram, as seen in Fig. 7.
Fig. 3. Comparison between RGB and binary macro-texture of Alvarrões ore obtained from a hypothetical half drill core reconstruction. 4
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Fig. 4. Grade histograms (wt%) for different square masks: (a) 18 mm; (b) 15 mm; (c) 12 mm; (d) 10 mm; (e) 9 mm; (f) 7 mm – Alvarrões ore.
4. Conclusions Pre-concentration at crushing sizes is a fundamental separation process and a promising solution for the processing of low-grade ores. According to that, it is crucial to develop proper methodologies to assess quantitative mineralogical data of macro-textures and comminuted particles at coarse sizes. Having access to that quantitative mineralogical data, Grade Histograms (wt%) can be obtained and used to build the UUC, which has been proved to be a tool to assess mineral liberation. During this work, a methodology to acquire the desired quantitative mineralogical data was developed and applied to the case of a Li-mica lepidolite ore from Alvarrões deposit, Center of Portugal. Then, the representation of UUC using the Henry curve showed to be a fast and accurate tool to assess the feasibility of pre-concentration. This methodology can be easily applied to photos of drill cores to get information about ore types and textures. For the studied case, the most promising theoretical scenario for pre-concentration would be the rejection of 40% mass with 7% Li losses. However, as this result was predicted as a perfect separation scenario, it should be considered that any real separation would lead to lower performances. When the methodology was applied to a pre-
Fig. 5. Joint histogram of size range [19.3/6.7]mm.
while LPD is practically non-liberated. This methodology can also be used to optimize the sorter settings, trying to approximate the experimental curves to the UUC, which is the limit of the physical separation given by the level of liberation produced by the comminution of the ore.
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Fig. 6. Henry UUC (left) and the representation of the reading procedure to simulate a cut-grade of 0.5 %Li2O (right). Table 3 Assessment of Pre-concentration feasibility. Cut-grade
%Yield
Concentrate grade (%Li2O)
%Recovery
0.0 0.5 1.0 2.0 3.0
90 72 61 40 26
2.2 2.7 3.0 3.9 4.5
100 96 93 77 59
Fig. 9. Identification of the graphical zones that represent the lack of mineral liberation (zone A) and the technical inefficiency (zone B).
Fig. 7. Experimental upgrading curve fitted by a mathematical model.
Fig. 10. identification of the influence of lack of liberation and technical efficiency in the global efficiency of the separation. Fig. 8. Comparison of the experimental results with ultimate upgrading descriptors using the Mayer curve.
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concentration by optical sorting of a Lithium-Mica ore, Mayer plots of the upgrading curves discussed in this paper point out to the following: i) UUC corresponds to a pre-concentration at the crushing sizes, in which non-valuables are more liberated than lepidolite; ii) the distance between the experimental curve and UUC indicates that a better separation performance can be achieved, acting in the technical component of the efficiency; iii) the optical sorter was more efficient when dealing with high-grade particles.
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Author contributions The manuscript was written through the contributions of all authors. All authors have approved the final version of the manuscript. CRediT authorship contribution statement Rui Sousa: Writing - original draft, Methodology, Software. Aurora Futuro: Investigation, Writing - review & editing, Validation. António Fiúza: Resources, Visualization. Mário Machado Leite: Conceptualization, Supervision, Data curation, Formal analysis. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment R. Sousa acknowledges the “Fundação para a Ciência e Tecnologia” for the scholarship programme with the reference SFRH/BD/114764/ 2016. References BCS, I., 2007. Mining Industry Energy Bandwidth Study. In: Program, I.T. (Ed.). U.S. Department. Bearman, R.A., 2013. Step change in the context of comminution. Minerals Eng. 43–44. Bond, F.C., 1961. Crushing and Grinding Calculations. Allis-Chalmers Manufacturing Company, pp. 16. Bowman, D.J., Bearman, R.A., 2014. Coarse waste rejection through size based separation. Minerals Eng. 62, 102–110. Bradshaw, D., 2014. The role of 'process mineralogy' in improving the process performance of complex sulphide ores. Carrasco, C., Keeney, L., Walters, S.G., 2015. Development of a novel methodology to characterise preferential grade by size deportement and its operational conditions. Minerals Eng. 91, 100–107. de Bakker, J., 2014. Energy use of fine grinding in mineral processing. Metall. Mater. Tans. 8–19. Disckson, B., 2017. Exploiting machine learning in cybersecurity, https://techcrunch. com/2016/07/01/exploiting-machine-learning-in-cybersecurity/. Accessed in: April, 2019.
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