Representation of Kinetics Models in Batch Flotation as Distributed First-Order Reactions

Vinnett, L.; Waters, Kristian E.

doi:10.3390/min10100913

Cited by 14 publications

(9 citation statements)

References 59 publications

(82 reference statements)

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“…( 5). (Bu et al, 2016;Vinnett and Waters 2020). Vinnett and Waters (2020) indicated that the same recovery can be obtained from second-order reaction with a single rate constant and first-order reaction with exponential.…”

Section: Kinetic Theorymentioning

confidence: 83%

“…(Bu et al, 2016;Vinnett and Waters 2020). Vinnett and Waters (2020) indicated that the same recovery can be obtained from second-order reaction with a single rate constant and first-order reaction with exponential. Besides, they reported that first-order reaction with exponential involves a fraction of floatable material with slow rate constants approaching to k = 0: 𝑅 = 5 6 0 9:; # (280 9:; #)…”

Section: Kinetic Theorymentioning

confidence: 87%

See 1 more Smart Citation

Kinetic Modelling and Optimization of Flotation Process of Electrum

Gül¹,

Aydın²

2021

Physicochem. Probl. Miner. Process.

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The investigation of flotation as an alternative method to cyanide leaching of gold ores is significant in terms of economic and environmental aspects. In this study, a gold ore sample containing 4.79 ppm Au and 7.72 ppm Ag was used. Gold and silver were observed to be present as liberated electrum or associated with or within quartz, galena, and sphalerite. Initially, five-stage rougher flotation tests were conducted, and then three-stage scavenger circuits and four-stage cleaning flotation circuits were performed in order to obtain high-content gold concentrate and decrease losses of Au and Ag in tailings. As a result of tests, the flotation concentrate assayed as 437 ppm Au and 511 ppm Ag was obtained with recoveries of 76.3% and 58.5%, respectively. This study reveals that the concentrates ready for direct smelting without any additional process can be obtained with flotation. In order to determine kinetic characteristic of electrum in the sample, the tests were conducted using firstorder model, first-order model with rectangular distribution of rate constants, second-order model and second-order model with rectangular distribution of rate constant. The second-order model was considered as most reasonable for fitting the recoveries of gold as a function of flotation time during the flotation process.

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Section: Kinetic Theorymentioning

confidence: 83%

Section: Kinetic Theorymentioning

confidence: 87%

Kinetic Modelling and Optimization of Flotation Process of Electrum

Gül¹,

Aydın²

2021

Physicochem. Probl. Miner. Process.

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“…Nevertheless, high electrolyte concent high electrical conductivity, which results in lower voltage values at the sam sity values. This leads to lower energy consumption [54]. The addition of an electrolyte to the slurry leads to an increase of the surface electric potential of the bubbles, thus promoting repulsive forces between bubbles and particles [51], however in cases of excess concentration of mineral salts during flotation, the pulp may have a suppressive effect on the recovery of some particles [52], while bubble aggregation has also been observed [50].…”

Section: Effect Of Electrolyte Concentration On Combined Flotationmentioning

confidence: 99%

Enhancing Fines Recovery by Hybrid Flotation Column and Mixed Collectors

et al. 2023

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The froth flotation technique can be considered one of the most efficient methods for the separation of minerals. Prior to utilizing any physicochemical separation method, the size of the mined ore must be decreased to facilitate the release of the valuable materials. This practice, along with the increased exploitation of ores that carry fine mineral particles caused the production of fine and ultrafine particles which are difficult to recover with classical enrichment methods, due to their different characteristics compared to coarser particles. It is established that fine and ultrafine particles are difficult to float, leading to losses of valuable minerals, mainly due to their low collision efficiency with bubbles. Moreover, fine particles require higher reagent consumption due to the fact that have a higher specific area, and finally, their flotation is limited by low kinetic energy. Flotation of fines can be enhanced by either decreasing bubble diameter or increasing their apparent size, or moreover, by enhancing the collector’s adsorption (their hydrophobic behavior) using alternative reagents (non-ionic co-collectors). In the present research, flotation experiments on a hybrid electrolytic flotation column that can produce microbubbles (−50 μm), were carried out for recovering fine magnesite (−25 μm) particles. In addition, the synergistic effect of anionic/non-ionic collectors were studied for the enhancement of fines recovery. Experimental flotation results so far designate the enhancement of fine magnesite particle recovery by approximately 8% with the addition of microbubbles. Finally, the synergistic effect of anionic/non-anionic collectors led to the improvement of flotation recovery by almost 12%.

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“…Discrete or continuous flotation rate distributions have been empirically justified by the heterogeneous kinetic responses by size (Yekeler and Sönmez, 1997;Abkhoshk et al, 2010;Bu et al, 2017a) and by other particle properties (Polat and Chander, 2000;Vinnett et al, 2021). Several studies have detailed, evaluated and compared different model structures for f(k) (Dowling et al, 1985;Polat and Chander, 2000;Ai et al, 2017;Bu et al, 2017b;Vinnett and Waters, 2020), showing their advantages with respect to single rate constants. Woodburn and Loveday (1965) studied the metallurgical performance of a continuous flotation cell in terms of f(k) and the residence time distribution h(t).…”

Section: Introductionmentioning

confidence: 99%

A sensitivity analysis of kinetic characterizations in continuous flotation circuits under moderate deviations with respect to perfect mixing

Vinnett¹,

Pino-Muñoz²,

Yianatos³

et al. 2022

Physicochem. Probl. Miner. Process.

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This paper studies the effect of moderate deviations with respect to perfect mixing on the estimated kinetic parameters in industrial flotation banks. Radioactive tracer tests and mass balance surveys were performed to characterize the mixing regimes and Cu kinetic responses. For three models (Single Rate Constant, Rectangular and Gamma), two approaches to incorporate the residence time distributions (RTD) in the kinetic characterizations of rougher banks were compared: (i) RTDs measured from the radioactive tracer tests; and (ii) pure perfect mixing in each flotation machine. The measured RTDs did not present significant bypass in the evaluated banks. In all cases, comparable model fitting was obtained with both RTD approaches, which indicates that the kinetic models add sufficient flexibility to compensate for moderate biases in the mixing regime. The studied kinetic models showed non-significant differences in the estimated maximum recoveries (R∞), mean (kmean) and median (k50) rate constants when comparing the process modelling from measured RTDs and pure perfect mixing. However, the Gamma model was more sensitive to the RTD assumption in terms of the shapes of the flotation rate distributions. From the results, kinetic characterizations focused only on model fitting, or on R∞ and kmean (or k50) estimations have low sensitivity to the assumption of perfect mixing when the RTDs present moderate deviations with respect to this regime. Special attention must be paid when characterizing floating components as the perfect mixing assumption may bias the shapes of the flotation rate distributions.

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Representation of Kinetics Models in Batch Flotation as Distributed First-Order Reactions

Cited by 14 publications

References 59 publications

Kinetic Modelling and Optimization of Flotation Process of Electrum

Kinetic Modelling and Optimization of Flotation Process of Electrum

Enhancing Fines Recovery by Hybrid Flotation Column and Mixed Collectors

A sensitivity analysis of kinetic characterizations in continuous flotation circuits under moderate deviations with respect to perfect mixing

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