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On the selection of the coarsest size class in flotation rate characterizations

Orellana Francisca, Rivera Marcelo, Benítez Matías, Belmonte Karyn, Vinnett Luis

Physicochemical Problems of Mineral Processing

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2023

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Vol. 59, iss. 5

art. no. 176950

EN

This paper studies size-by-size batch flotation kinetics for the separation of Cu at particle sizes +75 μm, investigating the responses in the -150/+75 μm, -212/+150 μm, -300/+212 μm, -355/+300 μm and +355 μm size fractions. The kinetic results were analyzed to identify classes limited by the maximum achievable recovery or low flotation rates. Combinations of these classes were investigated, emulating the selection of the coarsest size in a kinetic study. The impact of compositing size classes was discussed, emphasizing implications in the identification of difficult-to-float components. The -212/+75 μm classes reached steady recoveries at long flotation times, whereas the -355/+212 μm classes presented sustained increasing recoveries at extended flotation times. Flotation rate distributions in the -212/+75 μm classes exhibited mound-shaped distributions, indicating low fractions of rate constants close to zero (R∞-limited case). Conversely, the -355/+212 μm classes presented reverse J-shaped distributions, with a high fraction of valuable minerals with flotation rates close to zero (rate-limited case). Combining several size classes in the definition of the coarsest size fraction in kinetic characterizations proved to hide the flotation patterns of the less massive constituents (+212 μm classes). The +75 μm and +150 μm cumulative retained classes trended towards steady recoveries, consistently leading to mounded flotation rate distributions. This study highlighted the need for reliable methodologies to select size fractions in kinetic characterizations, as their arbitrary definitions may lead to a misinterpretation of the mineral losses when compositing classes with different flotation responses.

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Artificial neural network (ANN) modelling to estimate bubble size from macroscopic image and object features

Vinnett Luis, León Roberto, Mesa Diego

Physicochemical Problems of Mineral Processing

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2023

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Vol. 59, iss. 5

art. no. 185759

EN

Bubble size measurements in aerated systems such as froth flotation cells are critical for controlling gas dispersion. Commonly, bubbles are measured by obtaining representative photographs, which are then analyzed using segmentation and identification software tools. Recent developments have focused on enhancing these segmentation tools. However, the main challenges around complex bubble cluster segmentation remain unresolved, while the tools to tackle these challenges have become increasingly complex and computationally expensive. In this work, we propose an alternative solution, circumventing the need for image segmentation and bubble identification. An Artificial Neural Network (ANN) was trained to estimate the Sauter mean bubble size (D32) based on macroscopic image features obtained with simple and inexpensive image analysis. The results showed excellent prediction accuracy, with a correlation coefficient, R, over 0.998 in the testing stage, and without bias in its error distribution. This machine learning tool paves the way for robust and fast estimation of bubble size under complex bubble images, without the need of image segmentation.

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A discussion on the limitations of image analysis for determining bubble size in industrial flotation when using algorithms successfully tested from idealized images

Vinnett Luis

Physicochemical Problems of Mineral Processing

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2023

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Vol. 59, iss. 5

art. no. 174474

EN

This paper evaluates the capacity of an automated algorithm to detect bubbles and estimate bubble size (Sauter mean diameter, D32) from images recorded in industrial flotation machines. The algorithm is previously calibrated from laboratory images. The D32 results are compared with semi-automated estimations, which are used as "ground truth". Although the automated algorithm is reliable to estimate bubble size at laboratory scale, a significant bias is observed from industrial images for D32 >3.0-4.0 mm. This uncertainty is caused by the presence of small and large bubbles in the same population, with large bubbles forming complex clusters and being observed incomplete, limited by the region of interest. Flotation columns are more prone to this condition, which hinders the estimation of Sauter diameters. The results show the need for bubble size databases that include industrial images. As several image processing tools are currently available, software calibration from ideal bubble images (synthetic or from laboratory rigs) will mostly lead to biased D32 estimations in industrial flotation machines.

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

Vinnett Luis, Pino-Muñoz Catalina A., Yianatos Juan, Díaz Francisco, Henríquez Felipe

Physicochemical Problems of Mineral Processing

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2022

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Vol. 58, iss. 5

art. no. 152420

EN

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.