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Design, Modeling, Optimization and Control of Flotation Process

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A special issue of Minerals (ISSN 2075-163X). This special issue belongs to the section "Mineral Processing and Extractive Metallurgy".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 32121

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Dr. Fardis Nakhaei

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Guest Editor

School of Chemical and Minerals Engineering, North-West University, Potchefstroom 2531, South Africa
Interests: flotation; ultra-fine particle processing, surface chemistry; coal preparation; modeling; artificial intelligent; image analysis, , nano-bubbles
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Dr. Ahmad Hassanzadeh

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Guest Editor

Department of Geoscience and Petroleum, Faculty of Engineering, Norwegian University of Science and Technology, Andersens veg 15a, 7031 Trondheim, Norway
Interests: particle-bubble interactions; flotation machines; surface and colloidal chemistries; kinetics and thermodynamics; ultrafine grinding; gold and silver leaching
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Luis A. Cisternas

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Guest Editor

Department of Chemical Engineering and Mineral Process, Universidad of Antofagasta, Antofagasta 1240000, Chile
Interests: modeling; design; optimization; uncertainty; flotation; heap leaching; tailing; seawater
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Special Issue Information

Dear Colleagues,

The ultimate goal of a flotation process is to achieve the economically optimum combination of the desired mineral grade and recovery in the final concentrate from a feed of varying composition. The industrial operation of froth flotation faces many challenges, such as sudden decreases in the recovery and grade of recovered materials. The quality of the final concentrate determines the success of the downstream processes, and achieving the optimum metallurgical performance requires proper the characterization, optimization, and control of the process. The efficiency of a flotation circuit operation relies on several factors that are pertinent to mineral nature and structure (variability of ore feed, particle size, complex mineralogy, and morphology) as well as the type of instrumentation and operational parameters (design parameters, reagents, quality of process water, air flow rate, and solid content) used, which require both advanced theoretical and practical studies. Hence, new techniques in the fields of design, modelling, optimization, and control of flotation processes have attracted a great deal of attention.

This Special Issue is dedicated to the latest findings on methodologies, applications, and case studies in the field of the flotation to improve process efficiency, reduce energy consumption, and increase the sustainability of these processes. This Special Issue provides a wide range of research and practical topics, including those related to design, simulation and instrumentation, and process control. We welcome reviews, original articles, and multidisciplinary studies including but not limited to the following topics:

Conceptual or simulation of flotation processes;
Optimization of flotation processes (single or multi-objectives, uncertainty, and sensitivity analyses);
Novel perspectives in designing flotation circuits, machinery, and the minimization of energy consumption;
Modification and improvement of flotation circuits;
Numerical modelling of flotation processes (molecular modelling, computational fluid dynamics, intelligent computation, image analysis);
Kinetic models and their scale-up in industrial cells;
Process control (data management, automation, sensors, and measurements);
Mechanical, column, and pneumatic flotation cells (Jameson, Imhoflot^TM and Reflux^TM flotation cells);
Impact of operation parameters on designing flotation cells (gas hold-up, superficial gas velocity, bubble size distribution and orifice type, etc.);
Measurement and modelling of slurry residence time in flotation cell/circuits.

Dr. Fardis Nakhaei
Dr. Ahmad Hassanzadeh
Prof. Dr. Luis A. Cisternas
Guest Editors

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Keywords

froth flotation processes
optimization tools
modelling and simulation
froth control
cell design
flotation kinetics
modification and improvement of flotation circuits
gas dispersion
RTD measurement and modelling
particle–bubble modelling
first principal modelling
experimental design
mechanical and column cells
pneumatic flotation cells
experimental design

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Published Papers (11 papers)

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Editorial

Jump to: Research

3 pages, 159 KiB

Open AccessEditorial

Editorial for Special Issue “Design, Modeling, Optimization and Control of Flotation Process”

by Fardis Nakhaei, Ahmad Hassanzadeh and Luis A. Cisternas

Minerals 2024, 14(4), 391; https://doi.org/10.3390/min14040391 - 10 Apr 2024

Viewed by 1400

Abstract

Flotation is a significant and widely used processing technique, effectively separating valuable and gangue minerals [...] Full article

(This article belongs to the Special Issue Design, Modeling, Optimization and Control of Flotation Process)

Research

Jump to: Editorial

22 pages, 5117 KiB

Open AccessArticle

Studying Flotation of Gold Microdispersions with Carrier Minerals and Pulp Aeration with a Steam–Air Mixture

by Sergei Ivanovich Evdokimov, Nikolay S. Golikov, Alexey F. Pryalukhin, Viktor V. Kondratiev, Anatolii Mishedchenko, Alexandra Vl. Kuzina, Natalia Nikolaevna Bryukhanova and Antonina I. Karlina

Minerals 2024, 14(1), 108; https://doi.org/10.3390/min14010108 - 19 Jan 2024

Cited by 9 | Viewed by 1613

Abstract

This work is aimed at obtaining new knowledge in the field of interactions of polydisperse hydrophobic surfaces in order to increase the extraction of mineral microdispersions via flotation. The effect of high velocity and the probability of aggregating fine particles with large ones are used to increase the extraction of finely dispersed gold in this work. Large particles act as carrier minerals, which are intentionally introduced into a pulp. The novelty of this work lies in the fact that a rougher concentrate is used as the carrier mineral. For this purpose, it is isolated from three parallel pulp streams by mixing the rougher concentrate, isolated from the first stream of raw materials, with an initial feed of the second stream; accordingly, the rougher concentrate of the second stream is mixed with the initial feed of the third stream, and the finished rougher concentrate is obtained. In this mode of extracting the rougher concentrate, the content of the extracted metal increases from stream to stream, which contributes to the growth in its content in the end product. Moreover, in order to supplement forces involved in the separation of minerals with surface forces of structural origin in the third flotation stream, the pulp is aerated for a short time (about 15%–25% of the total) with air bubbles filled with a heat carrier, i.e., hot water vapor. Within this accepted flotation method, the influence that the surface currents occurring in the wetting film have on its thinning and breakthrough kinetics is proposed to be in the form of a correction to a length of a liquid slip in the hydrophobic gap. The value of the correction is expressed as a fraction of the limiting thickness of the wetting film, determined by the condition of its thickness invariability when the streams are equal in an interphase gap: outflowing (due to an action of the downforce) and inflowing (Marangoni flows and a thermo-osmotic stream). Gold flotation experiments are performed on samples of gold-bearing ore obtained from two deposits with conditions that simulate a continuous process. Technological advantages of this developed scheme and a flotation mode of gold microdispersions are shown in comparison with the basic technology. The purpose of this work is to conduct comparative tests on the basic and developed technologies using samples of gold-bearing ore obtained from the Natalka and Olimpiada deposits. Through the use of the developed technology, an increase in gold extraction of 7.99% and in concentrate quality (from 5.09 to 100.3 g/t) is achieved when the yield of the concentrate decreases from 1.86 to 1.30%, which reduces the costs associated with its expensive metallurgical processing. Full article

(This article belongs to the Special Issue Design, Modeling, Optimization and Control of Flotation Process)

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22 pages, 3808 KiB

Open AccessArticle

Studying the Flotation of Gold-Bearing Ores Using Carrier Minerals

by Sergei Ivanovich Evdokimov, Nikolay S. Golikov, Denis A. Zadkov, Elena V. Voitovich, Viktor V. Kondratiev, Aleksey A. Petrovskiy, Vladimir Yu. Konyukhov and Vitaliy A. Gladkikh

Minerals 2024, 14(1), 88; https://doi.org/10.3390/min14010088 - 11 Jan 2024

Cited by 6 | Viewed by 2414

Abstract

This work is aimed at the analysis of the development of flotation technology by applying carrier minerals. Based on the concepts of continuum mechanics, a theoretical analysis of the influence of the carrier minerals (wall) on the motion of a single solid particle is provided, taking into account their hydrodynamic interaction (in the case of low Reynolds numbers). A correction was obtained in the form of a ratio of the particle size to its distance from the wall to take into account the influence of the wall on the hydrodynamic force acting on the particle. The influence of the wall is manifested through a rapid approximation of the liquid vortex flow in the gap between the solid wall and the particle to the steady-state mode, accompanied by the suppression of the transverse movement of particles. When the liquid slides along a wall-mounted gas–liquid layer with a reduced viscosity, the liquid flow increases in the interfacial gap, which can be analyzed by a dimensionless correction that includes values describing the properties of a continuous medium (dynamic viscosity) and a disperse phase (geometric particle size). The reason for the decrease in the induction time when gold grains adhere to each other is assumed to be due to the forces of hydrophobic attraction (when the grains have a mirror-smooth surface) and the sliding of the flow along the hydrophobic surface of the particles along the gas layer (when the grains have a rough surface). When polydisperse particles are aggregated, the threshold energy of the fast coagulation was established to be lower than that arising during the interaction of monodisperse particles, whose aggregation requires a large depth of the potential pit. Performing natural experiments on the ore using a rougher concentrate as a carrier material showed that the concentrate yield decreases by 20.52% rel. In the second case, the gold extraction was higher by 4.69% abs. While maintaining the achieved level of gold extraction, the double mixing of the rougher concentrate and the initial feed increased the gold content in the rougher concentrate from 4.97 to 6.29 g/t. Full article

(This article belongs to the Special Issue Design, Modeling, Optimization and Control of Flotation Process)

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21 pages, 2944 KiB

Open AccessArticle

Experimental and Modelling Study of Pt, Pd, and 2E+Au Flotation Kinetics for Platreef Ore by Exploring the Influence of Reagent Dosage Variations

by Parisa Doubra, Candice Carelse, Deshenthree Chetty and Marian Manuel

Minerals 2023, 13(10), 1350; https://doi.org/10.3390/min13101350 - 23 Oct 2023

Cited by 1 | Viewed by 1721

Abstract

This study investigates the flotation kinetics of individual platinum-group elements (PGEs) and gold, namely Pt, Pd, and 2E+Au (i.e., Pt+Pd+Au), in the context of Platreef ore flotation. Experimental tests were conducted on a Platreef ore feed using various dosages of depressants, frothers, and collectors under controlled agitation and pH conditions. The recoveries of the individual PGEs were analysed using six kinetic models, with the modified Kelsall model identified as the most suitable for accurately describing the flotation kinetics and predicting elemental recovery. Notably, the model incorporates two rate constants (k_fast and k_slow) to account for the distinct flotation behaviours of the PGEs. The results indicate that Pt has the fastest floatability, followed by Pd and 2E+Au. The modified Kelsall model demonstrates high effectiveness in predicting the recovery of these PGEs. Three empirical correlations for Pt, Pd, and 2E+Au recoveries based on the modified Kelsall model are proposed, enhancing the understanding and optimisation of PGE recovery in Platreef ore flotation. Full article

(This article belongs to the Special Issue Design, Modeling, Optimization and Control of Flotation Process)

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24 pages, 5230 KiB

Open AccessArticle

A Model of Froth Flotation with Drainage: Simulations and Comparison with Experiments

by Fernando Betancourt, Raimund Bürger, Stefan Diehl, Leopoldo Gutiérrez, M. Carmen Martí and Yolanda Vásquez

Minerals 2023, 13(3), 344; https://doi.org/10.3390/min13030344 - 28 Feb 2023

Cited by 1 | Viewed by 2662

Abstract

The operation of a froth flotation column can be described by a nonlinear convection–diffusion partial differential equation that incorporates the solids–flux and drift–flux theories as well as a model of foam drainage. The resulting model predicts the bubble and (gangue) particle volume fractions as functions of height and time. The steady-state (time-independent) version of the model defines so-called operating charts that map conditions on the gas and pulp feed rates that allow for operation with a stationary froth layer. Operating charts for a suitably adapted version of the model are compared with experimental results obtained with a laboratory flotation column. Experiments were conducted with a two-phase liquid–bubble flow. The results indicate good agreement between the predicted and measured conditions for steady states. Numerical simulations for transient operation, in part for the addition of solid particles, are presented. Full article

(This article belongs to the Special Issue Design, Modeling, Optimization and Control of Flotation Process)

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12 pages, 3320 KiB

Open AccessArticle

The Correlation between Macroscopic Image and Object Properties with Bubble Size in Flotation

by Luis Vinnett, Iván Cornejo, Juan Yianatos, Claudio Acuña, Benjamín Urriola, Camila Guajardo and Alex Esteban

Minerals 2022, 12(12), 1528; https://doi.org/10.3390/min12121528 - 29 Nov 2022

Cited by 5 | Viewed by 1943

Abstract

This paper studies the correlation between different macroscopic features of image regions and object properties with the Sauter diameter (D₃₂) of bubble size in flotation. Bubbles were sampled from the collection zone of a two-dimensional flotation cell using a McGill Bubble Size Analyzer, and photographed bubbles were processed using image analysis. The Sauter mean diameters were obtained under different experimental conditions using a semiautomated methodology, in which non-identifiable bubbles were manually characterized to estimate the bubble size distribution. For the same processed images, different image properties from their binary representation were studied in terms of their correlation with D₃₂. The median and variability of the shadow percentage, aspect ratio, power spectral density, perimeter, equivalent diameters, solidity, and circularity, among other image or object properties, were studied. These properties were then related to the measured D₃₂ values, from which four predictors were chosen to obtain a multivariable model that adequately described the Sauter diameter. After removing abnormal gas dispersion conditions, the multivariable linear model was able to represent D₃₂ values (99 datasets) for superficial gas rates in the range of 0.4–2.5 cm/s, for four types of frothers and surfactant concentrations ranging from 0 to 32 ppm. The model was tested with 72 independent datasets, showing the generalizability of the results. Thus, the approach proved to be applicable at the laboratory scale for D₃₂ = 1.3–6.7 mm. Full article

(This article belongs to the Special Issue Design, Modeling, Optimization and Control of Flotation Process)

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50 pages, 34019 KiB

Open AccessArticle

Comparison of Fuzzy and Neural Network Computing Techniques for Performance Prediction of an Industrial Copper Flotation Circuit

by Ivana Jovanović, Fardis Nakhaei, Daniel Kržanović, Vesna Conić and Daniela Urošević

Minerals 2022, 12(12), 1493; https://doi.org/10.3390/min12121493 - 23 Nov 2022

Cited by 3 | Viewed by 2489

Abstract

This paper presents the development and validation of five different soft computing methods for flotation performance prediction: (1) two models based on fuzzy logic (Mamdani and Takagi-Sugeno fuzzy inference system) and (2) three models based on artificial neural networks. Copper content in the ore feed, collector dosage in the rougher and the scavenger flotation circuits, slurry pH in the rougher flotation circuit and frother consumption were selected as input parameters to estimate the copper grade and recovery of final concentrate, as well as the copper content in the final tailings of the flotation plant. The training and evaluation of the proposed models were performed on the basis of real process data collected by the multiannual monitoring of industrial flotation plant operation in “Veliki Krivelj Mine”. The results showed that the proposed soft computing-based models well describe the behavior of the industrial flotation plant in a wide range of circumstances. Among the proposed algorithms, artificial neural networks gave the most accurate predictions for the final copper concentrate grade and recovery (R² = 0.98 and R² = 0.99, respectively) and copper content in final tailings (R² = 0.87). At some points, fuzzy logic models are almost equally efficient, but artificial neural networks had lower values for all error functions. Full article

(This article belongs to the Special Issue Design, Modeling, Optimization and Control of Flotation Process)

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24 pages, 5874 KiB

Open AccessArticle

Prediction of Sulfur Removal from Iron Concentrate Using Column Flotation Froth Features: Comparison of k-Means Clustering, Regression, Backpropagation Neural Network, and Convolutional Neural Network

by Fardis Nakhaei, Samira Rahimi and Mohammadbagher Fathi

Minerals 2022, 12(11), 1434; https://doi.org/10.3390/min12111434 - 12 Nov 2022

Cited by 6 | Viewed by 2578

Abstract

Froth feature extraction plays a significant role in the monitoring and control of the flotation process. Image-based soft sensors have received a great deal of interest in the flotation process due to their low-cost and non-intrusive properties. This study proposes data-driven soft sensor models based on froth images to predict the key performance indicators of the flotation process. The ability of multiple linear regression (MLR), the backpropagation neural network (BPNN), the k-means clustering algorithm, and the convolutional neural network (CNN) to predict the amount of sulfur removal from iron ore concentrate in the column flotation process was examined. A total of 99 experimental results were used to develop the predictive models. Extracted froth features including color, bubble shape and size, texture, stability, and velocity were used to train the traditional predictive models, whereas in the CNN model the froth images were directly fed into the model. The results comparison indicated that the three-layered feedforward NN model (17-10-1 topology) and CNN model provided better predictions than the MLR and k-means algorithm. The BPNN model displayed a correlation coefficient of 0.97 and a root mean square error of 4.84% between the actual data and network output for both training and the testing datasets. The error percentages of the CNN, BPNN, MLR and k-means models were 10, 11, 15 and 18%, respectively. This study can become a key technical support for the application of intelligent models in the control of the operational variables for the flotation process used to desulfurize iron concentrate. Full article

(This article belongs to the Special Issue Design, Modeling, Optimization and Control of Flotation Process)

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17 pages, 7315 KiB

Open AccessArticle

An Improved Python-Based Image Processing Algorithm for Flotation Foam Analysis

by Wenkang Zhang, Dan Liu, Chunjing Wang, Ruitao Liu, Daqian Wang, Longzhou Yu and Shuming Wen

Minerals 2022, 12(9), 1126; https://doi.org/10.3390/min12091126 - 4 Sep 2022

Cited by 8 | Viewed by 3701

Abstract

For industrial flotation foam image processing, accurate bubble size measurement and feature extraction are very important to optimize the flotation process and to improve the recovery of mineral resources. This paper presents an improved algorithm to investigate mineral flotation foam image segmentation for mineral processing. Several libraries implemented for the Python programming language are used for image enhancement and compensation, quantitative analysis of factors influencing the image segmentation accuracy, and suggestions for improvement of the flotation foam image processing. The bubble characteristics-size and morphology-and the influence of the flotation conditions on the flotation foam image are analyzed. A Python implementation of the Retinex image compensation method-region-adaptive and multiscale-is proposed to address known issues of uneven illumination and shadows affecting flotation foam images, thereby improving brightness uniformity. Finally, an improved version of the watershed segmentation algorithm included in the Python Open Source Computer Vision library is used for segmentation analysis. The accuracy of the flotation foam image segmentation is 3.3% higher than for the standard watershed algorithm and the segmentation time is 9.9% shorter. Full article

(This article belongs to the Special Issue Design, Modeling, Optimization and Control of Flotation Process)

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26 pages, 8343 KiB

Open AccessFeature PaperArticle

Hybrid Serving of DOE and RNN-Based Methods to Optimize and Simulate a Copper Flotation Circuit

by Alireza Gholami, Meysam Movahedifar, Hamid Khoshdast and Ahmad Hassanzadeh

Minerals 2022, 12(7), 857; https://doi.org/10.3390/min12070857 - 5 Jul 2022

Cited by 4 | Viewed by 2491

Abstract

Prediction of metallurgical responses during the flotation process is extremely vital to increase the process efficiency using a proper modeling approach. In this study, two new variants of the recurrent neural network (RNN) method were used to predict the copper ore flotation indices, i.e., grade and recovery within different operating conditions. The model input parameters including pulp pH and solid content as well as frother and collector dosages were first analysed and then optimized using a two-step factorial approach. The statistical analysis showed a reliable correlation between operating parameters and copper grade and recovery with coefficients of 99.86% and 94.50%, respectively. The main effect plots indicated that pulp pH and solid content positively affect copper grade while increasing the frother and collector dosages negatively influenced the quality of the final concentrate. Despite the same effect from pulp pH, reverse effects from other variables were observed for copper recovery. Process optimization revealed that maximum copper recovery of 44.39% with a grade of 11.48% could be achieved under the optimal condition as pulp pH of 10, solid content of 20%, and frother and collector concentrations of 25 g/t and 9.9 g/t, respectively. Then, the predictive efficiency of long short-term memory (LSTM) and gated recurrent unit (GRU) networks with proper structure were evaluated using mean square error (MSE), root mean square error (RMSE), mean absolute percentage error (MAPE), and correlation coefficient (R²). The simulation results showed that the LSTM network with higher R² of 0.963 and 0.934 for copper grade and recovery, respectively, was more effective than the GRU algorithm with the corresponding values of 0.956 and 0.919, respectively. The results show that the LSTM model could be useful in predicting the copper flotation behaviour in response to changes in the operating parameters. Full article

(This article belongs to the Special Issue Design, Modeling, Optimization and Control of Flotation Process)

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23 pages, 8048 KiB

Open AccessArticle

Control Structure Design Using Global Sensitivity Analysis for Mineral Processes under Uncertainties

by Oscar Mamani-Quiñonez, Luis A. Cisternas, Teresa Lopez-Arenas and Freddy A. Lucay

Minerals 2022, 12(6), 736; https://doi.org/10.3390/min12060736 - 8 Jun 2022

Cited by 3 | Viewed by 2810

Abstract

Multiple-input and multiple-output (MIMO) systems can be found in many industrial processes, including mining processes. In practice, these systems are difficult to control due to the interactions of their input variables and the inherent uncertainty of industrial processes. Depending on the interactions in the MIMO process, different control strategies can be implemented to achieve the desired performance. Among these strategies is the use of a decentralized structure that considers several subsystems and for which a SISO controller can be designed. In this study, a methodology based on global sensitivity analysis (GSA) to design decentralized control structures for industrial processes under uncertainty is presented. GSA has not yet been applied for this purpose in process control; it allows us to understand the dynamic behavior of systems under uncertainty in a broad value range, unlike approaches proposed in the literature. The proposed GSA is based on the Sobol method, which provides sensitivity indices used as interaction measures to establish the input–output pairing for MIMO systems. Two case studies based on a semi-autogenous grinding (SAG) mill and a solvent extraction (SX) plant are presented to demonstrate the applicability of the proposed methodology. The results indicate that the methodology allows the design of 2 × 2 and 3 × 3 decentralized control structures for the SAG mill and SX plant, respectively, which exhibit good performance compared to MPC. For example, for the SAG mill, the determined pairings were fresh ore flux/fraction of mill filling and power consumption/percentage of critical speed. Full article

(This article belongs to the Special Issue Design, Modeling, Optimization and Control of Flotation Process)

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