Special Issue "Modeling, Design and Optimization of Multiphase Systems in Minerals Processing, Volume II"

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 (19 November 2021) | Viewed by 14110

Special Issue Editors

Prof. Dr. Luis A. Cisternas
E-Mail Website
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
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Freddy A. Lucay
E-Mail Website1 Website2
Guest Editor
School of Chemical Engineering, Pontificia Universidad Católica de Valparaíso, 2340000 Valparíso, Chile
Interests: modeling and simulation; process design; uncertainty quantification; optimization algorithm design; flotation; grinding; computational intelligence

Special Issue Information

After hundreds of years of the exploitation of mining resources, the demand for these resources has continued to increase. The demand will be maintained and increase in the future to face the significant challenges of engineering and society. To meet these challenges, tools are needed to help understand, improve, and facilitate more effective solutions. The use of modeling at all levels and types is undoubtedly one of those tools. A common feature in the processing of mining resources is the presence of multiphase systems, which are defined as systems in which two or more different phases (i.e., gas, liquid, or solid) are present. A series of phenomena associated with processes such as flotation, grinding, magnetic separation, and thickening are related to multiphase systems. With these antecedents, we have developed this Special Issue dedicated to the modeling, design, and optimization of multiphase systems in mineral processing to promote discussion, analysis, and cooperation between research groups. The Special Issue welcomes review articles, regular articles, and short notes that cover different methodologies for modeling, design, optimization, and analysis in problems of adsorption, leaching, flotation, and magnetic separation, among others. Tools for the study of multiphase systems at different time and size scales are also welcome such as molecular modeling, computational fluid dynamics, response surface methodology, artificial intelligence, multiscale modeling, uncertainty and global sensitivity analyses, and optimization.

Keywords

  • molecular modeling
  • intelligent computation
  • computational fluid dynamics
  • response surface methodology
  • optimization
  • design
  • solid–liquid systems
  • liquid–liquid systems
  • solid–gas systems
  • solid–liquid–gas systems
  • uncertainty

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Published Papers (11 papers)

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Editorial

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Editorial
Editorial for Special Issue “Modeling, Design, and Optimization of Multiphase Systems in Minerals Processing, Volume II”
Minerals 2022, 12(10), 1309; https://doi.org/10.3390/min12101309 - 17 Oct 2022
Viewed by 384
Abstract
The manuscripts published in the 2019 Special Issue “Modeling, Design, and Optimization of Multiphase Systems in Minerals Processing” [...] Full article

Research

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Article
Response Surface Methodology for Copper Flotation Optimization in Saline Systems
Minerals 2022, 12(9), 1131; https://doi.org/10.3390/min12091131 - 07 Sep 2022
Cited by 1 | Viewed by 781
Abstract
Response surface methodology (RSM) is one of the most effective tools for optimizing processes, and it has been used in conjunction with the Analysis of Variance (ANOVA) test to establish the effect of input factors on output factors. However, when this methodology is [...] Read more.
Response surface methodology (RSM) is one of the most effective tools for optimizing processes, and it has been used in conjunction with the Analysis of Variance (ANOVA) test to establish the effect of input factors on output factors. However, when this methodology is used in mineral flotation, its polynomial model usually performs poorly. An alternative is to use artificial neural networks (ANNs) in such situations. Within this context, the ANOVA test is not the best option for these model types; moreover, it requires statistical assumptions that are difficult to satisfy in flotation. This work proposes replacing the polynomial model of the RSM with ANNs and the Sobol methods to determine the influential input factors instead of the ANOVA test. This proposal is applied to two porphyry copper ores with a high content of pyrite, clay, and dilution media. In addition, this study shows how other computational intelligence techniques, such as swarm intelligence, can be incorporated into this type of problem to improve the learning process of ANNs. The results gave an adjustment of over 0.98 for R2 using ANNs, in comparison to values of around 0.5 when the polynomial model of RSM was utilized. On the other hand, the application of Global Sensitivity Analysis (GSA) identified the aeration rate and P80 size as the most influential variables in copper recovery under the conditions studied. Additionally, we identified significant interactions that affect the recovery of copper, with the interactions between the aeration rate, frother concentration, and P80 size being the most important. Full article
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Article
Accelerating Global Sensitivity Analysis via Supervised Machine Learning Tools: Case Studies for Mineral Processing Models
Minerals 2022, 12(6), 750; https://doi.org/10.3390/min12060750 - 14 Jun 2022
Cited by 2 | Viewed by 781
Abstract
Global sensitivity analysis (GSA) is a fundamental tool for identifying input variables that determine the behavior of the mathematical models under uncertainty. Among the methods proposed to perform GSA, those based on the Sobol method are highlighted because of their versatility and robustness; [...] Read more.
Global sensitivity analysis (GSA) is a fundamental tool for identifying input variables that determine the behavior of the mathematical models under uncertainty. Among the methods proposed to perform GSA, those based on the Sobol method are highlighted because of their versatility and robustness; however, applications using complex models are impractical owing to their significant processing time. This research proposes a methodology to accelerate GSA via surrogate models based on the modern design of experiments and supervised machine learning (SML) tools. Three case studies based on an SAG mill and cell bank are presented to illustrate the applicability of the proposed procedure. The first two consider batch training for SML tools included in the Python and R programming languages, and the third considers online sequential (OS) training for an extreme learning machine (ELM). The results reveal significant computational gains from the methodology proposed. In addition, GSA enables the quantification of the impact of critical input variables on metallurgical process performance, such as ore hardness, ore size, and superficial air velocity, which has only been reported in the literature from an experimental standpoint. Finally, GSA-OS-ELM opens the door to estimating online sensitivity indices for the equipment used in mineral processing. Full article
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Article
Simulation Algorithm for Water Elutriators: Model Calibration with Plant Data and Operational Simulations
Minerals 2022, 12(3), 316; https://doi.org/10.3390/min12030316 - 01 Mar 2022
Cited by 1 | Viewed by 1135
Abstract
A dynamic simulation algorithm based on 1-D transient convection/diffusion transport per particle size class is proposed to simulate a hydraulic classifier operated to selectively remove quartz from an iron oxide concentrate produced by processing the ore from an iron ore mine in northeastern [...] Read more.
A dynamic simulation algorithm based on 1-D transient convection/diffusion transport per particle size class is proposed to simulate a hydraulic classifier operated to selectively remove quartz from an iron oxide concentrate produced by processing the ore from an iron ore mine in northeastern Canada. The calibrated model is used to simulate the operation of dense bed hydraulic classifiers of different sizes and/or under different operating conditions. The simulator predicts the behavior and characteristics of the pulp at different depths within the classifier as a function of time. The simulator is validated by confronting the simulation results to experimental data obtained from sampling industrial and laboratory classifiers. The simulator is then used to assess the role of the fluidization or teeter water and of bed density on the quality of the produced separation of quartz from the valuable iron oxide of the processed ore. The knowledge acquired in the noise-free environment of simulation provides clues on the way to manipulate the hydraulic classifier operating variables in a process control strategy for an industrial scale unit. Full article
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Communication
Reducing the Dimensions of the Stochastic Programming Problems of Metallurgical Design Procedures
Minerals 2021, 11(12), 1302; https://doi.org/10.3390/min11121302 - 23 Nov 2021
Cited by 1 | Viewed by 687
Abstract
Process design procedures under uncertainty result in stochastic optimization problems whose resolution is complex due to the large uncertainty space, which hinders the application of optimization approaches, as well as the establishment of relationships between input and output variables. On the other hand, [...] Read more.
Process design procedures under uncertainty result in stochastic optimization problems whose resolution is complex due to the large uncertainty space, which hinders the application of optimization approaches, as well as the establishment of relationships between input and output variables. On the other hand, supervised machine learning (SML) offers tools with which to develop surrogate models, which are computationally inexpensive and efficient. This paper proposes a procedure based on modern design of experiments, deterministic optimization, SML tools, and global sensitivity analysis (GSA) to reduce the size of the uncertainty space for stochastic optimization problems. The proposal is illustrated with a case study based on the stochastic design of flotation plants. The results reveal that surrogate models of stochastic formulation enable the prediction of the structure, profitability parameters, and metallurgical parameters of designed flotation plants, as well as reducing the size of the uncertainty space via GSA and, consequently, establishing relationships between the input and output variables of the stochastic formulation. Full article
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Article
Incorporation of Geometallurgical Input into Gold Mining System Simulation to Control Cyanide Consumption
Minerals 2021, 11(9), 1023; https://doi.org/10.3390/min11091023 - 20 Sep 2021
Cited by 4 | Viewed by 1120
Abstract
The Alhué deposit (Melipilla, Chile) is an example of a hydrothermal Au-Ag-Zn(-Pb) vein system hosted within the volcanic rocks of the Las Chilcas Formation. The dominant ore minerals observed are free electrum and native gold associated with silver sulfosalts, and with magnetite and [...] Read more.
The Alhué deposit (Melipilla, Chile) is an example of a hydrothermal Au-Ag-Zn(-Pb) vein system hosted within the volcanic rocks of the Las Chilcas Formation. The dominant ore minerals observed are free electrum and native gold associated with silver sulfosalts, and with magnetite and base metal sulphides, including pyrite +/− sphalerite-galena-chalcopyrite. The alteration assemblage in the veins mainly consists of quartz epidote-chlorite-actinolite with lesser smectite, amphibole, and calcite-kaolinite-garnet. Mineralized veins also contain variable amounts of base metals, some of which (e.g., copper and iron) are considered harmful to the extraction of precious metals. Iron and especially copper minerals are known cyanide consumers; ore type classification schemes that do not consider the detrimental effects of such mineralogy or process elements can ultimately result in metal losses from ore feed restrictions, as well as spikes in cyanide consumption and higher operating costs. Mineralogical and geological variation can nonetheless be managed by applying alternating modes of operation as demonstrated in this paper; the decision to switch between modes is governed by current and forecasted stockpile levels feeding into the process. Simulations based on experiences at the Alhué deposit are provided that demonstrate the importance of standardized operational modes and their potential impact on cyanide consumption control. Full article
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Article
Experimental Uncertainty Analysis for the Particle Size Distribution for Better Understanding of Batch Grinding Process
Minerals 2021, 11(8), 862; https://doi.org/10.3390/min11080862 - 10 Aug 2021
Cited by 2 | Viewed by 1087
Abstract
Uncertainty in industrial processes is very common, but it is particularly high in the grinding process (GP), due to the set of interacting operating/design parameters. This uncertainty can be evaluated in different ways, but, without a doubt, one of the most important parameters [...] Read more.
Uncertainty in industrial processes is very common, but it is particularly high in the grinding process (GP), due to the set of interacting operating/design parameters. This uncertainty can be evaluated in different ways, but, without a doubt, one of the most important parameters that characterise all GPs is the particle size distribution (PSD). However, is the PSD a good way to quantify the uncertainty in the milling process? This is the question we attempt to answer in this paper. To do so, we use 10 experimental grinding repetitions, 3 grinding times, and 14 Tyler meshes (more than 400 experimental results). The most relevant results were compared for the weight percentage for each size (WPES), cumulative weight undersize (CWU), or the use of particle size distribution models (PSDM), in terms of continuous changes in statistical parameters in WPES for different grinding times. The probability distribution was found to be changeable when reporting the results of WPES/CWU/PSDM, we detected the over-/under-estimation of uncertainty when using WPES/CWU, and variations in the relationships between sizes were observed when using WPES/CWU. Finally, our conclusion was that the way in which the data are analysed is not trivial, due to the possible deviations that may occur in the uncertainty process. Full article
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Article
Toward the Operability of Flotation Systems under Uncertainty
Minerals 2021, 11(6), 646; https://doi.org/10.3390/min11060646 - 18 Jun 2021
Cited by 1 | Viewed by 1223
Abstract
The purpose of this work was to analyze the requirements for the operational feasibility of flotation systems as well as the effects of the selection of flotation equipment and metal price uncertainty. A procedure based on mathematical optimization and uncertainty analysis was implemented [...] Read more.
The purpose of this work was to analyze the requirements for the operational feasibility of flotation systems as well as the effects of the selection of flotation equipment and metal price uncertainty. A procedure based on mathematical optimization and uncertainty analysis was implemented to achieve this aim. The optimization included flotation and grinding stages operating under uncertainty, whereas the uncertainty analysis considered the Monte Carlo method. The results obtained indicate a small number of optimal flotation structures from the economic point of view. Considering the relationship between the economic performance and metallurgical parameters, we established that these structures exhibited favorable conditions for operating under uncertainty. Such conditions were proportional to the percentages representing each structure in the optimal set; i.e., a higher percentage of a structure implied a greater capacity to face operational and metal price changes. The set of optimal structures included configurations implementing cell banks, flotation columns, or both, indicating the influence of the flotation equipment type on the optimal structures. We also established the influence of metal price on the number of optimal structures. Therefore, the results obtained allowed us to separate the design of the flotation systems into two stages: first, a set of optimal structures exhibiting favorable conditions for facing uncertainty is determined; second, the optimal operation is established via resilience/flexibility approaches after the previous determination of the equipment design parameters. Full article
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Article
CFD Modeling and Simulation of the Hydrodynamics Characteristics of Coarse Coal Particles in a 3D Liquid-Solid Fluidized Bed
Minerals 2021, 11(6), 569; https://doi.org/10.3390/min11060569 - 27 May 2021
Cited by 6 | Viewed by 1235
Abstract
In this study, a Eulerian-Eulerian liquid-solid two-phase flow model combined with kinetic theory of granular flow was established to study the hydrodynamic characteristics and fluidization behaviors of coarse coal particles in a 3D liquid-solid fluidized bed. First, grid independence analysis was conducted to [...] Read more.
In this study, a Eulerian-Eulerian liquid-solid two-phase flow model combined with kinetic theory of granular flow was established to study the hydrodynamic characteristics and fluidization behaviors of coarse coal particles in a 3D liquid-solid fluidized bed. First, grid independence analysis was conducted to select the appropriate grid model parameters. Then, the developed computational fluid dynamics (CFD) model was validated by comparing the experimental data and simulation results in terms of the expansion degree of low-density fine particles and high-density coarse particles at different superficial liquid velocities. The simulation results agreed well with the experimental data, thus validating the proposed CFD mathematical model. The effects of particle size and particle density on the homogeneous or heterogeneous fluidization behaviors were investigated. The simulation results indicate that low-density fine particles are easily fluidized, exhibiting a certain range of homogeneous expansion behaviors. For the large and heavy particles, inhomogeneity may occur throughout the bed, including water voids and velocity fluctuations. Full article
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Article
Milling Studies in an Impact Crusher I: Kinetics Modelling Based on Population Balance Modelling
Minerals 2021, 11(5), 470; https://doi.org/10.3390/min11050470 - 30 Apr 2021
Cited by 2 | Viewed by 1387
Abstract
A number of experiments were conducted on a laboratory batch impact crusher to investigate the effects of particle size and impeller speed on grinding rate and product size distribution. The experiments involved feeding a fixed mass of particles through a funnel into the [...] Read more.
A number of experiments were conducted on a laboratory batch impact crusher to investigate the effects of particle size and impeller speed on grinding rate and product size distribution. The experiments involved feeding a fixed mass of particles through a funnel into the crusher up to four times, and monitoring the grinding achieved with each pass. The duration of each pass was approximately 20 s; thus, this amounted to a total time of 1 min and 20 s of grinding for four passes. The population balance model (PBM) was then used to describe the breakage process, and its effectiveness as a tool for describing the breakage process in the vertical impact crusher is assessed. It was observed that low impeller speeds require longer crushing time to break the particles significantly whilst for higher speeds, longer crushing time is not desirable as grinding rate sharply decreases as the crushing time increases, hence the process becomes inefficient. Results also showed that larger particle sizes require shorter breakage time whilst smaller feed particles require longer breakage time. Full article
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Article
Scale-Up of Decanter Centrifuges for the Particle Separation and Mechanical Dewatering in the Minerals Processing Industry by Means of a Numerical Process Model
Minerals 2021, 11(2), 229; https://doi.org/10.3390/min11020229 - 23 Feb 2021
Cited by 4 | Viewed by 3059
Abstract
Decanter centrifuges are frequently used for thickening, dewatering, classification, or degritting in the mining industry and various other sectors. Their use in an industrial process chain requires a sufficiently accurate prediction of the product and the machine behaviour. For this purpose, experiments on [...] Read more.
Decanter centrifuges are frequently used for thickening, dewatering, classification, or degritting in the mining industry and various other sectors. Their use in an industrial process chain requires a sufficiently accurate prediction of the product and the machine behaviour. For this purpose, experiments on a smaller pilot-scale are carried out for scale-up of a decanter centrifuge, which is usually a major challenge. Predicting the process behaviour of decanter centrifuges from laboratory tests is rather difficult. Basically, there are two common ways of scale-up: First, via analytical methods and the law of similarity, which often requires an enormous experimental effort. Second, using numerical models, which demands a mathematically and physically precise description of the multiple processes running simultaneously in such machines. This article provides an overview of both methods for scale-up of a decanter centrifuge. The concept of a previous developed numerical approach is introduced. Pros and cons of both scale-up methods are compared and further discussed. Experiments on lab-scale, pilot-scale, and industrial-scale decanter centrifuges with two different finely dispersed calcium carbonate water suspensions were carried out and simulations were done to investigate and prove the scale-up capability and transferability of the numerical approach. Full article
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