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This research aims to analyze the behavior of bubble size distribution in the HydroFloat® with seawater and tap water. The study characterized bubble size in a two-phase gas–water system in a fluidized-bed flotation cell. The impact of seawater was compared to tap water using two frothers, MIBC and polyglycol F507. The experimental design was used to investigate the influence of various parameters such as superficial air velocity, superficial liquid velocity, frother concentration, and seawater concentration on bubble size. The results indicate that the critical coalescence concentration followed the order of MIBC > F507. Bubble size decreases with increasing superficial liquid velocity, while the superficial gas velocity and frother/seawater concentration have the opposite effect. ANOVA results reveal that all linear factors are significant, the quadratic terms of the frother and seawater concentrations are significant, and the interaction term for the superficial air velocity–superficial liquid velocity is nonsignificant for bubble size. Global sensitivity analysis demonstrates that the variables significantly affecting bubble size are frother concentration and seawater concentration, followed by superficial water velocity. The superficial gas velocity has minimal impact on bubble size under the conditions studied.

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

The manuscripts published in the 2019 Special Issue “Modeling, Design, and Optimization of Multiphase Systems in Minerals Processing” [...]

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.

One of the main challenges of seawater desalination is a large volume of waste brine production that is commonly discharged into the sea and may threaten the marine ecosystem. This is critical in regions where conventional water resources are scarce and desalinated seawater is an alternative to meet water demand. Especially in regions where the mining industry is a key player in the economic development. The novelty of this research consists in the determination of the potential use of waste brine, discharged from the reverse osmosis process, as a source of industrial water in copper mining industry. To enable the waste brine applicability, there should be reduced calcium and magnesium ions concentration for improving copper recovery in the froth flotation process. The flotation tests were conducted in a batch cell with synthetic minerals composed of chalcopyrite, kaolinite, and quartz using different water qualities. The results showed that treated waste brine significantly improved copper recovery compared to untreated waste brine and seawater. Similar copper recovery was achieved when flotation test was performed with tap water and treated waste brine. Therefore, treated waste brine could provide a suitable water quality required in the froth flotation process as an alternative non-conventional water resource.

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.

Comminution is the stage with the largest energy consumption in the mining process. Therefore, several pre-treatments have been proposed to reduce the energy requirements of this stage. This work analyzed the effect of a heating pre-treatment on the Bond index. A conventional heating pre-treatment was applied to a Chilean copper ore. The ore was heated to temperatures from 300 to 600 °C using a conventional furnace, resulting in a reduction of 19% in the Bond work index. Due to the pre-treatment, the mineral cracked in several areas. Microfracture and composition analyses of these areas confirmed that crack generation in the ore is due to the thermal stress produced by the pre-treatment. The fracture analysis explains the reduction in the Bond work index, since crack generation started at similar temperatures to those at which the reduction in the Bond work index was observed. In addition, the analysis also shows that micro-cracks occur between and through different phases, which may have an impact on mineral liberation. These results also show that, under a moderate high temperature, an important reduction in energy consumption can be obtained.

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.

In this study, the potential of copper tailing deposits in Chile for the sequestration of carbon dioxide (CO2) via ex-situ mineral carbonation integrating the recovery of valuable metals was assessed. An inventory of tailing deposits and CO2 sources existing in Chile was constructed to determine the most suitable site for the installation of a future mineral carbonation plant and to evaluate the technical, economic, and environmental feasibility of CO2 capture, separation, and transport from the source to the mineral carbonation plant. The data of the inventory of tailings deposits in Chile were obtained from the National Service of Geology and Mining. For the thermoelectric plants installed in Chile, data of energy production were obtained from the Energy National Commission. Through the use of the technique for order preference by similarity to ideal solution (TOPSIS) method and sensitivity analysis, the optimum location in the region of Antofagasta to install a mineral carbonation plant was identified. In addition, the results show that in the region of Antofagasta five tailing deposits have the potential to sequester between 66 to 99 Mt of CO2. Meanwhile, thermoelectric plants in 2018 produced about 9.4 Mt of CO2 that is available to be sequestered, with a maximum generation potential of 21.9 Mt of CO2eq per year. The methodology and the study presented can be considered as a preliminary study to identify tailings that require further analysis.

Modeling the global markets is complicated due to the existence of uncertainty in the information available. In addition, the lithium supply chain presents a complex network due to interconnections that it presents and the interdependencies among its elements. This complex supply chain has one large market, electric vehicles (EVs). EV production is increasing the global demand for lithium; in terms of the lithium supply chain, an EV requires lithium-ion batteries, and lithium-ion batteries require lithium carbonate and lithium hydroxide. Realistically, the mass balance in the global lithium supply chain involves more elements and more markets, and together with the assortment of databases in the literature, make the modeling through deterministic models difficult. Modeling the global supply chain under uncertainty could facilitate an assessment of the lithium supply chain between production and demand, and therefore could help to determine the distribution of materials for identifying the variables with the highest importance in an undersupply scenario. In the literature, deterministic models are commonly used to model the lithium supply chain but do not simultaneously consider the variation of data among databases for the lithium supply chain. This study performs stochastic modeling of the lithium supply chain by combining a material flow analysis with an uncertainty analysis and global sensitivity analysis. The combination of these methods evaluates an undersupply scenario. The stochastic model simulations allow a comparison between the known demand and the supply calculated under uncertainty, in order to identify the most important variables affecting lithium distribution. The dynamic simulations show that the most probable scenario is one where supply does not cover the increasing demand, and the stochastic modeling classifies the variables by their importance and sensibility. In conclusion, the most important variables in a scenario of EV undersupply are the lithium hydroxide produced from lithium carbonate, the lithium hydroxide produced from solid rock, and the production of traditional batteries. The global sensitivity analysis indicates that the critical variables which affect the uncertainty in EV production change with time.

The combined use of the Radial Basis Function Network (RBFN) model with pretreated seawater by biomineralization (BSw) was investigated as an approach to improve copper tailings flocculation for mining purposes. The RBFN was used to set the optimal ranges of Ca2+ and Mg2+ concentration at different Ph in artificial seawater to optimize the performance of the mine tailings sedimentation process. The RBFN was developed by considering Ca2+ and Mg2+ concentration as well as pH as input variables, and mine tailings settling rate (Sr) and residual water turbidity (T) as output variables. The optimal ranges of Ca2+ and Mg2+ concentration were found, respectively: (i) 169–338 and 0–130 mg·L−1 at pH 9.3; (ii) 0–21 and 400–741 mg·L–1 at pH 10.5; (iii) 377–418 and 703–849 mg·L−1 at pH 11.5. The settling performance predicted by the RBFN was compared with that measured in raw seawater (Sw), chemically pretreated seawater (CHSw), BSw, and tap water (Tw). The results highlighted that the RBFN model is greatly useful to predict the settling performance in CHSw. On the other hand, the highest Sr values (i.e., 5.4, 5.7, and 5.4 m·h–1) were reached independently of pH when BSw was used as a separation medium for the sedimentation process.

The exploitation of mining resources has been fundamental for the development of humanity since before industrialization [...]

Multiphase systems are important in minerals processing, and usually include solid–solid and solid–fluid systems, such as in wet grinding, flotation, dewatering, and magnetic separation, among several other unit operations. In this paper, the current trends in the process system engineering tasks of modeling, design, and optimization in multiphase systems, are analyzed. Different scales of size and time are included, and therefore, the analysis includes modeling at the molecular level (molecular dynamic modeling) and unit operation level (e.g., computational fluid dynamic, CFD), and the application of optimization for the design of a plant. New strategies for the modeling, design, and optimization of multiphase systems are also included, with a strong focus on the application of artificial intelligence (AI) and the combination of experimentation and modeling with response surface methodology (RSM). The integration of different modeling techniques such as CFD with discrete element simulation (DEM) and response surface methodology (RSM) with artificial neural networks (ANN) is included. The paper finishes with tools to study the uncertainty, both epistemic and stochastic, based on uncertainty and global sensitivity analyses, which is present in all mineral processing operations. It is shown that all of these areas are very active and can help in the understanding, operation, design, and optimization of mineral processing that involves multiphase systems. Future needs, such as meso-scale modeling, are highlighted.

In mineral processing, the common requirement for progressively finer milling due to the decreasing of ore grades implies the need for more challenging water recovery conditions in thickeners. Several mining operations exist in arid areas, where water recovery becomes critical. The present paper explores the process of particle separation in batch inclined settlers where the downward facing wall is subject to heating. To this purpose, two-dimensional numerical simulations using a mixture model have been run for a number of combinations of temperature jumps at the downward facing fall, particle diameters, and concentrations. Results show that, for particle sizes on the order of 10 µm, heating has a significant effect on the particle settling velocity at the bottom, but it also promotes particle resuspension, affecting the particle concentration at the supernatant layer. The initial concentration also affects settling: for the concentration range tested (8%–15% by volume), when re-normalized by the average concentration, particle accumulation rates at the bottom were found to be lower for higher average concentrations, thus suggesting that the separation process is more efficient at lower concentrations.

The design of a flotation circuit based on optimization techniques requires a superstructure for representing a set of alternatives, a mathematical model for modeling the alternatives, and an optimization technique for solving the problem. The optimization techniques are classified into exact and approximate methods. The first has been widely used. However, the probability of finding an optimal solution decreases when the problem size increases. Genetic algorithms have been the approximate method used for designing flotation circuits when the studied problems were small. The Tabu-search algorithm (TSA) is an approximate method used for solving combinatorial optimization problems. This algorithm is an adaptive procedure that has the ability to employ many other methods. The TSA uses short-term memory to prevent the algorithm from being trapped in cycles. The TSA has many practical advantages but has not been used for designing flotation circuits. We propose using the TSA for solving the flotation circuit design problem. The TSA implemented in this work applies diversification and intensification strategies: diversification is used for exploring new regions, and intensification for exploring regions close to a good solution. Four cases were analyzed to demonstrate the applicability of the algorithm: different objective function, different mathematical models, and a benchmarking between TSA and Baron solver. The results indicate that the developed algorithm presents the ability to converge to a solution optimal or near optimal for a complex combination of requirements and constraints, whereas other methods do not. TSA and the Baron solver provide similar designs, but TSA is faster. We conclude that the developed TSA could be useful in the design of full-scale concentration circuits.

The environmental problems generated by waste from the mining industry in the mineral extraction for business purposes are known worldwide. The aim of this work is to evaluate the microalga Muriellopsis sp. as a potential remover of metallic ions such as copper (Cu2+), zinc (Zn2+) and iron (Fe2+), pollutants of acid mine drainage (AMD) type waters. For this, the removal of these ions was verified in artificial acid waters with high concentrations of the ions under examination. Furthermore, the removal was evaluated in waters obtained from areas contaminated by mining waste. The results showed that Muriellopsis sp. removed metals in waters with high concentrations after 4–12 h and showed tolerance to pH between 3 and 5. These results allow proposing this species as a potential bioremediator for areas contaminated by mining activity. In this work, some potential alternatives for application in damaged areas are proposed as a decontamination plan and future prevention.

The heap leaching of minerals is one of the more commonly used processes in the mining industry. This process has been modeled by many authors. However, the validation, verification, and implementation of these models are difficult since there is uncertainty about the operating conditions and the leaching model parameters. This work uses the uncertainty quantification, based on uncertainty and sensitivity analysis, for studying the model strength against uncertainties in heap leaching. The uncertainty analysis (UA) is used to quantify the effect of the magnitude of the uncertainties of the input variables on the recovery of heap leaching. Global sensitivity analysis (GSA) is used to study the nature of connections between the recovery and input variables of the leaching model. In addition, GSA facilitates the detection of whether a leaching model is over-parameterized. The information obtained allows studying some applications of the kinetic model. The Mellado et al. kinetic model is used as an example. The UA results indicate that the kinetic model can estimate the recovery behavior considering the full range of uncertainties of input variables. The GSA indicates that the kinetic model is over-parameterized on the uncertainties range considered; this conclusion contradicts the results when the local sensitivity analysis is used. However, the model shows a good correlation between the results of GSA and the kinetic behavior of heap leaching. In addition, the kinetic model presents versatility because it allows the determination of operating regions for heap leaching.

Caliche is a mineral exploited in northern Chile, from which iodine and Nitrate salts (saltpeter) are obtained. This ore is the most important source of iodine in the world and is processed mainly by heap leaching using water as a leaching agent. Heap leaching of caliche ore is carried out by the stacking of ROM (Run-Of-Mine) material, where the particle size distribution covers a wide range, from a few millimeters up to several decimeters, even diameters about 1 m. During the leaching, the multiple soluble species of caliche, which can reach total fractions larger than 40%, are dissolved at different rates, mainly controlled by their solubilities. When it occurs and unlike most other leachable ores, the particle size diminishes. The leaching modeling of several soluble species of caliche has been recently addressed; however, one of the main assumptions is the idealization that the heap is composed of particles of the same size. The present work aims to complement the previously formulated phenomenological models for caliche ore leaching, through a model that considers the simultaneous dissolution of two species from caliche with three different particle sizes. These two water-soluble species have different solubilities and dissolution rates and the conceptual model considers that both species are dissolved at the particle surface. When the most soluble species is being depleted, the particle collapses, leaving a remaining fraction of the less soluble species together with insoluble material. The less soluble species is now being dissolved from the collapsed material. This article also includes the experimental verification of the conceptual model using data obtained from column leaching tests conducted for this purpose, focusing on the dissolution of two soluble species: Nitrate and Magnesium.