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 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.
Highlights
Flotation circuits have included cell banks; changes in the processed ore, operational grinding conditions, technological developments, valuable metal prices, energy, and water consumption have generated an evolution from circuits to flotation systems
These systems include flotation cell banks, flotation columns, and grinding units, with an arrangement that is complex to determine as the design alternatives markedly increase as the number of processing stages increases [1]
Equipment selection, metal price uncertainty, and flotation and grinding stage uncertainty often are not studied as a whole during the design of flotation systems, as evidenced in works cited earlier and in other existing studies in the available literature (Table 1)
Summary
Flotation circuits have included cell banks; changes in the processed ore, operational grinding conditions, technological developments, valuable metal prices, energy, and water consumption have generated an evolution from circuits to flotation systems. To solve the MINLP problem under uncertainty, the fuzzy distributional robust optimization method based on possibility and necessity theories was implemented These works neither considered the selection of flotation equipment nor grinding stages, which are essential aspects of industrial practice. Equipment selection, metal price uncertainty, and flotation and grinding stage uncertainty often are not studied as a whole during the design of flotation systems, as evidenced in works cited earlier and in other existing studies in the available literature (Table 1) Another approach proposed in the literature to address the uncertainty in processes is flexibility and resilience, which are significant components of the operability of industrial processes; i.e., these are applied after designing the process. The main objective of this work is to establish, from the design point of view, the requirements necessary for the operational feasibility of flotation systems
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