Optimizing flotation circuits: A comprehensive approach using design of experiments and stochastic simulation in cycle test validation

Cycle flotation tests have been preferred for obtaining metallurgical projections based on laboratory flotation tests because they can simulate a continuous circuit similar to real flotation plants. However, cycle tests are typically conducted in the laboratory under a limited number of operating conditions, so the behavior of ores in these tests might only partially represent the complexity and variations seen in industry-scale flotation operations. To address this limitation, the current work introduces a methodology that integrates cycle tests with the design of experiments (DoE) and response surface methodology (RSM), as well as stochastic simulation to expand the range of tested conditions and identify optimal regions. The methodology involves four stages: definition and preliminary analysis, construction of metamodels, stochastic simulation, and experimental validation. The proposed approach is illustrated through closed/open cycle tests, covering flotation circuits with rougher, cleaner, and scavenger stages. Various output variables are evaluated, such as weight recovery, overall recovery, kinetics, and concentrate and tail grade. The study reveals that polynomial models were inefficient in fitting the experimental data accurately, leading to the use of Monte Carlo simulation to predict closed-cycle test results, which were later validated experimentally. Ultimately, this research provides valuable recommendations for the appropriate application of DoE and RSM in mineral processing.