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.

中文翻译：

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优化浮选回路：在循环测试验证中使用实验设计和随机仿真的综合方法


循环浮选测试一直是获得基于实验室浮选测试的冶金预测的首选，因为它们可以模拟类似于真实浮选厂的连续回路。然而，循环测试通常在实验室中在有限数量的操作条件下进行，因此矿石在这些测试中的行为可能只能部分代表工业规模浮选操作中的复杂性和变化。为了解决这一限制，目前的工作引入了一种方法，该方法将循环测试与实验设计 （DoE） 和响应面法 （RSM） 以及随机模拟相结合，以扩大测试条件的范围并确定最佳区域。该方法包括四个阶段：定义和初步分析、元模型构建、随机模拟和实验验证。所提出的方法通过闭式/开式循环测试进行说明，涵盖具有较粗、更清洁和清除阶段的浮选回路。评估各种输出变量，例如重量回收率、整体回收率、动力学以及精矿和尾部等级。研究表明，多项式模型在准确拟合实验数据方面效率低下，导致使用蒙特卡洛模拟来预测闭环测试结果，这些结果后来通过实验验证。最终，这项研究为 DoE 和 RSM 在矿物加工中的适当应用提供了有价值的建议。