Solution strategies to the stochastic design of mineral flotation plants

Abstract

The aim of this study is two-fold: first, to analyze the effect of stochastic uncertainty in the design of flotation circuits and second, to analyze different strategies for the solution of a two-stage stochastic problem applied to a copper flotation circuit. The paper begins by introducing a stochastic optimization problem whose aim is to find the best configuration of superstructure, equipment design and operational conditions, such as residence time and stream flows. Variability is considered in the copper price and ore grade. This variability is represented by scenarios with their respective probability of occurrence. The resulting optimization problem is a two-stage stochastic mixed integer nonlinear program (TS-MINLP), which can be extremely challenging to solve. For this reason, several solvers for this problem are compared and two stochastic programming methodologies are applied. The combination of these techniques allows the production of high quality solutions and an analysis of their sensitivity to epistemic uncertainty. The results show that the stochastic problem gives better designs because it allows operational parameters to adapt to the uncertainty of the parameters. The results also show that the flotation circuit structure can vary with the feed grade and copper price. The sensitivity analysis shows small to moderate variability with epistemically uncertain parameters.

Optimizing Flotation Circuit Recovery by Effective Stage Arrangements: A Case Study

“…These studies have shown that the flotation circuit configuration is not very sensitive to stage recovery [9,19]. The overall output suggests that choosing the best flotation circuit is not sensitive to the stage recovery, and as a result, only approximate values of the recovery can be used to select the optimal flotation circuit [6,9,20]. This paper using simple numerical examples shows that the assumption of circuit configuration insensitivity to the stage recovery is not correct in all cases.…”

“…This assumption may be very simplistic, but is commonly used in industrial operations [8]. Despite extensive researches had been done on the effect of design and operational parameters on the efficiency of flotation circuits, very few publications can be found in the literature that discusses the role of stage recovery on the overall circuit recovery and the effect of circuit configuration on the stage recovery [6,7,9,10]. Some previous studies have evaluated the circuit configuration with circuit analysis method assuming the same recovery in various flotation stages [7,11,12].…”

“…The present study is going to compare and evaluate the configuration of flotation circuits, assuming that an identical recovery in stages is an acceptable assumption and the results are valid for non-identical stage recovery. Recently, the effect of stage recovery on the overall circuit recovery has been investigated from two aspects of sensitivity and uncertainty analyses [6,7,9,17,18]. These studies have shown that the flotation circuit configuration is not very sensitive to stage recovery [9,19].…”

“…Recently, the effect of stage recovery on the overall circuit recovery has been investigated from two aspects of sensitivity and uncertainty analyses [6,7,9,17,18]. These studies have shown that the flotation circuit configuration is not very sensitive to stage recovery [9,19]. The overall output suggests that choosing the best flotation circuit is not sensitive to the stage recovery, and as a result, only approximate values of the recovery can be used to select the optimal flotation circuit [6,9,20].…”

A strategy for the identification of optimal flotation circuits

“…Thus, several studies have been developed to evaluate the effects of uncertainties in flotation process design (Montenegro et al, 2013(Montenegro et al, , 2015Jamett et al, 2015;Cisternas et al, 2015). These studies have noted that the optimal flotation circuit structure is not very sensitive to the stage recovery values.…”