Design of Cell-Based Flotation Circuits under Uncertainty: A Techno-Economic Stochastic Optimization

Abstract

The design of cell-based flotation circuits is often completed in two distinct phases, namely circuit structure identification and equipment sizing selection. While recent literature studies have begun to address the implications of stochastic analysis, industrial practice in flotation circuit design still strongly favors the use of deterministic metallurgical modeling approaches. Due to the complexity of the available mathematical models, most flotation circuit design techniques are constructed based on deterministic models. Neglecting the impact of various sources of uncertainty may result in the identification of circuit solutions that are only optimal in a narrow region of specific operating scenarios. One promising strategy to address this shortcoming is through the Sample Average Approximation (SAA) methodology, a stochastic approach to handling uncertainty that has been widely applied in other disciplines such as supply chain and facility location management problems. In this study, a techno-economic optimization algorithm was formulated to select the optimal size and number of flotation cells for a fixed circuit structure while considering potential uncertainty in several input parameter including feed grade, kinetic coefficients, and metal price. Initially, a sensitivity analysis was conducted to screen the uncertain parameters. After simplifying the optimization problem, the SAA approach was implemented to determine the equipment configuration (i.e., cell size and number) that maximizes the plant’s net present value while considering the range of potential input values due to parameter uncertainty. The SAA methodology was found to be useful in analyzing uncertainty in flotation kinetics; however, the approach did not provide a useful means to assess the influence of uncertainties in ore grade and metal price, as these values are not significant in determining equipment size but rather influence the optimal circuit structure, which was not considered in this study. Results from an application example indicate that the SAA approach produces optimal solutions not initially identified in a deterministic optimization, and these SAA solutions tend to provide greater robustness to uncertainty and variation in the flotation kinetics.

Techno-Economic and Life Cycle Cost Analysis through the Lens of Uncertainty: A Scoping Review

“…Net present value (NPV), payback Time (PBT), and return on investment (ROI) were used to investigate the profitability of this process. Amini and Noble [7] developed a techno-economic optimization method to identify the ideal size and quantity of flotation cells for a specific circuit configuration, taking into account the possibility of variability in various input parameters, including feed grade, kinetic coefficients, and metal price. In the first step, a sensitivity analysis was undertaken to identify the uncertain parameters.…”

“…Aleatory uncertainty is caused by intrinsic variability, whereas epistemic uncertainty results from a lack of knowledge [6]. However, many articles have been published over the years on methods and approaches for evaluating uncertainty (e.g., [7][8][9]), but there are few literature reviews on this topic. In addition, new and advanced uncertainty techniques are not yet utilized by techno-economics and life cycle cost analysts.…”