(235f) A Design Space Analysis for Quantifying Process Flexibility Under Disturbances: An Application to Froth Flotation

The world's transition to cleaner and more sustainable energy sources will significantly increase mineral and metal demand, which is challenging due to the decreasing grade and complexity of ores. To meet this challenge, improving the efficiency of current mineral separation processes while minimizing negative environmental impacts is crucial. The most extensively used method for separating valuable minerals from waste rock is called froth flotation. This separation process involves adding chemical reagents and air to stirred tanks. The reagents make the valuable mineral particles hydrophobic, causing them to repel water and attach to air bubbles. These bubble-particle aggregates rise to the top of the tank, forming a froth that overflows as a mineral-rich concentrate. In contrast, the waste rock particles, which do not attach to bubbles, leave the tank from the bottom. Due to the large-scale nature of this process, even a small improvement in the separation efficiency can result in a substantial increment in mineral recovery. However, efficiency improvements are not straightforward since froth flotation is a multiphase process with inherent instabilities and complex dynamics [1].

Incorporating computer-aided tools for design, optimization and control is crucial to deal with this complexity and improving the process's efficiency. To this end, we present the first study that implements a design space analysis technique that identifies acceptable operating regions, quantifies operational flexibility, and evaluates various operating points that can be used to enhance model-based control practices for froth flotation [2]. The framework comprises three core steps: 1) model validation & problem formulation, 2) design space identification, and 3) design space analysis. In the first step, a mathematical model of the process is validated. Then, the design problem is formulated by defining the design inputs (DIs), monitoring key performance indicators (KPIs), and the constraints. Next, in step 2, we perform quasi-random Sobol sampling to obtain the dataset based on the problem definition. Afterwards, the constraints are applied, and the design space is identified using alpha shapes. Finally, in step 3, we quantify acceptable ranges by identifying acceptable operating regions.

We investigate several design spaces with different combinations of DIs, using a dynamic flotation model developed by [3], which was calibrated and validated with laboratory-scale data [4]. In each case, we consider two manipulated variables and one disturbance. The manipulated variables are the superficial air velocity and pulp height set points, as they are commonly manipulated in the froth flotation process [5]. The disturbances considered are particle size, feed grade, solid content, and feed flowrate. The KPIs monitored are metallurgical recovery and concentrate grade as they are directly related to the economics of the process.The identified design spaces are used for the integrated analysis between manipulated variables, disturbances, and their impacts on performance and flexibility. Flexible operating points are identified, acceptable ranges quantified, Pareto fronts examined, and distributions of KPIs investigated for all disturbance cases.

The design analysis framework for flexibility quantification presented in this study is, undoubtedly, a significant step forward in optimizing mineral separation processes. To the best of our knowledge, this is the first time such an approach has been applied to froth flotation, making it a breakthrough in the field. This framework has the potential to lead to significant improvements in process performance and efficiency, which is crucial in supporting sustainable mining practices and meeting the rising demand for minerals in the green energy transition.

References

[1] P. Quintanilla, S. J. Neethling, and P. R. Brito-Parada, “Modelling for froth flotation control: A review,” Miner Eng, vol. 162, p. 106718, 2021, doi: 10.1016/j.mineng.2020.106718.

[2] S. Sachio, C. Kontoravdi, and M. M. Papathanasiou, “Model-Based Design Space for Protein A Chromatography Resin Selection,” Computer Aided Chemical Engineering, vol. 51, pp. 733–738, Jan. 2022, doi: 10.1016/B978-0-323-95879-0.50123-5.

[3] P. Quintanilla, S. J. Neethling, D. Navia, and P. R. Brito-Parada, “A dynamic flotation model for predictive control incorporating froth physics. Part I: Model development,” Miner Eng, vol. 173, no. November, p. 107192, 2021, doi: 10.1016/j.mineng.2021.107192.

[4] P. Quintanilla, S. J. Neethling, D. Mesa, D. Navia, and P. R. Brito-Parada, “A dynamic flotation model for predictive control incorporating froth physics. Part II: Model calibration and validation,” Miner Eng, vol. 173, no. November, p. 107190, 2021, doi: 10.1016/j.mineng.2021.107190.

[5] P. Quintanilla, D. Navia, S. J. Neethling, and P. R. Brito-Parada, “Economic model predictive control for a rougher froth flotation cell using physics-based models,” Miner Eng, vol. 196, p. 108050, May 2023, doi: 10.1016/J.MINENG.2023.108050.