(317a) Advances in Dynamic Modelling for Model Predictive Control for Froth Flotation

Froth flotation is a separation process used to separate valuable minerals from the waste rock, and it is the largest tonnage process of its kind. The process is carried out in stirred tanks where chemical reagents and air are added. The reagents make the valuable mineral particles hydrophobic, which causes 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. The waste rock forms a pulp phase that then leaves from the bottom of the tank as tailings.

Flotation is a multiphase process that exhibits inherent instabilities, and thus complex dynamics[1]. One of the most efficient ways to increase flotation performance is by implementing advanced controllers, such as Model Predictive Control (MPC). The effectiveness of MPC strategies relies on the model that represents the dynamics of the process, which has often hindered its application in froth flotation. MPC studies have primarily used kinetic models to phenomenologically represent the attachment-detachment of mineral particles in the pulp phase. While kinetic models can adequately represent the phenomena in the pulp phase, they are not suitable to model the complex phenomena in the froth phase. This is particularly relevant since froth phase phenomena are key drivers of froth performance yet are often neglected in flotation models. This study presents an overview of recent progress in modelling for froth flotation control, focusing on the development and implementation of a new dynamic flotation model that incorporates froth physics, which is thus suitable for MPC. The full model development is presented in [2]; it was calibrated and validated using experimental data, as shown in [3].

Unlike other flotation models for control in the literature, the model proposed here includes, for the first time, important variables related to froth stability, such as bursting rate and air recovery, as well as simplified phenomenological equations to calculate froth recovery and entrainment. The model also incorporates pulp-froth interface physics, which enables a more accurate prediction of relevant flotation variables. A comprehensive sensitivity analysis of the parameters involved in the model is presented, highlighting the predictions' relevance for overflowing bubble size and bursting rate. An analysis of the degrees of freedom of the model was also carried out and determined that two variables are available for control purposes, for which air and tailings flowrates were chosen.

Using the proposed dynamic model, a novel economic model predictive control (E-MPC) strategy was developed for a single froth flotation tank [4]. To ensure a global optimum for the flotation bank, a centralized E-MPC strategy was implemented. The E-MPC strategies were implemented in both simulations and a laboratory-scale flotation rig. The simulation results demonstrated a significant improvement in metallurgical recovery in all cases while maintaining the concentrate grade at a minimum of 20%. The implementation of E-MPC in the laboratory-scale flotation rig also improved recoveries, though some challenges in convergence were identified for flotation bank control due to the high computational demand of the centralized system. Further work is therefore needed to include algorithms that are less computationally demanding. Implementing the predictive control strategy has, nevertheless, provided encouraging results, demonstrating the model's potential for integration into a larger flotation control system.

[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] 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.

[3] 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.

[4] 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.