Yield stress of foam flow in porous media: The effect of bubble trapping

Foam behaves as a yield-stress fluid as it flows in a porous medium. Quasi-static analysis suggests that the yield stress arises from the non-smooth motion of foam films, denoted as lamellae, in pores. In order to study the effect of trapped lamellae on the motion of a moving lamella and consequently on the yield stress of foam, we conduct numerical simulations in the quasi-static limit. We propose a new method utilizing the surface energy minimization algorithm, which explicitly considers the connectivity of pores in a porous medium. We consider two different shapes of pore and vary the number of nearby trapped lamellae to investigate the effects of bubble trapping on the non-smooth and the smooth motion of a single lamella passing through a pore, respectively. We find that the trapped lamellae lead to the increased volume-averaged pressure drop and thus the increased yield stress. Notably, the motion of a lamella through a pore with rounded corners in the pore body becomes non-smooth, due to the presence of trapped lamellae. The results contribute to a better understanding of the yield stress of foam in porous media

Modelling the curing of agglomerated ores with comparison to micro-CT

Agglomeration and the associated curing process are critical as they both improve heap permeability and provide initial intimate contact between the leaching solution and the minerals. The evaporation of water from the agglomerate surface will drive liquid motion within agglomerates, redistributing dissolved species and increasing their concentration with the resultant potential for precipitation of previously dissolved species. Models have been proposed for the particle scale leach behaviour during the active irrigation phase of heap leaching, however no models currently exist for the leach behaviour during the curing process. The aim of this paper is therefore to propose and validate such a model by including important processes such as evaporation, unsaturated liquid transport, advective and diffusive transport of dissolved species, dissolution of mineral grains, and precipitation of species once saturation is reached. A set of small-scale column leaching tests were carried out, with the system being repeated scanned using X-ray Microtomography (micro-CT) over the course of the 65 day long curing experiments. Image analysis allowed the spatial distribution of both the initial mineral grains, as well as the precipitates to be tracked as a function of time. These were then used to demonstrate that the model captured the key features of the behaviour during the leaching process, as well as providing plausible ranges for the model parameters that could not be directly measured as input parameters. Both the model and the experiments showed that reprecipitation occurs preferentially towards the surface of the agglomerates. The model was also used to carry out a sensitivity analysis, with a key finding being that leach performance during curing improves with larger agglomerates and decreased evaporation rates. This is because of decreased loss of water. The particle size effect is the opposite of what would be expected during the subsequent leaching where mass transport into and out of the agglomerate is crucial, thus indicating the potential to optimise agglomerate size

A methodology to implement a closed-loop feedback-feedforward level control in a laboratory-scale flotation bank using peristaltic pumps

This paper describes the implementation of a level control strategy in a laboratory-scale flotation system. The laboratory-scale system consists of a bank of three flotation tanks connected in series, which mimics a flotation system found in mineral processing plants. Besides the classical feedback control strategy, we have also included a feedforward strategy to better account for process disturbances. Results revealed that the level control performance significantly improves when a feedforward strategy is considered. This methodology uses peristaltic pumps for level control, which has not been extensively documented even though: (1) peristaltic pumps are commonly used in laboratory-scale systems, and (2) the control implementation is not as straightforward as those control strategies that use valves. Therefore, we believe that this paper, which describes a proven methodology that has been validated in an experimental system, can be a useful reference for many researchers in the field.•Preparation of reagents to ensure that the froth stability of the froth layer is representative of an industrial flotation froth.•Calibration of instruments - convert the electrical signal from PLCs to engineering units.•Tuning PI parameters using SIMC rules by performing step-changes in each flotation cell

Development and Validation of a Dynamic Model for Flotation Predictive Control Incorporating Froth Physics

Data Availability Statement: The data that support the findings of this study are available from the corresponding author, P.Q, upon reasonable request.Paulina Quintanilla would like to acknowledge the National Agency for Research and Development (ANID) for funding this research with a scholarship from “Becas Chile”. The Society of Chemical Industry is also greatly acknowledged for the support granted by the SCI Messel Scholarship 2020

Economic model predictive control for a rougher froth flotation cell using physics-based models

The development of an economic model predictive control (E-MPC) strategy is presented. The strategy uses a novel dynamic flotation model that incorporates the physics of the froth phase in a flotation cell. The dynamic model was previously calibrated and validated using experimental data. Sensitivity analyses were conducted to select a suitable objective function that accounted for both process economics and control variable sensitivities. While the ultimate goal of a rougher flotation cell is to maximise the metallurgical recovery at a steady state for a specified minimum grade, it was evident that the incorporation of air recovery dynamics (which can be measured in real-time) and concentrate grade dynamics (calculated through first-principle models) led to the best results. The addition of a dynamic variable that can be easily measured online, i.e. air recovery, offers great potential to improve plant performance in existing froth flotation systems. Furthermore, a minimum concentrate grade was imposed in the E-MPC strategy. This acts as an economic constraint as it allows the metallurgical recovery to be optimised while ensuring that concentrate grade requirements are met. The dynamic optimisation problem for the E-MPC strategy was discretised using orthogonal collocations, and was implemented in Matlab using automatic differentiation via CasADi. Two typical manipulated variables were considered: air flowrate and pulp height setpoints. Based on laboratory-scale data, the implementation of the E-MPC strategy resulted in improvements ranging from +8 to +22 % in metallurgical recovery, while maintaining the specified grade. This is therefore an encouraging control strategy to explore in larger flotation systems

Economic model predictive control for a rougher froth flotation cell using physics-based models

Data availability: Data will be made available on request.Supplementary data are available online at: https://www.sciencedirect.com/science/article/pii/S089268752300064X#appSC .The development of an economic model predictive control (E-MPC) strategy is presented. The strategy uses a novel dynamic flotation model that incorporates the physics of the froth phase in a flotation cell. The dynamic model was previously calibrated and validated using experimental data. Sensitivity analyses were conducted to select a suitable objective function that accounted for both process economics and control variable sensitivities. While the ultimate goal of a rougher flotation cell is to maximise the metallurgical recovery at a steady state for a specified minimum grade, it was evident that the incorporation of air recovery dynamics (which can be measured in real-time) and concentrate grade dynamics (calculated through first-principle models) led to the best results. The addition of a dynamic variable that can be easily measured online, i.e. air recovery, offers great potential to improve plant performance in existing froth flotation systems. Furthermore, a minimum concentrate grade was imposed in the E-MPC strategy. This acts as an economic constraint as it allows the metallurgical recovery to be optimised while ensuring that concentrate grade requirements are met. The dynamic optimisation problem for the E-MPC strategy was discretised using orthogonal collocations, and was implemented in Matlab using automatic differentiation via CasADi. Two typical manipulated variables were considered: air flowrate and pulp height setpoints. Based on laboratory-scale data, the implementation of the E-MPC strategy resulted in improvements ranging from +8 to +22 % in metallurgical recovery, while maintaining the specified grade. This is therefore an encouraging control strategy to explore in larger flotation systems.Paulina Quintanilla would like to acknowledge the National Agency for Research and Development (ANID) for funding this research with a scholarship from “Becas Chile”

Evaluation of Changes in Feed Particle Size within an Economic Model Predictive Control Strategy for Froth Flotation

This study presents the evaluation of the impact of feed particle size on an Economic Model Predictive Control (E-MPC) strategy for a flotation bank. The effect of particle size was assessed under two scenarios: (1) assuming constant floatability with no dependency on particle size, and (2) assuming variable floatability as a function of particle size. The E-MPC strategy uses a dynamic model that includes froth physics, which was previously calibrated and validated using experimental data. Two typical control variables were considered: air flowrate and pulp height setpoints. The proposed objective function depends on three flotation variables: (1) dynamic air recovery, a measurable variable used to quantify froth stability and is directly related to flotation performance, (2) metallurgical recovery at steady-state, and (3) dynamic concentrate grade. A moving horizon estimator (MHE) was implemented to estimate the model states in both scenarios. Simulation results showed that the estimation of metallurgical indicators (concentrate grade and recovery) was significantly affected by changes in the floatability parameter. A poor estimate of floatability is likely to lead to very different results for the control strategy. Future research should focus on estimating and updating the most significant parameters of the dynamic model, such as floatability, with an appropriate sampling time

A methodology to implement a closed-loop feedback-feedforward level control in a laboratory-scale flotation bank using peristaltic pumps

Data availability: Data will be made available on request.This paper describes the implementation of a level control strategy in a laboratory-scale flotation system. The laboratory-scale system consists of a bank of three flotation tanks connected in series, which mimics a flotation system found in mineral processing plants. Besides the classical feedback control strategy, we have also included a feedforward strategy to better account for process disturbances. Results revealed that the level control performance significantly improves when a feedforward strategy is considered. This methodology uses peristaltic pumps for level control, which has not been extensively documented even though: (1) peristaltic pumps are commonly used in laboratory-scale systems, and (2) the control implementation is not as straightforward as those control strategies that use valves. Therefore, we believe that this paper, which describes a proven methodology that has been validated in an experimental system, can be a useful reference for many researchers in the field. • Preparation of reagents to ensure that the froth stability of the froth layer is representative of an industrial flotation froth. • Calibration of instruments – convert the electrical signal from PLCs to engineering units. • Tuning PI parameters using SIMC rules by performing step-changes in each flotation cell.Paulina Quintanilla would like to acknowledge the National Agency for Research and Development (ANID) for funding this research with a scholarship from “Becas Chile”. The Society of Chemical Industry (SCI) and the Institute of Metals, Minerals and Mining (IOM3) are also greatly acknowledged for funding the experiments at Universidad Técnica Federico Santa María, Chile

Hydrodynamics in a three-phase flotation system - fluid following with a new hydrogel tracer for Positron Emission Particle Tracking (PEPT)

Understanding the hydrodynamics of three-phase stirred tanks, such as froth flotation cells, is paramount for the characterisation of turbulence, stability and performance. Although positron emission particle tracking (PEPT) is known for its effectiveness in measuring the hydrodynamics of particles in opaque, high solid content systems, it has not been widely used for characterising the liquid phase. This work presents a new, neutrally buoyant, alginate hydrogel tracer, designed to emulate the density of the liquid phase, which is suitable for high-speed tracking with PEPT. PEPT experiments were conducted in a bench-scale flotation cell, comparing the new tracer to ion-exchange resin tracers previously used in this system. Results showed statistically significant differences in pathlines, residence time and velocity distribution among the tracers. Moreover, the hydrodynamics of the new tracer agree with existing CFD predictions for the liquid phase. This methodology enables the comprehensive study of relative flow behaviour in complex multiphase systems