A framework for polydisperse pulp phase modelling in flotation

Froth flotation is one of the most widely-used mineral processing operations. The pulp zone in flotation tanks is polydisperse in general and serves as a medium for the interaction between the solid particles and the gas bubbles in a liquid continuum, leading to particle–bubble attachment/detachment and bubble coalescence/breakage phenomena. To better predict the hydrodynamics and inform the design of e cient flotation equipment, it is therefore important to accurately model and simulate the evolution of the size distribution of the dispersed phases. This has created an urgent need for a framework that can model the pulp phase in an e cient manner, which is not currently available in the literature. The available software products are not e cient enough to allow for a tractable modelling of industrial-scale flotation cells and in some cases they cannot model the polydispersity of the dispersed phase at all. This work presents an e cient numerical framework for the macroscale simulation of the polydisperse pulp phase in froth flotation in an open-source finite element computational fluid dynamics (CFD) code that provides an e cient solution method using mesh adaptivity and code parallelisation. A (hybrid finite element–control volume) finite element framework for modelling the pulp phase has been presented for the first time in this work. An Eulerian–Eulerian turbulent flow model was implemented in this work including a transport equation for attached and free solid particles. Special care was taken to model the settling velocity of the free solids and the modification of the liquid viscosity due to the presence of these particles. Bubble polydispersity was modelled using the population balance equation (PBE), which was solved using the direct quadrature method of moments (DQMOM). Appropriate functions for bubble coalescence and breakage were chosen in the PBE. Mesh adaptivity was applied to the current problem to produce fully-unstructured anisotropic meshes, which improved the solution e ciency, while all simulations were executed on a multicore architecture. The model was validated for 2D simulations of a bubble column against experimental results available in the literature. After successful validation, the model was applied to the simulation of the pulp phase in a flotation column for monodisperse and polydisperse solids. Polydispersity of the solids was modelled for the first time in this work using three separate solid size classes. A clear dependence of the flotation rate on the particle size was noticed and the monodisperse solids simulations were shown to over-predict the flotation rate. Other than flotation, this open-source framework can be used for the simulation of a variety of polydisperse multiphase flow problems in the process industry

The role of microparticles on the shape and surface tension of static bubbles

HYPOTHESIS: Surface tension is a critical parameter in bubbles and foams, yet it is difficult to assess when microparticles are attached at the interface. By considering the interaction force between an air-liquid interface and microparticles, modified equations for sessile bubble tensiometry can be derived to determine the surface tension and shape of static microparticle-laden bubbles. EXPERIMENTS: A modified sessile bubble method, in which the forces between microparticles and the air-liquid interface are considered, was developed and used to analyse the surface tension of bubbles fully coated by a monolayer of silica microparticles of different sizes. The results are compared to those obtained using classical sessile bubble tensiometry. The new method is also used to investigate the contours of particle-laden bubbles of varying particle radius and contact angle. FINDINGS: While the classical sessile bubble method overestimates the surface tension, results obtained using the modified sessile bubble method show that the surface tension of static microparticle-laden bubbles remains the same as that of uncoated bubbles, with no dependency on the particle size. The discrepancy is due to the fact that microparticles attached to the air-liquid interface deform a bubble in a similar way that changes in surface tension do for uncoated bubbles

The selection of renewable energy technologies using a hybrid subjective and objective multiple criteria decision making method

The use of renewable energy technologies is a key factor for sustainable development but their selection from several alternatives is a difficult task that relies on the careful assessment of relevant criteria. While Multiple Criteria Decision Making (MCDM) methods have been used successfully in various renewable energy technology selection problems, the decision process becomes more challenging when preferential judgements are made on the basis of non-homogenous and imprecise input data, and when there is uncertainty due to disparities among decision makers. This paper presents a hybrid MCDM method capable of overcoming these problems by taking into account quantitative and qualitative data under a probabilistic environment in the context of group decision making. In this method, qualitative data is fuzzified and used along with quantitative data to develop a hybrid model. A coefficient factor allows decision makers to vary the weight of each quantitative model so that the resultant criteria weights and overall alternatives’ scores consider both subjective considerations and objective information. An example is presented to showcase the usability of the method developed for ranking and evaluating renewable energy technologies in the mining industry. In addition, the impact of different coefficient factors on the final results was assessed by means of sensitivity analysis. The results indicate that the method developed is able to minimise the loss of valuable objective information, caused by the subjective bias of qualitative weights during the evaluations, by adjusting the coefficient factors of the hybrid model during the calculations

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

Optimising froth stability of copper flotation tailings

Linking results from laboratory scale experiments to industrial flotation behaviour is challenging. Typically, such experiments involve batch tests in which the system does not operate at steady-state, making it difficult to infer the effects that operating conditions have on flotation performance. In order to overcome this limitation a 4-litre recirculating tank was previously developed at Imperial College London. This tank is capable of reaching, and operating at, steady-state by recycling overflowing concentrate back into the feed. As well as instruments to control operating conditions, it is fitted with a system of sensors that allow the surface of the froth to be dynamically monitored. From this information, it is possible to measure the air recovery a proxy for froth stability. Thus, this bench-scale tank can be used to understand the effect of differing operating conditions on flotation performance at steady state. However, so far, this cell has only been used to investigate idealised systems with only one or two species. Reprocessing of tailings dams is not only environmentally desirable but also increasingly economically feasible due to the declining head grades of primary deposits. There is also the added benefit of no further milling being required prior to flotation. However, the effects of fine and ultrafine particles on froth stability are not yet fully understood. In this work, the bench-scale continuous tank has been used for the first time to determine the flotation response of a complex feed, consisting of samples from a copper tailings dam, to changes in operating conditions. It was shown that the froth stability in the system is comparable to that of previous work and industrial tests, with a peak in air recovery being found at a superficial gas velocity of 1.13 cm/s. There is scope to optimise the froth stability of tailings flotation for enhanced metallurgical performance

Evaluation of collector performance at the bubble-particle scale

Particle attachment and detachment in froth flotation are complex processes and their measurement presents many challenges. Of particular interest is the effect of collectors at the bubble-particle scale, in order to assess the strength or collecting ability of these reagents. However, studies of the effect of collectors on particle attachment at the bubble-particle scale are scarce. In this work, we propose a methodology to characterise collector strength by measuring the attachment rate of particles to a capillary-pinned bubble. An image processing technique was developed to quantify bubble surface coverage over time, which was then used to determine particle attachment kinetics. The image analysis strategy is based on the sessile drop method and uses curve fitting to determine accurately the particle coverage. The methodology was used to assess the collecting ability of three chalcopyrite collectors. Interestingly, although very similar contact angle measurements were found for two of the collectors, they showed distinctly different particle attachment kinetics. It is proposed that this particle-bubble attachment method can be used to gain additional information not currently available from either contact angle measurements or bulk collector performance tests

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

The link between particle size and froth stability - Implications for reprocessing of flotation tailings

Historic tailings dams can often be considered as valuable mineral reserves due to the declining head grades of primary deposits. The reprocessing of such material is of great interest to the minerals processing industry, not only from an economic point of view, but also from an environmental one. However, tailings material is generally comprised of fine particles, which poses a challenge for its reprocessing using froth flotation due to reduced recoveries of these particle sizes. In addition, there is some debate as to the effect that these fine particles have on the froth stability, which in turn is linked to mineral recovery. In this work, air recovery was used as a measure of froth stability to determine the flotation response of a copper tailings ore to changes in particle size distribution and superficial gas velocity. The system exhibited a maximum in air recovery, which correlates well with the local peak in dynamic froth stability presented in previous work. This maximum in froth stability is also shown to correspond to an improvement in flotation performance, thus highlighting the importance of considering the link between particle size, air rate and froth stability when determining the flotation strategy for tailings reprocessing. The results are discussed in terms of the implications for the reprocessing plant from where the ore samples were obtained and, more generally, for the efficient flotation reprocessing of tailings

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

CFD modelling of particle classification in mini-hydrocyclones

This work presents validated Computational Fluid Dynamics (CFD) predictions of the effect that changes in vortex finder and spigot diameters have on the classification performance of mini-hydrocyclones. Mini-hydrocyclones (e.g. 10 mm in diameter) have been applied successfully to the separation of micron-sized particles since their bypass fraction is larger than the water recovery, which results in a high particle recovery to the underflow, as well as low water recovery. However, a larger bypass fraction can be a disadvantage when the purpose of the hydrocyclone is particle classification, because of the large amount of fine particles that are misplaced in the underflow. Although it is well known that changes in the outlets of the hydrocyclone affect its performance, there is limited research on the effect of these design parameters in mini-hydrocyclones, in particular with regard to particle classification. The aim of this study is to computationally explore the influence of spigot and vortex finder on the classification process. To this end, CFD simulations were carried out and the predictions experimentally validated in a 3D printed mini-hydrocyclone using glass beads (below 20μm) as the particulate system. The numerical results showed very good agreement with the experimental data for recovery of solids, concentration ratio, pressure drop and particle size distribution. A trade-off was observed between the solids recovery and concentration ratio, while the solids recovery was found to be inversely proportional to the pressure drop when vortex finder diameters were kept constant. It was found that the design that yielded the lowest recovery among those tested also resulted in a particle size distribution furthest away from that of the feed. We show how the model can be used to assess changes in design parameters in order to inform the selection of designs that exhibit lower energy requirements without compromising separation performance