Chemical Engineering and Processing - Process Intensification
Hydrodynamic study of a phosphate flotation cell by CFD approach
Graphical abstract
Introduction
Froth flotation is an efficient unit operation used essentially in the beneficiation and in the concentration of targeted minerals based on the difference in physicochemical properties of various mineral surfaces. It is commonly used to separate copper [5], lead [6], zinc [7], tin [8] minerals from gangue minerals. It uses the air bubbles as an agent to attach hydrophobic particles due to their strong adhesion and float them to the froth layer where they are collected in the form of a concentrate, while hydrophilic particles, depressed with a depressant reagent, settle in the bottom of the flotation cell and drain as tailings. This selective process is reached basically relying on the difference of surface physical properties, where valuable mineral particles are usually hydrophobic in nature or by addition of flotation reagents. The reverse flotation, consisting on floating the gangue minerals and retrieving the valuable ore from the tailings, is used in the purification of some minerals notably coal [9], silicate [10], iron [11]. Prasakh et al. reviewed various froth flotation processes based on different operating concepts [12]: cyclonic–static micro-bubble flotation column (FCSMC) [13], [14], electro-flotation (EF) [15], [16], [17], induced or dispersed air flotation (IAF) [18], [19], dissolved air flotation (DAF) [20], [21], [22], column flotation [23], [24] and jet flotation [25], [26].
With the computer revolution recorded in the last decades, many researchers have turned to CFD (computational fluid dynamics) for several mineral processes such as particle classification in hydro-cyclones [27], [28], electro-refining [29], pelletising process [30], mineral carbonation [31] and the process of our interest, the flotation [32], [33]. CFD simulations are a powerful tool that provides a realistic approach to simulate the flotation process and to predict the complex flow dynamics. The CFD overview on the local interactions intervening in this purification process as well as the hydrodynamic behavior contribute to the improvement of the process yield [1], [2]. Its advantage lies in the possibility of simulating different scales: laboratory-scale [34], [35], pilot-scale [36] and industrial-scale [37] with various operating conditions, providing relevant details about local and global parameters of the overall system.
In the case of complex multiphase flows, two different approaches prevail in the CFD studies held in the literature: The Eulerian–Eulerian (also called multi-fluid) approach and the Eulerian–Lagrangian model. Deng et al. [38] established a 2D, two-phase model based on the Eulerian-Eulerian formulation to investigate the effect of liquid and gas velocities on the flow patterns in a flotation column. Using the same multi-fluid approach Koh et al. [39] studied a multiphase flow considering liquid, particles and bubbles, investigated the velocity vectors, the gas phase distribution and the turbulent dissipation rate, then located the particle-bubbles collisions. Koh and Schwarz worked on the interactions between particles and bubbles namely collision, attachment and detachment for mono-sized [40], [41] and multi-sized bubbles and particles [42]. Sarhan et al. built a multi-fluid Eulerian model coupled with k–ϵ turbulence model and population balance equation in CFD code AVL FIRE with FORTRAN subroutines to find out the gas hold-up and the bubble hydrodynamics in a flotation column [43]. On the other hand, Desam et al. adopted the Eulerian–Lagrangian approach to study the effect of the geometry design, the bubbles diameter and the inlet velocity on the flotation process efficiency [44]. Xia et al. studied the global back mixing in a flotation column considering fluid–gas flow [45], the Eulerian formulation was used to describe the fluid flow through Navier–Stokes equations while the Lagrangian approach was used to track the bubble trajectories. Liu and Shwarz established CFD numerical simulations based on Lagrangian method for particle tracking and Eulerian approach for the flow behavior in a cylindrical domain in order to study bubble-particle collision efficiency [46].
To model the rotational motion in the flotation machine, two numerical approaches are distinguished: the sliding mesh (SM) [39] and the multiple reference frames (MRF) [47], [48], [49]. The SM approach is a fully transient approach, where the rotation of the impeller is explicitly taken into account. Meanwhile, the MRF approach predicts the steady flow field for a fixed position of the impeller relative to the overall system. Manka [50] modeled the rotor motion in the flotation tank using both approaches SM and MRF and obtained nearly similar results with an intensive computational cost engendered by the SM approach. Binxin evaluated the effect of the numerical approach in an agitated system, by using the converged results of the MRF approach as initial conditions for the sliding mesh approach. He obtained improved results when using the sliding mesh but much longer CPU time was required [51]. Hence, the MRF approach is recommended for its acceptable accuracy and low computing cost.
Under the constraint of exploiting mineable ore reserves of low bone phosphate of lime (BPL) grade, OCP Group (Morocco) has adopted the reverse froth flotation process in order to separate apatite from gangue minerals, essentially silicates and carbonates. Through this beneficiation process, improving BPL grade of washed phosphate and increasing the P2O5 recovery become feasible and it makes the exploitation of low grade ore economically profitable [52], [53]. Despite the froth flotation effectiveness, its excessive energy demand cannot be denied. Rinne and Peltola assessed that the lifetime energy consumption cost in the flotation constitutes two-thirds of the total life-cycle cost [54], it is considered as the first contributor in the operational cost. Responding to the increasing need of meeting the energy efficiency and the intensive growth of the flotation machine sizes [55], it is worth asking how much energy is consumed within flotation cells. Equally important, understanding how the three intervening phases in the flotation process namely liquid, air bubbles and solid interact, provides a good overview of the mixture behavior within the flotation cell.
The majority of the established works in the flotation field, deal with the chemical treatment [56], flotation kinetics [57] and the major interactions occurring during this process [58]. In this study, we are interested in the understanding of the hydrodynamic flow behavior within a flotation cell mechanically agitated. We aim to treat a multiphase hydrodynamic flow constituted by fluid (water) and particles (phosphate rock) intervening in a laboratory-scale flotation cell covering different aspects including the energy consumption and also the homogenization efficiency. The novelty of this work lies in the study of the hydrodynamic flow within the fluid sheath of a flotation cell having a complex and non conventional geometry, while taking into account all the essential equipments and the internal parts found in mechanically agitated flotation cells. Therefore, we have developed a CAD model that includes all the geometric singularities without any approximation that may have effect on the nature and the behavior of the flow within the cell. We dealt with a flotation cell having a cubic form, equipped with a Rushton turbine mounted vertically in the same axis with a stator (air diffuser). The investigation held in this study concerns sensitivity analysis in regards to two working parameters: the impeller rotational speed and the solid volume fraction. These two operating parameters are of extreme importance in the flotation process, because, under the constraint of increasing the production, the manufacturers may increase the solid volume fraction and the rotational speed expecting to get a satisfying purification yield but ignoring the consequent excessive energy consumption and missing the control of the solid distribution during the process. Accordingly, through this work we offer a global overview of the flow features within the flotation cell.
Section snippets
Mathematical models
The Eulerian–Eulerian formulation is used to perform numerical simulations of the flotation cell. This approach ensure the study of the dispersed phase as ensemble averaged and modeled with an Eulerian equation similarly to the continuous phase.
In the flotation process the phosphate volume fraction is relatively high. It is included between 14% and 20%, for this reason, the multi-fluid approach was adopted to study the fluid–solid flow. Thus, the phosphate particles and the fluid are treated as
Main hydrodynamic parameters
The major parameters that allow a clear understanding of the flow within an agitated system are essentially: the power consumption P, the power number Np, the Reynolds number Re, the pumping flow rate Qp, the flow number N, the mixing time θm, the vorticity criteria and the velocity field.
Procedure overview
First, we started by checking the reliability of the considered physical models describing the hydrodynamic flow in the flotation cell. Regarding this aim, we launched numerical simulations of the flotation tank without inserting the air diffuser, then we validated the obtained CFD results against some established works in the literature. Then, we worked on the complete geometry of the flotation cell including the air diffuser and we extended the study to cover two-phase flow by adding the
Results and discussions
The open source CFD tool OpenFoam 5.0 was used to solve the flow equations, the turbulence models and the transport equations. It is a highly flexible CFD code where every component can be customized to fit to the user's need. In monophase flow calculations, the algorithm SIMPLE is used for coupling the pressure with the velocity, while the PIMPLE algorithm is used in two-phase simulations. The relaxation factors used in the monophase simulations are 0.5 for U, k and ϵ and 0.3 for the pressure.
Conclusion
In this work a CFD study was elaborated in order to investigate the hydrodynamic flow behavior within a laboratory-scale phosphate flotation cell while the internal parts are taken into consideration. The Eulerian–Eulerian approach was used to describe mathematically the flow properties. The numerical results were compared to the experimental measurements published in the literature. A good agreement was shown in the CFD results order.
Two cases are treated, monophase flow simulations
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