CFD-PBM simulation of the column flotation unit of FCMC: Importance of gas–liquid interphase forces models

The cyclonic micro-bubble flotation column (FCMC) is an efficient flotation device for the separation of fine minerals, but its mechanisms are rarely studied using computational fluid dynamics (CFD). This paper reports the air–water two-phase computational fluid dynamics-population balance model (CFD-PBM) simulations for the column flotation unit of an FCMC. The shear stress transport (SST) k-ω model with curvature correction (CC) is used to simulate turbulence effects. Then, the interphase forces models considering bubble size distribution are selected according to the experimental data in a bubble column, which is in analogy to the column flotation unit of the FCMC. Finally, the optimal combination of interphase forces models (i.e., the Ishii–Zuber drag force model, the Hosokawa–Frank wall lubrication force model, and the Lopez de Bertodano turbulent dispersion force model) is applied to simulate an FCMC with a superficial gas velocity of 0.0144 m/s. The results show that the CFD-PBM simulation can achieve a relative error of 9.09% for gas volume fraction and −5.45% for bubble rising velocity, indicating the reliability of the selected combination of interphase forces models.     

An experimental study of copper sulfide flotation in a packed cyclonic–static microbubble flotation column

A method using a cyclonic–static microbubble flotation column packed with fluid guiding media was proposed for improving flotation efficiency of copper sulfide. The installation of packed fluid guiding media in a cyclonic–static microbubble flotation column was for changing flow pattern in 10 the column by avoiding strong cyclonic flow in the upper region of the column, which can cause bubble-particle detachment. Therefore, the attached particles can be more likely to enter the froth zone instead of swirling in the column. The flow rectification contributed to a smaller bubble size in the column and significantly reduced the number of big bubbles with diameter above 1 mm. This scenario was caused by the damping of swirling liquid motion where bubbles tended to 15 concentrate and coalescence in the center of an eddy. The packed fluid guiding media changed the hydrodynamics in the upper column from a cyclonic flow to a gentle flow and as a result improve the column separation. The application of packed fluid guiding media can decrease the bubble-particle detachment and the flotation recovery of copper sulfide could constantly improve with the installation of packed fluid guiding media in the FCSMC column.     

The Limits of Fine and Coarse Particle Flotation

The flotation behaviour of quartz particles was studied over the particle size range from 0.5 µm to 1000 µm and for advancing water contact angles between 0° and 83°. Flotation was performed in a column and in a Rushton turbine cell. Particle contact angle threshold values, below which the particles could not be floated, were identified for the particle size range 0.5–1000 µm, under different hydrodynamic conditions. The flotation response of the particles, either in a column or in a mechanically agitated cell with a similar bubble size, was comparable. Turbulence plays a role, as does bubble‐particle aggregate velocity and bubble size. The stability of the bubble‐particle aggregate controls the maximum floatable particle size of coarse particles. For fine particles, the flotation limit is dictated by the energy required to rupture the intervening liquid film between the particle and bubble. Flotation of very fine and large particles is facilitated with small bubbles and high contact angles. These results greatly extend our earlier observations and theoretical predictions.     

基于相群平衡模型的浮选气泡聚并模拟

气泡尺寸分布直接影响气浮分离效率,而聚并是导致气浮池内气泡尺寸变化的主要因素。首先用实验方法测量气浮接触区气泡尺寸分布,然后用计算流体力学方法对气泡/水两相流动及气泡聚并进行模拟,最后通过对实验和数值模拟结果进行对比建立基于相群平衡模型的浮选气泡聚并行为的模拟方法,分别运用Luo、Free molecular和Turbulent聚并模型对气浮接触区气泡聚并行为进行模拟。结果表明:Turbulent聚并模型计算所得气泡尺寸分布与实验值最接近,适合模拟接触区气泡聚并;气泡平均直径随高度升高先变大后保持不变,气泡聚并主要发生在接触区中下部;气泡的加入增强了接触区流动混乱程度,上部产生对称涡流,中下部呈由边壁向中心的水平流动。     

Bubble size distribution in a bubble column with vertical tube internals: Experiments and CFD-PBM simulations

Knowledge of bubble size distribution (BSD) is critical for controlling mass transfer and reaction in bubble column reactors. Installation of internals further complicates this issue. The effects of internals on BSD were systematically investigated through experiments and computational fluid dynamics-population balance model simulations. The experiments show a bimodal distribution of the volume-based BSD except at low superficial gas velocity of 0.01 m/s. Addition of 20% internals increases the small-bubbles fraction, making the first BSD peak more evident. Correspondingly, the simulation reveals a prominent decrease of turbulent dissipation rate and turbulent kinetic energy. Moreover, while the unresolved turbulent kinetic energy dominates in the empty columns, the resolved portion becomes the major component in the presence of internals. This suggests that internals may redistribute turbulent kinetic energy in each scale, which provides more insights into the complex flow characteristics in the presence of internals and process intensification.     

Picobubble Enhanced Fine Coal Flotation

Abstract

Froth flotation is widely used in the coal industry to clean ?28 mesh fine coal. A successful recovery of particles by flotation depends on efficient particle‐bubble collision and attachment with minimal subsequent particle detachment from bubble. Flotation is effective in a narrow size range beyond which the flotation efficiency drops drastically. It is now known that the low flotation recovery of particles in the finest size fractions is mainly due to a low probability of bubble‐particle collision while the main reason for poor coarse particle flotation recovery is the high probability of detachment. A fundamental analysis has shown that use of picobubbles can significantly improve the flotation recovery of particles in a wide range of size by increasing the probability of collision and attachment and reducing the probability of detachment.

A specially designed column with a picobubble generator has been developed for enhanced recovery of fine coal particles. Picobubbles were produced based on the hydrodynamic cavitation principle. They are characterized by a size distribution that is mostly below 1 µm and adhere preferentially to the hydrophobic surfaces. The presence of picobubbles increases the probability of collision and attachment and decreases the probability of detachment, thus enhancing flotation recovery. Experimental results with the Coalberg seam coal in West Virginia, U.S.A. have shown that the use of picobubbles in a 2″ column flotation increased fine coal recovery by 10–30%, depending on the feed rate, collector dosage, and other flotation conditions. Picobubbles also acted as a secondary collector and reduced the collector dosage by one third to one half.     

Experimental study on the influence of the orifice size on hydrodynamic characteristics and bubble size distribution of an external loop airlift reactor

The orifice size has a significant influence on hydrodynamic characteristics and bubble size distribution (BSD) in gas-liquid flow. However, the mechanism of the influence of orifice size on BSD and hydrodynamic characteristics in an external loop airlift reactor (EL-ALR) has not been fully revealed. In this work, the effects of the orifice size on hydrodynamic characteristics and BSD in a laboratory scale EL-ALR were investigated using the particle image velocimetry (PIV) technique and digital image analysis (DIA). The results show that the transition superficial gas velocity becomes greater when the orifice size is reduced. The time-averaged bubble velocity profiles along the riser radius are parabolic, and the shape of the time-averaged bubble velocity curve is strongly dependent on the orifice diameter. The larger the orifice diameter, the steeper the parabolas. For sparger with lager orifice diameters, the BSD curve is bimodal even at low superficial gas velocity, and its peaks shift to a larger equivalent bubble diameter. The bubble aspect ratio appears to be related only to the equivalent diameter of the bubbles, regardless of the diameter of the orifice. It has a defined relationship between the bubble aspect ratio and the bubble equivalent diameter, and a new correlation is obtained based on the experimental data. This study will help to gain an understanding of the influence of sparger orifice size on the hydrodynamic characteristics and BSD and provide a basis for numerical simulation.     

Hydrodynamic stability of a bubble column with a bottom-mounted point air source

Bubble column is widely used in both industrial and environmental applications. In this study, we examine the flow dynamics and stability of a bubble column driven by a point air source centrally mounted at the bottom using Phase Doppler anemometry (PDA). The model cylindrical bubble column had an inner diameter of 152 mm and was filled with the liquid to about 1 m height, above the point air source, which was made of a 30-mm diameter perforated air stone. The bubble diameters were within the range of 400–1300 μm. A customized setup was developed for accurate PDA measurements of the two phases, and detailed turbulent characteristics of the liquid phase velocity, bubble diameter, bubble velocity and the slip velocity were collected throughout the column. The comprehensiveness of the data set enabled a close examination of the hydrodynamic stability inside the column. Measurements were taken at three different air rates, namely 0.13, 0.25 and 0.38 L/min (corresponding to average gas volume fractions of 0.0065, 0.0138 and 0.0197, respectively). The results illustrated a large-scale coherent liquid circulation pattern inside the column. The circulation pattern in the upper column was relatively steady, while the pattern in the lower column was strongly unsteady with the probability density functions (pdf) for both the liquid and bubble velocities showing distinct twin peaks. An analysis based on the determination of the bubble drag forces and transversal lift forces is performed by decomposing the twin-peaked pdfs into two separated Gaussian distributions, one for the upward flow due to the bubble rises and the other for the downward flow due to circulation. Through the decomposition, a stability criterion can then be established by choosing the local bubble size as the representative length scale for the turbulent eddies inside the column. The analysis with the criterion illustrates why a steady circulation pattern was achieved in the upper column, and at the same time shows that the instability at the bottom column was induced by the low frequency meandering of the bubble swarm.     

Bubble size distribution in a flotation column

The bubbles that were generated in a flotation column were measured. The bubble size distributions were obtained both for air-water and air-water-coal systems. The size distribution pattern was fitted to different equations. It was found that the bubble size distribution in both the flotation and cleaning zones follows the Rosin-Rommler equation used to describe the particle size distribution in crushing. This study indicates that bubbles in the cleaning zone are always larger than those of the flotation zone and finer bubbles are generated when a mixture of frothers is used instead of individual frothers.     

An agitated bubble column for use in potash flotation

A novel, agitated bubble column was designed, constructed and operated for the purpose of potash flotation. This report describes the apparatus and presents some typical results regarding bubble size distribution, gas hold-up and flotation efficiency. It was found that the column produced mean bubble diameters and overall gas hold-ups that could be predicted by empirical correlations presented earlier in the literature for aerated, agitated tanks. The column also achieved both a high percentage recovery ( > 90%) and a high product purity (97%).     

Gas-liquid flow and bubble size distribution in stirred tanks

This work is aimed at investigating the turbulent two-phase flow and the bubble size distribution (BSD) in aerated stirred tanks by experiments and computational fluid dynamics (CFD) modelling. The experimental data were collected using a two-phase particle image velocimetry technique and a digital image processing method based on a threshold criterion. With the former technique, the liquid and the gas phase ensemble-averaged mean and r.m.s. velocities are measured simultaneously, while with the latter the dimensions of the bubbles dispersed inside the liquid are evaluated. On the modelling side, a CFD approach, based on the solution of Reynolds average Navier-Stokes equations in an Eulerian framework for both phases, is adopted. As for the bubble dimensions modelling, besides the mono-dispersed assumption, a population balance method, named MUSIG, with bubble break-up and coalescence models is considered. The BSD and the axial and radial velocity of the gas and the liquid phase are presented and discussed. The outcomes of the computational work are evaluated on the basis of the experimental results.     

Drag models coupled with CFD–PBM method for simulation in bubble columns

In this study, three-dimensional numerical simulation of gas–liquid flow in bubble columns was realized by using the computation fluid dynamics (CFD)–population balance model (PBM). The new drag model improves the stability-constrained multi-fluid (SCMF-C) model because of the consideration of the wake accelerating and the hindering effects for calculating the drag correction factor. The gas holdup, axial liquid velocity, and bubble size distribution (BSD) predicted by four drag models at 0.02 and 0.1 m/s were compared. The results revealed that the proposed drag model can provide excellent predictions for both bubbly and heterogeneous flows. Because the wake accelerating and the hindering effects were considered, reliable predictions were achieved for the gas holdup, and the problem of uniform gas holdup distribution was mitigated. Therefore, the SCMF-C model can be extended for nonuniform BSD. The gas holdup and liquid velocity increased, and the nonuniformity of radial results became pronounced at 0.1 m/s. The profiles of four drag models were similar at a low height, whereas the difference between the simulations of the four models became obvious with the variation of heights. The results of the four models were accurate, and the BSD was wide at 0.1 m/s. Subsequently, the feasibility of the four drag models was evaluated at 0.2 and 0.4 m/s. The results of the comparison revealed that the proposed drag model exhibited excellent feasibility at higher gas velocities and was powerful for the simulation of bubble columns.     

Hydrodynamics and simulation of air–water homogeneous bubble column under elevated pressure

A gas–liquid Eulerian computational fluid dynamics (CFD) model coupled with a population balance equation (PBE) was presented to investigate hydrodynamics of an air–water bubble column (1.8 m in height and 0.1 m in inner diameter) under elevated pressure in terms of pressure drop, gas holdup, mean bubble size, and bubble surface area. The CFD-PBE model was modified with three pressure correction factors to predict both the total gas holdup and the mean bubble size in the homogeneous bubbly flow regime. The three correction factors were optimized compared to experimental data. Increasing the pressure led to increasing the density, reducing the bubble size, and increasing the gas holdup. The bubble size distribution moved toward a smaller bubble size, as the pressure increased. The modified CFD-PBE model validated with experimental data and empirical models represented well hydrodynamics of the bubble column at P = 0.1, 1.5, and 3.5 MPa.     

Dynamics of gas–liquid flow in a rectangular bubble column: experiments and single/multi-group CFD simulations

Several flow processes influence overall dynamics of gas–liquid flow and hence mixing and transport processes in bubble columns. In the present work, we have experimentally as well as computationally studied the effect of gas velocity, sparger design and coalescence suppressing additives on dynamics of gas–liquid flow in a rectangular bubble column. Wall pressure fluctuations were measured to characterize the low frequency oscillations of the meandering bubble plume. Bubble size distribution measurements were carried out using high-speed digital camera. Dispersed gas–liquid flow in bubble column was modelled using Eulerian–Eulerian approach. Bubble population was represented in the model with a single group or multiple groups. Bubble coalescence and break-up processes were included in the multi-group simulations via a suitable population balance framework. Effect of superficial gas velocity and sparger configurations was studied using single-group simulations. Model predictions were verified by comparison with the experimental data. Role of bubble size in determining plume oscillation period was studied. Multi-group simulations were carried out to examine evolution of bubble size distribution. An attempt is made to understand the relationship between local and global (over all the dispersion volume) bubble size distribution. The models and results reported here would be useful to develop and to extend the applications of multi-group CFD models.     

High performance g.p.c. with crosslinked polystyrene gels: influence of particle size distribution

Spherical crosslinked polystyrene gel particles have been separated by air classification into fractions having average particle diameters in the range 10–40 μm. The particle size distributions have been shown to be narrow by Coulter Counter measurements. G.p.c. column performance improves as the average particle diameter decreases and columns packed with gel fractions having a number-average particle diameter below 20 μm give plate counts in excess of 3000 plates per foot. Plate height results as a function of eluent flow rate suggest that chromatogram broadening due to mobile phase dispersion is reduced in columns packed with spherical particles having a narrow size distribution.     

Effect of microbubbles and particle size on the particle collection in the column flotation

Particle-bubble collection characteristics from microbubble behavior in column flotation have been studied theoretically and experimentally. A flotation model taking into account particle collection has been developed by particle-bubble collision followed by the particle sliding over the bubble during which attachment may occur. Bubble size and bubble swarm velocity were measured as a function of frother dosage and superficial gas velocity to estimate the collision and collection efficiency. Separation tests were carried out to compare with theoretical particle recovery. Fly ash particles in the size range of <38, 38-75, 75-125, >125 mm were used as separation test particles. Theoretical collision and collection efficiencies were estimated by experimental data on the bubble behavior such as bubble size, gas holdup and bubble swarm velocity. Collection efficiency improved with an increase of the bubble size and particle size but decreased in the particle size up to 52 mm. Also, flotation rate constants were estimated to predict the optimum separation condition. From the theoretical results on the flotation rate constant, optimum separation condition was estimated as bubble size of 0.3-0.4 mm and superficial gas velocity of 1.5-2.0 cm/s. A decrease of bubble size improved the collection efficiency but did not improve particle recovery.     

PDA measurements in a three‐phase bubble column

Phase Doppler anemometry was used to quantify the flow characteristic of a three phases (liquid, solid, and bubbles) cylindrical bubble column driven by a point air source made of a 30‐mm diameter perforated air stone centrally mounted at the bottom. The cylindrical bubble column had an inner diameter of 152 mm and was filled with liquid up to 1 m above the point source. Acrylic beads with a nominal diameter of 3 mm were used as the solid phase. To match the density of the solid phase which was 1.05 kg/m³, the liquid density was raised to about 1.0485 kg/m3 by added salt. The bubble diameters generated were within the range of 600–2400 µm. The detailed turbulent characteristics of the liquid‐phase velocity, bubble diameter, bubble velocity, and solid velocity were measured at three different air rates, namely 0.4, 0.8, and 1.2 L/min (corresponding to average gas volume fraction of 0.0084, 0.0168, and 0.0258, respectively) for the homogeneous bubble column regime. With the addition of the solid phase, the flow field was found to be relatively steady compared to the two‐phase column referencing the probability density functions for both the liquid and bubble velocities. An analysis based on the determination of the drag forces and transversal lift forces was performed to examine the flow stability in the three‐phase bubble column. The analysis illustrated that how the added solid phase effectively stabilized the flow field to achieve a steady circulation in the bubble column and a generalized criterion for the flow stability in the three‐phase bubble column was derived. Further investigation for the transition and the heterogeneous bubble column regime with air rates at 2.0 and 4.0 L/min shown that this criterion can also be used as a general prediction of flow stability in this three‐phase bubble column. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2286–2307, 2013     

锥形鼓泡床内气含率特性的研究

本文分析了锥形鼓泡床内流型过渡、平均气含率及气含率轴向分布特性，考察了入口气体速度、静止液体（或淤浆）高度及淤浆浓度的影响，比较了与圆柱床的差异，结果表明对于鼓泡床内气体体积收缩的反应，用锥形床的冷态试验可以较精确地模拟其实际结果。     

Bubble size in a forced circulation loop reactor

BACKGROUND: The bubble size distribution in gas‐liquid reactors influences gas holdup, residence time distribution, and gas‐liquid interfacial area for mass transfer. This work reports on the effects of independently varied gas and liquid flow rates on steady‐state bubble size distributions in a new design of forced circulation loop reactor operated with an air–water system. The reactor consisted of a cylindrical vessel (～26 L nominal volume, gas‐free aspect ratio ≈ 6, downcomer‐to‐riser cross‐sectional area ratio of 0.493) with a concentric draft tube and an annular riser zone. Both gas and liquid were in forced flow through a sparger that had been designed for minimizing the bubble size. RESULTS: Photographically measured bubble size distributions in the riser zone could be approximated as normal distributions for the combinations of gas and liquid flow rates used. This contrasted with other kinds of size distributions (e.g. bimodal, Gaussian) that have been reported for other types of gas‐liquid reactors. Most of the bubbles were in the 3 to 5 mm diameter range. At any fixed low value of aeration rate (≤1.8 × 10^?4 m³s^?1), increase in the liquid flow rate caused earlier detachment of bubbles from the sparger holes to reduce the Sauter mean bubble size in the riser region. CONCLUSION: Unlike in conventional bubble columns where bimodal and Gaussian bubble size distributions have been reported, a normal bubble size distribution is attained in forced circulation loop reactors with an air–water system over the entire range of operation. Copyright © 2007 Society of Chemical Industry     

Studies in Solvent Extraction Using Polyaphrons. I. Size Distribution,Stability, and Flotation of Polyaphrons

Abstract

Predispersed solvent extraction (PDSE) is a promising technique for the treatment of wastewater containing low solubility, hydrophobic contaminants. A stable predispersed organic solvent in the form of polyaphrons of very small diameter results in high surface areas with a minimum energy requirement for mass transfer of solutes from the aqueous phase to the organic solvent. PDSE should greatly improve the performance of a conventional extraction process. This paper focuses on the characterization and size distributions of polyaphrons. Polyaphrons were generated using different cationic, anionic, and nonionic surfactants in water and an oil-soluble nonionic surfactant. Kerosene was used as the organic solvent to form the polyaphrons. Size distributions were obtained using a particle size analyzer. The optimal instrument parameters (sample quantity, optical parameters, run time, etc.) were identified for these measurements. The size distribution based on volume fraction was found to show a bimodal behavior, with peak size maxima between 1–3 and 10–30 μm for all the polyaphrons. The effects of different surfactant types, surfactant concentrations, and storage times on the size distribution spectrum of polyaphrons were studied. The size distribution of different polyaphrons before and after flotation in an aqueous column using colloidal gas aphrons (CGAs) was also studied. Flotation was deduced to occur as a result of electrostatic forces between the CGAs and polyaphrons.