Computational fluid dynamics modeling of the flow in a laboratory membrane filtration cell operated at low recoveries

Scaled-down models of industrial filtration units are often used in laboratory studies of membrane processes. Knowledge of the flow field and shear stresses at the membrane surface is vital for the accurate interpretation of bench scale experiments. In this paper, we present results of computational fluid dynamics modeling of the flow within the SEPA CF flat sheet membrane filtration cell operated at low recoveries. The problem was formulated as the steady-state isothermal laminar flow of incompressible Newtonian fluid. Pressure, velocity, and shear stress distributions were computed with resolution for different average inlet velocities. Flow was found to be unidirectional over most of the channel area with exception of the corners of the channel. Stagnation areas in dead ends of inlet and outlet tubes and in the channel areas behind duct entries as well as local regions of high shear in duct-channel transition areas were observed. The relation between the highest shear rate created in this geometry and the average inlet velocity is given.     

Particle–bubble interaction and attachment in flotation

Flotation is an important unit operation in the minerals industry, among others. Current state-of-the-art flotation modelling combines computational fluid dynamics (CFD) with user-defined algorithms based on the “induction time” concept to describe selective bubble–particle attachment and separation of hydrophobic and hydrophilic particles.We have undertaken experimental studies permitting direct observation of particle–bubble interaction and attachment at the microscale to provide empirical data for comparison with new theoretical predictions.Observations were made on a model system in which 150 μm glass particles were dropped onto a captive 1.3 mm air bubble formed in water within a glass cell. The interactions were recorded on high-speed digital video, permitting direct estimation of relevant parameters such as the approach velocity, and the duration of particle sliding over the bubble surface. A new experimental configuration has allowed the particle path toward, around, and away from the bubble to be totally unimpeded.Particle trajectories show a significant deviation at separations much larger than their own diameter; such deviations are due to the hydrodynamics. Comparisons with theoretical predictions indicate that the bubble surface exhibited mobility intermediate between “full slip” and “no slip”. Theoretical predictions for an immobile bubble surface were practically symmetrical about the bubble's equator, while asymmetry was apparent in the theoretical predictions for a mobile bubble surface. However, the strongest asymmetries were seen in the observed particle trajectories and speeds.Particles dropping more centrally were seen to slide over the surface of the bubble. In several cases the sliding particle ‘jumped in’ toward the bubble, which is interpreted as the precise moment of attachment. This provides for a direct estimate of the threshold duration to achieve attachment, i.e. “induction time”. Among the events observed were rotation of the particle upon jumping in, and particle jump-in below the bubble's equator. Explanations are proposed in terms of particle properties and flow phenomena.     

Particle entrainment model for industrial flotation cells

A simple empirical dimensionless model to calculate the mineral gangue recovered per size class (R_G,i) by entrainment, in terms of the water recovery (R_W), in an industrial flotation cell is presented. For modeling purposes, a dimensionless entrainment factor EF_i, corresponding to the ratio (R_G,i/R_W), was defined for each particle size class. From experimental data measured in an industrial 130 m³ flotation cell, it was found that EF_i was well correlated with the dimensionless ratio (d_P,i/δ) by

     

Oil droplet movement and micro-flow characteristics during interaction process between gas bubble and oil droplet in flotation

Flotation is an efficient pre-treatment technology for oily water. In this work, the interaction process between the moving oil droplet and the gas bubble was studied by high-speed camera and Bassset-Boussinesq-Oseen (BBO) theoretical model, and the experimental and simulation results of the oil droplet trajectory were compared. Moreover, the micro-particle image velocimetry system was utilized to observe the flow inside and outside of the moving oil droplet. The results show that the BBO model with the mobile bubble’s surface can reflect the velocity change trend of the oil droplet during the interaction process between the moving oil droplet and the gas bubble, but there are some significant differences between the experimental and simulation results. While the oil droplet is moving on the bubble’s surface, the velocity of the area near the contact point of oil droplet–gas bubble is less than that of the other areas inside the oil droplet. Meanwhile, the flow of water above the oil drop is more biased towards the gas bubble.     

CFD-based multiscale modelling of bubble-particle collision efficiency in a turbulent flotation cell

In this paper, bubble-particle collision efficiency in a turbulent flow is investigated from a multiscale modelling viewpoint. An integrated CFD-based scheme for the prediction of turbulent bubble-particle collision efficiency is developed. As part of this scheme, the effect of turbulence and the bubble wall effect on bubble-particle collision efficiency are systematically studied using a 3D low turbulent Reynolds number shear-stress-transport turbulence model. Example simulations and comparisons are carried out to illustrate the methodology. The method can also be applied to non-Newtonian slurries.     

Modeling and simulation of separation process in flotation system

In order to design a flotation circuit to remove ink and contaminants from slushed old corrugated container (OCC) pulp suspension, a model based on mass balance was developed. The model is a five fractional model, which handles mass flow rate of ink, fiber, fines, filler and dichloromethane (DCM) extractives. A detailed method of calculating the deinking selectivity of a material from experimental data, described in terms of reject ratio, is presented. Three flotation deinking systems were simulated. In a single stage flotation system, increasing the number of flotation cells improved cleanness of the accept pulp suspension while it decreased yield at the same time. Yield can be increased by adding a second stage and by introducing the accept flow of the second stage into the feed flow of the first stage. However, the cleanness of the accept pulp was deteriorated. It was shown that yield can be increased without compensating the cleanness of the accept pulp by utilizing the accept pulp from the second stage for another paper machine line instead of sending back to the feed flow of the first stage.     

Direct measurement of entrainment in large flotation cells

A key response variable to describe the metallurgical performance in a flotation cell is the concentrate grade. The mineral feed characteristics and conditioning determine the grade of the particles attached directly to the surfaces of the bubbles by true flotation, while the operating conditions, such as gas rate, bubble size, froth depth and others, determine the amount of gangue recovered by entrainment, which finally decreases the concentrate grade.In this paper, the recovery of liquid and solids by entrainment was evaluated by direct measurement of the fraction of liquid and solids reported to the concentrate in a 130 m³ mechanical flotation cell.The liquid and solids entrainment, per size classes (+ 150; − 150 + 45; − 45 µm), was measured by the radioactive tracer technique. The procedure consisted of introducing a tracer impulse at the cell feed entrance. The tracer time response was monitored on-line at the concentrate overflow and at the tailings discharge. Also, in order to obtain the quantitative distribution of the feed, samples were taken periodically from the concentrate and tailings streams, for a period of 4 residence times, during the tracer tests. This allowed the quantification of the mass of tracer reporting to both streams.Experimental results confirmed that solids entrainment with the froth was strongly dependent on particle size, and that the entrainment factor (EF = solid/water recovery ratio) was similar to that reported for smaller size cells under similar operations conditions.     

A simple model for the calculation of entrainment in flotation

Theoretical and experimental studies have been performed to analyze the entrainment of both hydrophilic and hydrophobic particles in flotation. A new model is proposed for the entrainment based on the water recovery trend. Two sets of timed flotation experiments were carried out to validate the model. These experiments were realized with quartz and pyrite as the only mineral in the pulp and with various frother concentrations and pulp densities. The chemical conditions of the pulp were adjusted to float pyrite as hydrophobic and to depress quartz as hydrophilic mineral. The solids recovery for each size fraction and water recovery was measured in these experiments. The proposed empirical model equation was checked against experimental observations. It was observed that the model equation well represented the entrainment-water relationship. Since hydrophilic mineral recovery mainly depends on the entrainment, the data obtained from quartz only tests were first fitted to the entrainment equation. The fit for quartz data was found to be satisfactory. This shows that the proposed model could be used to define the behavior of hydrophilic particles in a batch flotation test. The same model was applied for pyrite only tests and contribution of entrainment to hydrophobic mineral recovery was calculated. The results provided accurate interpretation of hydrophobic mineral entrainment, which is difficult to directly measure.     

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.     

永丰萤石矿粗精矿再磨浮选新工艺研究

本文研究了萤石—石英矿石的浮选，通过试验提出了粗精矿再磨浮选新工艺，各项指标较原工艺均有较大提高。     

A new experimental method for determining particle capture efficiency in flotation

A single bubble experiment has been developed for the determination of the capture efficiency of particles by bubbles in flotation under well-controlled hydrodynamics and physico-chemical conditions. In a glass column, small single bubbles (d_b=0.22−1.16 mm) are produced in pure water and then rise at their terminal velocity through a suspension consisting of spherical glass particles where bubble–particle capture takes place. The capture efficiency E_capt is calculated as the ratio of the number of particles captured by one bubble to the number of particles present in the volume swept out by this bubble. Images recorded at high optical magnification show that particles slip on the interface, then adhere to air bubbles individually or as aggregates and cover the rear part of bubble surface. The bubble's effective density and interface contamination level are increased by captured particles. As a result, bubble's rising velocity U_b is reduced along the experimental device. By establishing the relationship between capture efficiency E_capt, bubble rise velocity U_b and bubble clean angle θ_clean, a new approach to measure particle–bubble capture efficiency is proposed. This new experimental technique is applied to provide a new set of data for capture efficiency in the case of bubbles with a clean interface. E_capt is found to grow as d_b decreases and d_p increases, within the range between 0.02 and 0.20, which is in the order of magnitude of experimental results of Ralston and Dukhin (1999) as well as of numerical results of Sarrot et al. (2005). These data are favorably compared to numerical modeling of collision efficiency.     

Regrinding sulphide minerals — Breakage mechanisms in milling and their influence on surface properties and flotation behaviour

Changes in surface properties with grinding and regrinding play a key role in mineral flotation performance. Different particle breakage mechanisms in grinding mills may change the mineral surface properties in different ways, possibly leading to different mineral floatabilities depending upon the predominant breakage mechanism. The Magotteaux Mill^® and IsaMill were selected as representations of a tumbling and a stirred mill, respectively. The latter has a greater contribution to particle size reduction from the abrasion mechanism than the former which also has contributions from impact breakage.Mineral recovery decreased with size reduction through stirred mill regrinding (i.e., the IsaMill) employing ceramic media from 90%, achieved before regrinding (d₈₀ 80 μm regrind feed), to 71, 58, 20 and 5% achieved after regrinding to d₈₀ values of 60, 40, 20 and 10 μm, respectively. A similar trend of decreasing recovery was also observed with regrinding in the tumbling mill (i.e., Magotteaux Mill^®). Changes in mineral flotation behaviour were investigated with respect to (i) particle size, (ii) increase in surface area, and (iii) surface contamination with size reduction in the two different mills. The flotation of pyrrhotite with additional reagents illustrated that the total change in recovery through regrinding results mainly from the increase in surface area of the pyrrhotite afforded by size reduction. The effects of the predominating particle breakage mechanism on the change of mineral surface properties were studied through regrinding in the two different mills. In particular it was observed that the hydrophobicity/floatability of the coarse particles decreased to a greater extent with stirred mill regrinding than with tumbling mill regrinding at coarser regrind product sizes (d₈₀ 70 and 60 μm) presumably due to the greater contribution of the abrasion mechanism to size reduction afforded by the stirred mill. It was also observed that the difference in recovery for the same regrind product size from the two different mills decreased when approaching finer regrind sizes, which indicated that the particle breakage mechanisms of the different mills for fine regrind product size were not as influential as for coarse regrind product sizes.     

Modeling the liquid-phase oxidation of hydrocarbons over a range of temperatures and dissolved oxygen concentrations with pseudo-detailed chemical kinetics

The ability of pseudo-detailed chemical kinetic modeling to simulate the oxidation behavior of Exxsol D-80, a paraffin blend whose oxidative characteristics are representative of severely hydrotreated jet fuels, is assessed. The effects of temperature and initial dissolved O₂ concentration on oxidation are considered. A 17-step pseudo-detailed mechanism is shown to provide reasonable simulations of Exxsol D-80 oxidation over a range of temperatures, but not over a range of initial dissolved O₂ concentrations. The addition of alkyl-peroxy radical isomerization to the pseudo-detailed mechanism did not reconcile the initial dissolved O₂ limitation. With the addition of a peroxy radical decomposition reaction to the original 17-step pseudo-detailed mechanism, reasonable simulations of Exxsol D-80 oxidation over a range of temperatures and initial dissolved O₂ concentrations were obtained. Analysis of the rate parameters associated with peroxy radical decomposition suggests that aromatic hydrocarbons play a significant role in the oxidation of fuels, even at low (<1% by weight) aromatic levels.     

Determination of the collision frequency between bubbles and particles in flotation

Collision efficiency for a spherical bubble rising in a uniform concentration of small non-inertial particles is studied by direct numerical simulations (DNS). The Stokes number of the particles is negligibly small so that the particle trajectories follow the streamlines. The effect of the bubble interface contamination is studied for the flow surrounding the bubble using the spherical cap model. Numerical results are obtained for a wide range of bubble Reynolds number (based on bubble diameter d_b) ranging from 0.01 to 1000 and for different angles of contamination ranging from 0^° to 180^°. The collision efficiency is found to be increased with the Reynolds number and significantly decreased with the level of contamination. Correlations of the numerical results are proposed for efficiencies versus d_p/d_b (d_p being the particle diameter), bubble Reynolds number and interface contamination degree. For clean (respectively, fully contaminated) spherical bubbles, the efficiency evolves as d_p/d_b (respectively (d_p/d_b)²) whatever the bubble Reynolds number and the particle size. For partially contaminated bubbles, efficiency can be scaled with d_p/d_b or (d_p/d_b)² depending on both the level of contamination and the particle size.     

浮选数模及计算机模拟在选矿试验中的应用

可浮性k值的分布密度函数f(x)是常数k_m和k_p所唯一确定的г分布。概率微元f(k)dk的实验室闭路浮选可以用马尔科夫随机过程来描述,所导出的中矿浮选动力学模型是一组无穷递减等差数列。模型参数用回归法确定。只要进行一些较简单的试验,即可用按本模型编的程序在计算机上进行多种模拟试验。经实际验证模拟结果与试验结果吻合较好。     

Elastohydrodynamic theory for wet oblique collisions

This paper presents a model for oblique collisions of spherical particles with a plane surface covered with a thin liquid layer. Elastohydrodynamic theory developed previously for fully immersed collisions [Davis, Serayssol and Hinch 1986 JFM 63 479-497] is modified for the normal component of motion to account for the finite thickness of the liquid layer. The resulting time evolution of the film thickness profile is then used along with sliding lubrication to determine the tangential component of motion. The critical Stokes number (dimensionless ratio of particle inertia and viscous forces), below which no rebound is seen, is predicted in terms of the physical properties of the materials involved in the collision, as described by a compliance parameter representing a dimensionless measure of elastic deformation due to viscous forces. Beyond the critical Stokes number, the normal restitution coefficient is found to increase with the Stokes number and the compliance parameter, asymptoting to the dry restitution coefficient at high Stokes numbers. The lubrication suction resistance during rebound is limited by cavitation. The tangential restitution is independent of the impact angle and is linearly dependent on the ratio of the fluid layer thickness to the sphere radius, in addition to depending on the Stokes number and compliance parameter. The tangential restitution is found to be close to unity and is generally higher for a larger value of the compliance parameter. Moreover, the tangential restitution is seen to increase with the Stokes number at small compliance and decrease with the Stokes number at large compliance. The change in rotational velocity exhibits trends that are the reverse of the tangential restitution. Finally, closed-form expressions have been developed for describing the restitution coefficients and dimensionless change in rotational velocity.     

Modeling and Characterization of Air Emissions from Laboratory and Industrial Fluidized Beds

A fluidized bed model using several elutriation correlations was developed and tested against an operating fluidized bed used in a Fluidized Catalytic Cracker Unit (FCCU) and a 1:8.5 scale laboratory system. It was found that there was little variation between the emission rates predicted using different elutriation correlations, although the newly developed equations were slightly more accurate for the laboratory‐scale system. Although total emission rates were predicted with reasonable accuracy, the actual volatility and fluctuations seen in real fluidized beds emissions were not predicted. When the model was used to predict particle emission from the industrial FCCU, they preformed poorly, grossly overestimating the actual levels. It was determined that the attrition terms used in emission modeling were inappropriate and that the model preformed better without them, but still overestimated the actual emissions. This overestimation was greater in the industrial system compared with the smaller laboratory system. It was also found that the older elutriation terms were better for predicting industrial emissions compared with those of the smaller scale units.     

Modeling of flotation process in dispersed systems

Mathematical model of flotation in dispersed mixture of liquid, solid, and gas phases has been designed within the considerations of the mechanics of multiphase media with the assumption of the degree of mineralization of the bubble surface. The application of the designed model has been demonstrated based on the example of one-dimensional stationary flotation and it has been shown that the equations that describe the emergence of bubbles are singularly disturbed (“rigid”). The effect of size and concentration of bubbles, as well as volume content of dispersed particles, on flotation has been analyzed.     

Modeling of sedimentation of polydisperse spherical beads with a broad size distribution

This article deals with experimental and theoretical studies of the sedimentation of polydisperse agarose beads with broad particle size distributions. A light-extinction principle was used to measure the variation of solid concentration in the suspension with time and settling distance. Different experimental conditions have been used to show the influence of solid concentration and liquid density and viscosity on the settling behavior of the beads. The sedimentation process was described mathematically by a system of conservation law using Masliyah's hindered settling function. The physical properties of the beads and the optical properties of the suspension were carefully examined to enable a reliable comparison between experimental and simulation results. The model gives good predictions under all the conditions studied, showing its soundness in formulating the hindered settling process of polydisperse particles in a suspension.