A computational fluid dynamics model for the flotation rate constant,Part I: Model development

A Computational Fluid Dynamics (CFD) model for the prediction of the flotation rate constant in a standard Rushton turbine flotation tank was developed. The premise for the model development was the assumption that separation by flotation is a first order rate kinetic process. An Eulerian–Eulerian framework in conjunction with the dispersed k–ε turbulence model was supplemented with user defined functions to implement the local values of the turbulent flow into a kinetic model. Simulations were performed for quartz at different operational conditions. The numerical predictions were validated against experimental data and analytical computations using the fundamental flotation model of Pyke et al. (2003). The results showed that the CFD-based model not only captured the trend of experiments for a range of particle sizes but also that the CFD yielded improvements in the predictions of flotation rate constant compared with the theoretical calculations. It was found that the CFD model is able to predict the flotation rate constants of the quartz particles floating under different ranges of hydrophobicity, agitation speed and gas flow rates with lower root mean square deviation compared with the theoretical computations.     

Mixing characteristics of industrial columns in rougher circuit

The rougher circuit at Miduk Copper Concentrator, Iran, includes five Microcel™ flotation columns in parallel, each 12 m in height and 4 m in diameter. The main objective of this communication was to describe the mixing conditions of rougher columns using residence time distribution (RTD) data. A liquid radioactive tracer was employed to trace the material reported to tailing and concentrate. External scintillation detectors were used to record the tracer intensity without disturbing the flow pattern. Data analysis showed that large and small tank-in-series and N perfect mixers in series were the best models to present the flow pattern of liquid transferred to tailing and concentrate, respectively. Solids mean residence time from a theoretical model for counter-current columns was estimated. A 1.4:1 ratio between the residence time of liquids and solids was achieved. In order to complete the diagnosis, solid content and grade profiles along the collection and froth zone of one of the columns were also measured. The results of the present study showed that despite the presence of vertical baffles, the mixing conditions of industrial rougher columns were close to well mixed ones. The possible causes for mixing in industrial columns were described. As expected by increasing gas flow rate, the mean residence times of liquid transferred to both tailing and concentrate streams reduced and the mixing degree increased.     

A CFD-kinetic model for the flotation rate constant,Part II: Model validation

A Computational Fluid Dynamics (CFD) model was validated against published experimental data for the prediction of the flotation rate constant. An Eulerian–Eulerian framework was applied for modelling the multiphase flow inside a standard laboratory scale Rushton turbine flotation tank. The dispersed k–ε turbulence model simulated the turbulent effects inside the tank, while the collision, attachment and stability efficiencies were calculated using the local values of hydrodynamic parameters. Volume-weighted average flotation rate constants were simulated for chalcopyrite and galena and compared against published experimental data for the same physical setup. The results showed that both qualitatively and quantitatively the developed CFD-kinetic model can predict the flotation rate constants with an acceptable level of accuracy. Moreover, the validations of rate constants for the flotation of chalcopyrite and galena under various contact angles, agitation rates and gas flow rates confirmed the predictive capability of this numerical approach for further flotation modelling.     

Rougher flotation of copper sulphide ore using biosolids and humic acids

In the quest of new, less hazardous, and more ambient-friendly froth flotation reagents, the use of biosolids or humic acids as both collector and frother for the concentration of copper sulphide ores was investigated. Rougher flotation tests were conducted in Denver cells on a laboratory scale, and metallurgical indicators such as copper recovery, copper concentrate grade, and concentration and enrichment ratios were compared with those obtained under similar conditions but using conventional collectors and frothers for the industrial flotation of copper sulphide ores. With a dosage of 10% (w/w) biosolids, copper recovery and grade were 26% and 0.81%, respectively. The copper recovery and grade obtained with 1.5% (w/w) salt of humic acids were 29.7% and 3.5%, respectively. A significantly higher copper recovery (65.1%) was obtained with conventional industrial collectors and frothers, but the grade was also low (3.1% Cu). With the same dosage of humic substances, humic acid show that the flotation rate constant was significantly higher (0.2 min⁻¹) than that obtained with the same dosage of biosolids (0.09 min⁻¹). These results indicate that humic acids have more affinity than biosolids for copper-containing mineral species, and also show that biosolids and humic acids could be used as both collector and frother in the sulphide mineral concentration process by froth flotation. Because the distribution of iron in the concentrate obtained with biosolids is highest, these materials seem to have more affinity for pyrite.     

Flotation in a novel oscillatory baffled column

This paper presents an evaluation of an oscillatory baffled column (OBC) as a novel flotation device. The cell is based on a standard column design but employs a novel agitation mechanism where a series of baffle plates are oscillated sinusoidally through the fluid. This type of agitation has been shown to produce a more evenly distributed shear rate in the cell and allows the effect of agitation on particle–bubble contacting to be decoupled from gas dispersion effects. The column was first characterised in terms of mixing and gas dispersion, before being flotation tested using a quartz-amine system. Results indicated that the OBC was able to improve the flotation rate constant by up to 60% for fine particles (<30 μm) and by between 30% and 40% for coarser particles, relative to a standard flotation column. Interestingly, optimal flotation performance was obtained at power intensities orders of magnitude lower than those found in similar studies in stirred systems. This is believed to arise from the even distribution of shear in the OBC together with the oscillatory motion of the fluid in the cell. This oscillatory motion does not contribute to the average power intensity in the fluid and therefore results in more fluid motion per unit energy than would be obtained in a conventional stirred system. The OBC was therefore able to significantly improve flotation rates at power intensities orders of magnitude lower than those found in conventional cells.     

浮选柱的过去、现在及将来

介绍了国内外浮选柱的发展概况和部分浮选柱的结构。我国浮选柱与国外浮选柱相比,性能不相上下,但因我国电力不足,无法保证矿山供电,浮选柱经常停车,频繁放矿,金属矿物大量流失,选矿厂宁可再度采用浮选机。文中指出了我国浮选柱复苏的条件。     

近年浮选进展

通过浮选相关文献量的分布比较,从数量上描绘了浮选近5年的发展的概貌。重点评述了浮选以下几方面的发展：浮选设备（浮选机、浮选柱和磁力浮选设备）、浮选新药剂（捕收剂、起泡剂和调整剂）、泡沫中分选（粗粒浮选新方法）、载体浮选、无捕收剂浮选、物理作用（外加电场、磁化、超声波等）与浮选、生物浮选（生物捕收剂和调整剂）、浮选泡沫图象、硫化矿和铝土矿浮选等。此外,简述了国内近年浮选工业实践的进展。     

Characterization of large size flotation cells

Design and operating conditions of large size mechanical flotation cells were evaluated by comparing it with the actual operating conditions in a plant. The objective was to determine the time scale-up factor, typically based on empirical rules. Experiments were conducted on the rougher flotation circuit at Minera Escondida Ltd. The circuit consisted of self-aerated mechanical cells of 160 m³, arranged in six parallel banks with nine cells each.The rougher circuit flotation kinetics was evaluated from direct sampling and local mass balances around each cell of the bank. Adjusted overall mass balances were also developed. This information was used to fit different kinetic flotation models, and it was found that the rectangular distribution function was the most appropriate to describe the distributed rate constant for industrial operation. Then, a rougher flotation simulator was developed to describe the actual operation in terms of the operating variables (mass flow rate, solid percentage, feed grade) and the actual volumetric flow rate entering to each cell. In this study feed pulp samples were taken in parallel from the rougher circuit and were simultaneously floated in laboratory. The kinetic behavior was then modeled at a laboratory batch scale in order to determine the time scale-up factor between laboratory batch flotation data and industrial size flotation. The time scale-up factor observed for large sized cells, 160 m³, was found reasonably similar to those previously determined for self-aerated mechanical cells, but of lower size, operating at similar recoveries. In addition, the relative effect of mixing, between laboratory batch and an industrial flotation bank was quantified by the ϕ parameter, separating the impact that kinetic and mixing changes have on the time scale-up factor.In general, the rougher flotation operation was found to reach the predicted metallurgical target, and that the optimal separability criterion was also respected.The diagnostic generates information about the internal state of the process and helps to identify potential improvements for design, operation and control of the circuit.     

应用JKSimFloat进行矿物可浮性的模拟研究

由于浮选过程自身的复杂性以及众多因素对浮选过程的影响,浮选的建模一直比较困难。通常采用浮选一阶动力学模型进行浮选建模,本文根据一阶浮选速率k将矿物划分为不同的可浮性组分,通过最小化误差平方和的方法拟合得到不同可浮性组分的浮选速率,这将有利于对浮选的建模研究。     

会泽铅锌硫化矿异步浮选新技术研究

通过单因素和正交浮选试验研究了会泽方铅矿、黄铁矿与闪锌矿之间的浮选分离。根据浮选动力学基本原理,对方铅矿和黄铁矿的浮选动力学特性进行了分析。结果表明,基于总体平衡理论的分速浮选模型可以较好地模拟方铅矿和黄铁矿的浮选过程,浮选回收率模型拟合值与试验值之间的相关系数R2均达到0.999。研究认为,异步浮选新技术充分利用不同矿物及同种矿物可浮性和浮游速度特性,实现矿物的个性化、差异性浮选。进一步探讨了异步浮选新技术的理论背景,对选矿人员完善已有工艺及开发新技术具有一定的参考意义。     

Troubleshooting industrial flotation columns

Since the early 1980s flotation columns have been progressively incorporated in milling operations all over the world. Improvements in final concentrate grade, using single cleaning stages, have been in most cases the reason for using this new technology. However, the main disadvantage with respect to conventional mechanical cells is the large spread of'results, mainly in terms of recovery, which is normally compensated by a high circulating load and high capacities (overdesign).Besides normal changes in feed grade and flowrate, and the need for periodic maintenance for gas spargers, the following common troubles in plant practice are discussed: . improper calibration and maintenance of instrumentation to measure froth depth and gas rate . bias definition and estimation . uneven wash water distribution . uneven froth depth in baffled columns . lack of robustness of control strategiesProper boundaries for superficial wash water rate (0.1–0.2 cm/s), froth depth (0.5–1.0 m) and superficial gas rate (I-2 cm/s), based on fundamental knowledge and experience in large size columns, are suggested for stable operation. Unfortunately, the lack of coordination between these variables is an important limitation for metallurgical improvements.The effect of altitude on gas rate and gas holdup in flotation columns operating at 1500–4500 m over the sea level is analysed.     

速率常数在浮选过程中的变化机制研究进展

浮选动力学模型对描述浮选过程具有重要意义,浮选速率常数是模型构建的关键参数。深入研究速率常数与不同变量之间的数学关系,可以增加模型的精度和适用性|在不同操作条件下比较速率常数大小、观察其变化,为评价或优化浮选工艺、操作条件、药剂种类及用量、浮选设备性能等提供更有力的工具。文章介绍了浮选动力学模型随着速率常数的深入研究而不断发展的进程,论述了浮选速率常数K值的研究进展,简述了浮选速率常数的时间函数与分布函数的规律和发展以及K值在实践应用中发挥的作用。对推动浮选动力学不断发展的方向提出展望,深入探索浮选速率常数与微观变量的关系,建立新模型,并且优化拟合算法,精确求解模型中的主要参数,有助于精确地表达浮选过程。     

细粒矿物浮选技术和高效浮选柱研究进展

在分析细粒矿物浮选特性的基础上,综述了载体浮选、絮凝浮选、生物浮选、综合力场浮选等近年来应用广泛的新型细粒矿物浮选技术,并介绍了Jameson浮选柱、充填式浮选柱、旋流-静态微泡浮选柱这3种高效细粒矿物浮选柱,最后对细粒矿物浮选技术今后的研究方向进行了展望。     

大型浮选机自动控制——可编程调节器在工业控制中的应用

对我国研制的KYF—38型大型浮选机的控制对象特性进行了分析。对浮选机矿浆液面检测,提出了矿浆液面和泡沫层之间无明显分界面的模糊概念。针对选矿厂的气源情况,在充气量控制回路中,采用了提高执行机构比例度和设置控制死区的方式来改善充气量控制特性。控制系统在药剂、给矿条件不变情况下,以充气量和矿浆液面作为控制参数,实现铜粗选泡沫中的品位控制。控制系统采用了集散型的可编程调节器,工作可靠,组态灵活,其性能满足设计的要求,并通过工业试验证明该系统是切实可行的。     

Investigation of gas dispersion characteristics in stirred tank and flotation cell using a corrected CFD-PBM quadrature-based moment method approach

In this study, the population balance model (PBM) is coupled with computational fluid dynamics (CFD) to investigate the steady-state bubble size distribution in two types of process equipment namely, a standard Rushton turbine stirred tank reactor and a generic lab-scale flotation cell. The coupling is realized using Fluent 15.07 software, and the numerical model is validated for the stirred tank reactor. The population balance equation (PBE) is solved using the quadrature method of moments (QMOM) technique along with a correction procedure implemented to check and correct invalid moment sets. The breakage and coalescence of bubbles due to turbulence are considered. The breakage rate and daughter size distribution models proposed by Laakkonen et al. (2007) are considered. For modeling coalescence rate, models proposed by Coulaloglou and Tavlarides (1977) are considered. The interaction between the phases is handled by considering the drag model proposed by Lane et al. (2005) while ignoring the other interphase forces. The correction algorithm has been successfully implemented, and improved predictions of gas volume fraction and Sauter mean diameter (SMD, d₃₂) have been observed with a good match between the predictions and experimental measurements. The local SMD predictions are compared against predictions from the past studies and the superiority of the current approach for moderate gassing rates is established. The CFD-PBM approach is then used to study and characterize different flow regimes occurring in a generic mechanical flotation cell at different aeration rates and impeller rotation speeds. Also, power numbers are calculated from torque data and are found to drop considerably with an increase in aeration rate and impeller rotation speed as the flow regime approaches recirculating flow. The predicted SMD for flotation cell indicates that smaller bubbles are concentrated near the high turbulence impeller stream, the lower recirculation region, and close to the tank walls. On the other hand, large bubbles are formed in the upper tank region and are concentrated around the shaft during the flooding, loading, and transition flow regimes. In the future, the corrected QMOM approach will be further extended by implementing kinetic models capable of predicting the flotation rate constant using local bubble size information obtained from CFD-PBM simulations.     

Maximum size of floating particles in different flotation cells

Two flotation models, particle at the liquid-gas interface and particle-bubble aggregate, both based on balance of forces, were used for evaluation of experimental data relating the maximum size of floating particles d_max and their advancing contact angle. It was noticed, by comparing the experimental and model data, that for a given flotation device and material the maximum size of floating particle d_max increases with increasing particle hydrophobicity and at the same time the acceleration a, experienced by the d_max particle at the moment of rupture, decreases with particle hydrophobicity. The acceleration values change with cell dynamics and type of flotation device and are usually not available, therefore empirical apparent cell constants A, which characterize flotation dynamics and relate particle acceleration with advancing contact angle have been proposed instead. The values of A were determined by evaluation of experimental data relating d_max and advancing (detachment) contact angle for constant: particle density, medium density, surface tension, and flotation cell dynamics. Since A depends on particle density, a tentative formula was proposed to link A with density-independent flotation cell constant A_o. The values of A_o for selected flotation cells were calculated and presented.Using quartz as an example, it was shown in the paper that a positive advancing contact angle does not guarantee flotation because a prerequisite for flotation is non-zero receding contact angle.     

The implications of the froth recovery at the laboratory scale

This paper presents a critical review of the role of froth recovery in laboratory flotation kinetics tests. By conducting tests in the standard lab equipment (the Denver cell), it is demonstrated that, for typical scraping rates, the froth recovery is significantly lower than the 100% that is commonly assumed when interpreting lab kinetics data. Furthermore, it is shown that the curve of overall rate constant versus froth residence time, as defined by the scraping rate, is not linear, but increases quickly at faster scraping rates. These findings have important implications for scale-up. For one, differences in froth recoveries at the lab scale can lead to significant error in the modeled plant recoveries. For two, they undermine a key assumption used to derive and validate the linear relationship between collection rate constant and bubble surface area flux. This casts doubt on the assertion that it is only the collection rate—rather than the froth recovery, interface recovery, or some combination thereof—that is responsible for the observed collinearity between the bubble surface area flux and the overall rate constant.     

Flotation of high-grade fluorite in a short column under negative bias regime

This paper presents flotation results carried out on fluorite ore using a relatively short column, operated under negative bias regime and without wash water. The term short column is used from a kinetic point of view from which collection zone comes out to be around 8 m tall (the relation height/diameter appears valid for industrial size columns). Negative bias was achieved making tailing flow smaller than feed flow. Hence, part of the water is carried up within bubbles wakes. No wash water is added.It was found that, heavily loaded bubbles, formed in high-grade fluorite pulps, at negative bias, levitate easier than positive bias. Under such conditions, carrying capacity of columns seems to increase due to a decrease in downward velocity of pulp. Recovery increases considerably, resulting in a sort of rougher flotation. High recovery as well as grades was obtained under negative bias regime.     

Process mineralogy as a predictive tool for flowsheet design to advance the Kamoa project

The Kamoa resource, located in the Democratic Republic of the Congo, contains an array of copper sulphide minerals which are present as small grains, averaging 10–27 μm. An initial flowsheet was developed in 2011/12 for the prefeasibility study that was robust enough to handle flotation of all the copper sulphide minerals. Copper recoveries of the flowsheet were 85.4% for the hypogene ore and 83.4% for the supergene ore. Further work on the flowsheet required reduction of the SiO₂ grade of the concentrate, which at 19.1% negatively affected the downstream smelter processing, and also required improvement to copper grades and recoveries given the high grade of the ore. When new sample material became available as part of the Phase 6 drilling program, a fundamental reassessment of the ore and its flotation behaviour was conducted. Although mineralogical characterisation of the ore and liberation of the sulphides was quantified in previous phases of work, there was little understanding of the kinetics of each of the copper sulphide minerals and how they performed in the flowsheet. Comprehensive flotation kinetic tests at various primary grind sizes were performed. The corresponding timed concentrates of the three best performing grinds were characterised by QEMSCAN on a size-by-size basis to fully understand the flotation kinetics and liberation characteristics of the various copper sulphides. A simple and practical recovery model using minerals, particle size and liberation and association was developed from these data, and various flowsheet configurations were simulated. These simulations led to some robust process implications completely rearranging the flowsheet from the previous iteration into a more simple and economic configuration with better performance. The modelled data was confirmed with practically achieved data, extending the use of process mineralogy as a valid, predictive tool in process design. Additionally, the simulations using mineralogical, reduced empirical flotation testing needed to develop the new flowsheet.     

磁铁矿浮选柱反浮选中矿的研究

旋流-静态微泡浮选柱在磁铁矿阳离子反浮选中的工业应用,是国内首次将浮选柱成功应用于铁矿反浮选。为了更好地使用该新型设备,指出了在工业应用过程中出现的中矿问题,并在试验研究的基础上,提出了不同于传统浮选机流程的中矿处理方式。而中矿等一系列问题的解决,也完善了磁铁矿浮选柱阳离子反浮选工艺,为该工艺的应用开辟了更广阔的前景。