A model to relate the flotation rate constant and the bubble surface area flux in mechanical flotation cells

Two recent flotation models developed by the authors are discussed, viz. the bubble population balance model and the attachment-detachment model. The bubble population balance model describes the history of a bubble population in a flotation cell in terms of the sub-processes of bubble breakage and coalescence. The attachment-detachment model allows for the presence of a gas phase in the flotation cell, both in terms of a gas residence time and the attachment and detachment of mineral particles to/from bubbles. When combined the two models predict a near-linear region about a point of inflexion on the (simulated) response between the flotation rate constant (k) and the flux of bubble surface area through the flotation cell (S_b). It is proposed by the authors that this region corresponds to the linear k−S_b relationship observed in a recent research project on flotation kinetics in mechanical flotation cells by Gorain et al. (1997).     

Correlation of air recovery with froth stability and separation efficiency in coal flotation

Recent research progress in hard rock mineral flotation shows that froth stability can be represented by air recovery, which is defined as the fraction of air entering a flotation cell that overflows the weir in unburst bubbles, and that air recovery has strong correlation with the separation performance of mineral flotation. Yet no experimental work on air recovery has been devoted to coal flotation. This paper studies air recovery in coal flotation and examines the links between air recovery, froth stability and coal flotation performance. A series of experiments were conducted using a laboratory-scale mechanical flotation cell at various methyl isobutyl carbinol (MIBC) concentrations and aeration rates. It was found that air recovery has a strong correlation with dynamic froth stability determined by measuring the maximum froth height in a non-overflowing froth column. At a fixed aeration rate (hydrodynamic condition) and various MIBC concentrations, a strong correlation between air recovery and coal flotation performance was also observed.     

Bubble load estimation in the froth zone to predict the concentrate mass flow rate of solids in column flotation

The concentrate mass flow rate of solids of a flotation column was modeled based on geometrical principles and considering complete air recovery to the concentrate and bursting of a fraction of the bubbles that reach the top of froth. For the first consideration, the results show that concentrate mass flow rate of solids experimentally measured, is smaller than that estimated with the geometrical model. For the second consideration, bursting of a 0.45 fraction of the bubbles reaching the top of froth gave improved results (average relative error obtained under these circumstances is about 20%).     

Improving froth characteristics and flotation recovery of phosphate ores with nonionic surfactants

The beneficial effect of a series of nonylphenol polyethylene glycol ether surfactants were tested in the flotation of phosphate ores in which the mixtures of sodium oleate and dodecane were used as collectors. In order to elucidate the flotation results, equilibrium surface tension of single and binary surfactant solutions prepared with sodium oleate and nonionic surfactants were investigated. Synergism between surfactants was determined by observing the change in surface tension of solutions and by the calculation of interaction parameter from surface tension data. The lowering of surface tension of sodium oleate solutions was observed in the presence of nonionic surfactants. The interaction parameter between sodium oleate and a nonionic surfactant (i.e., NP-4) was calculated to be −0.21, showing attraction between the two surfactant molecules. The nonionic surfactant NP-4 was then tested in batch flotation of phosphate ores. The beneficial effect of nonionic surfactant was obtained at different collector dosages and surfactant combinations.     

Role of dixantogen in froth flotation

Mechanism of dixantogen action in froth flotation is discussed. It is shown that this reagent eliminates kinetic constraints during formation of a flotation complex, rather than improves hydrophobicity of a mineral surface.     

Influence of gas flow rate and frothers on water recovery in a froth column

Froth plays an important role in the froth flotation separation of minerals. In froth and foam liquid drains away due to gravity until equilibrium is reached and at the same time is carried upwards by the moving gas phase. This paper aims at better understanding of the influence of the superficial gas velocity and frothers on the liquid drainage in foam and liquid recovery rate from the froth column. The obtained experimental data shows that the available standard drainage theory does not properly describe the influence of gas flow rate and Dowfroth 250 frother on the liquid recovery rate. The theory overpredicts the liquid recovery rate from the froth column. The improvement of the standard theory by inclusion of the contribution of the vertex geometry to the liquid drainage in foam does not resolve this problem. It appears that the liquid drainage process in the froth column is controlled by the interfacial properties of the adsorbed surfactants at the gas–liquid interface.     

Optimisation of air rate and froth depth in flotation using a CCRD factorial design – PGM case study

Air rate and froth depth are the most commonly adjusted levers in PGM flotation plants. The optimisation of these levers on each flotation cell has traditionally been done by varying either air rate at a fixed froth depth or vice versa. This approach does not consider the interaction relationship between air rate and froth depth and this effect on flotation performance.Factorial type experimental designs are best suited for investigating interaction effects between variables. This paper presents the use of a factorial type of experimental design being the (CCRD) Central Composite Rotatable Design for plant scale flotation optimisation of air and froth depth. The results obtained include three dimensional response surfaces and models of flotation response variables such as 4E PGM recovery and grade as a function of air rate and cell level. This paper illustrates the experimental methodology and discusses the results for normalised 4E PGM grade and recovery for a rougher cell treating a Platreef ore.These results indicate that interaction effects of air and froth depth are significant and are more pronounced at conditions of higher air and shallower froth depth. In addition, indices which are based on an optimisation objective such as grade multiplied by recovery and/or grade multiplied by recovery squared allows application of this technique as an optimisation tool. These indices can be used to determine an optimum operating range for air and level with the consideration of interaction effects.     

A new method for flotation rate characterization using top-of-froth grades and the froth discharge velocity

A new methodology is proposed for flotation characterization in industrial operations. The approach considers the mineral recovery to be proportional to both the top-of-froth (TOF) grade and the froth discharge velocity down a bank of cells. The procedure allows for the identification of the fractional recovery profile from the discharge velocities and the TOF grades. In addition, if the total recovery of the bank is available, the cell recoveries can be estimated by scaling the fractional recoveries. For this purpose, a single parameter was used to scale the recoveries for each sampling survey in order to obtain the kinetic response along the flotation banks. Industrial tests were performed in two rougher banks; one bank consisted of six 250 m³ self-aerated cells in a 1-1-1-1-1-1 arrangement, and the other bank consisted of nine 130 m³ self-aerated cells in a 1-2-2-2-2 arrangement. The results showed good agreement with the recovery profiles obtained from the cell-by-cell mass balances along two industrial flotation banks.     

Evaluation of the selective detachment process in flotation froth

The improved selectivity between particles of varying degrees of hydrophobicity in flotation froths has been well documented in literature, especially in the deep froths utilized in flotation columns. The phenomenon is believed to be due to the selective detachment process whereby the least hydrophobic particles are released from the bubble surface upon bubble coalescence. To quantify the selective detachment process, column flotation experiments were performed under various operating conditions that provided varying amounts of reflux between the froth and collection zones. Entrainment was eliminated by the use of relatively coarse 250 × 75 micron material. The flotation column incorporated the ability to provide instantaneous stoppage of the process streams and separation between the collection and froth zones after ensuring steady-state operation of the column. The samples collected from the two zones and process streams were evaluated to quantify the flotation rate distribution of the particles comprising each sample. The flotation rate was used as an indicator of the degree of hydrophobicity and thus a relative measure of the binding force between the particle and bubble in the froth zone. The flotation rate data was used as input into well known flotation models to obtain the froth zone recovery rate and the quantity of material that refluxes between the collection and froth zones.     

Boundary conditions for gas rate and bubble size at the pulp–froth interface in flotation equipment

This paper describes the effective boundary conditions for the gas dispersion parameters of bubble size, superficial gas velocity and bubble surface area flux, in mechanical and column flotation cells. Using a number of previously derived correlations, with appropriate simplifying assumptions, and experimental data reported from plant practices, the boundary conditions were identified. Thus, it was shown that these constraints typically allow for a mean bubble diameter range of d_b = 1–1.5 mm and superficial gas rate of J_g = 1–2 cm/s, in order to maximize the bubble surface area flux, S_b = 50–100 s⁻¹. Under these conditions there is no carrying capacity limitation, while keeping a distinctive pulp–froth interface.     

提高某铅锌矿浮选回收率试验研究及实践

某铅锌多金属硫化矿中含有方铅矿、闪锌矿、黄铁矿、磁黄铁矿、银矿物、毒砂等。为提高资源利用率,加强回收有用矿物,采用优先浮选工艺流程,在铅浮选作业中,采用选择性组合药剂(硫酸锌+亚硫酸钠+DMDC)作为锌闪矿、黄铁矿、磁黄铁矿和毒砂抑制剂,采用选择性组合药剂(SK9011+乙硫氮)作为方铅矿、银矿物的捕收剂。在锌浮作业中采用石灰抑制黄铁矿、磁黄铁矿和毒砂,硫酸铜活化闪锌矿,丁基黄药为捕收剂,实现了锌硫矿物有效分选。在硫浮选作业中采用硫酸铜活化黄铁矿、磁黄铁矿,丁基黄药为捕收剂,使黄铁矿和磁黄铁矿有效回收。工业应用期间,铅回收率提高了3.03个百分点,银回收率提高了4.78个百分点,锌回收率提高了1.24个百分点;获得硫精矿硫品位46.07%,硫回收率73.06%。     

Influence of coal particles on froth stability and flotation performance

Solid particles have significant effect on flotation froth. In this research, the effects of coal particles of different size and hydrophobicity on froth stability and flotation performance were studied. The froth stability was measured in both the froth formation and froth decay processes by maximum froth height, froth half-life time and water recovery. The results show that fine particles of moderate hydrophobicity contributed most to maximum froth height in the froth formation process and were most favorable for flotation. Fine hydrophilic particles stabilized the froth in the froth formation process but the froth half-life time was very short due to the high water solid ratio. High hydrophobic particles of both fine and coarse size fractions greatly increased the froth half-life time in the froth decay process. But the froths were very rigid and the maximum froth heights were very low. The presence of fine hydrophobic particles was very unfavorable for the recovery of coarse particles.     

核极限学习机在浮选回收率中的研究与应用

浮选回收率是浮选过程中重要的生产指标。需要通过人工检测得到的浮选回收率,可知性具有较大的时间延迟,使工人不能及时有效地对生产做出相应控制调整。由于浮选过程相当复杂,变量维数高、关联性强、噪声大、检测信号不完备等因素,难以建立较精确的回收率预测模型。然而,人工智能与机器学习技术能在机理不清楚、信息不完备的情况下,对复杂系统建立基于数据驱动的经验模型。因此,本文为提高回收率检测的及时性、有效性,在分析浮选过程相关因素影响的基础上,提出基于核极限学习机建立浮选回收率的预测模型。仿真实验结果表明,该建模方法可有效辨识浮选过程中,输入数据与回收率测量值之间的非线性关系,且具有更高的预测精度与训练性能。     

Flotation rate distribution in the collection zone of industrial cells

The batch flotation process has been commonly characterized assuming a flotation rate distribution function F(k), e.g.: Dirac delta, Rectangular, Gamma or Weibull functions. The identification of F(k) for the collection zone of continuous industrial cells is more complex and to the authors knowledge, has not been reported yet.In this work, a novel procedure to estimate the flotation rate distribution from the collection zone of industrial flotation cells, using the radioactive tracer technique, is presented. The approach consists of measuring the impulse response of the floatable mineral tracer concentration, and non-floatable gangue tracer concentration (Residence Time Distribution, RTD), in the cell tailings. Then, the floatable tracer concentration can be compared with the model prediction, using the Gamma function and the RTD of the non-floatable tracer. Thus, the F(k) distribution parameters were obtained by means of the least-square estimation. The new approach was successfully tested in industrial rougher flotation cells of large size.     

煤泥浮选泡沫特征提取算法综述

介绍了浮选泡沫表面的物理特征、纹理特征和动态特征提取的主流算法,分析了各算法的优缺点,对解决现阶段人为判别泡沫状态比较困难的问题,实现浮选自动化,提高浮选工艺指标具有一定的指导意义。     

浮选中颗粒-气泡间相对运动研究进展

颗粒-气泡间相对运动的研究对浮选机理的认知至关重要,对新型浮选机的开发和提高浮选效率均具有指导意义,本文系统综述了颗粒-气泡间相对运动的研究进展。早期研究过程中,研究者忽略了颗粒和气泡性质的影响,将颗粒视为随流线运动的点,气泡视为刚性球体,利用流线方程对颗粒-气泡间的相对运动展开研究;随着认知过程的不断深入,颗粒和气泡物理化学性质的影响逐步得到了关注,研究者分别从颗粒惯性力、重力、形状和粗糙度以及气泡表面流动性等方面并展开了大量研究;颗粒-气泡间相对运动的试验研究多通过颗粒沉降法进行,研究对象由单个玻璃微珠发展为大量矿物颗粒,且出现了关于运动玻璃球与上升气泡之间相对运动的研究。研究表明,当颗粒粒度较细、密度较小时,利用流线方程对颗粒-气泡间相对运动的研究具有一定的适用性;当颗粒粒度较粗、密度较大时,需考虑正负惯性力、重力等因素对颗粒-气泡间相对运动的影响。此外,颗粒形状的不规则性会影响颗粒周围液体对颗粒的作用力,导致临界碰撞半径减小,且颗粒表面不规则的凸起会促进颗粒-气泡间水化膜的破裂,减少诱导时间,增大颗粒表面粗糙度有助于增强颗粒-气泡间的黏附强度。气泡表面的流动性可采用"滞留帽"模型进行分析,具有较好的适用性。对于颗粒-气泡间相对运动的试验研究主要采用颗粒沉降法,亲水玻璃微珠只能在气泡上半球滑行,到达气泡赤道位置附近后便离开气泡,疏水玻璃微珠会刺破颗粒-气泡间的水化膜,越过气泡赤道后会继续沿气泡表面滑行并最终黏附在气泡底部,煤颗粒与气泡的黏附效率随碰撞角和密度的增大而减小。然而目前的试验研究多集中于静水领域,对于浮选流场中颗粒-气泡间相对运动的试验研究尚需进一步探索。     

煤泥浮选气泡比表面积的计算方法

为了从基于分水岭变换分割后的煤泥浮选泡沫图像上获得更加准确的气泡大小的分布情况,需要计算气泡的比表面积.由于气泡的不规则性,使用等效椭圆比等效圆来计算面积、体积更能反应真实的气泡情况.通过对比表面积进行不同的加权,比较表明,使用气泡投影的横截面积作为加权系数是描述气泡分布情况最适合的方法.同时还讨论了气泡特征与浮选操作条件之间的关系,为计算机在线控制浮选过程建立基础.     

Physically sorbed collectors in froth flotation and their activity. Part I

It is demonstrated that the basic factor, identifying the capability to form a flotation complex, is the availability of a reagent sorbed physically on a particle surface and promoting the thinning-down of water interlayer between a mineral particle and a bubble at final stages of their approach. The numerical evaluation of the effect of physically sorbed collector on variations in the velocity of water discharge from an interlayer, partitioning a mineral particle and a gas bubble at the moment of their meeting is given. __________ Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 6, pp. 118–125, November–December, 2008.