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。     

Dynamic characterization of column flotation process laboratory case study

The objective of metallurgical column control is to achieve the economic optimum combination of concentrate grade and mineral recovery for any given feed. Metal prices and the cost of consumables will dictate the metallurgical concentrate and mineral recovery targets. Furthermore, experience has shown that collection zone height, air holdup and bias water flow rate are key parameters (controlled variables) that affect metallurgical performance. The collection zone height is related, mainly, with the residence time of the particles inside the collection zone, air holdup is correlated to the available surface area of air bubbles and bias water flow rate is an indirect measure of the cleaning action of the froth zone. However, these variables cannot be directly manipulated. Instead, wash water, air and underflow flowrates are the directly manipulated variables [1]. Therefore, if dynamic relationships could be established between the three manipulated variables and the three controlled variables, column metallurgical control may be improved. This study was an attempt to model these relationships using a tool known as System Identification, that includes Transient Analysis.The study consists in experimental tests, transient response analysis and identification of black box type models with cross validation.The experimental work was performed in a pilot scale laboratory flotation column of 3.2 m high by 80 mm of diameter. This flotation column operates in a plant with all the required instrumentation installed. The study considers the operation of the two phase air-water system.     

蓝晶石、石英及黑云母的浮选动力学研究

以十二胺为捕收剂,淀粉为抑制剂,采用单矿物分批浮选的方法,研究了蓝晶石、石英及黑云母在自然pH条件下的可浮性随浮选时间的变化关系,并对三种矿物的浮选动力学特性进行了分析。结果表明,浮选速度常数在浮选过程中不是恒定不变的,抑制剂淀粉的加入可显著扩大矿物之间浮游速度的差异,采用经典一级动力学模型对浮选过程进行了模拟,拟合后的石英、黑云母及蓝晶石模型回收率拟合值与试验值相关性R2分别为0.97、0.98和0.96,表明模型拟合精度较高可模拟矿物的浮选过程。     

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.     

高频超声波作用下黄铁矿的浮选性能及动力学研究

研究了超声波作用下黄铁矿的浮选行为。结果表明,在磨矿细度为-0.074 mm占57%、丁基黄药200 g/t、起泡剂20 g/t的浮选最佳条件下,在超声波频率为135 kHz和功率为100 W时可以使黄铁矿回收率提高13.86%。通过超声波浮选和常规浮选的动力学分析发现,高频超声波对-150+100μm粒级的黄铁矿影响最大,使回收率提高了7.54%;对该粒级的试验数据利用五个动力学模型拟合可知,一阶经典模型的拟合效果最好,动力学方程可分别表示为超声波浮选:ε=26.27[1-exp（-0.601t）]、常规浮选:ε=18.01[1-exp（-0.671t）]。利用SEM分析发现,超声波主要通过对黄铁矿表面的清洗作用,去除了表面罩盖的矿泥等脉石矿物,提高了黄铁矿的回收率。      

六偏磷酸钠对菱镁矿与白云石浮选分离动力学的影响

以油酸钠为捕收剂,研究了六偏磷酸钠对菱镁矿和白云石浮选行为和浮选动力学特性的影响。结果表明：不添加六偏磷酸钠时两种矿物可浮性相近,分离困难;在矿浆pH值为9-11.5的区间里,添加适量的六偏磷酸钠,菱镁矿仍保持较好的可浮性和较高的浮游速度,而白云石的可浮性和浮游速度大幅降低,从而有利于两种矿物浮选分离。菱镁矿和白云石的浮选分别符合经典一级动力学模型和二级矩形分布模型。     

Geometallurgical modelling of the Collahuasi flotation circuit

The flotation rate constant was modelled as a function of air dispersion properties and the complete feed particle size distribution by using the collision–attachment–detachment approach and introducing a parameter (Ф) which represents the inherent floatability of the ore. It was found that this parameter Ф is characteristic of the geometallurgical unit and does not depend on the main operating conditions. The parameter Ф is dimensionless and can be estimated either from laboratory testwork or directly from an industrial kinetics survey and can be used to predict industrial operation, provided that the other components of the model are evaluated under actual operation conditions. An empirical expression for the maximum achievable recovery – infinite time recovery – is also presented. The complete model, including flotation rate constant and infinite time recovery, was tested showing good correlation at both laboratory and industrial scale. At industrial scale the model was able to predict metallurgical results in a time frame of several weeks at Compañia Minera Doña Inés de Collahuasi SCM, showing an average relative error of less than 2%.     

黑钨矿、白钨矿及萤石异步浮选动力学研究

以苯甲羟肟酸为捕收剂,采用分批浮选试验方法,研究了柿竹园黑钨矿、白钨矿及萤石可浮性随浮选时间的变化关系,并根据浮选动力学基本原理,对白钨矿、黑钨矿及萤石的浮选动力学特性进行了分析。结果表明,浮选速度常数K值在浮选过程中是不断变化的,调整剂柠檬酸可显著扩大矿物浮游速度之间的差异,在原有经典动力学模型的基础上,通过适当改进导出了分速浮选动力学方程的一般形式,分速模型对浮选数据的拟合精度优于经典动力学模型。研究认为,异步浮选技术能实现矿物的个性化、差异性浮选,充分体现了"和谐的精细工艺技术"的重要特征。     

Mathematical models of the column flotation process a review

Mathematical modelling is a valuable quantitative instrument, which is being effectively employed to the column flotation process in order to predict its metallurgical performance. This paper presents an up-to-date assessment of the various mathematical models for column flotation currently available under the categories of kinetic models and non-kinetic models and also identifies a number of associated shortcomings.     

Influence of operating parameters on the flotation of apatite

Flotation of apatite is complicated, owing to its physicochemical similarity with other minerals in phosphate ores. Despite this, relatively few studies have been done on the effect of operating parameters, such as the mode of milling, pulp conditions and collector dosage on the kinetics of apatite flotation. In this technical note, the results of batch flotation tests and the fitting of a first-order kinetic model to assess the influence of operating variables on the flotation kinetics are discussed. Pulp pH, collector dosage and pulp temperature affected recovery significantly, but the mode of milling (wet or dry) did not. All factors influenced the concentrate grade, except for the collector dosage, while the milling mode was the only factor that did not affect the flotation kinetics significantly.     

难浮煤泥浮选速率试验研究

针对主导粒级为细粒级的难浮煤泥,进行了窄粒度级和全粒度级的浮选速度试验。结果表明：浮选速度由快到慢的粒级依次为0.125～0.074、0.250～0.125、〈0.074、0.500～0.250、〉0.500 mm。粗粒级煤粒因其质量大、脱附概率高、部分连生体表面疏水性较差,需在高能量输入条件下,通过较长时间的矿化作用...     

不同粒级白云石浮选动力学研究

采用单矿物浮选试验研究了在溶液pH值为4时,三种粒级的白云石在捕收剂LA浓度不同和转速不同条件下的累计回收率随浮选时间的变化规律。结果表明,提高转速和LA的浓度对粗粒级白云石的回收率具有重要影响,对于中间粒级白云石的浮选回收率影响不大,但能显著缩短浮选平衡时间,中间粒级的白云石累计回收率最高可达99.00%。采用四种经典动力学模型对试验数据进行拟合,结果表明白云石的浮选过程更加符合一级动力学模型,不同转速和不同浓度LA条件的拟合优度R2均大于0.96。     

Development of a flotation model incorporating liberation characteristics

A liberation/flotation model has been developed to evaluate flotation performance, in which the grade distribution of composite particles is incorporated explicitly. The grade distribution of particles at a given size fraction was calculated using a predictive liberation model developed by the authors. Flotation behaviour of these particles in narrow size fractions were evaluated using batch flotation tests. The recovery of particles in narrow size/grade classes at various flotation times under a given flotation environment were obtained from SEM images of mounted specimens of feed, concentrate and tailings samples using image analysis techniques.By describing the size, grade and recovery data of particles in narrow size/grade classes by separate matrices, a transformation matrix technique has been developed that can predict the flotation performance of a composite sample of an ore comprising various size classes. It has been shown that the predicted results agree well with the observed results.This liberation/flotation model has wide applications in geometallurgical testing and design, where the downstream flotation performance is to be determined with limited availability of ore samples and their liberation characteristics. It also alleviates the deficiencies involved with flotation models that assumes first order behaviour.     

Application of neural networks to predict locked cycle flotation test results

The performance of a continuous flotation circuit is influenced by the flotation variables and the number of stages of a flotation circuit is dependent on flotation conditions, such that the interrelation between the flotation conditions and the number of stages must be carefully determined to obtain acceptable metallurgical performance from the circuit. The locked cycle test is a useful tool for simulation of continuous flotation circuits. However, it is a time-consuming and tedious procedure. A simulation method used to predict locked cycle test results from data from individual batch tests is available in the literature. In order to develop an optimum circuit configuration for a specific ore, several batch flotation tests for the first cycle of the locked cycle test have to be conducted to predict the metallurgical performance of various circuit types. Therefore, an integrated simulation method, which uses experimental data and the results of this simulation method has been developed to structure a neural network model for prediction of locked cycle tests results without additional experiment and calculation. In training and testing of the neural network model, results of the simulation method were used as the output data set and the flotation conditions of the batch tests were used as the input data set. Apart from the training and testing data, results of the LCT for several circuit types were predicted in order to validate the neural network model and to determine its performance on both: interpolation and extrapolation. Because the neural network model was trained using results of the simulation method, the use of the neural network model did not lead to any improvement in predictions of actual LCT results. However, the results of this study indicate that the neural network model can be used to simulate various circuit types with an error of less than 4%, instead of the simulation method. Consequently, the neural network model, as an alternative to the simulation method, can be used to determine the effects of changes in certain flotation variables on the number of cleaner and scavenger stages in a flotation circuit.     

Flotation of PGM-containing minerals: Plant-wide regression and prediction of circuit performance

A crucial step in the processing of PGM-bearing reefs in South Africa is the flotation of the sulfidic minerals from the host rock. Flotation plays a crucial role in reducing the mass of material to be processed further downstream by smelting, converting and hydrometallurgical refining. However, flotation has the lowest recovery of valuable metals along the processing chain. As a result, small improvements in efficiency in flotation have an enormous benefit to the company’s performance. Modelling and simulation play an important role in circuit optimisation, due to the ability to test and examine multiple options in a small amount of time without affecting the operational circuit. Unfortunately flotation is extremely difficult to model and simulate due to the complexity of the mechanism and the large number of variables involved. Whole circuit modelling is even more difficult, for the reasons already mentioned as well as maintaining a consistent mass balance in the face of multiple recycle streams. The purpose of this work is to construct a whole-circuit model of a flotation circuit, and use the model to predict the effect of changes to the flotation circuit. A goal in the construction of the model was to use as few parameters as possible. The work presented in this paper is focused on the regression of the parameters of a first-order kinetic flotation model to actual pilot plant data. The performance of the model was then validated by predicting the behaviour of a modified flotation circuit.The regression showed excellent correlation with actual plant data on a bank by bank basis. Using the regressed parameters directly on a modified circuit configuration, the model was able to predict the circuit behaviour when compared to plant data.     

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.     

The interaction of flash flotation with closed circuit grinding

Flash flotation is an important unit operation within many grinding circuits. It provides an opportunity for the valuable mineral to be recovered as early as possible in the processing plant. This prevents liberated valuable mineral from building up in the recirculating load of the mill, and reduces the occurrence of overgrinding. Overgrinding can place a significant limitation on overall recovery, because it causes the production of valuable fines that are difficult to recover by flotation.The flash flotation cell is fed by the cyclone underflow in a closed grinding circuit. This feed stream represents the optimal particle size distributions of valuable mineral and gangue for flotation kinetics, selectivity and grade. The flash cell treats the recirculating load of the ball mill, and therefore influences the performance of both the mill and the hydrocyclone classifier. The effect of a flash cell in the grinding circuit is difficult to determine since flash cells in Australia are introduced at the design stage and so no plant data is available before and after the introduction of the flash flotation unit. By establishing a computer simulation of the closed-circuit grinding with flash flotation, the interaction of flash flotation with grinding can be estimated. The models can be used to predict the effect of various changes to the operating conditions on circuit performance as well as the expected grinding performance in the absence of flash flotation. This enables the effect of flash flotation and any possible benefits to be evaluated.The model was developed from unit models of the ball milling, hydrocyclone classification and flash flotation processes. An empirical model was used for the flash cell, and generic models were fitted to the ball mill and hydrocyclone based on the matrix model and the Plitt model respectively. The data required for the development of the models was obtained from plant surveys of the Kanowna Belle gold mine and laboratory batch grinding and flotation tests.The model accurately represents the plant grinding and flash flotation circuit while operating under normal conditions. Simulation of the circuit using the model enabled the effect of variations to flash cell operating conditions on the flash concentrate, recirculating load and cyclone overflow to be determined.     

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.     

Effects of hydrodynamic parameters on entrainment and flotation performance

The separation selectivity and efficiency of the flotation process depends not only on differences in the physico-chemical surface properties of various minerals within an ore, but also on the hydrodynamics of flotation. The hydrodynamics relate directly to many sub-processes of the flotation, such as suspension of particles in the pulp, dispersion of the air into bubbles and the probability of particle–bubble collision. Mechanical entrainment plays a major role in the quality of the flotation concentrate and the separation selectivity. Therefore, the effects of some important hydrodynamic parameters on both the entrainment and the flotation performance were investigated by means of a fractional factorial experimental design. Furthermore, many flotation tests were performed in order to generate sufficient data for use in empirical modelling and neural network based modelling, in light of the results of the experimental design. The adaptability and reliability of the models developed, depending on the treatment of available experimental data, have been studied comprehensively. Evaluation of the observed and predicted results demonstrated that the effect of some chemical and hydrodynamic parameters of the flotation process on both the metallurgical performance and entrainment in the training region, can successfully be predicted, with an error of less than 6%, by using the developed neural networks models without particular assumptions and additional experiments. In order to prove the validation of the empirical and neural networks models developed and to compare their performances, a few additional tests were conducted under predetermined flotation conditions. The results of these additional flotation tests indicated that the neural network models were consistently more accurate than the empirical models with a negligible error.     

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.