The empirical prediction of bubble surface area flux in mechanical flotation cells from cell design and operating data

In the operation of mechanical flotation cells, the dispersion of gas into fine bubbles may be expressed by three indicators : bubble size, gas holdup and superficial gas velocity. Taken together, these properties determine the bubble surface area flux (S_b) in the cell, which has been found to have a strong correlation with the flotation rate constant (k). Previous work by the authors has indicated that it is possible to predict the value of k for a known ore in a cell from a knowledge of the bubble surface area flux generated in that cell.In order to make good use of this finding, an empirical model has been developed to predict S_b in mechanical flotation cells, using data from extensive pilot industrial scale test programs. The model is able to predict Sb from cell operating conditions, impeller design and feed properties. The model has been validated for different types and cell sizes, impeller types and ore types, in different independent investigations carried out at several concentrators in Australia and South Africa.This paper outlines the development of the model, the parameter estimation, and the validation using a number of additional data sets.     

Gas dispersion and de-inking in a flotation column

The role of four gas dispersion parameters in ink particle collection was investigated in 4″ and 20″ flotation columns. Gas holdup (ε_g) and superficial gas velocity (J_g) were measured on-line and bubble size (d_b) was estimated using drift flux analysis that enabled bubble surface area flux (S_b) to be calculated. Operating with approximately zero froth depth ink recovery as a function of retention time (controlled by underflow rate) was determined. Using a mixing model, the collection zone flotation rate constant (k_c) was estimated from the recovery––time data. The rate constant was not related to J_g or d_b but was linearly dependent on ε_g and S_b, similar to findings in mineral flotation studies.     

On the relationship between hydrodynamic characteristics and the kinetics of column flotation. Part I: Modeling the gas dispersion

Modeling of flotation has been the subject of many investigations aiming at better understanding the process behavior per se, and as well for process design, control and optimization purposes. With this regard, the importance of hydrodynamic characteristics, either as manipulated or measured variables, are paramount. The interfacial area of bubbles (I_b) is introduced in Part 1 of this paper as a hydrodynamic variable providing more information about the size distribution than the commonly used bubble surface area flux (S_b). Experimental evidence shows that the bubble size distribution can exhibit normal, lognormal, and even multi-modal shape. Unlike the Sauter mean diameter (d₃₂) and S_b, the interfacial area of bubbles is derived from the complete bubble size distribution, and takes into account these specific characteristics. Fundamental expressions are proposed to allow characterising I_b using the population mean and standard deviation. Experimental results indicate that for lognormal bubble size distributions, I_b correlates well with the gas hold-up and d₃₂. Part 2 of the paper analyzes the correlation of gas dispersion characteristics with flotation rate constant.     

The JKMRC high bubble surface area flux flotation cell

The High Bubble Surface Area Flux Flotation Cell (HS_bFC) is a 16-litre mechanical flotation cell with a bottom driven impeller, which is operated continuously. Bubble formation is carried out using an in-line mixer which enables the cell to achieve superficial gas velocities (Jg) equivalent to those generated in industrial flotation cells (0.7–1.2 cm/s). At the same time, the cell produces considerably smaller bubble sizes; consequently, a high bubble surface area flux (S6) can be generated.     

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.     

Effect of impeller rotational speed on the size dependent flotation rate of galena in full scale plant cells

The first three rougher cells in the lead circuit of the Elura concentrator (formerly Pasminco Australia Limited) were selected as the plant cells for investigation. Metallurgical surveys were performed and various hydrodynamic measurements taken, allowing the galena flotation rate constant and the bubble surface area flux (S_b) in these cells to be calculated over a wide range of gas flow rates, and at two impeller rotational speeds. It was determined that altering the impeller rotational speed did not significantly change the rate constant dependency on S_b when flotation was considered on an unsized basis.The analysis was further extended to examine the same cells parameters on a size-by-size basis. The results obtained have been used to identify differences in the flotation behaviour of the various particle size fractions, independently of surface hydrophobicity. It is shown that the physical conditions for effective flotation of fine (<9 μm) and coarse (>53 μm) particle size fractions differ substantially, suggesting that a specific hydrodynamic environment will favour a high flotation rate for fine galena, which may be detrimental to the recovery of coarse galena, and vice versa. These observations are in accord with metallurgical practice that suggest that it is difficult to improve fine particle flotation without also compromising coarse particle stability efficiency simply by modifying the cell hydrodynamics alone. A fundamental flotation model was applied to quantify differences in the flotation rate of the various particle size fractions with impeller rotational speed.     

Gas dispersion properties: bubble surface area flux and gas holdup

Bubble surface area flux has been related to flotation performance and advocated as a key “machine variable”. Analysis of available data suggests that bubble surface area flux (S_b) and gas holdup (ε_g) are related by S_b ∼ 5.5 ε_g. This was the case for flotation columns and mechanical cells, both laboratory and plant scale, over the approximate range S_b < 130s⁻¹ and ε_g < 25%. A relationship is expected given their similar dependence on gas rate and bubble size (both increase as gas rate increases and bubble size decreases). Reasons that a relationship may be obscured, especially in full size units because of the difficulty in defining the overall S_b and ε_g, are discussed. The possibility to replace S_b by ε_g as the machine variable has the advantage that gas holdup is easier to measure.     

CFD modelling of bubble–particle attachments in flotation cells

In recent years, computational fluid dynamic (CFD) modelling of mechanically stirred flotation cells has been used to study the complexity of the flow within the cells. In CFD modelling, the flotation cell is discretized into individual finite volumes where local values of flow properties are calculated. The flotation effect is studied as three sub-processes including collision, attachment and detachment. In the present work, these sub-processes are modelled in a laboratory flotation cell. The flotation kinetics involving a population balance for particles in a semi-batch process has been developed.From turbulent collision models, the local rates of bubble–particle encounters have been estimated from the local turbulent velocities. The probabilities of collision, adhesion and stabilization have been calculated at each location in the flotation cell. The net rate of attachment, after accounting for detachments, has been used in the kinetic model involving transient CFD simulations with removal of bubble–particle aggregates to the froth layer.Comparison of the predicted fraction of particles remaining in the cell and the fraction of free particles to the total number of particles remaining in the cell indicates that the particle recovery rate to the pulp–froth interface is much slower than the net attachment rates. For the case studied, the results indicate that the bubbles are loaded with particles quite quickly, and that the bubble surface area flux is the limiting factor in the recovery rate at the froth interface. This explains why the relationship between flotation rate and bubble surface area flux is generally used as a criterion for designing flotation cells. The predicted flotation rate constants also indicate that fine and large particles do not float as well as intermediate sized particles of 120–240 μm range. This is consistent with the flotation recovery generally observed in flotation practice. The magnitude of the flotation rate constants obtained by CFD modelling indicates that transport rates of the bubble–particle aggregates to the froth layer contribute quite significantly to the overall flotation rate and this is likely to be the case especially in plant-scale equipment.     

Estimation of the actual bubble surface area flux in flotation

The bubble surface area flux, S_B, defined as the ration between the superficial gas rate J_G and the Sauter mean bubble diameter D₃₂, has been widely used to describe the gas phase dispersion efficiency in flotation machines, and from this predict flotation performance, notable mineral recovery to forecast plant economics.In this work, results of bubble size distribution (BSD) generated in a pilot column are analyzed. Using video and image analysis techniques, the impact of different sampling rates on the BSD was evaluated. Measurements were carried out for D₃₂ = 1–2 mm, J_G = 0.5–1.5 cm/s and two frother concentration, with a maximum sampling rate of 100 fps. In addition, the bubble rise velocity in the bubble swarm was measured, as a function of the individual bubble diameter, for different operational conditions.The identification of the BSD depends on the proper selection of the visual field and sampling rate for acquisition and processing of bubble images. Distortion in the estimation occurs because a larger holdup of small bubbles is observed, relative to the overall data set, due to their lower velocity.The actual BSD was obtained by correcting the observed population, considering the effect of bubble rise velocity. Thus, the actual bubble surface area flux, S_B, was calculated. The results were evaluated at a pilot scale (air–water system) as well as an industrial plant scale (air-pulp system).     

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.     

Modeling of bubble surface area flux in an industrial rougher column using artificial neural network and statistical techniques

Previous studies in mechanical and column flotation cells have shown that bubble surface area flux (S_b) is an appropriate indicator of gas dispersion in a flotation cell which has a relatively strong correlation with flotation rate constant. In the present investigation, based on extensive tests conducted in an industrial Metso Minerals CISA flotation column (4 m in diameter and 12 m in height) in a rougher circuit, S_b as a function of the most significant operating variables which affect gas dispersion in a flotation column (i.e. superficial gas velocity, slurry density (solids%) and frother dosage/type) was modeled using artificial neural network (ANN) and statistical (non-linear regression) techniques. The models were developed taking into consideration a data set consisting of 82 experimental tests conducted in an industrial rougher column (at a copper concentrator in Iran) operating under a variety of experimental conditions.This paper outlines the development of the models and validation using a number of randomly selected datasets. Limitations of the present models are discussed and comments and recommendations on further investigations are given.     

The hydrodynamics of an operating flash flotation cell

Key parameters for evaluating the hydrodynamic conditions within an operating flash flotation cell have been investigated. Profiles of the slurry at increasing depth within the cell have shown a strong trend of increasing slurry density (per cent solids) and coarseness (P₈₀), with a clear indication of segregation on the basis of particle specific gravity. Results of local gas dispersion measurements, taken with the Anglo-Platinum Bubble Sizer, show that bubble coalescence is occurring at shallower depths within the cell and there is a clear trend of decreasing gas velocity (J_g) with increasing depth at the axial location of measurement. Due to access restrictions gas dispersion measurements were taken close to the cell wall, but all data obtained falls well below the recommended minimum values for mechanically driven conventional flotation cells. However, the flash flotation environment is significantly different to a conventional cell, with higher per cent solids and a significantly coarser feed material, making this comparison qualitative (as unfortunately within the literature, there exists no other flash flotation data sets of this nature on which to base a comparison). The residence time distribution of solids indicates a significant amount of short-circuiting and/or internal recycle within the cell. Yet despite these findings, this cell contributes up to half of the pyrite recovery to the final concentrate at a very high grade.     

Relationship between the bubble surface flux that overflows and the mass flow rate of solids in the concentrate of flotation processes

This paper presents the relationship between the bubble surface flux that overflows and the mass flow rate of solids in the concentrate. Even though this study was carried out in a flotation column, the knowledge derived from this paper may be applied to all froth flotation processes. The experimental set up was equipped with an image analysis system to estimate the froth bubble diameter and the air recovery. This study describes the difference between the bubble surface flux entering the froth zone (S_bI) and the flux that arrives to the top of the froth (S_bT) and then overflows to the concentrate (S_bO), the latter being most directly related to the mass flow rate of solids in the concentrate. It was observed that the superficial area of the overflow increased with increasing collector addition and air flow rate, but decreased with increasing froth depth and particle size distribution. Visual evidence and experimental results suggest that, it is common that the superficial area of air that overflows in the concentrate is covered by particles. Only when this condition is almost achieved does overflows occur; otherwise, a high level of coalescence and bubble bursting take place at the froth surface. This was concluded after finding compatible trends between the estimated and predicted mass flow rates of solids in the concentrate, when a tractable geometrical model was used (R² = 0.8).     

Gas dispersion measurements in industrial flotation cells

For nearly 100 years, the flotation plant metallurgist has often wondered what is happening ‘beneath the froth’. To assist in unravelling this mystery, new technology has been developed as part of the Australian Mineral Industries Research Association (AMIRA) P9 project, to measure gas dispersion characteristics (such as gas hold-up, superficial gas velocity and bubble size) in industrial flotation cells. These measurements have been conducted in a large number of cells of different types and sizes by researchers from the Julius Kruttschnitt Mineral Research Centre (JKMRC) and JKTech. A large database has been developed and the contents of this database are described in this paper.Typical cell characterization measurements show a wide spread in values, even in the same cell types and sizes performing similar duties. In conventional flotation cells, the typical gas hold-up values range from 3% to 20%, bubble sizes range between 1 and 2 mm, and superficial gas velocity ranges from 1 to 2.5 cm/s.The ranges of cell characterization measurements given in this paper will enable plant personnel to compare their operation to other similar types of operations from around Australia and the rest of the world, giving opportunities for further improvement to flotation plant operations.     

Bubble spargers in column flotation: Adaptation to precipitate flotation

The limiting factor for metal-organic precipitate flotation in a column is the level of aggregate stability under the turbulence created by the rising bubbles. The hydrodynamic conditions in a 75 mm diameter pilot column were optimised by using different bubble spargers (Microcel, Flotaire, Imox) and by varying the gas flow rate into the bubble sparger, feed flow rate in the column, type and concentration of frother and recirculating pump flow rate. With the bubble spargers used, the average bubble diameter ranges from 0.30 and 1.10 mm, with up to 25% gas hold-up. The parameters influencing average bubble diameter are the superficial gas velocity and the recirculating pump flow rate. For optimal concentrations (10 to 20 mg/1), the type of frother has a negligible role.Strong interaction occurs between superficial gas and feed velocities and recirculating pump flow rate for bubble size control. The optimum operating conditions must accordingly be maintained to prevent carryover of small bubbles into the recirculating pump or the purified solution. An example of the Mo precipitate flotation confirms the assumption made for the effect of bubble size and dissipation energy on the separation results. reserved.     

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.     

Review of hydrodynamics and gas dispersion in flotation cells on South African platinum concentrators

Hydrodynamic and gas dispersion parameters, obtained from industrial flotation cells on South African Platinum concentrators, are reviewed in this paper. Hydrodynamic results show that power intensities are slightly higher than those typically observed in industrial flotation cells while impeller tip speeds and Froude numbers are within the range found in industrial cells. Gas dispersion results show that air flow rates, air flow numbers and air flow velocities vary significantly from cell to cell but are within the range typically found in industrial flotation cells. Gas dispersion results also show reasonably broad variations in bubble size, gas holdup and superficial gas velocity, although bubble surface area fluxes are shown to lie within a fairly narrow range of 50–70/s.