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.     

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).     

Prediction of the metallurgical performances of a batch flotation system by image analysis and neural networks

It is now generally accepted that froth appearance is a good indicative of the flotation performance. In this paper, the relationship between the process conditions and the froth features as well as the process performance in the batch flotation of a copper sulfide ore is discussed and modeled. Flotation experiments were conducted at a wide range of operating conditions (i.e. gas flow rate, slurry solids%, frother/collector dosage and pH) and the froth features (i.e. bubble size, froth velocity, froth color and froth stability) along with the metallurgical performances (i.e. copper/mass/water recoveries and concentrate grade) were determined for each run. The relationships between the froth characteristics and performance parameters were successfully modeled using the neural networks. The performance of the developed models was evaluated by the correlation coefficient (R) and the root mean square error (RMSE). The results indicated that the copper recovery (RMSE = 2.9; R = 0.9), concentrate grade (RMSE = 1.07; R = 0.92), mass recovery (RMSE = 1.94; R = 0.94) and water recovery (RMSE = 3.07; R = 0.95) can be accurately predicted from the extracted surface froth features, which is of central importance for control purposes.     

Operating parameters that affect the carrying capacity of column flotation of a zinc sulfide mineral

Test work performed in a pilot-scale flotation column (4 m height × 0.057 m diameter) processing an industrial zinc concentrate (51% w/w Zn as sphalerite, 10.5% Fe, 0.77% Pb, 0.62% Cu, 7.3% NSG, d₈₀ = 110 μm), confirmed the findings of previous work conducted by the authors, that showed there exists a limit in the mass flow rate of solids that can be processed in the column without adversely affecting recovery and solids carrying-rate; this limit is related to the onset of an unusual accumulation of gas in the lower section of the cell due to overloading of gas bubbles. In the present work, the effect of slurry rate (J_t = 0.3–1.7 cm/s) and slurry density (15–35% w/w solids) onto solids recovery and solids carrying-rate were studied under the following experimental conditions: J_g = 1.45 cm/s, 15 ppm Dowfroth, pH = 9.5 and 60 g isopropyl xanthate/ton; froth depth = 0.3 m. The results showed that solids carrying-rate may be maximized by operating the column with a combination of a relatively dense slurry and a relatively small slurry rate. The above behavior is explained in terms of the solids load that air bubble transport under the different operating conditions imposed, which is reflected by the axial air-holdup profile established in the column, as a result of the accumulation of overloaded bubbles in the lower part of the collection zone. It is argued that the slurry rate plays an important role on the onset of this phenomenon since it directly affects the rising velocity of overloaded bubbles, thus being the responsible of such unusual accumulation of gas and of phenomena such as bubble coalescence and lost of bubble surface area.     

Froth transport characterization in a two-dimensional flotation cell

A study of the froth bubble transport in a two-dimensional (2D) flotation cell was performed. Experiments were developed as a 2 × 2 factorial design, in which the effect of superficial air rate (1.2–1.8 cm/s) and froth depth (2–4 cm) on the froth transport for a two phase (air–water) system was characterized.Using image analysis techniques, bubble residence times, air recovery, bubble path and bubble size increase through the froth were obtained. This information was complemented by froth surface velocity measurements using the Visiofroth system.It was found that bubbles transported from the pulp–froth interface up to the overflow, showed a minimum residence time for bubbles entering the froth near the lip wall. Also, the air-recovery significantly changes in a range of 7–20% at different operating conditions.Higher residence times promoted bubble size increase by coalescence for bubbles transported from the interface. Conversely, for lower residence times, a smaller increase in bubble size was observed.     

Hydrodynamic and kinetic characterization of industrial columns in rougher circuit

In the present investigation the relationship between collection zone rate constant (k_c) and gas dispersion parameters, viz. bubble size (d_b), superficial gas velocity (J_g), gas hold-up (ε_g) and bubble surface area flux (S_b) was evaluated. Experiments were conducted in an industrial (4 m in diameter and 12 m high) and a pilot (0.1 m in diameter and 4 m high) flotation column in rougher circuit at Miduk copper concentrator in Iran. Gas hold-up was measured using pressure difference technique and mean bubble sizes were estimated from a drift flux analysis. It was found that the collection zone rate constant was not correlated with d_b and J_g solely but was linearly dependent on ε_g and S_b for the range of interest. Collection efficiency (E_k) and floatability factor (P) in the industrial columns were quantified (E_k = 3.1%; P = 7.7 × 10^?3). The influence of operating parameters comprising superficial gas velocity, slurry solids% and frother dosage/type on S_b and flotation kinetics was discussed. Analysis of available industrial data suggested that S_b and ε_g were related by S_b = 4.46ε_g over the range 30 < S_b < 60 s^?1 and 7% < ε_g < 14%.     

The relationship between the peak in air recovery and flotation bank performance

Air recovery, or the fraction of air entering a cell that overflows the cell lip as unburst bubbles, is an important measure of froth stability as it affects the flow of bubble surface to the concentrate. An experimental campaign was carried out over the first four cells of the rougher bank at a South African platinum mine in order to find the relationship between froth stability and flotation performance as a function of air flowrate.The results showed that a peak in air recovery was observed as the air rate increased. Furthermore, this corresponded to the air flowrate at which the highest overall recovery was obtained. This can be explained by understanding the resulting changes in the structural features of the froth such as bubble loading and the flow of bubble surface and suggests that improved flotation performance can be achieved by operating a bank under conditions that result in a maximum in froth stability.     

Froth zone characterization of an industrial flotation column in rougher circuit

In this investigation the froth zone of an industrial column (4 m “diameter” × 12 m “height”) in rougher circuit was characterized. Experiments were carried out at Miduk copper concentrator, Iran. Miduk is a unique copper processing plant which utilizes columns in rougher circuit. Cleaning and selectivity actions in the rougher froth were illustrated using solids and grade profiles along with RTD data. The impact of froth depth (FD) on overall rate constant (k) and k–S_b relationship was evaluated. Dependency of overall flotation kinetics on froth depth and gas velocity (J_g) was modeled by k = 4.97(FD)^?0.87(J_g)^0.80. Froth recovery (R_f) was estimated and modeled in terms of froth residence time of slurry (FRT_Slurry) as R_f = R_f,maxexp(?k × FRT_Slurry). Finally, the correlation between k, S_b (indicative of the collection zone performance) and FRT_Slurry (indicative of the froth zone performance) was modeled by k = 0.02 (FRT_Slurry)^?0.62(S_b)^0.82.     

Packing of particles on the surface of bubbles

In this paper, geometrical packing models were derived to determine the coverage of particles on an air bubble. Nearly spherical glass beads of two size fractions and galena particles were used in the study. The coverage of air bubbles by glass beads was carried out in the concentration range 2.74 × 10^?5–1.65 × 10^?3 mM of CTAB. The results indicated that coverage at all concentrations could be approximated with a hexagonal model with monodispersed particles using the value of d_[4,3]. This could be done with a relative deviation of the packing factor within 15%. The coverage of an air bubble by galena particles was carried out in a collectorless environment. The best models were found to be a hexagonal or square cell using the value of d_[1,0]. Experimental observations on particle packing are given and implications for the froth phase of flotation are discussed.     

Evaluation of models for air recovery in a laboratory flotation column

One of the more interesting recent topics in flotation modelling is the association between the fraction of air that overflows to the concentrate as unbroken bubbles (air recovery, α) and concentrate recovery. This paper analyses several models to estimate air recovery. These models were tested using experimental data obtained with a laboratory flotation column (2 m high; 0.095 m diam.), which was used to float sphalerite. Predictions from these models were compared with the results obtained by image analysis. The aim of this last technique was to have a reference measurement, quantifying by visual detection (manual method) the bubbles bursting on the surface. Based on the experimental results, the best models were identified. This kind of comparison is valuable for simulator developers.     

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.     

Effect of entrainment in bubble load measurement on froth recovery estimation at industrial scale

Froth recovery was calculated in a 130 m³ mechanical cell of a rougher flotation circuit. This was done by bubble load determinations along with mass balance surveys. Valuable grade in the bubble load decreased in the −38 μm due to fine particles entrained to the chamber of the device. The effect of fine particle entrainment on froth recovery was evaluated. A comparison between results from the raw bubble load data (assuming all particles were transported by true flotation) with those from corrected bubble load information (subtracting fine particle entrainment) was carried out. Entrainment occurred due to hydraulic transport in the bubble rear, which corresponds to the worst case scenario for froth recovery estimation. Results showed that the relative error was less than 0.3%, which allowed validation of the bubble load measurement as an effective methodology for froth recovery estimation at industrial scale.     

Froth flotation of sphalerite: Collector concentration,gas dispersion and particle size effects

This experimental work on sphalerite flotation investigated the effect on flotation performance of three particle size fractions, namely, coarse (d₈₀ = 100 μm), medium (d₈₀ = 39 μm) and fine (d₈₀ = 15 μm), bubble size distribution, superficial air velocity, and collector dosage. Bubble size distributions were characterized with the image analysis technique. The two-phase (liquid–gas) centrifugal pump and frother addition (MIBC, 5–30 ppm) allowed generating bubble diameters between 150 and 1050 μm, and air holdup ranging from 0.2% and 1.3%. Main results showed that each particle-size distribution required an optimal bubble-size profile, and that sphalerite recovery proceeded from mechanisms involving true flotation (when J_g = 0.04 cm/s and 1.9 × 10⁻⁴ M SIPX). However, cluster-flotation occurs at high collector dosage (when J_g = 0.04 cm/s and d₃₂ between 285 and 1030 μm), and requiring further investigation.     

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.     

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.     

Bank profiling and separation efficiency

Various authors have discussed methods of optimising a bank of flotation cells. In this paper, JKSimFloat is used to investigate the effect of recovery profiling and mass pull profiling (i.e., mass distribution to cells in a bank) on the separation efficiency between floatable minerals and against entrained gangue.In the case of two floatable minerals, a balanced recovery profile was found to be optimal: supporting and extending previous analysis. In the case of separation of a floatable mineral from entrained gangue, the entrainment model that links water overflow rate to solids overflow rate was employed. When the value of b in the entrainment model is greater than one, a balanced mass pull profile was found to be optimum. The evidence for b > 1 is briefly reviewed; no example has been found where b < 1. Most of the profiles were controlled in the software by altering the bubble surface area flux distribution; a sensitivity analysis was performed using other variables.Recovery profiling was tested as part of a bank optimisation campaign at a talc operation in Timmins, Canada. Using air and frother as manipulated variables, it was found that as the rougher bank was moved toward a balanced profile the final plant product showed improvement in grade and yield.     

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.     

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.     

Frother-related research at McGill University

Over the past ten years the Mineral Processing group at McGill University has developed techniques to determine gas dispersion properties (gas superficial velocity, gas holdup, bubble size and bubble surface area flux) in flotation machines. This work is finding application in metallurgical diagnostics and cell characterization. The picture, however, will remain incomplete until the impact of chemistry on bubble production, and hence on gas dispersion, is understood. This has prompted investigations into frothers.There are two areas addressed in this communication: frother analysis and frother characterization.Coincident with the centenary, for 100 years there was no convenient frother analysis procedure. A colorimetric technique originally developed for alcohols had been applied to MIBC (Parkhomovski, V.L., Petrunyak, D.G., Paas, L., 1976. Determination of methylisobutylcarbinol in waste waters of concentration plants. Obogashchenie Rud 21 (2), 44–45). Using this as a starting point, the technique was successfully extended to a wide range of commercial frothers and shown to be robust against most common ‘contaminants’. The technique is readily used on-site and some observations from plant surveys are described.Characterization of frothers has taken two routes, determining water carrying rate and investigating properties of thin bubble films.Second only to transporting particles the recovery of water by bubbles has the most influence on metallurgy. The question posed was whether this ‘water carrying’ property could be related to frother type. In a specially designed column the volume rate of water to the overflow per unit cross-sectional area (‘carrying rate’, J_wo) and gas holdup (ε_g) at controlled froth depths were measured. The J_wo–ε_g relationship proved approximately linear and dependent on frother type, with four frother ‘families’ being identified.Bubble thin films have been studied for soaps and the techniques were adapted for frothers. From infrared analysis it became apparent that the frother molecule, while itself not seen, had an impact on organizing water molecules, apparently forming a film of bound water on the bubble surface. Exploiting the interference pattern generated in UV/Vis the film thickness (d) was determined; for MIBC d was less than 160 nm while for DF250 d was ∼600 nm. Taking a representative frother from the four families identified above, the water carrying rate at a given gas holdup increased with film thickness.Possible implications of the findings on the role of frother in bubble production are explored.     

Factors involving the solids-carrying flotation capacity of microbubbles

Dissolved air flotation (DAF) is a technique used extensively for separating fine particles in water and wastewater treatment, but, unfortunately, its use is still limited for froth flotation of minerals. This appear to be due to the very low lifting power of the microbubbles (40–70 μm) and low airflow rate because of the low solubility of air in water. Thus, the efficiency of DAF in treating mineral particles has shown to be poor and as a solid/liquid separation technology is limited to slurries with no more than 3% solids. This work presents results showing (measuring) the limits of DAF as a function of particle size distribution, solids content and air superficial velocity. Interestingly, the microbubbles were found to be not selective with respect to particle size, floating both fine and coarse particles, which is most likely due to the existence of several mechanisms acting on the flotation of particles by these minute bubbles.