Modelling of residence time distribution of liquid and solid in mechanical flotation cells

This paper presents the results of modelling the residence time distribution (RTD) in mechanical flotation cells, measured in several plants, using the radioactive tracer technique. Results include mechanical cells of 100–300 m³ operated with effective residence times from 2 to 7 min. Data were obtained in forced air and self-aerated cells for liquid and non-floatable solids (per size classes). Different RTD model structures including perfect mixing, Large and Small Tanks in Series (LSTS) and by-pass flow plus perfect mixing were evaluated and compared for single cells. The actual mixing regimes were related to the effective residence times and cell designs based on the model fitting. By-pass flow percentages were typically lower than 10%, therefore the perfect mixing model plus a dead time was a suitable model structure in most cases.On the other hand, the arrangement of cells in series was in most cases effective in reducing the bypass flow observed in single cells. In addition, the N mixed tanks-in-series model was used to represent the mixing regime along flotation banks, which were operated with mean residence times in the range of 18–53 min. Results showed that the N equivalent tanks-in-series values were closer to the actual values in most cases. In some applications, slight by-pass propagation was observed because of circuit layout, problems with the level control system, solid settling and/or high flowrates.     

Study of gas holdup and pressure characteristics in a column flotation cell using coal

Present work has been carried out to observe the effect of process variables (gas flow rate, feed flow rate, solid concentration and frother concentration) on gas holdup and pressure characteristics in flotation column using coal. Gas holdup has been estimated using phase separation method while piezometers have been used to obtain column’s axial pressure profile. It was observed that gas holdup in collection zone was affected by both air as well as feed flow rates. Up to 6% change in gas holdup may occur when the feed flow rate changes from 1–2 cm/s. It was also observed that addition of coal decreased the gas holdup while addition of methyl isobutyl carbinol (MIBC) had opposite effect. Almost linear variation in columns axial pressure characteristics has been observed with gas flow rate. An empirical relationship between gas holdup in the flotation column with column’s axial pressure difference was developed.     

Comparing the effect of salts and frother (MIBC) on gas dispersion and froth properties

The Raglan concentrator (Xstrata Nickel) does not employ frother. It was considered this might be the result of the high salt content in the process water (ca. 30 000 ppm). Two-phase (solution–air) and three-phase (slurry–air) tests were undertaken in a laboratory column to quantify the effect of inorganic ions present in the water (a range of polyvalent ions). The measurements focused on gas dispersion (bubble size and gas holdup) and froth overflow rate. The results were compared to a typical frother (MIBC) system. The two-phase tests revealed reduced bubble size, increased gas holdup and limited froth formation in salt solutions. The gas holdup correlated with ionic strength. At an ionic strength ca. 0.4 (=0.4 M NaCl) the increase in gas holdup was comparable to ca.10 ppm MIBC. In three-phase tests on a sulphide ore, bubble size and froth overflow rate were again comparable between 0.4 M NaCl and 10 ppm MIBC. The observations help explain why the Raglan plant can operate without frother addition.     

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.     

Effect of frothers and dodecylamine on bubble size and gas holdup in a downflow column

Bubble size and gas holdup were characterized in a two phase gas–water system in a laboratory downflow column. The effect of the cationic surfactant dodecyl amine (MW 185, HLB 10.7) and the frothers MIBC (MW 102, HLB 6.05) and polyglycol F507 (MW 425, HLB 8.63) on the bubble size and gas holdup were investigated. In addition, the effect of blends of MIBC-dodecyl amine (DDA) and F507-DDA on these parameters was assessed. The bubble Critical Coalescence Concentration (CCC) followed the order MIBC > DDA > F507. When blending the frothers with DDA at a concentration below its CCC, the frother CCC decreased and bubbles of finer size were obtained below and above the frother CCC. Static surface tension measurements of aqueous solutions with frothers and DDA as well as with frothers-DDA blends show coadsorption of DDA at the air/aqueous solution interface. The surface tension of aqueous solutions prepared with the blends decreased with the addition of DDA and varied linearly with the frother concentration within the concentration range studied. The gas holdup in the downflow column was determined by the bubble size and decreased with the bubble size. It is shown that frother-DDA blends gave the lowest gas holdup in the downflow column. This work is relevant for the reverse flotation of quartz from iron ores using amine collectors in cells with downflow systems.     

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.     

Tangential velocity measurements in a conical hydrocyclone operated with a fibre suspension

The tangential velocity flow field in a conical hydrocyclone was measured using a self-cleaning pitometer. The influence of pulp fibre concentration on the tangential velocity profile was of particular interest.The measurements showed that the pulp fibres had a strong influence on the tangential velocity profile. When operating the hydrocyclone with pure water, the velocity profile showed the typical combination of free-vortex-like rotation close to the hydrocyclone wall and solid-body-like rotation in the proximity of the hydrocyclone axis. This profile changed significantly when pulp fibres were added. At a low fibre concentration (1.2 g/l), the fibres smoothened the transition between the free-vortex-like and the solid-body-like region of the velocity profile. The location of the maximum tangential velocity moved to a larger radius. At higher fibre concentration (7.5 and 11 g/l), the free-vortex-like behaviour in the outer area was virtually suppressed. Due to networking, the fibre suspension in the entire hydrocyclone behaved as a solid body.The radial acceleration profile and tangential rate-of-strain profile were determined. Based on these profiles, a hypothesis was proposed explaining the well-known observation that fractionation efficiency decreases significantly at higher fibre concentrations.     

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.     

Modelling of entrainment in industrial flotation cells: Water recovery and degree of entrainment

Entrainment in flotation can be considered as a two-step process, including the transfer of the suspended solids in the top of the pulp region just below the pulp–froth interface to the froth phase and the transfer of the entrained particles in the froth phase to the concentrate. Both steps have a strong classification characteristic. The degree of entrainment describes the classification effect of the drainage process in the froth phase. This paper briefly reviews two existing models of degree of entrainment. Experimental data were collected from an Outokumpu 3 m³ tank cell in the Xstrata Mt. Isa Mines copper concentrator. The data are fitted to the models and the effect of cell operating conditions including air rate and froth height on the degree of entrainment is examined on a size-by-size basis. It is found that there is a strong correlation between the entrainment and the water recovery, which is close to linear for the fines. The degree of entrainment decreases with increase in particle size. Within the normal range of cell operating conditions, few particles coarser than 50 μm are recovered by entrainment. In general, the degree of entrainment increases with increase in the air rate and decreases with increase in the froth height. Air rate and froth height strongly interact with each other and affect the entrainment process mainly via changes in the froth retention time, the froth structure and froth properties. As a result, other mechanisms such as entrapment may become important in recovering the coarse entrained particles.     

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.     

Frother persistence: A measure using gas holdup

Persistence here refers to the how long a frother remains effective in producing small bubbles, one of its prime functions in flotation. One way to evaluate is to track gas holdup over time while air is sparged into a column: if frother is depleted bubble size will start to increase consequently increasing bubble rise velocity and hence decreasing gas holdup. Persistence of nine frothers was evaluated in this manner. Polyglycol frothers exhibited high persistence with gas holdup virtually constant over 50 h compared with alcohol frothers. The alcohols divided into two groups, one showing steady decline in gas holdup, e.g., 1-hexanol, and a second group exhibiting a sharp decline at a given time, e.g., MIBC. Tests on MIBC showed increasing concentration extended persistence while increasing gas velocity and increasing bubble size decreased persistence. The decrease in gas holdup was related directly to measured decrease in frother concentration. It appears that the transport of frother to and through the froth and from froth to atmosphere needs to be considered.     

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.     

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.     

Effect of gas rate and impeller speed on bubble size in frother-electrolyte solutions

In a flotation cell, bubble size is a function of both coalescence and breakup phenomena. Two phase tests, conducted in a conventional 5.5 L Denver mechanical flotation cell, studied the effect of impeller speed, gas flow rate and frother concentration on bubble size in various electrolyte-frother solutions. The addition of frother to a synthetic sea salt did reduce the measured bubble size (at certain mechanical conditions); whereas the effect of frother addition to NaCl was too small (when compared to measurement errors) to make significant conclusions. This led to more detailed CCC curves (0–50 ppm MIBC) for NaCl, NaCl + MgCl₂, NaCl + CaSO₄, and NaCl + KCl solutions, at constant electrolyte concentrations, to be conducted. They showed an increase in bubble size with the addition of MIBC. This was attributed to the saturation of frother at the air-water interface, reducing local surface tension gradients that help produce smaller bubbles. This occurrence is typically masked in traditional CCC curves due to the dominance of coalescence effects at low frother concentrations.     

Factors affecting the floto-elutriation process efficiency of a copper sulfide mineral

Coarse mineral particles exhibit poor conventional flotation efficiency because of many factors, including the low carrying capacity of bubbles, bubble/particle adhesion problems due to cell turbulence, and low degrees of liberation (low hydrophobicity). Many attempts to improve the recovery of coarse fractions have been explored, such as floto-elutriation operating at a high solid content while dispersed in a fluidized (or expanded) bed formed with a continuous injection of compressed air and an uprising water flow. This work analyzed the comparative performances of floto-elutriation (FE) and conventional flotation (CF) on a classified copper sulfide mineral feed as an example of a difficult-to-liberate low-grade ore. Contrary to expectations, CF and FE (Hydrofloat) displayed similar particle recovery rates with feed size distributions for P80s of 130, 240 and 280 μm. However, metallurgical recoveries from classified fractions of −297+210 μm were 25% higher in FE than in CF and as expected, coarse (+297 μm) particles were not recovered in the CF, but in the FE. The recovery of fine fractions in the FE process was due to high hydraulic entrainment and surprisingly the recovery of intermediate and liberated fractions (+74−149 μm) was very low, due to its low air hold-up. However, the enhancement of the holdup in FE increased the recovery of these mid-sized fractions. Because of the hydraulic carryover caused by the bubbles and water elutriation, the metallurgical grades obtained in all cases were very low compared to conventional bench flotation. It is believed that this FE equipment works better with coarse, narrowly classified particles and high-grade feeds and that performance decreases for low-grade ores requiring high liberation. Certain features of these findings are visualized.     

Impact of talc on pulp and froth properties in F150 and 1-pentanol frother systems

The role of frother controlling bubble size and froth properties is reasonably well understood in the air–water system. A concern is how well this relates to the three-phase flotation condition. As a model hydrophobic solid talc was used. A column was run at fixed froth depth and air rate with overflow and underflow recycled. Four frothers were examined, two polyglycols, polypropylene glycol (F150), polypropylene methyl ether (DF250), and two alcohols, 1-heptanol and 1-pentanol. At steady state, pulp zone gas holdup and bubble size were measured along with water and solids overflow rate as a function of talc addition. For 1-heptanol and DF250 there was no impact of talc on bubble size or gas holdup. For 1-pentanol the presence of talc had no effect on bubble size but gas holdup increased; in contrast, for F150 addition of talc increased bubble size and decreased gas holdup. There was a reversal in water overflow rate between the F150 and 1-pentanol on adding talc, the 5:1 ratio in favour of F150 in air–water becoming 3:1 in favour of 1-pentanol at 5 wt% talc. The solids overflow rate likewise favoured 1-pentanol in presence of talc.The increase in bubble size in the talc/F150 system implies coalescence, as further evidenced by the bubble size distribution becoming bi-modal. The mechanism proposed was a combination of talc adsorbing frother from solution, demonstrated by TOC analysis of residual frother, and directly from the bubble surface due to the orientation of adsorbed F150. In the talc/pentanol case the increase in gas holdup was attributed to bubbles not being at terminal velocity and attached talc particles increasing deceleration, i.e., slowing bubble rise. The increase in water overflow rate in the talc/pentanol system corresponds to increased froth stability imparted by hydrophobic solids. Froth stabilization by talc with F150, however, is offset by the increased bubble size that means less water is carried into the froth. The reversal in water overflow ranking of the frothers can, therefore, be interpreted as due to frother/solid interactions. Similar interactions may account for reversals noted in other systems.     

The effect of hydrodynamic parameters on probability of bubble–particle collision and attachment

In this study the dependence of the impeller speed on the particle size variation was investigated on the quartz particles using laboratory mechanical flotation cell. Maximum recovery was obtained at 1100 rpm. For either more quiescent (impeller speed <900 rpm) or more turbulent (impeller speed >1300 rpm) conditions, flotation recovery decreased steadily. Furthermore, amount of collision probabilities is calculated using various equations. According to this study, maximum collision probability was obtained around 48.35% with impeller speed of 1100 rpm, air flow rate of 15 l/h and particle size of 545 μm and minimum collision probability was obtained around 2.43% with impeller speed of 700 rpm, air flow rate of 15 l/h and particle size of 256 μm. Maximum attachment probability was obtained around 44.16% with impeller speed of 1300 rpm, air flow rate of 75 l/h and particle size of 256 μm. With using some frothers such as poly propylene glycol, MIBC and pine oil, probability of collision increased, respectively. Maximum collision probability was obtained around 65.46% with poly propylene glycol dosage of 75 g/t and particle size of 545 μm.     

Study of residence time distribution and mill hold-up for a continuous centrifugal mill with various G/D ratios in a dry-grinding environment

It is important to determine the residence time distribution (RTD) of a mill in order to predict the performance of the mill. In this study, the residence time distribution of a continuous centrifugal mill was measured experimentally by using aluminum powder as a tracer in a dry-grinding environment. Aluminum powder was placed into the continuous centrifugal mill chamber as a pulse under a steady-state condition, and then, the discharge time and proportional concentration of the tracer was measured using a metal detector at various G/D ratios and feed rates. During the measurement procedure, the mill product was collected and analyzed with regard to the size distribution to investigate the relationship between the mill product and the characteristics of RTD. In addition, the mill hold-up data was also analyzed after measurement. These test results can be used to predict the mill product size distribution in combination with a kinetic grinding model.