A flotation column simulator based on hydrodynamic principles

doi:10.1016/0301-7516(91)90063-O

International Journal of Mineral Processing

Volume 33, Issues 1–4, November 1991, Pages 355-368

https://doi.org/10.1016/0301-7516(91)90063-O Get rights and content

Abstract

Based on the hydrodynamic principles of bubble-particle interactions, a simulation package has been developed to predict the performance of flotation columns for sulfide flotation. The input variables to the simulator include particle size, bubble size, particle hydrophobicity, feed rate, feed composition, aeration rate, wash water rate, column height, etc. The problems associated with carrying capacity limit and froth overloading have also been considered in the model development. The simulation results show that operating a column considerably beyond this limits creates a circulating load between the froth and pulp phases, which is helpful for improving the product grade. Since the simulator is based largely on first principles, it can be useful for scale-up, control, optimization and trouble-shooting.

References (12)

G.S. Dobby et al.
Particle size dependence in flotation derived from a fundamental model of the capture process
Int. J. Miner. Process.
(1987)
R. Espinosa-Gomez et al.
Flotation column carrying capacity: Particle size and density effects
Miner. Eng.
(1988)
G.H. Luttrell et al.
Determination of the probability of bubble-particle adhesion using induction time measurements
G.S. Dobby et al.
Flotation column scale-up and modeling
Can. Inst. Min. Metall. Bull.
(1988)
O. Levenspiel
Chemical Reaction Engineering
G.H. Luttrell et al.
A computer-aided design pack-age for column flotation

There are more references available in the full text version of this article.

Cited by (16)

A dynamic model of fluidized-bed flotation
2019, IFAC-PapersOnLine
The concept of fluidized-bed flotation (FBF) (e.g. HydroFloat^TM) was recently introduced to improve the recovery of coarse particles (425 to 1180 µm). In spite of encouraging results from the first industrial applications dating back more than a decade, FBF still remains an emerging technology in the global mining industry. This paper presents a dynamic model of a FBF cell based on first principles describing volume conservation balances and macro hydrodynamic conditions. It was specifically developed to address process design, monitoring, and control problems. The model relies on the drift-flux theory to predict the flow of three populations (free particles, attached particles and bubbles) throughout the proposed vertical mixer-in-series framework. A calibration of empirical parameters on literature data demonstrates the ability to reproduce the effect of operating parameters (airflow rate, fluidization water flow rate and bed height) on steady-state recovery as long as the equipment operates at low turbulence.
Hydrodynamic study of two phase flow of column flotation using electrical resistance tomography and pressure probe techniques
2017, Separation and Purification Technology
Citation Excerpt :
The addition of mineral particles shows the impact on bubble interactions. From the two-phase hydrodynamic column flotation data using Luttrell and Yoon model [65], the rate constant and mineral recoveries can be easily calculated for any distinct particle sizes suitable for flotation process. Comparatively, the ERT technique offers more advantages over conventional probing methods.
Gas dispersion characteristics are very important to design and selection of flotation process for the fine particle separation. Although the separation of flotation process heavily depends on hydrophobicity of given solid particles, but their rate of attachment and detachment depends on local gas dispersion characteristics. In this work, gas dispersion characteristics in a 100 mm laboratory column flotation have been investigated by exploring the flow behavior in terms of the local and mean gas hold-up, bubble rise velocity and bubble size distribution across the column. This experimental data has been used to demonstrate the validation of the two-fluid CFD model predictions in the column flotation. The column hydrodynamics are estimated by using high speed dual planar Electrical Resistance Tomography (ERT) system and pressure transducers. In all the experiments, water is used as the liquid phase and air (bubbles) as the disperse phase. Using the ERT system, measurement of two phase distributions are examined for a wide range of design and operating conditions of the column including different spargers and frother dosage, where the flow changes from homogenous to transition bubbly flow. It is confirmed by ERT that the gas-holdup increases with an increase in the sparger porosity, air superficial velocity, liquid height and liquid feed flow rate. To test the reliability of ERT measurements, simultaneously a set of pressure transducers is used to obtain the sectional average gas holdup and validated. It is observed that bubble density occupancy is more at center region of the column and gas holdup value increases with the increase of gas superficial velocity. Dynamic gas disengagement technique is utilized to measure bubble rise velocity and sauter mean bubble diameter. At end this ERT data has been used to validate two-fluid CFD model (modified with suitable drag and lift forces via user defined functions) predictions in the column and found a close agreement.
Comparison of flash and column flotation performance in an industrial sulphide rougher application
2016, Minerals Engineering
A survey has been conducted on a refractory gold (pyrite) concentrator which utilises flash flotation on the cyclone underflow stream and a flotation column on the cyclone overflow stream. Both cells are considered to be performing a first rougher operation on their respective streams. A comparison of the size and nature of the target mineral for flotation (pyrite) in the concentrates from both these unit operations has shown that they both recover predominantly liberated pyrite in the fine and intermediate size classes (−150 μm). The flash flotation machine on this particular circuit recovers fast floating well liberated particles, with a minimal froth depth and short residence time; while the rougher column has a very deep froth and long residence time. To date no comparison of a flash flotation cell and a column cell has been published in the literature and the results presented here are the first of their kind to the best of the authors’ knowledge.
Analysis of the liberated pyrite recovery data has culminated in the development of a mathematical relationship which takes the form: $k_{fi}^{2} \propto k_{ci} * m_{Ri}$ . This relates the first order rate constants for liberated pyrite in the flash flotation machine (k_f) and the rougher flotation column (k_c) for each size class (i) in the floatable size range (+38/−150 μm), using the mass recovery (m_R) of each size class within the flash flotation machine. To account for the considerable differences in both feed properties and operating strategy of the two flotation machines, the rate constant data was normalised using the mass recovery of the total solids to concentrate by the flash flotation machine, allowing a relationship to be developed.
The ability to relate these two very different unit operations via particle specific properties provides impetus for further investigation into the methods used to analyse flotation data. The similarities of both the properties of the recovered pyrite particles and the rate constants of both machines for the size range +38/−106 μm are also of interest for the possibility of mill discharge (cyclone feed) flotation. The rougher column receives the fine split of the cyclone feed, while the flash flotation machine receives the coarse split, if a single machine could be used to recover all these particles in a single stage it would result in considerable cost savings to the industry via decreased plant footprint and operating costs, most notably via reduced water and reagent consumption.
A phenomenological model for an industrial flash flotation cell
2014, Minerals Engineering
Citation Excerpt :
Robust correlations exists where Jg lies within a normal range, the lower limit of which is 0.5 cm/s; however from the available data taken from within the operating flash cell, all measured Jg values were less than 0.35 cm/s (Newcombe et al., 2013a). Models for flotation columns proposed by Alford (1992), Luttrell and Yoon (1991) and Massinaei et al. (2009) require operating variables such as gas dispersion properties, slurry viscosity and density to be known. The degree of mixing is taken to be constant within a vessel, but has been shown to vary considerably with the per cent solids (Mills and O’Connor, 1990) which has implications for the adaption of this model to flash flotation cell in which the per cent solids are very high and also change substantially with height in the cell.
The measured slurry properties of an operating industrial flash flotation cell treating a refractory gold ore have been tested using a number of different modelling methods, including: axial dispersion; classification/partitioning; sedimentation dispersion; and rate equations. Limited success was achieved with the conventional approach to describing flotation vessels and instead a novel approach of interpreting the data from within the cell was developed. This method uses the residence time from within the quiescent/settling zone of the cell (the region between the mixing zone surrounding the impeller and the froth zone). In this situation particle residence time in the settling zone increases with increasing height in the cell, and axial profile data can be used to determine recovery by size at varying heights relative to the mixing zone. Valuable mineral (pyrite) recovery is observed to decrease with increasing residence time in the settling zone, predominantly as a function of the internal cell geometry (inner cone). Plotting the log first order kinetic rate constant for each size class k_i versus the residence time within the settling zone of the cell, τ_s, a near linear relationship becomes evident which is described by the relationship: $k_{i} = α_{i} e^{- β_{i} τ_{s}}$ ; where α and β are empirically fitted parameters for each size class i.
The residence time within each zone has been assumed to be constant for all size classes considered for this initial part of the model development work, as a very detailed residence time distribution study would be required to determine the variation in residence time for each size class.
Numerous mass balancing approaches have been tested, some of which attempted to incorporate the froth phase, however due to the complexities of trying to model the froth the most accurate fit was obtained when the froth zone was excluded from mass balancing calculations. In this case, β was found to be essentially constant across all size classes considered, at an average value of −1.41 (with a standard deviation of 0.056). The average value of β changes with the method of mass balancing used, with the attempts to incorporate the froth bringing in a greater level of deviation from the average. The value of α changes with size, and follows a pattern similar to a recovery by size curve, peaking through the size range of optimal floatability (−212/+53 μm). The shape of this curve, and also the values of α for each size class considered are similar regardless of the mass balancing method used.
Whether these two parameters (α and β) are intrinsic to the ore, the machine or the system as a whole would take a considerable amount of detailed sampling from within the flash flotation cell under consideration and consequent analysis work which were beyond the scope of this initial study. The relationships developed here require validation in other systems, however if they are found to be robust and universal, would allow for the unit recovery to be calculated using standard hydrodynamic equations.
Fine coal beneficiation by column flotation
2014, Fuel Processing Technology
Citation Excerpt :
Main features of the more advanced sparger systems such as the microcel sparger system (Microcel™ column) are non-plugging ability, externally mounted for easy maintenance and also it can produce smaller bubbles (0.1 to 0.4 mm), which provide a higher flotation rate. It can also achieve a higher degree of turbulence inside the static mixer to produce smaller bubbles [13]. It has found wide applications in the coal industry in plants such as Alpha Inc. (Middle Fork etc., USA), Horizon Ltd. (Marrowbone, USA), and BHP (Peak downs and Saraji, Australia) [22].
The amenability of beneficiating a fine hard coal from Hwa-Sun coal mine using column flotation has been studied using a CoalPro flotation column developed by Canadian Process Technologies (CPT). After initial testwork using a batch flotation cell to determine the optimal flotation conditions, tests were carried out to compare its performance with the column. The results showed that the performance of the column was far superior to that of the conventional cell owing to the large fines content present in the coal. It was established that a stable froth column of 40 cm in height and a suitable balance between froth and collection zone could be maintained at 1.0 cm/s superficial gas rate. A suitable reagent scheme and the optimal operating conditions that minimized adverse effects generally encountered in treating fine coal, such as gangue entrainment, have been identified. An increase in water recovery significantly decreased ash rejection implying entrainment of fine ash particles. Column flotation is capable of producing an acceptable clean coal concentrate of 85% combustible recovery with 81% ash rejection at a maximum separation efficiency of 62%, compared to conventional flotation which has 70% recovery with 70% ash rejection at an efficiency of 42%.
Errors in the estimation of size-by-liberation flotation rate constants
2012, Minerals Engineering
The description of froth flotation kinetics has been acknowledged as an essential step towards gaining a more comprehensive understanding of flotation operations. Mathematical models have adopted either continuous or discrete descriptions of specific rate constants. Particularly, the latter framework makes it possible to link discrete specific rate constants to physical properties of the mineral particles, such as particle size and mineral liberation. One aspect of such models usually overlooked is the evaluation of the uncertainty involved in the computation of relevant variables intimately related with the flotation performance such as recovery and specific rate constants, among others. This work aims at assessing the error in the estimation of specific overall flotation rate constants from the P9 flotation model (Savassi, 1998).
The case study presented in this work is based on Welsby et al. (2010). The error was computed using the derivative form of propagation error analysis without considering covariance terms. The specific variances of the different variables were obtained from measurements described in Welsby et al. (2010) or estimated based on the available literature. The estimated error was found to be sensitive to the specific variances. The error was estimated in two cases, namely best and worst case scenario. The average coefficients of variation of k_ij were 11% and 121% for the best and worst case scenario respectively. In the best case scenario, the major contributor to the variances of the discrete specific overall flotation rate constants is residence time, while in the worst case scenario the main contributor was the recovery expressed by size and liberation classes.
The work has exposed the need for information on the uncertainties implicit in the measurements of flotation quantities, which is current by lacking.

View all citing articles on Scopus

View full text

A flotation column simulator based on hydrodynamic principles

Abstract

Int. J. Miner. Process.

Miner. Eng.

Flotation column scale-up and modeling

Can. Inst. Min. Metall. Bull.

Chemical Reaction Engineering

A computer-aided design pack-age for column flotation