How to Determine the Height of Column Flotation

How to Determine the Height of Column Flotation

Pneumatic flotation units are fast replacing conventional flotation cells in both scavenging and cleaning duties. One such unit that has received wide acceptability in industry is the flotation column. While many consider column flotation to be a recent development, its roots date back to the mid-1910s where it was first commercially tested at Inspiration Copper Company (Gahl, 1915). However this early design was not commercially successful as it was plagued by solid settlement on the gas distributor. In an attempt to overcome the solid settlement problem, Simkovich (1952) used a flotation column cell with a low speed stirrer installed near the base of the unit. selection criteria.

Selection of Recovery Zone Height

Chemical Kinetic Approach to Column Sizing

For first order kinetics, the performance may be predicted from the knowledge of kinetic data and the parameters of the flow model. The behavior of solid particles in the flotation column is described using the sedimentation dispersion model. Thus, only the rate constant k, and the mixing parameters of the process vessel or age distribution of the particles, are required for predicting the conversion (or recovery). Accordingly, the fractional recovery is given by:

column-flotation-fraction-recovery

column-flotation-fraction-recovery-2

where Ur and Vp are the slurry and particle settling velocities in the recovery zone, L is the recovery zone height, Ep and εg are the particle dispersion coefficient and gas hold-up respectively. Quite recently, O’Connor et al. (1994) have introduced the concept of a terminal recovery in Eq. 1 to account for the presence of floatable particles that are not recovered at infinite time. Thus for a given recovery, the required particle residence time (or column height) is determined from Eq. 1-4 in an iterative manner.

 

column-flotation variation of sphalerite recovery

In both cases, it can be seen that increasing the recovery zone height does not necessarily result in increased recoveries. In the same manner, the product, kτp, is also independent of recovery zone height. If we assume that the rate constant does not vary with height, this can only mean that the particle residence time is also constant. This would imply that the particle collection process is actually occurring in a relatively constant height which is independent of the actual recovery zone height.

Use of L/D Ratio – In determining the height of a flotation column, the particle residence time needed to achieve a target recovery is determined as described above. From the particle residence time, the volume of flotation cell may be calculated from the slurry flow rates necessary to achieve the target production rates. The column height may be estimated using rule of thumb practices in the industry. In general, design engineers strive to maintain a length to diameter (L/D) ratio of at least five.

In operations where columns are employed to replace existing conventional cells, the volume required may also be estimated from comparable practice. For example, Clinger and McGregor (1987) carried out an extensive survey of flotation column installations. They compiled data on the volume ratios employed where flotation columns replaced mechanical cells. The flotation column to mechanical cell volume ratios encountered varied from 0.4:1 to 1.54:1 with an average value of 0.98:1.

A Mass Transfer Approach to Column Sizing

In view of the inadequacies inherent in the present approach to the selection of flotation column height, a new procedure which is based on fundamental principles was recently presented in the literature (Ityokumbul, 1992 a, b). According to this procedure, the performance equation is given by:

column-flotation-equation

where z is height of recovery zone required for a given recovery, R, a is the bubble interfacial area, k’ the particle transfer rate constant, Γm is the maximum bubble load, Ur and Vp are the slurry velocity in the recovery zone and particle settling velocity respectively. In Eq. 5, the terms k’Γm, (Ur+Vp)/akΓm and -1n(1-R) are equivalent to the interface mass transfer coefficient, height of a transfer unit, HTU, and number of transfer units, NTU, respectively. The maximum NTU cannot be varied at will. It is determined by the maximum recovery which is a function of the degree of liberation of the mineral, reagent dosage, hydrophobicity of the particles, gas and slurry velocities, feed slurry concentration, etc.

column-flotation estimate heights of transfer unit

Column Throughput

Parekh et al. (1990) carried out a parametric study of column flotation for fine coal cleaning. They identified three major variables affecting the recovery/yield and grade: column height, air flow rate and frother concentration. As indicated above, the effect of column height may not be as significant as their results suggest. The last two parameters, air flow rate and frother concentration, control the bubble size in column flotation. For sparging through porous media, Xu and Finch (1990) have shown that:

column-flotation-equation-2

where n is a constant in the range 0.2 to 0.5, and Rg is the ratio of column cross-sectional area to the surface area of the sparger. It follows from the foregoing that the column throughput should be a function of the gas flow rate. Strictly speaking, the column throughput should be a function of the bubble surface generation rate which is the product of the gas flow rate and the specific bubble surface area.

column-flotation survey summary

what really determines the height in column flotation