Modeling the Sauter Mean Bubble Diameter in Mechanical, Forced-air Flotation Machines

Abstract

There currently exists no available model for predicting the Sauter mean bubble diameter, D32, from the key process variables for mechanical flotation machines. This is seen as a significant shortcoming since flotation is a surface area (of bubbles) dependent process, the key metric being the bubble surface area flux, Sb, defined as 6 Jg/ D32, where Jg is the superficial gas velocity. Knowledge of how key variables affect the bubble size distribution (BSD), and hence Sb, is seen as an essential component of process understanding and optimization. The objective of this work was to develop a mathematical expression for D32 based on the key process variables of frother type and concentration, superficial gas velocity, power intensity (impeller tip speed), liquid viscosity, and altitude (elevation above sea level). In order to effectively measure the BSD that links to the Sb leaving the pulp phase, a relatively large 700 liter cell, a Metso RCS™ 0.8 m3 pilot unit, was selected. This unit, having an internal shelf baffle, produced separation of turbulent (near impeller) and quiescent (near froth) regions, ensuring that the measured BSD was truly reflective of the surface area flux leaving the pulp zone. Failure to adequately address this has been a shortcoming of work by others. The Metso unit was powered by a variable speed drive that permitted an 8-fold increase in power intensity covering the full range of industrial impeller tip speed (4.6 to 9.2 m/s). Five frothers were tested, covering a broad range in types including alcohols and polyglycols, Viscosity was modeled by varying water temperature between 4 and 40 oC. Altitude was modeled by varying gas density, an air-helium mixture fed to a smaller 5.5 liter laboratory Denver cell. The McGill gas dispersion sensors; bubble viewer and Jg probe, were used for measurement. The work showed that the effect on D32 for all frothers can be normalized to the same set of curves when dividing concentration by a frother's CCC95 value. The notion of CCC95 is introduced and is equivalent to Laskowski's CCC (critical coalescence concentration) but more suitable for mathematical analysis and model development. It represents the frother concentration (ppm) for which 95% reduction in D32 has been achieved. Frother concentration was found to be the variable with the largest impact on D32 and is modeled with an exponential decay function that reaches a limiting bubble size at frother concentration exceeding the CCC95 value. Higher CCC95 results in a lower limiting bubble size. It appears that the CCC95 value for a frother may be predicted from its' basic molecular structure using the Hydrophile-Lipophile Balance/Mol. Wt. parameter. It was also found that the CCC95 value for a frother increases with increasing Jg. D32 was found to depend on Jg0.5 with a notional "bubble creation size" at Jg = 0 cm/s. The dependence on viscosity relative to that at 20 oC was a power relationship having an exponent of 0.776, while similarly, that for simulated altitude (gas density relative to air density at sea level)) showed less dependency with an exponent of -0.132. Surprisingly, impeller speed was found not to have any significant effect on D32 across the range representing an 8-fold increase in power intensity and a doubling of impeller tip speed.The overall D32 model, developed in a 2-phase air-water system, shows very good agreement with measured plant data from 5 operating sites worldwide, representing 3-phase (air-water-solids) flotation systems. The Sb- Jg curves produced by the model can be used as a "road-map" to benchmark plant operation as illustrated by a case study from the Lac des Iles palladium mine in Ontario. This approach is seen as a significant development for process understanding and optimization.