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 ki versus the residence time within the settling zone of the cell, τs , a near linear relationship becomes evident which is described by the relationship: ki=αie-βiτski=αie-βiτs; 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.