Gas‐Liquid Mass Transfer Approach applied to the Modeling of Flotation in a Bubble Column

Abstract

A kinetic model developed to describe flotation in a bubble column is presented. This model, developed on the basis of the theory of mass transfer in gas-liquid flows, makes explicit in its formulation the effect of the superficial saturation of bubbles on the kinetics of flotation. The model is applied to the simulation of flotation column experiments for which the classical first-order models, commonly used in flotation modeling, are insufficient to represent the flotation kinetics. The results of the simulations obtained under different hypotheses of simplification and compared to experimental data show that the model succeeds in representing the flotation kinetics in these cases.

Toward a Multiphase Local Approach in the Modeling of Flotation and Mass Transferin Gas-Liquid Contacting Systems

“…The application of mass transfer theory to flotation process has been previously suggested by Jameson et al (1977) and Ityokumbul (1992).The later proposed, for the collection zone of a flotation column, a kinetic model based on a mass balance at the gas-liquid interfaces where the rate of particle attachment to the bubbles is assumed to be proportional to the particle concentration in the liquid and to the presence of non-saturated bubble surface. Chahed & Mrabet (2008) have built on this model and have proposed a more complete formulation. They also tried to comment some reductions of this formulation in comparison with the common first order model of flotation and with the model proposed by Ityokumbul (1992).…”

“…Commenting the model of Ityokumbul (1992), Chahed & Mrabet (2008) assume the hypothesis considering that the surface load b C is generally small as compared to the maximum surface load mb C , allows to neglect b C in the first term in the rhs of equation (6), but certainly does not allow, in the general case, to neglect the last term. This term represents the rate of detachment of the particles and when neglected, the model degenerates so much so that it becomes impossible to represent the effect of the surface load of bubble on its potential carrying capacity.…”

“…This term represents the rate of detachment of the particles and when neglected, the model degenerates so much so that it becomes impossible to represent the effect of the surface load of bubble on its potential carrying capacity. In order to avoid this loss of generality, Chahed & Mrabet (2008) proposed to keep the term of detachment but they neglected b C in the first term of the second member of the mass balance (6) against mb C . In these conditions, the model (6) reduces to:…”

“…The kinetic model based on gas-liquid mass transfer theory presented above has been applied to two cases of literature experimental data, Chahed & Mrabet (2008). The first set of experiments is due to Bensley et al (1985) and concerns the flotation of fine coal particles in a bubble column.…”

“…In both experiments, classical first order models are insufficient and the simulations produced by Chahed & Mrabet (2008) showed how it is pertinent to use mass transfer approach to describe the flotation kinetics in bubble columns. The simulation of the first set of experiments shows that, when the irreducible concentration is suitably adjusted from the experiments, the kinetics of flotation can be adjusted and the model reproduces correctly the experimental results, with an irreducible concentration * R χ greater than 20% , figure (2).…”