The transition from first to zero order flotation kinetics and its implications for the efficiency of large flotation cells

Abstract

Flotation cells have traditionally been modelled using first order kinetics, often distributed over multiple floatable species. This description is valid as long as the kinetics are not restricted by the available bubble surface area. If this carrying capacity limit is approached, the behaviour will transition toward zero order kinetics with respect to the concentration of floatable species in the pulp, with this transition being associated with a significant degradation in performance. In this paper we develop a model which describes the transition from first to zero order kinetics. A dimensionless group is introduced, which is the ratio of the flotation rate under first order kinetics to the rate at maximum bubble carrying capacity. At values of this dimensionless group much less than 1 the kinetic equation reduces to the familiar k-Sb relationship, but with a progressive deviation away from first order kinetics as the value increases through 1, with zero order kinetics obtained for values of the dimensionless group much greater than one. This dimensionless group is a function of the cell size, being proportional to the ratio of the cell volume to its cross-sectional area. Since mechanical flotation cells continue to get larger, mainly due to the capital and operating cost benefits that they provide for a given residence time, the potential for deleterious zero order effects is likely to increase. This is also why zero order behaviour is virtually never encountered at the laboratory scale. The propensity for zero order kinetics also increases with both the floatability and concentration of floatable material in the pulp, as well as with the fineness of the grind. This means that cleaner cells are likely to be very susceptible to exhibiting zero order kinetics, while scavenger cells are likely to continue to exhibit first order kinetics for any foreseeable flotation cell size. The cell size at which zero order kinetics effects will degrade the performance of rougher cells will be very system dependent. Since the cell size has a large impact on the zero order transition it cannot be predicted directly from laboratory scale kinetic tests. It is thus important to be able to diagnose it at the industrial scale. The paper presents a method for using down the bank data to determine if there is a significant zero order effect, with the method being applied to a number of sampling campaigns undertaken by the authors. In one of the data sets a significant zero order effect is observed, with the new kinetic model being able to fit the experimental data.