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Ph.D. Igor Bobin, January 10, 2017
THE IMPROVED EQUATION OF FLOTATION KINETICS WITH DELAY
Ph.D. Igor Bobin, April 3, 2016
Kinetics of flotation reflects the flotation results in the transitive states and is characterized by dependency of the recovery R of floatable mineral in concentrate from time t, i.e. R=f(t). The main purpose of the flotation kinetics is a quantitative description of the flotation process in time. The flotation kinetics of monomineral particles is usually described in mineral processing by the K.F. Beloglazov’s equation or by other similar equations.
However, the equation of K. Beloglazov (as other flotation kinetics equations, too) has a number of disadvantages [2]:
1. Limit of the recovery of valuable component is always taken as 100 %, which is not true. With flotation, the actual recovery of valuable component never reaches 100 %.
2. In practical calculations, the slope of curve R=f(t) is taken into account rather rudely: by selection of the parameter k, which gives a considerable error in the calculation of flotation kinetics.
3. For many minerals the flotation kinetics can’t be described only by an exponential dependence, since there is a delay due to the surface properties of minerals. For such minerals dependence R=f(t) has a pronounced S-shaped form with a delay (Fig. 2).
Thus, the limiting factor of the theory and practice of the ore flotation is still imperfection of the used models of the flotation kinetics. More...
Ph.D. Igor Bobin, Ph.D. Natalia Petrovskaya, December 19, 2015
The requirement for further enhancing the accuracy of modeling necessitates use in a model increasingly complex differential equations. For example, in applications requiring higher accuracy of calculations, for mathematical description of the flotation kinetics and the flotation rate can be used the inertial models of second or higher order with delay. Especially recommended to use similar models (4) and (5) to describe the kinetics and dynamics of the flotation of minerals with S-shaped experimental curves of the time. In this case, in the simulation, the shape of the analytical curves of kinetics and dynamics corresponds to the shape of the experimental curves. What could be more important in the optimization of the ore flotation process. Practical simulation of flotation kinetics with Bobin’s equations (2), (3), (4) and (5) may be performed using any system of computer mathematics. For example MATLAB. Bobin’s equation (1) is less demanding on the researcher's toolbox, you'll only have possession of MS Excel or even a manual calculation. More.....
USAGE OF INERTIAL MODEL OF 1ST ORDER WITH DELAY FOR ANALYSIS OF KINETICS OF FLOTATION
I. Bobin, N. Petrovskaya. 2008. Tsvetnie Metaly, № 10, Moscow, pp. 30-33.
The model allowing to describe correctly kinetics and speed of flotation of raw mineral material of any kind are proposed. The model take into account delay in extraction of a component in concentrate, upper limit of component’s extraction, inclination of e(t) parameter* and can be considered as universal analytical tool for investigation of kinetics and speed of flotation. It is recommended to use the model for optimization of technological schemes and algorithms of control of flotation.
* e(t) – kinetics of flotation (component’s extraction)
Key words: kinetics of flotation, speed of flotation, inertial model, copper-zinc ore, delay, extraction.
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