International Journal of Minerals, Metallurgy and Materials
Volume 17, Number 5, October 2010, Page 526
DOI: 10.1007/s12613-010-0353-1
Corresponding author: Saeed Chehreh Chelgani E-mail: Sos4552@gmail.com
© University of Science and Technology Beijing and Springer-Verlag Berlin Heidelberg 2010
Estimation of froth flotation recovery and collision probability based
on operational parameters using an artificial neural network
Saeed Chehreh Chelgani
1)
, Behzad Shahbazi
2)
, and Bahram Rezai
3)
1) Surface Science Western, Research Park, University of Western Ontario, London Ont. N6G 0J3, Canada
2) Mining Engineering Department, Science and Research Branch, Islamic Azad University, Tehran 1477893855, Iran
3) Amirkabir University of Technology, Tehran 158754413, Iran
(Received: 19 October 2009; revised: 23 November 2009; accepted: 17 December 2009)
Abstract: An artificial neural network and regression procedures were used to predict the recovery and collision probability of quartz flota-
tion concentrate in different operational conditions. Flotation parameters, such as dimensionless numbers (Froude, Reynolds, and Weber),
particle size, air flow rate, bubble diameter, and bubble rise velocity, were used as inputs to both methods. The linear regression method
shows that the relationships between flotation parameters and the recovery and collision probability of flotation can achieve correlation coef-
ficients (R
2
) of 0.54 and 0.87, respectively. A feed-forward artificial neural network with 3-3-3-2 arrangement is able to simultaneously esti-
mate the recovery and collision probability as the outputs. In testing stages, the quite satisfactory correlation coefficient of 0.98 was achieved
for both outputs. It shows that the proposed neural network models can be used to determine the most advantageous operational conditions
for the expected recovery and collision probability in the froth flotation process.
Keywords: flotation; recovery; collision; probability; neural networks
1. Introduction
Derjaguin and Dukhin were the first to describe bub-
ble-particle interactions in flotation by considering surface
forces. They considered that, before adhering on the surface
of an air bubble, the particles must pass through three dis-
tinct zones, hydrodynamic, diffusiophoretic, and wetting
zones [1].
The primary aim in flotation is the selective attachment
of hydrophobic particles to air bubbles under dynamic con-
ditions (agitation, mixing, and vortex formation) generated
by the action of an impeller when the process is carried out
by mechanical cells. Therefore, it is useful to consider the
extent of hydrodynamic parameters which influence the flo-
tation performance, since they play a major role in parti-
cle/bubble collision, attachment, and transport within an en-
vironment that hold some degree of turbulence [2-4]. The
influences of some dimensionless hydrodynamic parameters,
such as Reynolds number (Re), Froude number (Fr), and
Weber number (We), on the microflotation performance of
quartz coarse particles were studied in this paper.
Besides surface forces, hydrodynamic interaction also
plays a very important kinetic role in determining the colli-
sion efficiency between particles, the state of particulate
suspension, and flotation. The extent of the hydrodynamic
effect is determined by the character of the liquid field
flowing around the particles, which is dependent on the type
of flow in turn, i.e., the Reynolds number. Hydrodynamic
forces influence the rates of aggregate growth and breakup
in several ways [5-9]. Bubble-particle capture is the very
heart of the froth flotation process for the selective flotation
of mineral particles. In addition, bubble-particles are pro-
duced as a result of a comminuting process, which inevita-
bly produces a distribution of particle sizes. The bub-
ble-particle capture process is clearly of key interest to the
mineral processor, each particle possesses a flotation rate
constant that reflects, in part, both the particle size and the
degree of hydrophobicity. There have been a few successful