2441
The Sensitivity of Kinetic Characterizations to the Selection of
Flotation Intervals in Batch Tests
Luis Vinnett, Marcelo Rivera, Matías Benítez, Francisca Orellana
Department of Chemical and Environmental Engineering, Universidad Técnica Federico Santa María
Francisca Justel
Department Metallurgical and Materials Engineering, Universidad Técnica Federico Santa María
ABSTRACT: Batch tests were conducted to recover copper minerals by flotation. Seven flotation intervals were
chosen to characterize kinetic responses in terms of: maximum recoveries, R∞, and flotation rate distributions,
f(k). The responses were subsampled, removing one datapoint at a time to obtain seven datasets with six time-
recovery data. These datasets were fitted to the Single Flotation Rate, Rectangular and Gamma models. The
R∞-f(k) pairs of the latter proved to be less sensitive to changes in the flotation intervals. A scale-up procedure
was performed, showing significant uncertainties in the predicted recoveries when the R∞-f(k) pairs resulted
strongly influenced by different flotation intervals.
Keywords: flotation kinetics, batch tests, flotation rate distribution, scale-up.
INTRODUCTION
Flotation is the most widely used technique for separating
and concentrating valuable minerals. Internal parameters
and operating conditions, such as mineral liberation, par-
ticle size, gas flowrate, froth depth and reagent dosage, as
well as the three-phase nature of this process, makes flota-
tion modeling not straightforward (Bergh et al., 2018 Bu
et al., 2017). This modeling involves the construction of
mathematical representations that describe the interactions
among multiple variables and incorporate critical phenom-
ena in the mineral separation. These representations can
be as kinetic models, empirical models, and first-principle
models (Finch &Dobby, 1991 Villeneuve et al., 1995
Gharai &Venugopal, 2015), from which the former have
received special attention due to their applicability in scal-
ing-up procedures.
Flotation models are used to simulate and predict pro-
cess performances under different conditions, such as varia-
tions in feed properties, changes in reagent schemes and
dosages, evaluation of different control strategies, changes
in machine geometry and circuits, among others (Gharai
&Venugopal, 2015). These models are also used to evalu-
ate process efficiencies, optimize operating parameters, and
make well-informed decisions to improve the recovery of
valuable minerals. Although significant progresses have
been made in flotation modeling, there are still difficulties
in predicting macroscopic metallurgical results from the
physical and chemical phenomena involved in the collec-
tion and separation processes. Thus, kinetic modelling con-
tinues being one of the most commonly used strategy for
flotation characterization.
The first kinetic model [Equation (1)] was proposed
by Garcia-Zuñiga (1935) for batch flotation, which
The Sensitivity of Kinetic Characterizations to the Selection of
Flotation Intervals in Batch Tests
Luis Vinnett, Marcelo Rivera, Matías Benítez, Francisca Orellana
Department of Chemical and Environmental Engineering, Universidad Técnica Federico Santa María
Francisca Justel
Department Metallurgical and Materials Engineering, Universidad Técnica Federico Santa María
ABSTRACT: Batch tests were conducted to recover copper minerals by flotation. Seven flotation intervals were
chosen to characterize kinetic responses in terms of: maximum recoveries, R∞, and flotation rate distributions,
f(k). The responses were subsampled, removing one datapoint at a time to obtain seven datasets with six time-
recovery data. These datasets were fitted to the Single Flotation Rate, Rectangular and Gamma models. The
R∞-f(k) pairs of the latter proved to be less sensitive to changes in the flotation intervals. A scale-up procedure
was performed, showing significant uncertainties in the predicted recoveries when the R∞-f(k) pairs resulted
strongly influenced by different flotation intervals.
Keywords: flotation kinetics, batch tests, flotation rate distribution, scale-up.
INTRODUCTION
Flotation is the most widely used technique for separating
and concentrating valuable minerals. Internal parameters
and operating conditions, such as mineral liberation, par-
ticle size, gas flowrate, froth depth and reagent dosage, as
well as the three-phase nature of this process, makes flota-
tion modeling not straightforward (Bergh et al., 2018 Bu
et al., 2017). This modeling involves the construction of
mathematical representations that describe the interactions
among multiple variables and incorporate critical phenom-
ena in the mineral separation. These representations can
be as kinetic models, empirical models, and first-principle
models (Finch &Dobby, 1991 Villeneuve et al., 1995
Gharai &Venugopal, 2015), from which the former have
received special attention due to their applicability in scal-
ing-up procedures.
Flotation models are used to simulate and predict pro-
cess performances under different conditions, such as varia-
tions in feed properties, changes in reagent schemes and
dosages, evaluation of different control strategies, changes
in machine geometry and circuits, among others (Gharai
&Venugopal, 2015). These models are also used to evalu-
ate process efficiencies, optimize operating parameters, and
make well-informed decisions to improve the recovery of
valuable minerals. Although significant progresses have
been made in flotation modeling, there are still difficulties
in predicting macroscopic metallurgical results from the
physical and chemical phenomena involved in the collec-
tion and separation processes. Thus, kinetic modelling con-
tinues being one of the most commonly used strategy for
flotation characterization.
The first kinetic model [Equation (1)] was proposed
by Garcia-Zuñiga (1935) for batch flotation, which