2676 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
mineral particles attached to bubbles by making the miner-
als to be recovered hydrophobic (Figure 1).
(Source: Wills et al., 2006)
When determining the optimal time required for froth
flotation, the ratio of valuable minerals recovered from the
feed to the concentrate (i.e., the recovery) and the content
of valuable minerals in the concentrate (i.e., the grade) are
usually quantified (Wills et al., 2006). Many studies have
investigated the relationship between recovery and flota-
tion time, and several kinetic models have already been
suggested (Agar et al., 1998 Wills et al., 2006 Stanojlović
et al., 2014). However, the suggested kinetic models are
not suitable for calculating the grade of concentrate at an
arbitrary time, and therefore, their practical application in
the mineral processing plant is limited.
The objective of this work is first to characterize the
ASR-char composition and then to upgrade the carbon-
containing particles using froth flotation. In addition, a
new kinetic model has also been developed to calculate the
grade of valuables in the concentrate at an arbitrary flota-
tion time.
NEW KINETICS MODEL
The modified first-order rate equation (Agar et al. 1998
Mlynarczykowska et al. 2006) is one of the kinetic models
usually adopted to calculate the recovery as a function of
the flotation time. In the modified first-order rate equa-
tion, the relationship between recovery and flotation time
is represented by Eq. 1:
e f f =-
3
-kt ^t ^1 h h (1)
where t is the flotation time (s), ε(t) is the recovery (%)
at a flotation time t, ε∞ is the recovery at the equilibrium
conditions (i.e., the maximum recovery), and k is the rate
constant (1/s). The constant k is a coefficient represent-
ing the float velocity of a particle (Mlynarczykowska et al.
2006). On the other hand, the grade GN (%)of any com-
ponent MN recovered in the concentrate can be calculated
using Eqs. 2 and 3 using the calculated value of recovery
εN (%).
w mN
N N #f= (2)
......G w w w
w
N
N
N
1 2
=++++(3)
where wN is the mass of the MN component in the concen-
trate (g), and mN is the mass of the MN component in the
feed ore (g). However, using Eq. 3, it is impossible to calcu-
late the recovery of various components in a multi-compo-
nent material like ASR-char. Therefore, by narrowing down
the denominator of Eq. 3 to wN’ (the mass of component
MN’) and adopting a coefficient b, a new kinetic model (Eq.
4) was derived from Eq. 1.
...G th b w w w
w
N'
N
1 2
#=++
+
^a (4)
METHODOLOGY
Size Distribution Analysis
The ASR-char sample was first collected using the quarter
sampling technique. Then, a portion was analyzed using a
laser diffraction particle size analyzer (Microtrac MT3000)
to quantify and measure the size distribution of the parti-
cles. In addition, ASR-char was classified by size to prepare
three different size fractions named: SR-Sieve, SR-Cyclone,
and SR-Wind, which were also subject to the same size dis-
tribution analysis.
Figure 1. Principle of froth flotation
mineral particles attached to bubbles by making the miner-
als to be recovered hydrophobic (Figure 1).
(Source: Wills et al., 2006)
When determining the optimal time required for froth
flotation, the ratio of valuable minerals recovered from the
feed to the concentrate (i.e., the recovery) and the content
of valuable minerals in the concentrate (i.e., the grade) are
usually quantified (Wills et al., 2006). Many studies have
investigated the relationship between recovery and flota-
tion time, and several kinetic models have already been
suggested (Agar et al., 1998 Wills et al., 2006 Stanojlović
et al., 2014). However, the suggested kinetic models are
not suitable for calculating the grade of concentrate at an
arbitrary time, and therefore, their practical application in
the mineral processing plant is limited.
The objective of this work is first to characterize the
ASR-char composition and then to upgrade the carbon-
containing particles using froth flotation. In addition, a
new kinetic model has also been developed to calculate the
grade of valuables in the concentrate at an arbitrary flota-
tion time.
NEW KINETICS MODEL
The modified first-order rate equation (Agar et al. 1998
Mlynarczykowska et al. 2006) is one of the kinetic models
usually adopted to calculate the recovery as a function of
the flotation time. In the modified first-order rate equa-
tion, the relationship between recovery and flotation time
is represented by Eq. 1:
e f f =-
3
-kt ^t ^1 h h (1)
where t is the flotation time (s), ε(t) is the recovery (%)
at a flotation time t, ε∞ is the recovery at the equilibrium
conditions (i.e., the maximum recovery), and k is the rate
constant (1/s). The constant k is a coefficient represent-
ing the float velocity of a particle (Mlynarczykowska et al.
2006). On the other hand, the grade GN (%)of any com-
ponent MN recovered in the concentrate can be calculated
using Eqs. 2 and 3 using the calculated value of recovery
εN (%).
w mN
N N #f= (2)
......G w w w
w
N
N
N
1 2
=++++(3)
where wN is the mass of the MN component in the concen-
trate (g), and mN is the mass of the MN component in the
feed ore (g). However, using Eq. 3, it is impossible to calcu-
late the recovery of various components in a multi-compo-
nent material like ASR-char. Therefore, by narrowing down
the denominator of Eq. 3 to wN’ (the mass of component
MN’) and adopting a coefficient b, a new kinetic model (Eq.
4) was derived from Eq. 1.
...G th b w w w
w
N'
N
1 2
#=++
+
^a (4)
METHODOLOGY
Size Distribution Analysis
The ASR-char sample was first collected using the quarter
sampling technique. Then, a portion was analyzed using a
laser diffraction particle size analyzer (Microtrac MT3000)
to quantify and measure the size distribution of the parti-
cles. In addition, ASR-char was classified by size to prepare
three different size fractions named: SR-Sieve, SR-Cyclone,
and SR-Wind, which were also subject to the same size dis-
tribution analysis.
Figure 1. Principle of froth flotation