950 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
simulation have been described previously (Huang et al.,
2022 Gupta et al., 2023 Gupta &Yoon, 2024). Figure 2
shows the flotation circuit, which consists of a rougher flo-
tation bank where a low-grade copper ore is fed to remove
most of free gangue minerals. The plant consisted of four
rougher banks, each consisting of five 4,500 ft3 mechani-
cally agitated cells in series. The overall plant throughput
was ~5,000 tph. The froth product of the rougher bank was
then upgraded in the coarse-cleaners flotation circuit. The
coarse-cleaner concentrate was reground to improve libera-
tion, followed by column flotation in the cleaner circuit.
The flotation circuit was run in a closed loop so that the
cleaner-scavenger tail (CST) was returned to the rougher
bank to allow the slow-floating particles to be recovered by
giving them longer retention times.
Circuit simulations began with the analysis of the min-
eral liberation (mij) matrix of the feed to the rougher flota-
tion bank as obtained from a 2-D surface liberation analysis
using a TIMA. The liberation data were used to determine
the particles of different liberation classes (j) using the
Cassie-Baxter equation (1948),
cos cos cos a b a b2 j 1 1 2 i i1 i2 =+[9]
in which a1 and a2 are the surface liberation, θ1 and θ2 are
contact angles of the target and gangue mineral, respec-
tively. and b1 and b2 are correction factors. We assumed
that b1 =0.8, and b2 =1.0 to account for the stereographic
errors associated with determining locking factors. In deter-
mining, we also assumed that θ1 =70° and 150° for KAX-
and SC-coated target mineral (chalcopyrite), respectively,
while θ2 =2° for gangue minerals (e.g., quartz). Table 1
shows the
j i values determined from the mij matrix.
Table 1. Values of
j i obtained Using Eq. [9]
Surface Liberation
0–10 10–30 30–50 50–100
KAX 15.7 31.5 45.1 63.3
SC 23.8 48.6 71.2 105.7
The values obtained using the Cassie-Baxter equation
and presented in Table 1 were used to determine the hydro-
phobic force (Fhp) that decays with thickness h of a thin liq-
uid film (TLF) of water formed between two hydrophobic
surfaces as follows,
r
Fhp K
6h 1
2
131 =-[10]
in which K131 is a hydrophobic force constant. In the pres-
ent work, the force constant was determined using a K131
vs. θ plot established by Pazhianur and Yoon (2003).
The K131 values determined from constant angles as
described above were then combined with the hydrophobic
force constant (K232) between two air bubbles using the
combining rule (Yoon et al., 1997),
Figure 2. A flowsheet for the processing of a low-grade porphyry copper ore. CST is recycled as a
circulating load
simulation have been described previously (Huang et al.,
2022 Gupta et al., 2023 Gupta &Yoon, 2024). Figure 2
shows the flotation circuit, which consists of a rougher flo-
tation bank where a low-grade copper ore is fed to remove
most of free gangue minerals. The plant consisted of four
rougher banks, each consisting of five 4,500 ft3 mechani-
cally agitated cells in series. The overall plant throughput
was ~5,000 tph. The froth product of the rougher bank was
then upgraded in the coarse-cleaners flotation circuit. The
coarse-cleaner concentrate was reground to improve libera-
tion, followed by column flotation in the cleaner circuit.
The flotation circuit was run in a closed loop so that the
cleaner-scavenger tail (CST) was returned to the rougher
bank to allow the slow-floating particles to be recovered by
giving them longer retention times.
Circuit simulations began with the analysis of the min-
eral liberation (mij) matrix of the feed to the rougher flota-
tion bank as obtained from a 2-D surface liberation analysis
using a TIMA. The liberation data were used to determine
the particles of different liberation classes (j) using the
Cassie-Baxter equation (1948),
cos cos cos a b a b2 j 1 1 2 i i1 i2 =+[9]
in which a1 and a2 are the surface liberation, θ1 and θ2 are
contact angles of the target and gangue mineral, respec-
tively. and b1 and b2 are correction factors. We assumed
that b1 =0.8, and b2 =1.0 to account for the stereographic
errors associated with determining locking factors. In deter-
mining, we also assumed that θ1 =70° and 150° for KAX-
and SC-coated target mineral (chalcopyrite), respectively,
while θ2 =2° for gangue minerals (e.g., quartz). Table 1
shows the
j i values determined from the mij matrix.
Table 1. Values of
j i obtained Using Eq. [9]
Surface Liberation
0–10 10–30 30–50 50–100
KAX 15.7 31.5 45.1 63.3
SC 23.8 48.6 71.2 105.7
The values obtained using the Cassie-Baxter equation
and presented in Table 1 were used to determine the hydro-
phobic force (Fhp) that decays with thickness h of a thin liq-
uid film (TLF) of water formed between two hydrophobic
surfaces as follows,
r
Fhp K
6h 1
2
131 =-[10]
in which K131 is a hydrophobic force constant. In the pres-
ent work, the force constant was determined using a K131
vs. θ plot established by Pazhianur and Yoon (2003).
The K131 values determined from constant angles as
described above were then combined with the hydrophobic
force constant (K232) between two air bubbles using the
combining rule (Yoon et al., 1997),
Figure 2. A flowsheet for the processing of a low-grade porphyry copper ore. CST is recycled as a
circulating load