XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 57
Reynolds numbers, n ~5 (Garside, and Al-Dibouni, 1977).
For a mono-density system, the dimensionless density term,
p w
p susp t t
t t
-
-
d n,
reverts to (1–f) where f is the volume fraction of the solids.
Equation 7 is then equivalent to the Richardson and Zaki
(1954) equation.
We have previously found Equation 7 to be remark-
ably effective in describing the process of gravity separation
(Patel et al., 2008 Syed et al., 2018). Consider a suspension
with a density of 1500 kgm–3. A silicate particle of density
2675 kgm–3 has a dimensionless density of 0.70 hence an
effective volume fraction of 0.30. However, a hematite par-
ticle of density 5100 kgm–3 has a dimensionless density of
0.88 and hence an effective volume fraction of only 0.12.
Both species perceive a common pressure gradient through
the suspension and, logically, interpret that gradient in
terms of their density, meaning the lower density species
experiences a stronger level of hindered settling (Galvin et
al,1999).
Combining Equations 5 and 7 with uTt=utsin(θ), and
noting that at the critical separation condition rp=D50,
gives the superficial channel velocity. That is,
sin^ih
Ul
zut D
D50
3d
w
susp
n-
50
1
t
t
=
-
-
d n
(8)
Consider the critical condition defining whether a par-
ticle of a given size and density reports to the overflow of
the Reflux Classifier. The suspension density is fixed, and
the velocity of the superficial flow through the channel is
fixed. We know that as the particle density decreases, the
level of hindered settling increases which means the criti-
cal separation condition accommodates a particle of larger
diameter. This means the value of m should decrease as the
suspension density increases, which in turn should improve
the gravity separation.
In this paper we use Equation 8 to describe the variation
in the separation density, D50, with the particle diameter, d.
We use two specific case studies reported by Rodrigues et al
(2023) to help assess the effectiveness of the simple analyti-
cal model. It is recognised full validation to establish the
limitations will require further investigation.
PROCESS DESCRIPTION
The feed suspension enters the Reflux Classifier at an
elevated position as shown in Figure 1. Most of the volu-
metric flow reports to the overflow, the underflow being
constrained by the lower fluidized bed, and the PID set-
point density control conditions required for the release of
underflow. Particle segregation occurs within the inclined
channels, leading to the build-up in the suspension den-
sity within the vertical section of the Reflux Classifier. With
the setting of a suitable fluidization velocity, a lower bed of
fluidized particles develops. Equation 7 should also apply
to the fluidized bed, however here the suspension density
will typically be much higher. This means that lower den-
sity particles should be progressively rejected from the bed,
in an upwards direction. This well-known phenomenon
which underpins conventional teetered bed separators is
referred to as “inversion” (Moritomi et al., 1986).
The system evolves toward steady state. Increasingly,
the denser particles segregate from the system of inclined
channels. The dense, ultrafine, particles then accumulate
just below the inclined channels due to their inability to
settle against the strong upwards flow velocity produced by
the entering feed. Ultimately, a dense plume effect is created
that falls en-masse, sinking below the feed entry elevation.
These particles then transport readily towards the lower
fluidized bed. The finest particles however are impeded
by the fluidization entering through the base. Ultimately
the ultrafine dense particles and the relatively coarse low-
density particles accumulate, and each eventually partition
between the overflow and the underflow.
In the context of the theoretical model, a suspension
with a density, rsusp, develops naturally over time, through-
out the vertical zone above the fluidized bed. This suspen-
sion becomes dominated by the higher density minerals
hence the density is reached at a relatively low volume frac-
tion of solids. This suspension, which is ultimately well
mixed with the incoming feed, enters the inclined channels
with a superficial velocity, U′. These two parameters then
establish the critical separation condition linking the par-
ticle density and the particle diameter. This link, which is
the subject of the analysis in this paper, governs the particle
partitioning between the underflow and the overflow.
ASSESSMENT OF LAMINAR FLOW-
HINDERED SETTLING MODEL
Rodrigues et al (2023) investigated the upgrading of an
iron ore feed nominally 80% finer than 150 mm using the
Reflux Classifier. A series of 13 experiments was conducted
covering a broad range of conditions. The feed was very
well liberated between low density silicates and high-den-
sity hematite. Thus, a binary approach was applied to the
analysis to deduce the partition surface for each separation.
It is noted that the volumetric flow rate and hence chan-
nel velocity was known however the internal suspension
density was not measured. Thus, this work determines the
suspension density necessary to achieve agreement with
Reynolds numbers, n ~5 (Garside, and Al-Dibouni, 1977).
For a mono-density system, the dimensionless density term,
p w
p susp t t
t t
-
-
d n,
reverts to (1–f) where f is the volume fraction of the solids.
Equation 7 is then equivalent to the Richardson and Zaki
(1954) equation.
We have previously found Equation 7 to be remark-
ably effective in describing the process of gravity separation
(Patel et al., 2008 Syed et al., 2018). Consider a suspension
with a density of 1500 kgm–3. A silicate particle of density
2675 kgm–3 has a dimensionless density of 0.70 hence an
effective volume fraction of 0.30. However, a hematite par-
ticle of density 5100 kgm–3 has a dimensionless density of
0.88 and hence an effective volume fraction of only 0.12.
Both species perceive a common pressure gradient through
the suspension and, logically, interpret that gradient in
terms of their density, meaning the lower density species
experiences a stronger level of hindered settling (Galvin et
al,1999).
Combining Equations 5 and 7 with uTt=utsin(θ), and
noting that at the critical separation condition rp=D50,
gives the superficial channel velocity. That is,
sin^ih
Ul
zut D
D50
3d
w
susp
n-
50
1
t
t
=
-
-
d n
(8)
Consider the critical condition defining whether a par-
ticle of a given size and density reports to the overflow of
the Reflux Classifier. The suspension density is fixed, and
the velocity of the superficial flow through the channel is
fixed. We know that as the particle density decreases, the
level of hindered settling increases which means the criti-
cal separation condition accommodates a particle of larger
diameter. This means the value of m should decrease as the
suspension density increases, which in turn should improve
the gravity separation.
In this paper we use Equation 8 to describe the variation
in the separation density, D50, with the particle diameter, d.
We use two specific case studies reported by Rodrigues et al
(2023) to help assess the effectiveness of the simple analyti-
cal model. It is recognised full validation to establish the
limitations will require further investigation.
PROCESS DESCRIPTION
The feed suspension enters the Reflux Classifier at an
elevated position as shown in Figure 1. Most of the volu-
metric flow reports to the overflow, the underflow being
constrained by the lower fluidized bed, and the PID set-
point density control conditions required for the release of
underflow. Particle segregation occurs within the inclined
channels, leading to the build-up in the suspension den-
sity within the vertical section of the Reflux Classifier. With
the setting of a suitable fluidization velocity, a lower bed of
fluidized particles develops. Equation 7 should also apply
to the fluidized bed, however here the suspension density
will typically be much higher. This means that lower den-
sity particles should be progressively rejected from the bed,
in an upwards direction. This well-known phenomenon
which underpins conventional teetered bed separators is
referred to as “inversion” (Moritomi et al., 1986).
The system evolves toward steady state. Increasingly,
the denser particles segregate from the system of inclined
channels. The dense, ultrafine, particles then accumulate
just below the inclined channels due to their inability to
settle against the strong upwards flow velocity produced by
the entering feed. Ultimately, a dense plume effect is created
that falls en-masse, sinking below the feed entry elevation.
These particles then transport readily towards the lower
fluidized bed. The finest particles however are impeded
by the fluidization entering through the base. Ultimately
the ultrafine dense particles and the relatively coarse low-
density particles accumulate, and each eventually partition
between the overflow and the underflow.
In the context of the theoretical model, a suspension
with a density, rsusp, develops naturally over time, through-
out the vertical zone above the fluidized bed. This suspen-
sion becomes dominated by the higher density minerals
hence the density is reached at a relatively low volume frac-
tion of solids. This suspension, which is ultimately well
mixed with the incoming feed, enters the inclined channels
with a superficial velocity, U′. These two parameters then
establish the critical separation condition linking the par-
ticle density and the particle diameter. This link, which is
the subject of the analysis in this paper, governs the particle
partitioning between the underflow and the overflow.
ASSESSMENT OF LAMINAR FLOW-
HINDERED SETTLING MODEL
Rodrigues et al (2023) investigated the upgrading of an
iron ore feed nominally 80% finer than 150 mm using the
Reflux Classifier. A series of 13 experiments was conducted
covering a broad range of conditions. The feed was very
well liberated between low density silicates and high-den-
sity hematite. Thus, a binary approach was applied to the
analysis to deduce the partition surface for each separation.
It is noted that the volumetric flow rate and hence chan-
nel velocity was known however the internal suspension
density was not measured. Thus, this work determines the
suspension density necessary to achieve agreement with