58 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
the experimental data. Clearly further work is needed to
help validate the approach. The provision of two additional
pressure transducers located below the system of inclined
channels would provide a real time measure of the sus-
pension density entering the inclined channels in future
experiments.
Two cases studies are examined in the following
Sections. The first, referred to as Run 1, was effectively the
outlier of the study, involving a very low volumetric feed
rate of 2 L/min. This experiment produced the poorest
upgrade of the iron ore but the highest recovery. The feed
solids concentration was at the higher level of the study,
hence led to a higher viscosity due to the ultrafine clays. The
second, referred to as Run 13, was more consistent with the
other experiments, but had the highest feed rate of 8 L/
min. This experiment produced the highest upgrade, and
a satisfactory recovery. The feed solids concentration was
at the lower level of the study, hence had a lower viscosity.
The particle terminal settling velocities referred to
in this paper were calculated using the Zygrang Sylvester
equation (1981). It is important to note that we based the
terminal settling velocity of the particles on the density
and viscosity of the water, not on so-called pseudo prop-
erties of the suspension. Those pseudo properties were in
effect addressed through the hindered settling function.
However, the ultrafine clays do produce a viscosity effect
that can be considered as a change in the property of the
water. Rodrigues et al (2023) established that the viscosity
increased exponentially with increasing concentration of
the 0–20 mm overflow solids. It is very difficult to estab-
lish the relevant viscosity despite the existence of systematic
measurements given the suspension entering the inclined
channels is very different to the overflow that emerges. A
viscosity double that of water was ultimately used for Run
1 while a viscosity equivalent to that of water was used for
Run 13.
In the above work, the upper lamellae consisted of
40 inclined channels, each 1000 mm long, with angle of
inclination of 70°. The plate thickness was 0.55 mm. The
channel perpendicular cross-section was 1.8 mmx100 mm.
Thus, the channel velocity was readily calculated using the
volumetric flow rate reporting to the overflow. The two
cases described below involved very different flow veloci-
ties. The theoretical model applied here has neglected the
effects of shear induced inertial lift (King and Leighton,
1997). It is highly likely there was no inertial lift in Run
1, given the low velocity, and highly probable there was
inertial lift in Run 13, given the higher velocity (Rodrigues
et al., 2023).
Analysis of Run 1—Low Volumetric Feed Rate
In the paper by Rodrigues et al (2023), Run 1 was con-
ducted at the lowest volumetric feed rate of 2.0 L/min with
a solids concentration of 27 wt%. We have set the viscosity
to double that of water. The full component balance of the
flow streams is summarised below in Table 1 showing the
total overflow rate was 1.80 L/min, which corresponds to a
superficial channel velocity of 0.0042 m/s.
The objective here is to find the combination of the
particle density and particle diameter that aligns with a
common suspension density and channel velocity. The
channel velocity was 0.0042 m/s and the suspension den-
sity was set at 1500 kgm–3. The particle density was deter-
mined implicitly to obtain the correct channel velocity.
For example, the terminal settling velocity of a particle of
diameter, d=10 mm, and density, rp=5201 kgm–3 in water
is ut=0.000118 m/s. The calculated channel velocity, Ul ,is
obtained using Equation 8. That is,
..18
.9397
.U'
3 10 10
1 8 10 1 10
5201 1000
5201 1500 0
0 0042 /s m
3
4
##
###
##
=-
-
=
-6
--4
b l
Each line of calculation in Table 2 produces the same
channel velocity, meaning the analysis has established the
critical link between the particle separation density and the
particle diameter.
Figure 3 shows the variation in the separation density
with particle diameter for Run 1 (Rodrigues et al., 2023)
via the orange triangles. Note there is strong variation in
the separation density with the particle diameter, with
m~0.46. This strong dependence is in part attributed to
Table 1. Run1 Component balances of flow streams
Basis Feed Fluidization Underflow Overflow
Water (L/min) 1.83 0.12 0.20 1.74
Solids (L/min) 0.18 0.00 0.12 0.07
Total (L/min) 2.01 0.12 0.33 1.80
Water (kg/min) 1.83 0.12 0.20 1.74
Solids (kg/min) 0.68 0.00 0.48 0.20
Total (kg/min) 2.50 0.12 0.68 1.94
the experimental data. Clearly further work is needed to
help validate the approach. The provision of two additional
pressure transducers located below the system of inclined
channels would provide a real time measure of the sus-
pension density entering the inclined channels in future
experiments.
Two cases studies are examined in the following
Sections. The first, referred to as Run 1, was effectively the
outlier of the study, involving a very low volumetric feed
rate of 2 L/min. This experiment produced the poorest
upgrade of the iron ore but the highest recovery. The feed
solids concentration was at the higher level of the study,
hence led to a higher viscosity due to the ultrafine clays. The
second, referred to as Run 13, was more consistent with the
other experiments, but had the highest feed rate of 8 L/
min. This experiment produced the highest upgrade, and
a satisfactory recovery. The feed solids concentration was
at the lower level of the study, hence had a lower viscosity.
The particle terminal settling velocities referred to
in this paper were calculated using the Zygrang Sylvester
equation (1981). It is important to note that we based the
terminal settling velocity of the particles on the density
and viscosity of the water, not on so-called pseudo prop-
erties of the suspension. Those pseudo properties were in
effect addressed through the hindered settling function.
However, the ultrafine clays do produce a viscosity effect
that can be considered as a change in the property of the
water. Rodrigues et al (2023) established that the viscosity
increased exponentially with increasing concentration of
the 0–20 mm overflow solids. It is very difficult to estab-
lish the relevant viscosity despite the existence of systematic
measurements given the suspension entering the inclined
channels is very different to the overflow that emerges. A
viscosity double that of water was ultimately used for Run
1 while a viscosity equivalent to that of water was used for
Run 13.
In the above work, the upper lamellae consisted of
40 inclined channels, each 1000 mm long, with angle of
inclination of 70°. The plate thickness was 0.55 mm. The
channel perpendicular cross-section was 1.8 mmx100 mm.
Thus, the channel velocity was readily calculated using the
volumetric flow rate reporting to the overflow. The two
cases described below involved very different flow veloci-
ties. The theoretical model applied here has neglected the
effects of shear induced inertial lift (King and Leighton,
1997). It is highly likely there was no inertial lift in Run
1, given the low velocity, and highly probable there was
inertial lift in Run 13, given the higher velocity (Rodrigues
et al., 2023).
Analysis of Run 1—Low Volumetric Feed Rate
In the paper by Rodrigues et al (2023), Run 1 was con-
ducted at the lowest volumetric feed rate of 2.0 L/min with
a solids concentration of 27 wt%. We have set the viscosity
to double that of water. The full component balance of the
flow streams is summarised below in Table 1 showing the
total overflow rate was 1.80 L/min, which corresponds to a
superficial channel velocity of 0.0042 m/s.
The objective here is to find the combination of the
particle density and particle diameter that aligns with a
common suspension density and channel velocity. The
channel velocity was 0.0042 m/s and the suspension den-
sity was set at 1500 kgm–3. The particle density was deter-
mined implicitly to obtain the correct channel velocity.
For example, the terminal settling velocity of a particle of
diameter, d=10 mm, and density, rp=5201 kgm–3 in water
is ut=0.000118 m/s. The calculated channel velocity, Ul ,is
obtained using Equation 8. That is,
..18
.9397
.U'
3 10 10
1 8 10 1 10
5201 1000
5201 1500 0
0 0042 /s m
3
4
##
###
##
=-
-
=
-6
--4
b l
Each line of calculation in Table 2 produces the same
channel velocity, meaning the analysis has established the
critical link between the particle separation density and the
particle diameter.
Figure 3 shows the variation in the separation density
with particle diameter for Run 1 (Rodrigues et al., 2023)
via the orange triangles. Note there is strong variation in
the separation density with the particle diameter, with
m~0.46. This strong dependence is in part attributed to
Table 1. Run1 Component balances of flow streams
Basis Feed Fluidization Underflow Overflow
Water (L/min) 1.83 0.12 0.20 1.74
Solids (L/min) 0.18 0.00 0.12 0.07
Total (L/min) 2.01 0.12 0.33 1.80
Water (kg/min) 1.83 0.12 0.20 1.74
Solids (kg/min) 0.68 0.00 0.48 0.20
Total (kg/min) 2.50 0.12 0.68 1.94