XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2111
contributing to the differences observed between average
density cut size and cut sizes of different components in the
feed containing multi-size/multi-density particles. Utilising
the new artificial mineral mixture experiments and a data
from natural ore experiments, reported by (Padhi 2021)
[27], the improved component cut size (d50i) model pro-
posed is given equation 11.
Re
tan^ih
cos`
D Kdl D
Do
D
Du
D
Di
D
Lc
V
V i
d
1
2
.187
.22b
c c c
c c
t
hi
1.093
0
0
50i
2
1
=
t
t
-1.0
-0.436
-0.936
-0.1988 -1.034 c
c
c
c
c
c
`
m
m
m
m
m
m
jj
l
(11)
The d50i equation contains a component hindered settling
velocity with a power coefficient value of 0.22 times of
density ratio of the components, which is a different func-
tion to what was suggested by Narasimha et al (2014) [2],
and Plitt et al (1980) [8], for single-component systems. In
this formulation, ρ1 ρ2. Multi-component settling veloc-
ity proposed by Masliyah (1979) [26] with Richardson &
Zaki (1954) [25] is used for Vhi. The multicomponent clas-
sification model equations are fitted with 53 bi-component
classification data and 14 natural ore data. Comparisons
of predicted against the observed cut sizes for bi compo-
nent mixtures and natural ores are shown in Figure 6a and
Figure 6b, respectively. The model equation for component
sharpness of separation is shown in Equation 12.
V Cc
Vh1 .036
o
1
0
a =m ,V Cc
Vh2 .33
2
0
0
a =m
/tan
cos`
C K
Dc
D
Dc
L
D
D
R g
V i
2h
1
180
.27 .016
.868
max
ag
u
f
s f
w
m
c
c
o t
0.567 1.887
0.127
0.182 0.187
0 2 0
0
t
t
n
n
=-
c
c
c ^
d
e
^t
c
`
b
m
m
m
n
h
m
o
jj
l
(12)
where ρsi and ρsl represent pure component and slurry mix-
ture densities respectively. The constant C is dependent on
feed material characteristics, cyclone design variables and
the form of the relationship is used from the single average
density particle classification.
Since density has an influence on the mass split, an
additional solids recovery model equation was developed
and is shown in Equation 13. The equation for Rf used in
the solids recovery model equation is given in Equation 14.
**R R K
.14 .44
si f i silica f
mag sil- susp
o
mix
1 0
t t
t t
n
n
=+-
-
d b n l (13)
tanb
R Kw D
Do
D
Du
R g
V
D
Lc
V
Vh i
2
1
2
.829
max
f
u c
t
w c
t f
s f
2.2062 2
0 2.424
0.523
1.793
i n
nm
t
t
=
-
-1.06787 -0.20472
-0.7118
-0.8843
f
c
c
e
^t
b
c
c
`cos`
d
m
l p
m
l
h o
m
m
jj
n
(14)
Figure 7. Validation of multi-component model predictions with experimental data component wise for (a) sharpness of
separation and (b) solids recovery
contributing to the differences observed between average
density cut size and cut sizes of different components in the
feed containing multi-size/multi-density particles. Utilising
the new artificial mineral mixture experiments and a data
from natural ore experiments, reported by (Padhi 2021)
[27], the improved component cut size (d50i) model pro-
posed is given equation 11.
Re
tan^ih
cos`
D Kdl D
Do
D
Du
D
Di
D
Lc
V
V i
d
1
2
.187
.22b
c c c
c c
t
hi
1.093
0
0
50i
2
1
=
t
t
-1.0
-0.436
-0.936
-0.1988 -1.034 c
c
c
c
c
c
`
m
m
m
m
m
m
jj
l
(11)
The d50i equation contains a component hindered settling
velocity with a power coefficient value of 0.22 times of
density ratio of the components, which is a different func-
tion to what was suggested by Narasimha et al (2014) [2],
and Plitt et al (1980) [8], for single-component systems. In
this formulation, ρ1 ρ2. Multi-component settling veloc-
ity proposed by Masliyah (1979) [26] with Richardson &
Zaki (1954) [25] is used for Vhi. The multicomponent clas-
sification model equations are fitted with 53 bi-component
classification data and 14 natural ore data. Comparisons
of predicted against the observed cut sizes for bi compo-
nent mixtures and natural ores are shown in Figure 6a and
Figure 6b, respectively. The model equation for component
sharpness of separation is shown in Equation 12.
V Cc
Vh1 .036
o
1
0
a =m ,V Cc
Vh2 .33
2
0
0
a =m
/tan
cos`
C K
Dc
D
Dc
L
D
D
R g
V i
2h
1
180
.27 .016
.868
max
ag
u
f
s f
w
m
c
c
o t
0.567 1.887
0.127
0.182 0.187
0 2 0
0
t
t
n
n
=-
c
c
c ^
d
e
^t
c
`
b
m
m
m
n
h
m
o
jj
l
(12)
where ρsi and ρsl represent pure component and slurry mix-
ture densities respectively. The constant C is dependent on
feed material characteristics, cyclone design variables and
the form of the relationship is used from the single average
density particle classification.
Since density has an influence on the mass split, an
additional solids recovery model equation was developed
and is shown in Equation 13. The equation for Rf used in
the solids recovery model equation is given in Equation 14.
**R R K
.14 .44
si f i silica f
mag sil- susp
o
mix
1 0
t t
t t
n
n
=+-
-
d b n l (13)
tanb
R Kw D
Do
D
Du
R g
V
D
Lc
V
Vh i
2
1
2
.829
max
f
u c
t
w c
t f
s f
2.2062 2
0 2.424
0.523
1.793
i n
nm
t
t
=
-
-1.06787 -0.20472
-0.7118
-0.8843
f
c
c
e
^t
b
c
c
`cos`
d
m
l p
m
l
h o
m
m
jj
n
(14)
Figure 7. Validation of multi-component model predictions with experimental data component wise for (a) sharpness of
separation and (b) solids recovery