Environmental Engineering Reference
In-Depth Information
d
m
(
t
)
Cp
∗
(
p
∗
(
=
f
(
t
)+
t
)−
t
)−
γ
(
t
)
Dm
(
t
),
(5.19)
dt
where
f
is the fresh ore feed,
C
is the classification matrix and
D
is a lower triangular
matrix defined as
M
p
H
m
R
−
1
K
E
R
D
=
.
(5.20)
The variable
H
m
is the ore content in the grinding chamber,
M
p
is the mill power
draw, matrix
K
E
is a diagonal matrix with
K
i
being the specific grinding rate of the
production of fines below size interval
i
,and
R
is a unitary lower triangular matrix.
Assuming perfect mixture, the ore discharged from the grinding chamber is given
by
p
∗
H
m
m
p
∗
=
.
(5.21)
The classification matrix
C
is a diagonal matrix, its elements being a function of the
mill pulp solid percentage, defined as
p
s
.
The power draw model is given by the Austin empirical model:
=
H
f
/(
H
f
+
W
)
H
m
+
W
+
W
b
kD
2
.
5
L
M
p
=
(
1
−
AJ
)
f
(
φ
)
,
(5.22)
V
m
where
D
and
L
are the diameter and length of the SAG mill,
V
m
is the internal mill
volume,
J
is the volumetric mill fraction occupied by the total hold-up, and
W
b
is
the mass hold-up of steel balls. Function
f
depends on the critical speed fraction
φ [15]. The parameters
k
and
A
are experimental parameters.
The water balance is given in terms of inflow water
q
f
and discharge flow from
the mill, which is given by the following empirical expression:
(
φ
)
α
1
H
m
)
q
p
=(
α
0
+
W
,
(5.23)
where α
0
and α
1
are experimentally adjusted.
Thus, the final expression for water balance is
dW
(
t
)
α
1
H
m
=
q
f
(
t
)−(
α
o
+
)
)
W
(
t
).
(5.24)
dt
(
t
f
f*
p
p*
Grinding
K
Classification
C
C p*
Figure 5.7
Block diagram of a SAG mill
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