Environmental Engineering Reference
In-Depth Information
+
White
noise
+
G(Z
-1
)
Stream junction
s
-
+
Internal disturbance generator
s
kj
Flowrate mean
value
Zero-dynamics separator
+
+
Flowrate
variation
f
G(Z
-1
)
Flowrate full value generator
Transfer function or feed
disturbance generator
Figure 2.14
Basic elements of an empirical model of a mineral separation plant
This empirical full model implicitly contains the mass conservation Equations
2.8, in the absence of component transformation as assumed in the operating condi-
tions defined by the previous selected basic units. Mass conversation for component
i
is written
dm
i
dt
=
f
i
M
i
B
i
z
M
i
f
i
=
M
i
(
f
i
−
)=
(
t
)
for
i
=
0to
n
+
1
(2.120)
since the constraint
M
i
f
i
0 is valid for the nominal state values. A representation
of the model for a single flotation cell is given in Figure 2.15. The same structure
can be used for all the stream components and for all the nodes of a complex plant.
The model requires, in addition to the steady-state values
f
, the knowledge of
the separation coefficients
s
kj
, the transfer function coefficients, and the variance of
the driving white noise vector ξ
including ξ
i
and ξ
s
. Both the empirical and the
phenomenological models contain numerous parameters to be calibrated. This is
why it is interesting to look at sub-models for dynamic data reconciliation.
=
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