Environmental Engineering Reference
In-Depth Information
J
Figure 2.10
BILMAT™ reconciliation algorithm
i
=
1
(
c
i
−
c
i
)
3
2
i
=
1
(
z
i
−
z
i
)
3
2
J
c
=
+
.
(2.101)
σ
c
i
σ
z
i
Then the Lagrange function is derived with respect to the six metal mass fractions
and the two Lagrange multipliers, and the derivative equations set to 0. The solution
of this system of eight unknown variables into eight equations leads to
c
1
−
λ
c
F
1
σ
c
1
c
1
=
c
2
−
λ
c
F
2
σ
c
2
c
2
=
(2.102)
c
3
−
λ
c
F
3
σ
c
3
c
3
=
with
F
1
c
1
F
2
c
2
F
3
c
3
−
−
=
λ
c
(2.103)
F
1
σ
c
1
+
F
2
σ
c
2
+
F
3
σ
c
3
for copper, and similar expressions for zinc. The reconciled values obtained from
Equations (2.102) are optimum only for the selected particular values of the flowrates.
To minimize the overall criterion
F
j
σ
F
j
3
j
=
1
F
j
−
J
=
J
c
+
,
(2.104)
Search WWH ::
Custom Search