Environmental Engineering Reference
In-Depth Information
This geometric distribution also governs the relationships between the extents
e
ðÞ
k
of the chemical reactions C
k
!
C
k
+1
:
e
ðÞ
2
α
e
ðÞ
1
=
e
ðÞ
3
2
e
ðÞ
2
=
α
e
ðÞ
e
ðÞ
1
3
e
4+
=
½
α
=
−ð Þ
1
e
ð
WGS
=
e
ð
1
+2
e
ð
2
+3
e
ð
3
+
n
C
,
a
e
e
ðÞ
4+
β
ð
Eq
:
7
:
6
Þ
The chain growth probability parameter
α
and the CO-to-CO
2
conversion factor
β
are fixed inputs in this simplified model: 0.70 <
α
< 0.95 and 0.02 <
β
< 0.10.
7.6) counts 25 variables and 15 equations.
Assuming that the nine inlet flows are obtained from an upstream unit in the
flow sheet, there is 1 degree of freedom remaining. It is customary for any con-
version block in a flow sheet to specify the degree of conversion of one of the
main reactants. In the FT conversion case, we choose the degree of conversion
The set of equations (7.4
-
η
of carbon monoxide (CO):
−ð Þ
φ
2
,
CO
−
φ
3
,
CO
= 0 with 0
1
:
25 <
η
<0
:
75
ð
Eq
:
7
:
7
Þ
η
For the conversion factor
, one has to specify a target value within a preset
range as an input to a design computation. The model is mathematically well
posed. If model parameters
α
β
η
and
, the conversion target
, and the inlet flows
φ
2
,
{
7.7) suffices to determine the extents
of the reactions {
e
}, the averaged composition {
n
a
,MW
a
} of the fuel product,
and the outlet flows {
∗
} are given, the set of equations (7.4
-
φ
3
,
∗
}.
2.
Molar Balances and Separation Factors for Syngas Recovery and Recycle
The effluent from the FT conversion unit is separated into a fuel product stream
(C
4+
), a water stream, a recycle syngas, and a gas purge. A purge is always
needed to vent any inert components entering the process system to avoid
infinite build-up. Two operations are combined in the separator block of
Figure 7.12: a physical separation into liquids (some C
2
and C
3
and all C
4+
and the bulk of the water) and gas. The gas stream is immediately split into a
syngas recycle stream (fraction
r
) and a purge stream (fraction 1
r
).
Equation 7.8 gives the molar balances and recycle of all species
i
:
−
Þ
:
φ
3
,
i
−
φ
4
,
i
−
φ
5
,
i
=0
Molar balances for all species
ii
=1,
ð
…
,9
rS
ðÞ
i
φ
3
,
i
−
φ
4
,
i
=0
Recovery of species
i
for recycle to conversion
:
ð
Eq
:
7
:
8
Þ
0<
S
ð
i
<1
The separation parameters
f
g
indicate the separation fractions of spe-
cies
i
for recycle. The recycle factor {0
≤
r
< 1} indicates the fraction actually
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