Environmental Engineering Reference
In-Depth Information
for the sake of computational simplicity that in this example only four hydrocarbon
species are considered, C
1
-
C
3
and the C
4+
lump in the form of C
n
a
H
2
n
a
+2
rather than
having the full range of species (>100).
A remark is due regarding simplifications to be made here with respect to the FT
conversion modeling. At this functional level of design (level 3), one can still avoid
detailed mechanistic modeling of chemical equilibrium and rate limited reactions.
Instead, some practically sound assumptions (based on prior experience with labora-
tory experiments and existing process plants) can be made about ranges for the degree
of conversion of CO and the fraction of the converted CO ending up as CO
2
. The
effect of such assumptions is the replacement of nasty, nonlinear reaction equilibrium
equations for the methanation and WGS reactions by much simpler (bi)linear expres-
sions. A mechanistic approach to FT reaction kinetics is discussed in Chapter 17.
The resulting simplified model is based on molar balances for all species involved,
using empirical estimates for the expected degrees of conversions. The model equa-
tions are shown in the following, aiming to make a clear distinction between the spe-
cies balances, rates of change by reactions and separations, and design targets imposed
by the designers.
1.
Molar Balances with Flows and Extents of Reactions in the
FT Conversion Block
Equation 7.4 shows the molar balances for all species, including the extents of
the reactions, with
the molar flow rate. The hydrocarbon lump C
4+
, covering
the species range C
4
-
φ
C
∞
, is the main fuel product:
φ
2
,
Ar
−
φ
3
,
Ar
=0
3
e
ðÞ
1
5
e
ðÞ
2
7
e
ðÞ
3
e
ðÞ
4+
+
e
ð
WGS
−
φ
3
,
H
2
φ
2
,
H
2
Þ
e
−
−
−
−
ð
2
n
a
+1
=0
φ
2
,
H
2
O
+
e
ðÞ
+2
e
ð
2
+3
e
ðÞ
e
ðÞ
4+
−
e
ð
WGS
−
φ
3
,
H
2
O
=0
+
n
a
e
1
3
e
ðÞ
1
2
e
ðÞ
2
3
e
ðÞ
3
e
ðÞ
4+
e
ð
WGS
−
φ
3
,
CO
=0
φ
2
,
CO
−
−
−
−
n
a
e
−
+
e
ð
WGS
−
φ
3
,
CO
2
=0
φ
2
,
CO
2
+
e
ðÞ
1
φ
2
,
CH
4
−
φ
3
,
CH
4
=0
+
e
ðÞ
2
φ
2
,
C
2
−
φ
3
,
C
2
=0
+
e
ðÞ
3
φ
2
,
C
3
−
φ
3
,
C
3
=0
e
ðÞ
4+
φ
2
,
C
4+
+
e
−
φ
3
,
C
4+
=0
ð
Eq
:
7
:
4
Þ
The molar quantities of hydrocarbon species (C
k
) with a chain length of
k
car-
bon atoms satisfy a geometric distribution: C
k
+1
=
α
α
<1.
The composition of the hydrocarbon lump (C
4+
) is characterized by two
averaged variables:
C
k
, with
k
> 0 and 0 <
ðÞ
1
Average number of carbon atoms
n
a
=4
ð Þ
=
−
3
−ð Þ
1
:
:
:
ð
Eq
7
5
Þ
ðÞ
2
Averagemolecular mass
MW
C
4+
=14
n
a
+2
:
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