Environmental Engineering Reference
In-Depth Information
upper bound is imposed on this molar fraction. This bound puts a ceiling on
syngas conversion by limiting the amount of reaction water being formed. In
a mechanistic reactor model, fundamental thermodynamic equations are needed
to model the gas
liquid-phase equilibrium with possible condensation of water.
The simplified water constraint is given as
-
x
3
,
H
2
O
X
9
i
=1
φ
3
,
i
−
φ
3
,
H
2
O
=0
x
3
,
H
2
O
≤
x
mað Þ
with
x
mað Þ
3
,
H
2
O
=0
:
22 = input data
ð
Þ
ð
Eq
:
7
:
15
Þ
3
,
H
2
O
8.
Check on Overall Model Consistency: Square, Full-Rank Set of Equations
The process model contains 80 variables and 80 equations. The count of variables
arises from the following: 5 streams × 9 species flows (
) + 5 extents (
e
)+2prod-
uct variables (
n
a
,MW
a
)+9separationfactors,
S
+ 10 (feed fractions
x
+totalfeed
flow) + 5 design factors (
φ
α
,
β
,
η
,
r
,
λ
) + 2 product flows (mass, molar) + 2 per-
formance variables
x
H
2
O
,
. The 80 equations are the sum of 16 equations
(conversion block related) + 27 (separator block) + 9 (mixer) + 18 (feed speci-
fications) + 1 (production rate) + 2 (performance) + 6 design specifications for
α
ð
ε
C
Þ
, and
F
5
,
C
4+
.
There are no linear dependencies between the equations,
so the system of equations can be solved. The model has many linear equations
and a few bilinear ones. The bilinear equations reduce to linear ones if the given
numerical values for the physical parameters in Equation (7.6), for the separa-
tion factors in Equation (7.9), and for the molar fractions in Equation (7.12) are
substituted. One may solve the resulting linear model (A
,
β
,
η
,
r
,
λ
:
x
=
b
, where square
matrix A has full rank) in parallel. A sequential approach can start with solving
the CO balances and the CO conversion equation (7.7), enabling to determine
all extents of reactions and thus solving the other species balances.
9.
Analysis of a Base Case Design: Species Flows in a Stream Table
The specifications for the base case design variables are given in Table 7.3.
Table 7.4 specifies the reaction conditions and performance variables. The
resulting flows of the main species (reactants and products) are given in a stream
TABLE 7.4 Reaction conditions and performance variables for FT process
Reaction conditions
Average carbon number of C
4+
lump (
−
)
13.0
kmol
−1
)
Average molecular weight of C
4+
lump (kg
184.0
s
−1
)
Extent of reaction to C
1
(kmol
0.00686
s
−1
)
Extent of reaction to C
2
(kmol
0.00617
s
−1
)
Extent of reaction to C
3
(kmol
0.00556
s
−1
)
Extent of reaction to C
4+
lump (kmol
0.05000
s
−1
)
Extent of WGS reaction to CO
2
(kmol
0.03429
Performance variables
Water fraction in reactor outlet stream 3 (−)
0.20056
Carbon atom efficiency (−)
0.75918
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