Environmental Engineering Reference
In-Depth Information
requires two
c
ðÞ
i
Solving two equations with four unknowns
,c
i
0
ðÞ
,
i
=H
2
,CO
more specifications:
1. The H
2
/CO ratio will increase toward the center of the particle due to faster
diffusion of hydrogen. For that reason, the perfect stoichiometric ratio is only
imposed as an upper bound in the particle center:
ðÞ
c
CO
z
c
H
2
z
z
=0
−
α
:
=3
ðÞ
2. At the outer surface, the CO concentration is given, while the H
2
concentration
is a degree of freedom to match the previous center condition:
=c
ðÞ
m
−3
z
=r
c
CO
ðÞ
CO
=0
:
2
kmol
:
Typical numerical values (right order of magnitude) for the model parameters
(at 500 K) are:
0×10
−3
s
−1
m
−3
cat
α
=0
:
9;
a
=6
:
kmol
2×10
−9
m
2
D
CO
=5
:
ð
s
−1
Þ
;
D
H
2
=2
:
7
D
CO
m
2
ð
s
−1
Þ
5×10
−3
m
r=0
:
ðÞ
;
s
CO
=
−
1;
s
H
2
=
−
ð
3
−
α
Þ
a. Given the concentration distribution equations with boundary conditions,
derive and report the expressions for the H
2
concentration at the outer surface
c
ðÞ
H
2
and the expressions for the H
2
and CO concentrations in the center.
b. Use these expressions to compute the concentrations in the center and the
H
2
/CO ratio at the outer surface
ð
σ
H
2
=
CO
Þ
. Check by which fraction (
μ
)
this
ratio is
smaller
than the ideal
stoichiometric ratio of 3
−
α
,
where
μ
=
σ
H
2
=
CO
=
ð
3
−
α
Þ
.
17.3
A Fischer
Tropsch slurry bubble column reactor is shown in Figure 17.4.
Small catalyst particles are suspended in the liquid product (a mix of hydrocar-
bons and water), while syngas is vigorously bubbled through the liquid. Due to
intense mixing, the compositions of the liquid and the gas are uniform within
each phase throughout the reactor, i.e., independent of the location in the reac-
tor. The reactants, CO and H
2
, are only partially converted in such a reactor.
A fraction of the unconverted syngas is recycled and mixed with fresh syngas
feed. The main issue is the determination of the composition of fresh syngas
meeting a target H
2
/CO ratio for the gas phase. This latter target must be
a suitable one for the Fischer
-
-
Tropsch reactions in the catalyst particles
exposed to the gas.
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