Environmental Engineering Reference
In-Depth Information
Example 17.2 Thiele modulus and effectiveness factor
If catalyst particles are relatively large and the reaction rate is fast, the diffusion rate
might be too slow to provide the center of the catalyst particle with enough reactant
to maximize the reaction rate. This can be expressed by the Thiele modulus (see
also Chapter 9):
r
r
Th
=
d
p
6
ρ
cat
D
eff
,
CO
c
CO
,
b
where d
p
is the particle diameter,
r
is the reaction rate expressed per kg cat,
ρ
cat
is
the catalyst density,
D
eff,CO
is the effective CO diffusion coefficient (taking into
account catalyst porosity and pore tortuosity), and c
CO,b
is the bulk concentration
of CO. We assume that at 500 K
D
eff,CO
is 5.20 × 10
−9
m
2
s
−1
,
m
−3
,
ρ
cat
is 2500 kg
m
−3
. If the Thiele modulus is small (
and c
CO,b
is 300 mol
1), there are no dif-
fusion limitations; if the Thiele modulus becomes larger, diffusion starts to play a
role and the effective reaction rate is lower than the intrinsic reaction rate. From the
Thiele modulus, we can calculate the catalyst effectiveness factor:
reaction ratewith diffusion limitation
reaction rate at bulk conditions
=
tanh
Th
Th
η
≡
Calculate the catalyst effectiveness factor at 500 K with the reaction rate calculated
in Example 17.1 (
F
= 3) for catalyst particles of 2 mm, which is a typical size used
in a fixed bed. What is your conclusion? What happens if the catalyst activity is
increased so that
F
becomes 10? What is the effectiveness factor for typical slurry
catalyst particles with a diameter of 50
μ
m?
Solution
s
4
0×10
−3
6
54 × 10
−3
Th
=
2
:
:
2500
=0
:
899;
η
=0
:
796
20 × 10
−9
5
:
300
The effectiveness factor is lower than 1, showing that there are some diffusion lim-
itations. If we increase
F
, the reaction rate increases with a factor 3.33, leading to an
effectiveness of 0.567. Since the reaction becomes faster and the diffusion rate stays
the same, the diffusion limitations become worse. For slurry catalyst particles of only
50
μ
m in diameter, the effectiveness factor is 1.00, so there is no diffusion limitation.
17.3 SYNTHETIC NATURAL GAS SYNTHESIS
An alternative approach for chemical conversion of syngas into fuel is the production
of SNG. It is sometimes also called substitute natural gas or green gas, but the latter
term can also encompass methane produced by anaerobic digestion. The synthesis of
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