Environmental Engineering Reference
In-Depth Information
a. Derive the H
2
and CO molar balances over the reactor
mixer system.
Each balance specifies a relation between the concentrations in the fresh syngas
and the gas inside the reactor. The balance equations will contain the following
parameters:
-
recycle
-
The degree of conversion of CO in this reactor (
X
), relative to intake to reactor
The recycle ratio (
r
) of the unconverted syngas
The conversion of H
2
relative to the CO conversion in reaction stoichiometry
(3
−
α
)
b. Using these balances, show how the H
2
/CO molar ratio
in the fresh
syngas feed can be related to the corresponding ratio in the gas inside the reactor
ð
σ
H
2
=
CO
Þ
ð
x
H
2
=
CO
Þ
. The gas in the reactor is well mixed, so the H
2
/CO ratio of the syngas
exit stream is equal to the ratio inside.
c. Compute the molar H
2
/CO ratio
ð
x
H
2
=
CO
Þ
in the fresh syngas meeting a target
H
2
/CO ratio in the gas inside the reactor
ð
σ
H
2
=
CO
Þ
. This target ratio is expressed
as a fraction (
μ
) of the ideal stoichiometric H
2
/CO ratio for the Fischer
-
Tropsch
reactions:
σ
H
2
=
CO
=
μ
ð
3
−
α
Þ
.
The following numerical values are applicable:
Chain growth probability:
α
= 0.9
Reduction factor:
= 0.8
Degree of CO conversion:
X
= 0.6
Recycle fraction for syngas:
r
= 0.8
μ
PROJECTS
P17.1
Develop a process block diagram with molar balances for the conversion of
methanol to DME, reaction equation (RX. 17.5), based on thermodynamic
considerations.
a. Use Gibbs free energies of the reaction components (see data tables in topics
on chemical engineering thermodynamics) to derive the Gibbs free energy
change of the reaction. Compute the associated reaction equilibrium con-
stant at 500 K. The reaction of methanol to DME occurs in the gas phase
at 10 bar(a). When reporting your results, mention the thermodynamic
equations used (e.g., from Chapter 5 in this topic or other textbooks).
b. Determine the equilibrium conversion of methanol at 500 K, assuming
that the reacting species are not involved in any other reactions. Decide
if recovery and recycling of unconverted methanol are desirable. If the
methanol conversion is sufficiently high (typically >98%), the cost of feed
recovery and recycling often is larger than the extra economic benefit
derived from a fuller use of the feed.
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