entropy
Technical Note
Entropy Analysis of Solar Two-Step Thermochemical
Cycles for Water and Carbon Dioxide Splitting
Matthias Lange *, Martin Roeb, Christian Sattler and Robert Pitz-Paal
Received: 3 November 2015; Accepted: 7 January 2016; Published: 11 January 2016
Academic Editors: Michel Feidt, Daniel Tondeur, Jean-Noël Jaubert and Romain Privat
German Aerospace Center (DLR), Institute of Solar Research, Linder Höhe, 51170 Köln, Germany;
[email protected] (M.R.); [email protected] (C.S.); [email protected] (R.P.-P.)
* Correspondence: [email protected]; Tel.: +49-2203-601-4758; Fax: +49-2203-601-4141
Abstract: The present study provides a thermodynamic analysis of solar thermochemical cycles for
splitting of H2 O or CO2 . Such cycles, powered by concentrated solar energy, have the potential to
produce fuels in a sustainable way. We extend a previous study on the thermodynamics of water
splitting by also taking into account CO2 splitting and the influence of the solar absorption efficiency.
Based on this purely thermodynamic approach, efficiency trends are discussed. The comprehensive
and vivid representation in T-S diagrams provides researchers in this field with the required
theoretical background to improve process development. Furthermore, results about the required
entropy change in the used redox materials can be used as a guideline for material developers.
The results show that CO2 splitting is advantageous at higher temperature levels, while water
splitting is more feasible at lower temperature levels, as it benefits from a great entropy change
during the splitting step.
Keywords: solar; thermochemical cycle; CSP; water splitting; CO2 splitting; T-S diagram;
efficiency; entropy
1. Introduction
Fossil fuel depletion and the ongoing climate change lead to the need for a sustainable energy
system. One important pillar of an energy system is the availability of fuels. Today, almost all fuels
consumed worldwide are based on petroleum or natural gas, i.e., our mobility relies on unsustainable
raw materials.
In order to improve this situation in the future, great research effort is put into the production
of sustainable fuels, mainly hydrogen and synthetic hydrocarbons. One possible way to produce
hydrogen and carbon monoxide is to apply solar-driven thermochemical cycles for water splitting
or CO2 splitting. The obtained gases can be either used directly as a fuel or further processed in
a Fischer–Tropsch plant to generate synthetic hydrocarbons. Many thermochemical cycles have been
investigated and evaluated in the past [1–4]. The cycle which is subject to most research activities in
this area today is the two-step cycle based on a redox reaction as follows [5]:
1.
2.
Endothermic reduction of a metal oxide (MO):
MOx Ñ MOx´δ ` δ{2 O2
(1)
MOx´δ ` CO2 Ñ MOx ` δ CO
(2)
MOx´δ ` H2 O Ñ MOx ` δ H2
(3)
Splitting step (for H2 O or CO2 )
Entropy 2016, 18, 24; doi:10.3390/e18010024
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Several
thermodynamic evaluations
evaluationsofofthese
these
cycles,
especially
water-splitting
Several thermodynamic
cycles,
especially
the the
water-splitting
cyclecycle
havehave
been
been
conducted
In our
group,
we intend
to revive
thermodynamic
analysis
of these
cycles
conducted
[6–9].[6–9].
In our
group,
we intend
to revive
the the
thermodynamic
analysis
of these
cycles
in
in
a
different
way,
based
on
vivid
graphical
representation.
Further,
we
extend
the
existing
work
by
a different way, based on vivid graphical representation. Further, we extend
work by
analyzing
analyzing the
the thermodynamic
thermodynamic exigencies
exigenciesfor
fordifferent
differentprocess
processparameters
parameters(temperatures,
(temperatures,pressures).
pressures).
This
way,we
weobtain
obtainthethe
maximum
efficiency
as well
the required
entropy
which
the
This way,
maximum
efficiency
as well
as theasrequired
entropy
change change
which the
material
material
to undergo.
In a previous
publication
we presented
the methodology
of the
needs to needs
undergo.
In a previous
publication
[10], we [10],
presented
the methodology
of the analysis
analysis
on T-S diagram
representation.
The
work
was to
limited
to the water-splitting
based onbased
T-S diagram
representation.
The work
was
limited
the water-splitting
process process
and the
and
the influence
of the
solar efficiency
not
taken
into account.
The paper
present
paper the
extends
the
influence
of the solar
efficiency
was not was
taken
into
account.
The present
extends
analysis
analysis
by considering
CO2 and
splitting
and comparing
to waterFurther,
splitting.
the solar
by considering
also CO2 also
splitting
comparing
it to wateritsplitting.
theFurther,
solar efficiency
is
efficiency
discussed
and its
on theprocess
theoretical
process
efficiency is presented.
discussed is
and
its influence
oninfluence
the theoretical
efficiency
is presented.
2. One-Step
One-StepCycle
Cycleand
andSolar
SolarEfficiency
Efficiency
2.
2.1. Direct
Direct Gas
Gas Splitting—Thermolysis
Splitting—Thermolysis
2.1.
In reality,
reality, direct
direct splitting
splitting of
of water
water and
and CO
CO22 isis not
not as
as trivial
trivial as
as presented
presented in
in this
this paragraph.
paragraph.
In
However,
for
the
relevant
temperature
range
this
representation
is
sufficient,
especially
because
the
However, for the relevant temperature range this representation is sufficient, especially because the
present section
purpose
only.
In order
to completely
split water
at 1 baratinto
oxygen
present
sectionhas
hasan
anexplanatory
explanatory
purpose
only.
In order
to completely
split water
1 bar
into
and
hydrogen,
a
temperature
of
about
4315
K
is
necessary.
This
high
temperature
is
a
result
of
the
large
oxygen and hydrogen, a temperature of about 4315 K is necessary. This high temperature is a result
enthalpy
of formation
and the
low entropy
change
between change
H2 O and
the product
H2
of
the large
enthalpy of
of water
formation
of water
and the
low entropy
between
H2O gases
and the
and O2 . The
T-SHrepresentation
of one-step water splitting and subsequent recombination at ambient
product
gases
2 and O2. The T-S representation of one-step water splitting and subsequent
temperature
is
shown
in
Figure
1. The
andvalues
in all subsequent
recombination at ambient temperature
is entropy
shown invalues
Figureshown
1. The here
entropy
shown here figures
and in
in
this
paper
are
temperature-dependent
and
were
generated
with
the
thermochemistry
software
all subsequent figures in this paper are temperature-dependent and were generated with
the
FactSage
[11,12].
thermochemistry software FactSage [11,12].
Figure 1. T-S diagram of one step splitting of 1 mol H2O/CO2 at 1 bar and 100% conversion.
Figure 1. T-S diagram of one step splitting of 1 mol H2 O/CO2 at 1 bar and 100% conversion.
The water-splitting curve in Figure 1 encloses an area which represents the energy of formation
The (237
water-splitting
in Figure
1 encloses
an areafrom
which
the energy
of for
formation
of
of water
kJ/molH2O).curve
This energy
could
be extracted
allrepresents
water-splitting
cycles,
example
water
(237
kJ/mol
).
This
energy
could
be
extracted
from
all
water-splitting
cycles,
for
example
H
O
2
by recombining hydrogen
and oxygen in an ideal fuel cell. In addition to the water-splitting cycle,
by recombining
hydrogen
and oxygen
an ideal fuel of
cell.
In addition
to the water-splitting
Figure
1 also shows
the simplified
T-S in
representation
direct
CO2 splitting.
Comparing thecycle,
two
Figure
1
also
shows
the
simplified
T-S
representation
of
direct
CO
splitting.
Comparing
the
two
2
cycles, CO2 splitting seems to be more feasible, because the maximum process temperature is lower.
cycles,
CO
splitting
seems
to
be
more
feasible,
because
the
maximum
process
temperature
is
lower.
The larger 2entropy change in the case of CO2 splitting leads to an increased width of the enclosed
The larger
change
in the case
CO2Ksplitting
to an to
increased
width This
of the
area.
Thus, entropy
the upper
temperature
beingof3346
is lowerleads
compared
H2O splitting.
is enclosed
the case,
area. Thus,
upper
temperature
being
is lower
compared
tokJ/mol
H2 O splitting.
This is the case,
although
thethe
Gibbs
free
energy change
is 3346
largerKfor
CO2 splitting
(257
CO), resulting in a larger
althougharea
the Gibbs
free 1.
energy change is larger for CO2 splitting (257 kJ/molCO ), resulting in a larger
enclosed
in Figure
enclosed
inhigh
Figure
1.
Due area
to the
process
temperatures, the theoretical efficiency of direct splitting processes is
Due
to
the
high
process
temperatures,
theoretical
direct splitting
processes
high. The splitting-cycle efficiency
ηsc is the
based
on the efficiency
net heat. of
input
assuming
idealis high.
heat
The splitting-cycle
is based
net heat input
Q NET assuming
ideal heat
recovery.
recovery.
This heatefficiency
recovery ηissc the
resultonofthe
a pinch-point
analysis
with minimum
temperature
difference of 0 K. Such ideal heat recovery is assumed for all processes throughout this publication.
2
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This
heat
recovery
is the result of a pinch-point analysis with minimum temperature difference of 0 K.
Entropy
2016,
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Such ideal heat recovery is assumed for all processes throughout this publication. In the case of water
In
the casethe
of enumerator
water splitting,
theefficiency
enumerator
in the efficiency
formulation
is theofGibbs
free energy
of
splitting,
in the
formulation
is the Gibbs
free energy
formation
of water
formation
water
f,H2O. splitting,
CO2 splitting,
the ´
benefit
is).(ΔG
f,CO2
− ΔG
). general
This leads
to
∆Gf,H2 O . Inofthe
caseΔG
of CO
theofbenefit
is (∆Gf,CO
This
leads
tof,CO
the
form:
∆Gf,CO
2 In the case
2
the general form:
∆G f
ηsc “ . Δ
(4)
=Q
(4)
NET
of direct
direct CO
CO22splitting
splitting(η(ηscsc= =
90.6%)
advantageous
compared
efficiency
90.6%)
is is
advantageous
compared
to to
thethe
efficiency
of
The efficiency of
of direct
water
splitting
= 82.8%).
This
advantage
duetotothe
thefact
factthat
thatthe
the evaporation
evaporation of
of water
direct
water
splitting
(n(n
sc =
This
advantage
is isdue
sc 82.8%).
takes place at a low temperature. Such a low temperature input to a process
process decreases
decreases its
its efficiency.
efficiency.
2.2. Solar
Solar Absorption
Absorption Efficiency
Efficiency
2.2.
The solar
describes
to which
extent
the solar
reachingreaching
the receiver
The
solarabsorption
absorptionefficiency
efficiency
describes
to which
extent
the radiation
solar radiation
the
can be used
byused
a coupled
process
as thermal
energy.
It is
strongly
receiver
can be
by a coupled
process
as thermal
energy.
It is
stronglydependent
dependenton
onthe
the receiver
receiver
temperature and
and the
the concentration
ratio C
C [13].
ratio describes
the ratio
temperature
concentration ratio
[13]. The
The concentration
concentration ratio
describes the
ratio between
between
the
collector
aperture
area
and
the
absorber
aperture
area.
Rising
the
receiver
temperature
as well
well as
as
the collector aperture area and the absorber aperture area. Rising the receiver temperature as
lowering the
ratio
leads
to increased
thermal
reradiation
of the receiver.
reradiation
lowering
theconcentration
concentration
ratio
leads
to increased
thermal
reradiation
of theHigh
receiver.
High
results
in
low
solar
absorption
efficiencies.
This
relation
is
displayed
in
Figure
2.
reradiation results in low solar absorption efficiencies. This relation is displayed in Figure 2.
Figure 2. Maximum absorption efficiency of a black body at different temperatures and
Figure 2. Maximum absorption efficiency of a black body at different temperatures and
concentration ratios.
concentration ratios.
In the current analysis, whenever we take the solar absorption efficiency into account, we
In the
analysis,
whenever
wethe
take
the solartemperature,
absorption efficiency
account,
we assume
assume
thecurrent
receiver
temperature
to be
reduction
because into
at this
temperature
the
the
receiver
temperature
to
be
the
reduction
temperature,
because
at
this
temperature
the
endothermic
endothermic reaction takes place. Further, we set the concentration ratio to a constant value of
reaction
Further,
we set but
the for
concentration
ratio toprocesses
a constantitvalue
of be
C =aimed
4000. at
This
is
C
= 4000.takes
This place.
is a quite
high value,
high temperature
should
such
a
quite
high
value,
but
for
high
temperature
processes
it
should
be
aimed
at
such
high
values
to
avoid
high values to avoid drastic thermal losses. Using solar towers together with secondary optics, such
drastic
thermal losses.
Using
solar
towers[14].
together
with secondary
optics,efficiency
such highηabs
concentration
high
concentration
ratios
can be
reached
Considering
the absorption
, the overall
ratios
can
be
reached
[14].
Considering
the
absorption
efficiency
η
,
the
overall
solar
to
useful work
abs
solar to useful work efficiency ηtot is defined as:
efficiency η tot is defined as:
(5)
= ηabs
× ηsc
tot “
abs ˆ
sc
ηtot
(5)
During
the reader
reader should
should keep
keep in
in mind
mind that
that this
this efficiency
efficiency formulation
formulation
During the
the following
following study,
study, the
represents
an
ideal
thermodynamic
description
far
from
real
applications.
With
a
concentration
represents an ideal thermodynamic description far from real applications. With a concentration ratio
ratio
of
C=
= 4000,
the required
required temperatures
temperatures for
for the
the direct
direct splitting
splitting cannot
cannot be
be reached.
reached. The
The concentration
concentration
of C
4000, the
ratios
requiredtotoreach
reachcomplete
complete
direct
splitting
to 8000
2 splitting) and 20,000
ratios required
direct
gasgas
splitting
are are
closeclose
to 8000
(CO2(CO
splitting)
and 20,000 (H2 O
(H
2O splitting). Such high concentration ratios are technically not feasible.
splitting). Such high concentration ratios are technically not feasible.
3
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18, 24 at Normal Pressure, Gas Phase Only
2.3. TwoEntropy
Step 2016,
Splitting
2.3. Two
Step Splitting
at Normal
Pressure,before
Gas Phase
Only
Direct
splitting
has been
discussed
and
considered technically not feasible, even when
aiming at lower
conversion
which
would
relax
the
temperature
exigenciesnot
butfeasible,
at the same
time require
Direct splitting has been discussed before and considered technically
even when
high temperature
gas conversion
separationwhich
[5]. Therefore,
cycles which
aiming at lower
would relaxthermochemical
the temperature exigencies
but at increase
the same the
timeentropy
require
separation
thermochemical
cyclesintroduced.
which increase
theof many
difference
andhigh
thustemperature
widen thegas
enclosed
area[5].
inTherefore,
the T-S diagram
have been
Out
and thus
widen the
enclosed area in
the T-S
diagramcycling
have been
introduced.
Out
possibleentropy
cycles difference
with different
numbers
of intermediate
steps,
two-step
based
on redox
reactions
of many possible cycles with different numbers of intermediate steps, two-step cycling based on
has drawn most attention of the solar fuels research community [15,16]. In our previous paper we
redox reactions has drawn most attention of the solar fuels research community [15,16]. In our
explainprevious
the two-step
processwater-splitting
in detail [10].
Here,inwe
directly
compare
it to the CO2
paper water-splitting
we explain the two-step
process
detail
[10]. Here,
we directly
splittingcompare
process.
At
first,
we
introduce
only
the
gas
phase
entropy
change,
as
this
is
most
generic
and
it to the CO2 splitting process. At first, we introduce only the gas phase entropy change,
as
generic independent
and the basis ofofallthe
processes
independent
of theThe
redox
material
choice.
The T-S3 shows
the basisthis
of isallmost
processes
redox material
choice.
T-S
diagram
in Figure
diagram in Figure
3 CO
shows
the water-splitting
andoxidation
the CO2-splitting
process.
Theto oxidation
the water-splitting
and the
-splitting
process.
The
temperature
is
set
1600
K for both
2
temperature is set to 1600 K for both processes. In the following, the CO2-splitting cycle is explained
processes. In the following, the CO2 -splitting cycle is explained in detail.
in detail.
Figure 3. T-S diagram for splitting of one mole of water/CO2. Oxidation temperature is set to 1600 K,
Figure 3.
T-S diagram for splitting of one mole of water/CO2 . Oxidation temperature is set to 1600 K,
all pressures are 1 bar.
all pressures are 1 bar.
The cycle starts with heating CO2 from ambient to the oxidation temperature. Then each CO2
molecule loses one oxygen atom to the redox material resulting in the product gas carbon monoxide.
The cycle starts with heating CO2 from ambient to the oxidation temperature. Then each CO2
In this step, the entropy decreases, because diatomic CO has lower degree of freedom than triatomic
molecule loses one oxygen atom to the redox material resulting in the product gas carbon monoxide.
CO2. In the next step, the redox material is heated to the reduction temperature. At this temperature,
In this step,
the
entropy
because
diatomic
CO has
lower
degree
of isfreedom
than triatomic
oxygen
evolves
fromdecreases,
the redox material
leading
to a strong
entropy
increase.
This
the endothermal
CO2 . Inreduction
the nextstep
step,
the
redox
material
is
heated
to
the
reduction
temperature.
At
this
which requires solar energy input. As the oxygen and the CO evolve at differenttemperature,
parts
of
the
process,
are kept
separately
so that
mixing increase.
is not regarded
the
oxygen evolves from they
the redox
material
leading
to aentropy
strongofentropy
This ishere.
the In
endothermal
following
step,
oxygen
and
CO
are
cooled
to
ambient
temperature.
Then
they
are
finally
recombined
reduction step which requires solar energy input. As the oxygen and the CO evolve at different parts
to CO2. In this recombination step, useful work equivalent to the enclosed area in the diagram (Gibbs
of the process, they are kept separately so that entropy of mixing is not regarded here. In the following
free energy of formation) can be extracted. There are three options to draw the T-S diagrams above
step, oxygen
and CO are cooled to ambient temperature. Then they are finally recombined to CO2 .
the oxidation temperature:
In this recombination step, useful work equivalent to the enclosed area in the diagram (Gibbs free
1. In real processes, the product gases (CO and H2 respectively for CO2/water splitting) are not
energy of formation) can be extracted. There are three options to draw the T-S diagrams above the
heated above oxidation temperature. Therefore, one could exclude their contribution to the
oxidation temperature:
overall entropy in the graphs. Then, the entropy would actually drop to zero at the reduction
1.
2.
to the entropy of oxygen at the reduction temperature. When cooling the
In realtemperature
processes,and
therise
product
gases (CO and H2 respectively for CO2 /water splitting) are not
oxygen down from the reduction temperature, the product gas entropy would need to be added
heatedleading
abovetooxidation
temperature.
Therefore, one could exclude their contribution to the
a distorted graph, which would be difficult to capture for the reader. Therefore, we
overalldid
entropy
in the
not choose
this graphs.
option. Then, the entropy would actually drop to zero at the reduction
temperature
and contribution
rise to the entropy
of oxygen
at thealso
reduction
temperature.
Whenwhile
cooling the
2. The entropy
of the product
gases could
be considered
to stay constant
reduction
place. In thetemperature,
T-S representation,
this option
result
in a straight
oxygenthe
down
fromtakes
the reduction
the product
gaswould
entropy
would
need toline
be added
upwards
after
the
oxidation
reaction
and
in
a
slight
change
of
slope
at
T
ox in the curve
leading to a distorted graph, which would be difficult to capture for the reader. Therefore, we did
representing the cooling of all gases. This kind of representation is easy to grasp visually, but
not choose this option.
4
The entropy contribution of the product gases could also be considered to stay constant while the
reduction takes place. In the T-S representation, this option would result in a straight line upwards
after the oxidation reaction and in a slight change of slope at Tox in the curve representing the
cooling of all gases. This kind of representation is easy to grasp visually, but may be confusing,
Entropy 2016, 18, 24
5 of 12
because entropy terms from gases at different temperatures would be added and represented by
Tred . Therefore, we also did not consider this way of representation.
In the T-S diagrams shown in this paper, the product gas is always heated to the reduction
may be confusing, because entropy terms from gases at different temperatures would be added
temperature
to avoid the confusion which may come up with option 1 or 2. In real applications
and represented by only one line at Tred. Therefore, we also did not consider this way
this heating
would not take place. As long as ideal heat recovery is assumed, which is the case in
of representation.
this
study,
the
heating ofshown
CO tointhe
reduction
temperature
not influence
efficiency.
3. In the T-S diagrams
this
paper, the
product gasdoes
is always
heated tothe
thecycle
reduction
Thus,
this
is
just
a
question
of
display
and
has
no
effect
on
the
outcome
of
the
analysis.
temperature to avoid the confusion which may come up with option 1 or 2. In real applications
Entropy
2016,line
18, 24at
only one
3.
this heating would not take place. As long as ideal heat recovery is assumed, which is the case
In theinprocesses
shown
in Figure
3, all
are set
to 1 bar. Thus,
degree
freedom
this study,
the heating
of CO
topressures
the reduction
temperature
does the
not only
influence
theofcycle
to adjust efficiency.
the area enclosed
by
the
curves
is
the
reduction
temperature
(the
oxidation
temperature
Thus, this is just a question of display and has no effect on the outcome of the analysis.
was set to a fixed value of 1600 K). Although the reduction temperatures still reach very high values
In the processes shown in Figure 3, all pressures are set to 1 bar. Thus, the only degree of
of above 2500 K, they could be radically reduced compared to the one-step process. Further, the
freedom to adjust the area enclosed by the curves is the reduction temperature (the oxidation
CO2 -splitting
cycle
has
a slightly
temperature
than
the water-splitting
temperature
wasstill
set to
a fixed
valuelower
of 1600reduction
K). Although
the reduction
temperatures
still reach cycle.
very
The
the reduction
temperature
be lowered
duetotothe
theone-step
two-step
approach
high extent
values to
of which
above 2500
K, they could
be radicallycan
reduced
compared
process.
is determined
by the
shaded areas
Figure
due to temperature
second step.than
These
Further, the
CO2-splitting
cycleinstill
has 3alabelled
slightly extra
lowerarea
reduction
theareas
water-splitting
cycle. between the one-step and the two-step splitting. It can be directly observed
represent
the difference
The extent
to which
reduction
temperature
can
lowered
due to In
thethe
two-step
approach
is
that the impact
of the
secondthe
step
is larger
in the case
ofbe
water
splitting.
following
paragraph,
determined
by
the
shaded
areas
in
Figure
3
labelled
extra
area
due
to
second
step.
These
areas
we give a possible explanation for this difference. However, for a thorough understanding, an ab initio
represent
the difference
the one-step
andof
thethis
two-step
analysis
is required,
which between
is not within
the scope
work.splitting. It can be directly observed
that the impact of the second step is larger in the case of water splitting. In the following paragraph,
Oxidizing the product gases CO and H2 to CO2 and H2 O respectively leads to an entropy decrease,
we give a possible explanation for this difference. However, for a thorough understanding, an ab
mainly
because the number of moles in the gas is reduced. However, the extent of this entropy change
initio analysis is required, which is not within the scope of this work.
differs remarkably
the two
the H
case
of CO2 splitting,
change
Oxidizingbetween
the product
gasessplitting
CO andprocesses.
H2 to CO2Inand
2O respectively
leadsthe
to entropy
an entropy
is more
than
80%
larger
than
in
the
case
of
water
splitting.
This
only
applies
for
the
temperature
decrease, mainly because the number of moles in the gas is reduced. However, the extent of this
rangeentropy
at which
water
is gaseous
(being
the relevant
temperature
range
A possible
change
differs
remarkably
between
the two splitting
processes.
In in
thethis
casecontext).
of CO2 splitting,
the entropy
change
is more than
80%the
larger
in the case
of water
splitting.
only applies
for
explanation
for this
discrepancy
is that
CO2than
molecule
is linear,
while
the H2This
O molecule
is nonlinear.
the temperature
rangerotational
at which and
waterfour
is gaseous
(beingdegrees
the relevant
temperature
range
thisthree
Therefore,
CO2 has two
vibrational
of freedom,
while
H2 Oinhas
context).
possible
explanation
for this of
discrepancy
thatthe
theenergy
CO2 molecule
is linear,
while
therotational
H2O
rotational
andA three
vibrational
degrees
freedom.isAs
spacing
between
the
molecule is nonlinear. Therefore, CO2 has two rotational and four vibrational degrees of freedom,
energy states is closer compared to vibrational energy states, molecules with more rotational freedom
while H2O has three rotational and three vibrational degrees of freedom. As the energy spacing
have more possibilities to distribute energy resulting in larger entropy [17]. Nevertheless, CO2 has
between the rotational energy states is closer compared to vibrational energy states, molecules with
higher
absolute entropy than H O, because it is a larger, heavier molecule. But relative to its weight,
more rotational freedom have2 more possibilities to distribute energy resulting in larger entropy [17].
waterNevertheless,
has high entropy
leads toentropy
the low
entropy
decrease
H2 with
CO2 haswhich
higher absolute
than
H2O, because
it is when
a larger,recombining
heavier molecule.
But O2 .
As a straightforward
consequence
to
the
above,
the
reduction
of
water
to
hydrogen
leads
to
a large
relative to its weight, water has high entropy which leads to the low entropy decrease when
entropy
decrease H
compared
CO2 to CO.
recombining
2 with O2. to
Asreducing
a straightforward
consequence to the above, the reduction of water to
hydrogen leads
a large
entropy in
decrease
compared
to areducing
CO2 to CO. gap between oxidation
Resulting
fromtothis
difference
entropy
change,
large temperature
Resulting
from
this
difference
in
entropy
change,
a
large
temperature
gap between
oxidation
and reduction leads to an advantage of the water-splitting process in terms
of potential
to lower
and
reduction
leads
to
an
advantage
of
the
water-splitting
process
in
terms
of
potential
to
lower
the
the reduction temperature. An example of such a case is displayed in Figure 4. Here, the
oxidation
reduction temperature. An example of such a case is displayed in Figure 4. Here, the oxidation
temperature is set to 800 K and all other conditions are the same as in Figure 3.
temperature is set to 800 K and all other conditions are the same as in Figure 3.
Figure 4. T-S diagram for splitting of one mole of water/CO2. Oxidation temperature is set to 800 K,
Figure 4. T-S diagram for splitting of one mole of water/CO2 . Oxidation temperature is set to 800 K,
all pressures are 1 bar.
all pressures are 1 bar.
5
Entropy 2016, 18, 24
6 of 12
Entropy 2016, 18, 24
Entropy 2016, 18, 24
Figure 5. Reduction temperatures corresponding to oxidation temperature with all gases at 1 bar. At
Figure 5. Reduction temperatures corresponding to oxidation temperature with all gases at 1 bar.
oxidation temperatures below 1100 K, water splitting can be performed at lower reduction
At oxidation temperatures below 1100 K, water splitting can be performed at lower reduction
temperatures than CO2 splitting.
temperatures than CO2 splitting.
Figure 5. Reduction temperatures corresponding to oxidation temperature with all gases at 1 bar. At
Concluding
the above,
it is
instructive
show can
the be
resulting
reduction
when
oxidation from
temperatures
below
1100
K, water to
splitting
performed
at lowertemperature
reduction
Concluding
from
theCO
above,
it is instructive
to show is
thedisplayed
resulting in
reduction
temperature
when
temperatures
than
2 splitting.
changing
the oxidation
temperature.
This dependency
Figure 5.
At an oxidation
changing
the of
oxidation
temperature.
dependency
is displayed
in Figure
5. At an oxidation
temperature
about 1100
K, the twoThis
processes
have the
same reduction
temperature.
At higher
Concluding
from
theK,
above,
it is instructive
to
show
thesame
resulting
reduction
temperature when
temperature
of
about
1100
the
two
processes
have
the
reduction
temperature.
At higher
oxidation temperatures, CO2 splitting leads to lower reduction temperatures, while water splitting
is
changing
the oxidation
Thisto
dependency
is displayed
in Figurewhile
5. At water
an oxidation
oxidation
temperatures,
COtemperature.
leads
lower reduction
temperatures,
splitting is
2 splitting
advantageous
at lower oxidation
temperatures.
temperature of about 1100 K, the two processes have the same reduction temperature. At higher
advantageous
at lower
temperatures.
The
impact
of thisoxidation
trend
the efficiency
is displayed
Figure 6. Itwhile
shows
thesplitting
ideal process
oxidation
temperatures,
CO2on
splitting
leads to lower
reduction in
temperatures,
water
is
The
impact
of
this
trend
on
the efficiency
is displayed
insolar
Figure
6. It shows
theRegarding
ideal process
efficiency
η
sc
as
well
as
the
total
efficiency
η
tot
which
includes
absorption
losses.
the
advantageous at lower oxidation temperatures.
efficiency
η
as
well
as
the
total
efficiency
η
which
includes
solar
absorption
losses.
Regarding
the
sc
tot
process efficiency
ηscof
, the
2-splitting
process isisadvantageous
in the6.complete
range
subject
to this
The impact
thisCO
trend
on the efficiency
displayed in Figure
It shows the
ideal
process
process
efficiency
,be
the
-splitting
is advantageous
the
range
to this
efficiency
asη sc
well
asCO
the2total
efficiency
ηtotthat
which
solarin
absorption
losses.
Regarding
the
analysis.
This ηissc can
explained
by
theprocess
fact
theincludes
extra area
due
tocomplete
the second
stepsubject
(as shown
in
analysis.
is caninbe
by2the
fact that
thearea
extra
area
to the
second
(astoshown
process
efficiency
ηthe
scexplained
, the
COof
2-splitting
process
is advantageous
indue
the
complete
range step
subject
this
Figure
3) This
is smaller
case
CO
splitting.
This
itself
has
a poor
efficiency,
because
heat atina
Figure
3) is smaller
in the
case
of CO
splitting.
This
area
itself
has
poor
efficiency,
because
heat
This islevel
can
be
byThus,
fact
that
the extra
area
due
to a
the
second
step
shown
2the
high analysis.
temperature
isexplained
dumped.
the
process
with
the
smaller
extra
area(ashas
the in
higher
Figure
3)
is
smaller
in
the
case
of
CO
2 splitting.
This
area
itself
has
a
poor
efficiency,
because
heat
at
a
at
a
high
temperature
level
is
dumped.
Thus,
the
process
with
the
smaller
extra
area
has
the
higher
efficiency ηsc. This trend is reversed when taking the solar absorption efficiency into account. A large
high temperature
level
is dumped.
Thus,
the process
with
the smaller
extra area
hasaccount.
the higher
efficiency
. This trend
is reversed
when
taking
the solar
absorption
efficiency
extra areaη scwhich
considerably
reduces
the upper
process
temperature
is into
rewarded
byA large
good
efficiency
η
sc. This trend is reversed when taking the solar absorption efficiency into account. A large
extra
area
which
considerably
reduces
the
upper
process
temperature
is
rewarded
by
good
absorption
absorption efficiencies. Thus, at low oxidation temperatures which typically lead to large extra areas,
extra area which considerably reduces the upper process temperature is rewarded by good
efficiencies.
Thus, at low
temperatures
which
typically
large extra areas, the overall
the overall
efficiency
ηtot oxidation
ofThus,
water
splitting
is higher
compared
tolead
CO2 to
splitting.
absorption
efficiencies.
at low
oxidation
temperatures
which
typically
lead to large extra areas,
efficiency η tot of water splitting is higher compared to CO2 splitting.
the overall efficiency ηtot of water splitting is higher compared to CO2 splitting.
Figure
6. Comparison
of
efficienciesofofwater
water splitting
splitting and
2 splitting. Total efficiency is strongly
Figure
6. Comparison
Comparison
of efficiencies
efficiencies
andCO
CO
2 splitting. Total efficiency is strongly
Figure
6.
of
of water splitting
and
CO
2 splitting. Total efficiency is strongly
dependent on reduction temperature.
dependent
on
reduction
temperature.
dependent on reduction temperature.
2.4. Two Step Splitting at Reduced Pressure, Gas Phase Only
2.4. Two Step Splitting at Reduced Pressure, Gas Phase Only
2.4. Two Step Splitting at Reduced Pressure, Gas Phase Only
Up to now, the pressure of all gases was kept at 1 bar in order to introduce the concepts and
Up
to
now, the
pressure of
all
gasesreal
was
kept
at 1 in
barorder
in
order
to introduce
the concepts
and
show
dependencies.
However,
applications
with
oxygen
pressure
in
theshow
Up to general
now, the
pressure of all
gases was
kept
at 1 barwork
toreduced
introduce
the concepts
and
showreduction
general
dependencies.
However,
real
applications
work
with
reduced
oxygen
pressure
in the
step. ThisHowever,
is accomplished
by
either
sweeping
with
inert
gas
reducing
the oxygen
general
dependencies.
real applications
work with
reduced
oxygen
pressure
in thepartial
reduction
reduction step. This is accomplished by either sweeping with inert gas reducing the oxygen partial
6
6
Entropy 2016, 18, 24
7 of 12
step. This is accomplished by either sweeping with inert gas reducing the oxygen partial pressure
or by reducing the total pressure with vacuum pumps. Thermodynamically, these two options are
Entropy 2016, 18, 24
equivalent, so they will not be treated separately in the following.
Entropy 2016, 18, 24
Typically,
reduction
is reduced
about 10´4 –10´5 bar
in two
order to
pressure orthe
by oxygen
reducingpressure
the totalduring
pressure
with vacuum
pumps.toThermodynamically,
these
options
are
equivalent,
sotemperature.
they will not be
treated
separatelyrepresentations
in the following.of the two cycles with low
further
lower
the
reduction
The
T-S
diagram
pressure or by reducing the total pressure with vacuum pumps. Thermodynamically, these two
Typically,
the oxygen
pressure
during
reduction
is7.reduced
to aboutthe
10−4–10−5 bar in order to
oxygen
pressure
during
reduction
are
shown
in Figure
Ininthe
options
are equivalent,
so they will
not
be treated
separately
the figure,
following. entropy of the products
´
4
further
lower
the
reduction
temperature.
The
T-S
diagram
representations
of
the
two
with low the
−4–10
−5 cycles
with oxygen
pressure
1 bar and
10 during
bar is labelled
the benefit
Typically,
theofoxygen
pressure
reductiontoisshow
reduced
to aboutof10lowering
barthe
in pressure:
order to
oxygen pressure during reduction are shown in Figure 7. In the figure, the entropy of the products
further
loweristhe
reductionand
temperature.
The T-S diagram
representations
of the two
cycles
with
lowin the
oxygen
entropy
increased
thus the
enclosed
area
of
the
cycle
increases,
too.
This
results
with oxygen pressure of 1 bar and 10−4 bar is labelled to show the benefit of lowering the pressure:
oxygentopressure
during decrease
reductionthe
are reduction
shown in Figure
7. In the figure,
the entropy
of the
products
possibility
considerably
temperature.
In the case
of Figure
7, the
reduction
the oxygen entropy is increased and thus
the enclosed area of the cycle increases, too. This results in
−4 bar
withplace
oxygen
pressure
ofK,1 while
bar andat10
is labelled tothe
show
the benefit
of lowering the pressure:
can take
below
ambient
reduction
temperature
the possibility
to 2000
considerably
decrease
the pressure
reduction temperature.
In
the case of would
Figure need
7, theto be
the
oxygen
entropy
is
increased
and
thus
the
enclosed
area
of
the
cycle
increases,
too.
This
results
in
well above
2400
K.take place below 2000 K, while at ambient pressure the reduction temperature would
reduction
can
the possibility to considerably decrease the reduction temperature. In the case of Figure 7, the
The
of this
temperature
reduction on the efficiency is shown in Figure 8, exemplarily for
needeffect
to be well
above
2400 K.
reduction can take place below 2000 K, while at ambient pressure the reduction temperature would
Toxidation =
1000
K.
The
process
efficiency
η sc ison
hardly
affectedisby
reducing
the pressure,
because
The effect of this temperature reduction
the efficiency
shown
in Figure
8, exemplarily
for the
need to be well above 2400 K.
Toxidation =effect
1000 K. The process
efficiency η
is hardly
affectedatbyoxidation
reducing the
pressure, because
dominating
the efficiency
issc the
dump
temperature.
Only the
a slight
The effect limiting
of this temperature
reduction
onheat
the efficiency
is shown in Figure
8, exemplarily
for
dominating
effect
limiting
the lowering
efficiency the
is the
heat dump
at oxidation
temperature.
Only
a slight
decrease
can
be
observed
when
pressure,
because
the
heat
input
takes
place
at
Toxidation = 1000 K. The process efficiency ηsc is hardly affected by reducing the pressure, because thelower
decrease can
be observed
when
lowering
the pressure,
because the heat
input
takes
place at
lower
temperatures.
Ineffect
strong
contrast
that,
reducing
the pressure
quite
a large
benefit
taking
dominating
limiting
thetoefficiency
is the heat
dump at brings
oxidation
temperature.
Only when
a slight
temperatures. In strong contrast to that, reducing the pressure
brings quite a large benefit when
´
5
decrease the
can solar
be observed
whenefficiency.
lowering the
pressure,
because
the heat
inputefficiency
takes placecan
at lower
into account
absorption
From
1 bar to
10 bar,
the
total
almost
be
taking into account the solar absorption efficiency. From 1 bar to 10−5 bar, the total efficiency can
temperatures.
In strong
contrast
to that, reducing
the pressure
brings
doubled,
because the
reduction
temperature
is decreased
by about
600 quite
K. a large benefit when
almost be doubled, because the reduction temperature is decreased by about 600 K.
taking into account the solar absorption efficiency. From 1 bar to 10−5 bar, the total efficiency can
almost be doubled, because the reduction temperature is decreased by about 600 K.
Figure 7. T-S diagram of splitting one mole of H2O/CO2 with reduced pressure. Oxidation
Figure
7. T-S diagram
one molelines
of Hof
reduced
pressure.
temperature
2 O/CO
2 with
temperature
is set of
tosplitting
1000 K. Entropy
oxygen
release
at 1 bar
and 10−4Oxidation
bar are shown
to
Figure 7. T-S diagram of splitting one mole of H2O/CO2 ´4
with reduced pressure. Oxidation
is set visualize
to 1000 K.
Entropy
lines
of
oxygen
release
at
1
bar
and
10
bar
are
shown
to
visualize
the
effect
the effect of reduced pressure.
temperature is set to 1000 K. Entropy lines of oxygen release at 1 bar and 10−4 bar are shown to
of reduced pressure.
visualize the effect of reduced pressure.
Figure 8. Influence of reducing the pressure on the reduction temperature and the efficiency;
Tox = 1000 K.
Figure 8. Influence of reducing the pressure on the reduction temperature and the efficiency;
Figure 8. Influence of reducing the pressure on the reduction temperature and the efficiency;
Tox = 1000 K.
Tox =However,
1000 K. when interpreting this increase of the total efficiency, one should consider that
applying a vacuum as well as flushing with inert gas bring along large irreversibilities reducing the
However, when interpreting this increase of the total efficiency, one should consider that
efficiency [8,18,19].
Therefore, thethis
pressure
reduction
should
mainly
be considered
as aconsider
technical
However,
when interpreting
increase
total
efficiency,
one should
applying a vacuum
as well as flushing
with
inert of
gasthe
bring
along
large irreversibilities
reducing the that
advantage rather than an efficiency boost.
efficiency
[8,18,19].
the pressure
considered
as a technical
applying
a vacuum
as Therefore,
well as flushing
withreduction
inert gasshould
bring mainly
along be
large
irreversibilities
reducing
advantage rather than an efficiency boost.
7
7
Entropy 2016, 18, 24
8 of 12
the
efficiency [8,18,19]. Therefore, the pressure reduction should mainly be considered as a technical
Entropy 2016, 18, 24
advantage rather than an efficiency boost.
2.5. Two Step Splitting at Reduced Pressure, Gas and Solid Phase
2.5. Two Step Splitting at Reduced Pressure, Gas and Solid Phase
A possible approach in system design is to define the temperature limits which are technically
A possible approach in system design is to define the temperature limits which are technically
reasonable and then use a material which can work at these temperatures. A typical material
reasonable and then use a material which can work at these temperatures. A typical material candidate
candidate for such an approach is ceria. It can be reduced from CeO2 to CeO2-δ with values of δ
for such an approach is ceria. It can be reduced from CeO2 to CeO2´δ with values of δ reaching from
reaching from 0 to 0.5. In the relevant temperature range, ceria does not undergo a phase change, but
0 to 0.5. In the relevant temperature range, ceria does not undergo a phase change, but δ increases
δ increases steadily with increasing temperature and decreasing oxygen pressure. The entropy
steadily with increasing temperature and decreasing oxygen pressure. The entropy change in the
change in the material per mole of oxygen released is considerably higher at low values of δ [20]. The
material per mole of oxygen released is considerably higher at low values of δ [20]. The explanation for
explanation for this effect is the higher configurational disorder caused by the first oxygen atoms
this effect is the higher configurational disorder caused by the first oxygen atoms leaving the crystal
leaving the crystal structure. The drawback of low values of δ is a high thermal mass which needs to
structure. The drawback of low values of δ is a high thermal mass which needs to be cycled between
be cycled between oxidation and reduction temperature at low fuel generation rates. Thus, the lower
oxidation and reduction temperature at low fuel generation rates. Thus, the lower the δ, the more
the δ, the more important becomes solid phase heat recovery [7,21].
important becomes solid phase heat recovery [7,21].
For a complete analysis of a specific redox material, it is important to also consider the enthalpy
For a complete analysis of a specific redox material, it is important to also consider the enthalpy
of reaction. Only then, it can be determined if a certain process can be accomplished at selected
of reaction. Only then, it can be determined if a certain process can be accomplished at selected
temperature levels. But in this analysis we want to point out the entropy requirement and discuss it
temperature levels. But in this analysis we want to point out the entropy requirement and discuss it
in a vivid way together with the efficiency. The enthalpy of reaction is assumed to be always of the
in a vivid way together with the efficiency. The enthalpy of reaction is assumed to be always of the
value which is necessary to make the reaction feasible. This idealization should be kept in mind
value which is necessary to make the reaction feasible. This idealization should be kept in mind when
when dealing with specific materials. Thus, in this paper we show the highest possible efficiency
dealing with specific materials. Thus, in this paper we show the highest possible efficiency which
which could be reached with materials perfectly matching the process conditions.
could be reached with materials perfectly matching the process conditions.
Figure 9 shows the T-S diagram with typical process parameters in the range of recent projects
Figure 9 shows the T-S diagram with typical process parameters in the range of recent projects
realizing solar thermochemical cycles [22]. The reduction takes place at 1700 K and a pressure of 10−5
realizing solar thermochemical cycles [22]. The reduction takes place at 1700 K and a pressure of 10´5
bar. The oxidation temperature is set to 1300 K. In order to keep the representation of the T-S
bar. The oxidation temperature is set to 1300 K. In order to keep the representation of the T-S diagrams
diagrams consistent and generic, we do not include the absolute entropy value of a possible redox
consistent and generic, we do not include the absolute entropy value of a possible redox material.
material. Instead, we only include the entropy difference during oxidation and reduction. The
Instead, we only include the entropy difference during oxidation and reduction. The dashed lines in
dashed lines in Figure 9 represent the gas phase entropy only. The required extra entropy change
Figure 9 represent the gas phase entropy only. The required extra entropy change which needs to be
which needs to be undergone by the redox material in order to reach the necessary ΔG is also
undergone by the redox material in order to reach the necessary ∆G is also marked in the figure.
marked in the figure.
Figure 9. T-S diagram of splitting one mole of H2O/CO2 at defined reaction temperatures. The
Figure 9. T-S diagram of splitting one mole of H2 O/CO2 at defined reaction temperatures. The entropy
entropy change required by the redox material is marked.
change required by the redox material is marked.
Analogous to the example in Figure 9, we determined the required entropy change in the redox
Analogous
to the process
exampleconditions,
in Figure 9,see
weFigure
determined
the
requiredtemperature
entropy change
in theon
redox
material
for different
10. The
oxidation
is varied
the
material
for
different
process
conditions,
see
Figure
10.
The
oxidation
temperature
is
varied
on
the
x-axis, the reduction temperature is varied by setting the temperature difference between oxidation
x-axis,
the reduction
is =varied
setting
the
temperature
and reduction
to dT =temperature
200 K and dT
400 K.by
The
results
are
shown for adifference
reductionbetween
pressureoxidation
of 0.1 bar
and
reduction
to
dT
=
200
K
and
dT
=
400
K.
The
results
are
shown
for
a
reduction
pressureexigencies
of 0.1 bar
and 10−5 bar. The graphs show that at oxidation temperatures above 1100 K, the entropy
regarding the redox material are less demanding in the case of CO2.
8
Entropy 2016, 18, 24
9 of 12
and 10´5 bar. The graphs show that at oxidation temperatures above 1100 K, the entropy exigencies
regarding the redox material are less demanding in the case of CO2 .
Entropy 2016, 18, 24
Entropy 2016, 18, 24
Figure 10. Required entropy change in the redox material per mole of H2O/CO2.
Figure 10. Required entropy change in the redox material per mole of H2 O/CO2 .
Figure 10. Required entropy change in the redox material per mole of H2O/CO2.
However, at oxidation temperatures below 1100 K, the opposite is the case: water-splitting does
However,
ataoxidation
temperatures
1100 material.
K, the opposite
is thecan
case:
water-splitting
does
not require
such
high entropy
change inbelow
the redox
This trend
again
be explained
by
However,
at oxidation
temperatures
below
1100 K, the opposite
is the case:
water-splitting
does
not
require
such
a
high
entropy
change
in
the
redox
material.
This
trend
can
again
be
explained
the
area
which
the entropy
second step
generates
in the material.
T-S diagram
Figure
3). If that
area playsby
a
not extra
require
such
a high
change
in the redox
This(see
trend
can again
be explained
by the extra
area whichisthe
second
step
generates
intemperatures—the
the T-S diagram (see
Figure 3). Ifprocess
that area
dominant
role—which
the
case
at
low
process
water-splitting
is
the extra area which the second step generates in the T-S diagram (see Figure 3). If that area plays a
plays a dominant
role—which
is the case
at low
temperatures—the
water-splitting
process
is
advantageous,
because
the
entropy
change
in process
the gas
phase during oxidation
is larger.process
Further,
dominant role—which
is the
case at
low
process
temperatures—the
water-splitting
is
advantageous,
because
the
entropy
change
in
the
gas
phase
during
oxidation
is
larger.
Further,
lower
lower
reductionbecause
pressures
lead tochange
a decrease
of the
redox material
change.
advantageous,
thealso
entropy
in the
gasrequired
phase during
oxidationentropy
is larger.
Further,
reduction
pressures
also lead
tolead
a decrease
of the required
redox
material
entropy
change.set
The
total
efficiency
ofalso
the
process
shown
inthe
Figure
11 for
the material
same
parameter
used in
lower
reduction
pressures
to a is
decrease
of
required
redox
entropy
change.
The
of
the
is
11
set
in
Figure
10.total
The efficiency
effect of the
temperature
onFigure
the efficiency
hassame
been parameter
discussed before
[10].
The
total
efficiency
of oxidation
the process
process
is shown
shown in
in
Figure
11 for
for the
the
same
parameter
set used
used
in
Figure
10.
The
effect
of
the
oxidation
temperature
on
the
efficiency
has
been
discussed
before
[10].
It
can be10.
summarized
asthe
follows:
at low
oxidation temperatures
the heat
loss accompanied
with[10].
the
Figure
The effect of
oxidation
temperature
on the efficiency
has been
discussed before
It
as
at
heat
accompanied
with
the
oxidation
step is dominating
the efficiency.
If that temperatures
heat loss takesthe
place
higher
temperatures,
It can
can be
be summarized
summarized
as follows:
follows:
at low
low oxidation
oxidation
temperatures
the
heatatloss
loss
accompanied
with the
the
oxidation
step
is
dominating
the
efficiency.
If
that
heat
loss
takes
place
at
higher
temperatures,
the
efficiency
at the
oneefficiency.
point the If
influence
thattakes
heat place
loss isatoverruled
by the positive
oxidation drops.
step is However,
dominating
that heatofloss
higher temperatures,
the
efficiency
drops.
However,
at
one
point
the
influence
of
that
heat
loss
is
overruled
by
the
positive
effect
of
rising
heat
input
temperatures.
Then,
the
efficiency
rises
again
with
rising
temperatures.
efficiency drops. However, at one point the influence of that heat loss is overruled by the positive
effect
effect of
of rising
rising heat
heat input
input temperatures.
temperatures. Then,
Then, the
the efficiency
efficiency rises
rises again
again with
with rising
risingtemperatures.
temperatures.
Figure 11. Total theoretical efficiency of solar water splitting at different process conditions.
Figure 11. Total theoretical efficiency of solar water splitting at different process conditions.
Figure 11. Total theoretical efficiency of solar water splitting at different process conditions.
Further, lower reduction pressures are beneficial for the absorption efficiency, as discussed
aboveFurther,
when considering
the gaspressures
phase only.
difference
to dTas
= 200
K, the
lower reduction
areReducing
beneficialthe
fortemperature
the absorption
efficiency,
discussed
Further,
lower
reduction
pressures
are
beneficial
for
the
absorption
efficiency,
as
discussed
efficiency
drops
remarkably.
is again
dueReducing
to the large
influence
of thedifference
heat loss during
above when
considering
theThis
gas phase
only.
the
temperature
to dT =oxidation.
200 above
K, the
when
considering
the
gas
phase
only.
Reducing
the
temperature
difference
to
dT
=
200
K,
the
efficiency
Figure
12 shows
an example
suchdue
a process
with influence
low dT. The
strong
influence
the large
efficiency
drops
remarkably.
This isofagain
to the large
of the
heat loss
duringofoxidation.
dropsassociated
remarkably.
Thissecond
again
dueof
the large
influence
thedT.
heat
loss
during
oxidation.
area
to the
step
istoclearly
In
thisof
case,
the
heat
released
duringofoxidation
Figure
12 shows
anis example
such
a visible.
process
with
low
The
strong
influence
the large
should
be coupled
to second
a secondary
Energetically,
the thermochemical
cycle
could
surely
area associated
to the
step isprocess.
clearly visible.
In this case,
the heat released
during
oxidation
always
with
secondary process.
processesEnergetically,
using all waste
and thus leading
the Carnot
should be
be extended
coupled to
a secondary
theheat
thermochemical
cycletocould
surely
efficiency
between with
the secondary
reduction processes
temperature
ambient
Technically
and
always be extended
usingand
all waste
heattemperature.
and thus leading
to the Carnot
economically
however,
such
an approach
is not always
efficiency between
the
reduction
temperature
andfeasible.
ambient temperature. Technically and
economically however, such an approach is not always feasible.
Entropy 2016, 18, 24
10 of 12
Figure 12 shows an example of such a process with low dT. The strong influence of the large
area associated to the second step is clearly visible. In this case, the heat released during oxidation
should be coupled to a secondary process. Energetically, the thermochemical cycle could surely always
be extended with secondary processes using all waste heat and thus leading to the Carnot efficiency
between the reduction temperature and ambient temperature. Technically and economically however,
such an approach is not always feasible.
Entropy 2016, 18, 24
Figure 12. T-S diagram of splitting one mole of H2O/CO2 at an oxidation temperature of 1300 K and a
Figure 12. T-S diagram of splitting one mole of H2 O/CO2 at an oxidation temperature of 1300 K and
reduction temperature of 1500 K.
a reduction temperature of 1500 K.
3. Conclusions
3. Conclusions
We have conducted a comprehensive study on the efficiency of solar thermochemical splitting
We have conducted a comprehensive study on the efficiency of solar thermochemical splitting
cycles. The study is based on an approach using mainly T-S diagrams, hence emphasizing graphical
cycles. The study is based on an approach using mainly T-S diagrams, hence emphasizing
explanations rather than the underlying equations. A previous study analyzing the purely
graphical explanations rather than the underlying equations. A previous study analyzing the purely
thermochemical process efficiency of water splitting was extended. On the one hand, CO2-splitting
thermochemical process efficiency of water splitting was extended. On the one hand, CO2 -splitting
cycles were analyzed and compared to the previous results. On the other hand, the solar absorption
cycles were analyzed and compared to the previous results. On the other hand, the solar absorption
efficiency was included in the overall efficiency calculation.
efficiency was included in the overall efficiency calculation.
CO2 splitting is in many cases advantageous compared to water splitting regarding the
CO2 splitting is in many cases advantageous compared to water splitting regarding the efficiency.
efficiency. This is due to the higher entropy change which occurs when recombining CO with
This is due to the higher entropy change which occurs when recombining CO with oxygen compared to
oxygen compared to H2. However, when splitting CO2, the low entropy change in the gas phase
H2 . However, when splitting CO2 , the low entropy change in the gas phase during the oxidation step
during the oxidation step can lead to higher demands regarding the redox material. The entropy
can lead to higher demands regarding the redox material. The entropy difference in the solid between
difference in the solid between the oxidized and the reduced state needs to be higher in some cases,
the oxidized and the reduced state needs to be higher in some cases, especially when operating at
especially when operating at low temperatures.
low temperatures.
The study has theoretical thermodynamic character only and should therefore only help
The study has theoretical thermodynamic character only and should therefore only help
understanding the general principles of the analyzed cycles. Real applications have to cope with
understanding the general principles of the analyzed cycles. Real applications have to cope with many
many other factors like heat recovery from solids, efficiency cutbacks due to means to create an
other factors like heat recovery from solids, efficiency cutbacks due to means to create an oxygen
oxygen deficient atmosphere and many more. This should be kept in mind when interpreting the
deficient atmosphere and many more. This should be kept in mind when interpreting the efficiency
efficiency values. Furthermore, the redox material entropy values shown here are only valid in
values. Furthermore, the redox material entropy values shown here are only valid in combination
combination with certain enthalpies of reaction. Therefore, no specific material analysis was
with certain enthalpies of reaction. Therefore, no specific material analysis was conducted here.
conducted here. Also especially at low temperatures, slow kinetics may impede the process to
Also especially at low temperatures, slow kinetics may impede the process to practical infeasibility.
practical infeasibility. Thus, this study does not intend to present real process efficiencies, but rather
Thus, this study does not intend to present real process efficiencies, but rather to provide the relevant
to provide the relevant thermodynamic background every process developer should have when
thermodynamic background every process developer should have when trying to bring theory
trying to bring theory into practice.
into practice.
Acknowledgments: The research leading to these results has received funding from the European Union's
Acknowledgments:
research(FP7/2007-2013)
leading to theseforresults
hasCells
received
funding from
European Initiative
Union’s
Seventh Framework The
Programme
the Fuel
and Hydrogen
Jointthe
Technology
Seventh
Framework
Programme
for theand
Fuel
Cells and Hydrogen
Joint
Technology
Initiative
under grant
agreement
n° 325361 (FP7/2007-2013)
and from the Initiative
Networking
Fund of the
Helmholtz
Association
of
German Research Centers (Grant Identifier VH-VI-509).
Author Contributions: Robert Pitz-Paal initiated the paper and did general consulting. Martin Roeb and
Christian Sattler helped improving the manuscript and interpreting the results. Matthias Lange wrote the paper
and conducted the numerical analysis. All authors have read and approved the final manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
Entropy 2016, 18, 24
11 of 12
under grant agreement n˝ 325361 and from the Initiative and Networking Fund of the Helmholtz Association of
German Research Centers (Grant Identifier VH-VI-509).
Author Contributions: Robert Pitz-Paal initiated the paper and did general consulting. Martin Roeb and
Christian Sattler helped improving the manuscript and interpreting the results. Matthias Lange wrote the
paper and conducted the numerical analysis. All authors have read and approved the final manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
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