step-by-step methodology of solar reactor design for emission-free generation of hydrogen
DESCRIPTION
dsaTRANSCRIPT
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Step-by-step methodology of developing a solar reactor foremission-free generation of hydrogen
Nesrin Ozalp*, Vidyasagar Shilapuram
Mechanical Engineering Department, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar
a r t i c l e i n f o
Article history:
Received 10 November 2009
Received in revised form
30 January 2010
Accepted 6 February 2010
Available online 25 March 2010
Keywords:
Solar reactor
Solar cracking
Methane decomposition
Hydrogen
Thermodynamics
Kinetics
a b s t r a c t
This study presents a methodology to develop a solar reactor based on the thermody-
namics and kinetics of methane decomposition to produce hydrogen with no emissions.
The kinetic parameters were obtained in the literature for two cases; methane laden with
carbon particles and methane without carbon particles. Results show that there is signif-
icant difference in experimentally obtained and theoretically predicted methane conver-
sion. The paper also presents a parametric study on the effects of temperature, pressure
and the inuence of inert gas composition, which is fed along with methane, on the
thermodynamics of methane decomposition. Results show that there is signicant effect of
the inert gas presence in the feeding gas mixture on the equilibrium of methane conver-
sion and product gas composition. Results also show that higher conversions are obtained
when the carbon particles laden with methane. The step-by-step reactor design method-
ology for homogenous methane decomposition and the parametric study results presented
in this paper can provide a very useful tool in guiding a solar reactor design and optimi-
zation of process operating conditions.
2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.
1. Introduction
Natural gas, which is mainly composed of methane, is an
excellent source of hydrogen because of its high ratio of
hydrogen to carbon [1]. One of the other good aspects of using
natural gas as a feedstock is that it can be thermally decom-
posed into its components without any toxic or greenhouse
gas emissions once the solar energy is used as a process heat.
Hydrogen production via solar direct thermal decomposition
of natural gas is referred as solar cracking, where carbon
black comes as a byproduct. Although solar cracking of
natural gas has a lower endothermicity compared to that of
steam reforming of methane, non-catalytic methane decom-
position requires higher temperatures (15002000 K) in order
to obtain reasonable hydrogen yield [2]. Therefore, catalytic
decomposition of methane has recently attracted attention of
researchers because of its potential to lead to the development
of a CO2 free hydrogen production process and higher
hydrogen yield [3].
Catalytic decomposition of methane can be achieved via
steam reforming [4] or without introducing water into the
media [5]. Once methane is solar thermally split using carbon
particles as catalyst, the process efciency enhances reason-
ably [611], because, carbon particles provide nucleation sites
for heterogeneous decomposition reactions, and serve as
a radiant absorbent [12,13]. Muradov et al. [11] studied the
characteristics of catalytic effects of an expanded range of
carbon materials on the methane decomposition, and sug-
gested a uidized bed reactor conguration for thermocata-
lytic decomposition of methane. On the other hand, Hirsch
and Steinfeld [14] solar thermally cracked methane by intro-
ducing carbon particles into their vortex ow reactor, where
* Corresponding author. Tel.: 974 686 2832; fax: 974 423 0066.E-mail address: [email protected] (N. Ozalp).
Avai lab le at www.sc iencedi rect .com
journa l homepage : www.e lsev ie r . com/ loca te /he
i n t e r n a t i on a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 4 4 8 4 4 4 9 5
0360-3199/$ see front matter 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.ijhydene.2010.02.032
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carbon particles enhanced the heat transfer in the reaction
chamber. Therefore, one of the key factors to achieve higher
conversion efciencies in methane cracking solar reactor is
the presence and transport of carbon particles.
Reactor volume and the operating parameters of a solar
reactor aredecidedbasedon the thermodynamics andkinetics
of the chemical reaction system to achievemaximumpossible
conversion/product yield [15]. There have been few studies on
the design of hydrogen producing solar reactors for two step
water splitting cycle [16,17], gasicationof petroleumcoke [18],
solar reformingofnatural gas [4], zincproductionfromthermal
dissociation of zinc oxide [15,1922] and for solar cracking of
natural gas [5,14]. However, the above literature mostly focus
on the mechanical design instead of giving details on the
process design, which comes from thermodynamics and
kinetics, e.g. although they provide the kinetics and thermo-
dynamics of the process, there are few details on linking
kinetics with the reactor design. Besides, since the reactor
concepts and process engineering are different for liquid
phase, gas phase and solid phase reactions, a solar reactor
design for hydrogen generation from methane cracking is
different from the solar reactors design for zinc oxide decom-
position, gasication of petroleum coke, solar reforming of
natural gas, and two step water splitting [23]. Therefore, this
study provides a step-by-step methodology for the design and
development of a solar thermal reactor for methane decom-
position based on the thermodynamics and kinetics of this
process. The paper also gives the optimum conguration for
the highest possible methane conversion by providing
a comparison of methane decomposition with and without
carbon particles. Finally, the main issues associated with the
development of a solar reactor for methane decomposition
from the kinetics found in literature are discussed in detail.
2. Previous studies on the thermodynamicsand kinetics of solar methane decomposition
Kogan andKogan [24] usedNASACET-85 computer program to
run the thermochemical equilibrium calculations, where they
plotted themole fractionofunreactedmethaneasa functionof
temperature and pressure when methane is used as a feeding
gas. On the other hand, Sinaki et al. [25] gave the thermody-
namic equilibrium based on the NASA-Lewis Thermodynamic
data in terms of hydrogen mole fraction for various tempera-
tures andpressures. However, they did not include the particle
inception and particle phase processes of the solid carbon in
their thermodynamic calculations. Other studies on the ther-
modynamic equilibrium composition are done by Hirsch et al.
[2] using the HSC Outokumpu code, and Abanades et al. [26] by
using Gemini software. A thermodynamic study done by Dahl
et al. [27] shows that methane decomposition starts above
600K, and the temperatures greater than1500Kare required to
achieve nearly complete decomposition. All of the above
thermodynamic studies were done formethane as the feeding
gas, e.g. there is no study giving thermodynamic calculations
when an inert gas is mixed with methane in the feeding gas.
Furthermore, the above thermodynamic studies in literature
do not state whether carbon is assumed as solid phase or as
a uid in the calculations.
As for the studies done on the kinetics of methane decom-
position, they can be categorized into two groups: (1) when
there is no carbon particles in the feed gas [25,28,29], and (2)
when the feed gas is laden with carbon particles [611,13]. For
example, Sinaki et al. [25] modied the mechanism of soot
formation in combustion of hydrocarbons to develop a kinetic
model for homogenous thermal decomposition of methane.
Rodat et al. [28] studied the kinetics ofmethanedecomposition
in a tubular solar reactor using Dsmoke software. They
obtained a kinetic expression for the overall dissociation
reaction fromthe reactormodel assumingaplugowandnon-
catalytical reaction. On the other hand, Wyss et al. [29]
obtained the best t kinetic parameters by minimizing the
sum of squares of the residuals for methane conversions
determined experimentally and theoretically. Most of the
literature available on the kinetics of methane decomposition
using carbon particles states that reaction order is 0.5 and it is
the same for different carbon samples as well. It is also stated
that the activation energies of the carbon particles and the
reaction mechanism are all the same for activated carbon
samples regardless of the type and the supplier [611].
Conversely, Trommer et al. [13] assumed methane decompo-
sition as a rst order and estimated the kinetic parameters
accordingly. Table 1 summarizes the kinetic parameters
available in literature for methane decomposition when
carbon particles are laden with methane, and when there is
only methane in the feed gas.
3. Results and discussion
3.1. Thermodynamics
We can see from Table 2 that in most of the studies on solar
cracking of methane, inert gas at different mole fractions is
used along with the methane feeding gas. As stated earlier,
there is no information on the literature regarding the equi-
librium product gas composition when an inert gas is mixed
withmethane feed. Since the thermodynamics changes when
pure methane is used as feeding gas vs. when methane is fed
with an inert gas, it is important to study the effect of inert gas
to methane ratio in the feeding gas to estimate the equilib-
rium product gas composition accordingly. Furthermore,
thermodynamic studies of the above literature do not
mention whether carbon is assumed as a solid or as a uid in
their thermodynamic equilibrium calculations. The chemical
reaction equilibrium is different for uid phase reactions and
for the reactions with solid components [30]. Hence, in the
present thermodynamic calculations, reaction coordinate of
carbon is not considered for the estimation of product gas
composition. Because; the fugacity of carbon is roughly equal
to the vapor pressure, which would be extremely negligible,
and besides, the amount of solid carbon cannot inuence the
extent of this reaction [31]. Therefore, the calculations are
performed for solid carbon assuming that it does not occupy
signicant volume. Furthermore, we also studied the effect of
inert gas at different mole fractions in the methane feeding to
see what would be the product gas composition. To calculate
the thermodynamic equilibrium compositions, the following
methodology was used:
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Step 1: Calculate the standard heat of reaction and standard
Gibbs energy change of reaction.
Step 2: Estimate the heat of reaction for the assumed reaction
temperature or obtain the heat of reaction as a func-
tion of temperature with the standard heat of reaction
and from thermodynamic tables of heat capacity data.
Step 3: Calculate the equilibrium constant at the reaction
temperature as follows:
(i) From standard Gibbs energy change of reaction, nd
the factor, K0, represents equilibrium constant at
reference temperature.
(ii) Find the factor,K1, thathas themajor temperatureeffect.
(iii) Find the factor, K2, accounts for small temperature
inuence resulting from the enthalpy change with
temperature.
(iv) Calculate the, K, equilibrium constant at the reaction
temperature from the above factors.
where
K0hexp
DG00RT0
(1)
K1hexp
DH00RT0
1 T
T0
(2)
The temperature dependency of heat capacity is given by
CP=R A BT CT2 DT2; where the constants A, B, C, D arethe characteristics of the particular substances involved in the
reaction.
K2hexp
(DA
lns
s 1
s
12DBT0
s 12s
16DCT20
s 12s 2s
12DD
T20
s 12s2
)3
KhK0K1K2 (4)
Step 4 Estimate the reaction coordinate from the equilibrium
constant relation involving composition, pressure and
temperature.
Step 5 Calculate themole fraction of the species present in the
product gas from the relation of reaction coordinate
involving mole fraction of the species and stoichio-
metric numbers.
Formethane decomposition, i.e. CH4g/Cs 2H2g, thestoichiometric numbers for methane, carbon and hydrogen
are 1, 1 and 2 respectively. Therefore, the mole fractions ofthe species are related to the reaction coordinate and the
stoichiometric numbers by the following equations:
yCH4 hCH34;0
h0 e
(5)
yH2 hH2;0 23h0 3
(6)
yinerts h0 hCH4;0 hH2;o
h0 3
(7)
PP0
1K
( hH2;0 23
2h0 3
hCH4;0 3
)
(8)
With the increase in temperature, equilibrium constant (K )
estimated from the thermodynamic data of pure species
shows that K 1. This indicates that complete conversion is
practically possible and that the reaction can be considered as
irreversible.
Fig. 1 shows the effect of temperature and the inert gas
mole fraction in the methane feeding on the equilibrium
product gas composition. We can see from the gure that the
product gas is composed of unreacted methane, inert gas and
hydrogen. Since the reaction is endothermic, equilibrium
methane conversion is increased with an increase in
Table 1 Kinetic parameters of methane decomposition with carbon and without carbon presence in the feed gas.
Without carbon With carbon
Rodat et al. [28] Wyss et al. [29] Trommer et al. [13] Muradov et al. [9]
K0 (s1) Ea (KJ/mol) n K0 (s
1) Ea (KJ/mol) n K0 (s1) Ea (KJ/mol) n K0 (mol/m
3 s Pa0.5) Ea (KJ/mol) n
6.6 1013 370 1 5.8 108 156 7.2 1.07 106 147 1 1.6812 108 201 0.5
Table 2 Summary of the range of operating conditions and the experimental ndings available in literature.
Flamant group[5,26,28,3235,50,51]
Weimer group[27,29,3740]
Kogan group[25,4449]
Steinfeld group[14,4143]
Reactor volume, liter 0.005 & 0.23 0.035 & 4.166 2.514 & 4.33 0.45 & 1.57
Reactor temperature, K 11802073 15332173 10001550 10001600
Inert used Ar H2 and/or Ar Ar and/or He Ar and/or N2Total inlet ow rate, liter/min 0.930 3.024 8.620
Methane inlet mole fraction 0.0760.3 0.030.8
Residence time, s 0.0130.244 0.061.6 0.9110
Conversion 0.1160.98 0.541.00 0.0680.988
H2 yield 0.20.9 0.3840.925
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temperature. Hence, decrease in methane mole fraction
results with an increase in hydrogen mole fraction.
Figs. 2 and 3 show the effect of pressure and temperature
on equilibrium mole fraction of methane and hydrogen. To
see the inuence of pressure on product gas composition,
pressure ratios (P/P0) of 0.5, 1, 5 and 10 were tested. For the
same temperature, it was observed that when the pressure is
decreased, methane mole fraction is decreased while
hydrogen mole fraction is increased. This is because; when
the pressure is decreased, higher methane conversion is
achieved resulting with an increase in hydrogenmole fraction
in the product gas composition. Furthermore, we know that
duringmethane decomposition, 1 mol of methane gives 2mol
of hydrogen, and 1 mol of solid carbon. According to the Le
Chateliers principle, since the product gas mole numbers are
higher than the mole numbers of the reactant, maximum
hydrogen yield is obtained at low pressures. This theoretical
explanation has been experimentally observed by Flamant
group of CNRS [32].
Figs. 4 and 5 show the effect of inert gas composition in the
methane feeding gas on the product gas equilibrium mole
fraction of methane and hydrogen. A wide range of mole
Fig. 1 Estimation of equilibrium product gas composition.
Fig. 2 Effect of temperature and pressure on the mole
fraction of methane in product gas.
Fig. 3 Effect of temperature and pressure on the mole
fraction of hydrogen in product gas.
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fractions of methane, e.g. from 0.1 to 1, in the feeding gas was
studied. It can be seen from the gures that the effect of inert
gas in the methane feeding signicantly changes the equilib-
rium composition. Basically, by increasing the inert gas
content in the feeding gas, methane decomposition is
increasing. Since the inert gas has signicant effect, methane
and hydrogen mole fraction in the product gas decreases in
spite of an increase in hydrogen mole fraction. It is also
observed that when the temperature is above 1000 K, the
effect on the hydrogen mole fraction is signicant. All these
results are consistent with the fundamental principles of
thermodynamics [30,31].
3.2. Kinetic study
Table 2 summarizes the literature on solar hydrogen genera-
tion from methane decomposition with and without carbon
laden ows with respect to range of operating conditions, and
experimentally obtained performance parameters, such as
conversion and hydrogen yield [5,14,2629,3151]. There have
been various solar reactor congurations tested by different
groups to investigate the effects of carbon seeding in a nozzle
type reactor [26,3436], tubular reactor [28,32,50,51], uid-wall
aerosol ow reactor [27,29,3740], tornado ow reactor
[24,25,4449], and vortex ow reactor [2,1214,4143]. All these
studies have tried to solve the carbon blockage problem,
enhance the heat transfer, reduce kinetic limitations, obtain
uniform temperature, and effectively utilize the solar radia-
tion. For example, Abanades and Flamant [33] states that
indirect heating provides a major advantage because the
reacting ow is separated from the solar irradiation zone, and
therefore, particles do not deposit on the window.
Alternatively, Trommer et al. [13] states that direct solar
irradiation of the reactants enhances the heat transfer and
reaction kinetics, which cannot be achieved by indirect heat
transport. However, in real situation, reaction kinetics does
not depend on the reactor conguration and direct or indirect
heating, but, on the presence or absence of carbon particles in
the methane feeding. On the other hand, since reactor
conguration and direct/indirect heating alters the tempera-
ture inside the reactor, it may have indirect effect on the
kinetics of the methane decomposition because of the
temperature dependent term.
For the non-catalytic/with no carbon particles part of this
present study, experimental data of Rodat et al. [32], and
Abanades et al. [35] were used. Theoretical methane conver-
sions were calculated using the kinetic parameters given in
Table 1 of Rodat et al. [28]. As for the catalytic/with carbon
laden ows part of this present study, experimental data was
taken from Hirsh et al. [14] and Maag et al. [42]. On the other
hand, kinetics data of Trommer et al. [13] was used for the
theoretical methane conversion predictions, where a plug
ow reactor model was assumed. In both no carbon and
carbon laden ows, experimental data and kinetic parameters
are chosen from their same respective research group for
theoretical and experimental comparison. This shows how
much their kinetic parameter agrees with their experimental
results. The comparisons of the theoretical and experimental
methane conversions are given in Fig. 6. These results show
Fig. 4 Effect of inert gas on the mole fraction of methane
in products.
Fig. 5 Effect of inert gas on the mole fraction of hydrogen
in products.
Fig. 6 Experimental vs. theoretically obtained conversions
using kinetic parameters.
i n t e r n a t i on a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 4 4 8 4 4 4 9 54488
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that there is a signicant difference in experimentally
observed and theoretically predicted methane conversion
for case with no carbon and for the case with carbon
laden ow.
Furthermore, experimental conversion data for methane
decomposition without carbon seeding are taken from Rodat
et al. [32] and Dahl et al. [40] to make a comparison. Experi-
mental data from these research groups [32,40] are chosen for
the same operating conditions of temperature and residence
time (s z 0.010.012) as shown in Table 3. Theoretical
conversions are predicted by using the kinetic parameters of
Rodat et al. [28] andWyss et al. [29]. Since it is a non-catalytical
reaction, it is expected that the kinetics and the methane
conversion should be the same for experimental results and
theoretical predictions made by both the groups. However, as
shown in Table 3, experimentally obtained conversion does
not match with the theoretically predicted conversion.
Therefore, it is not very clear which kinetic parameters from
the literature should be selected for reactor design. As it is
stated by Wyss et al. [29] and Dahl et al. [40], we have no
control over the estimation errors since the kinetic data was
taken from the literature of another work. However, probably
the error in the experimentally obtained data might be
because of the large sensitivity of k0. Furthermore, the indi-
vidual condence intervals on the activation energy, Ea, and
the pre-exponential factor, k0, are often deceiving because the
joint condence region is quite narrow and asymmetric.
Trommer et al. [13] says that the conversion predictions with
temperature and residence time from their kinetic parameters
have not been experimentally validated because the vortex
ow reactor used in their study did not allow for stable oper-
ation with variable mass ow rates. Therefore, predictions
may be invalid for very small residence times and at very high
temperatures.
The above results show that methane conversions found
from theory vs. through experiments show large variation. If
we refer to Table 1 to compare the activation energies found
through the kinetics studies by these groups, there is
a signicant difference. It can be also observed that there is
a scatter in the values of the pre-exponential term. Therefore,
these discussions suggest that further research may be
needed to the nd what would be the most accurate kinetics
for this reaction. Our use of the kinetic data from these above
sources during the subsequent design of our solar reactor
geometry should be viewed as a rst approximation.
The performance parameters, such as; methane conver-
sion and hydrogen production, changes with temperature,
residence time and feed ow rates. In this study, the following
methodology was used to test the solar reactor performance
under different reaction conditions found in literature.
(1) Presume a rector volume V, temperature T, and methane
feed rate nCH4;0 (ln/min).
(2) Calculate the residence time s and methane molar feed
rate, FCH4;0 .
(3) Find the kinetic rate constant, k, from literature.
(4) Calculate theXCH4 fromplug owperformance equation by
solving equation (5) using MATLAB or from analytical
expression. The performance equation for plug ow is
given as in equation (5).
VFCH4;0
sCCH4;0
VvCH4;0CCH4;0
Z XCH40
dXCH4rCH4
(9)
(5) Calculate the hydrogen production rate, FH2 , from the
stoichiometry balance i.e.,
FH2 2$FCH4;0$XCH4 (10)
Total number of moles varies with reaction during the
methane decomposition especially if inert gases are used
along with methane feeding. Hence, for the case of ow
systemswith variable volume ow, such as; plug ow reactors
and mixed ow reactors, concentration must be expressed
appropriately in terms of the expansion factor (a) in the rate
expressionrCH4 [30,52]. The calculation of expansion factor toincorporate the effect of inert gas composition in themethane
feed and the volume change during the reaction is explained
in the next section.
The design expression, e.g. Equation (9), relates the reactor
volume, feed rate, and the mole fraction of methane in the
feeding gas to the kinetics of the reaction. Hence, the Equation
(5) can be used either for reactor design or for the analysis of
design variables to see the effects of chosen reactor volume on
the reactor performance. Our objectives are (1) to conduct the
reaction at lower temperatures with maximum methane
conversion, and (2) to use the kinetics found in literature to
calculate methane conversion for methane feed with carbon
and without carbon cases. To achieve these objectives, we
chose different reactor volumes to study the effects of resi-
dence time, temperature, and methane feed gas composition
on methane conversion and hydrogen production. For reactor
volume of 2.26 L, effects ofmethane feed rate and temperature
on methane conversion and hydrogen production were
calculated and tabulated in Table 4 using Wyss et al. [29]
kinetics. Similarly, calculations were also made based on
plug ow reactor assumption for pure methane as feeding
gas using the kinetics given in Table 1.
The volumetric feed rate ofmethane is normally calculated
from the net power absorbed by the solar reactor. Given the
desired total solar power in a solar furnace, net power
absorbed by the reactor can be estimated by accounting the
power loss by re-radiation. The volumetric ow rate of the
reactant was estimated by matching the net power absorbed
by the solar reactor with the enthalpy of the reaction [53]. On
the other hand, methane conversion was obtained by using
different kinetics found in literature for the same set of
operating conditions, such as temperature and residence
time. Wide range of methane conversion was observed due to
Table 3 Comparison of methane conversions found bytheoretical prediction and experimentally observation fornon-catalytical decomposition.
T (K) Experimental conversion Predicted conversion
Dahlet al. [40]
Rodatet al. [32]
Wysset al. [29]
Rodatet al. [28]
17101723 0 0.67 0.65 0.96
17401773 00.07 0.62 0.66 1
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Table 4 Methane conversion and hydrogen production estimations usingWyss et al. [29] kineticswithout carbon seeding.
T k vCH4;0 s FCH4;0 XCH4 FH2
900 0.5 1 135.72 0.045 0.624182 0.056
2 67.86 0.090 0.579885 0.104
3 45.24 0.134 0.551659 0.148
4 33.93 0.179 0.53054 0.190
10 13.572 0.448 0.456972 0.410
1000 4.1 1 135.72 0.045 0.731415 0.066
2 67.86 0.090 0.699659 0.125
3 45.24 0.134 0.679375 0.183
4 33.93 0.179 0.664163 0.238
10 13.572 0.448 0.610784 0.547
1100 22.7 1 135.72 0.045 0.796008 0.071
2 67.86 0.090 0.77188 0.138
3 45.24 0.134 0.756465 0.203
4 33.93 0.179 0.744901 0.267
10 13.572 0.448 0.704287 0.631
1200 93.9 1 135.72 0.045 0.837802 0.075
2 67.86 0.090 0.818617 0.147
3 45.24 0.134 0.806359 0.217
4 33.93 0.179 0.797162 0.286
10 13.572 0.448 0.76486 0.685
1300 312.6 1 135.72 0.045 0.866404 0.078
2 67.86 0.090 0.850602 0.152
3 45.24 0.134 0.840505 0.226
4 33.93 0.179 0.83293 0.299
10 13.572 0.448 0.806322 0.723
1400 876.6 1 135.72 0.045 0.88687 0.079
2 67.86 0.090 0.873488 0.157
3 45.24 0.134 0.864938 0.233
4 33.93 0.179 0.858524 0.308
10 13.572 0.448 0.835991 0.749
1500 2142.0 1 135.72 0.045 0.902053 0.081
2 67.86 0.090 0.890468 0.160
3 45.24 0.134 0.883065 0.237
4 33.93 0.179 0.877511 0.315
10 13.572 0.448 0.858003 0.769
1600 4681.3 1 135.72 0.045 0.913657 0.082
2 67.86 0.090 0.903444 0.162
3 45.24 0.134 0.896919 0.241
4 33.93 0.179 0.892023 0.320
10 13.572 0.448 0.874826 0.784
1700 9331.7 1 135.72 0.045 0.922749 0.083
2 67.86 0.090 0.913611 0.164
3 45.24 0.134 0.907773 0.244
4 33.93 0.179 0.903393 0.324
10 13.572 0.448 0.888006 0.796
1800 17 229.1 1 135.72 0.045 0.930024 0.083
2 67.86 0.090 0.921746 0.165
3 45.24 0.134 0.916458 0.246
4 33.93 0.179 0.91249 0.327
10 13.572 0.448 0.898552 0.805
1900 29 821.8 1 135.72 0.045 0.93595 0.084
2 67.86 0.090 0.928373 0.166
3 45.24 0.134 0.923533 0.248
4 33.93 0.179 0.919901 0.330
10 13.572 0.448 0.907144 0.813
2000 48 862.9 1 135.72 0.045 0.940853 0.084
2 67.86 0.090 0.933857 0.167
3 45.24 0.134 0.929386 0.250
4 33.93 0.179 0.926033 0.332
10 13.572 0.448 0.914252 0.819
2100 76 383.6 1 135.72 0.045 0.944965 0.085
2 67.86 0.090 0.938455 0.168
3 45.24 0.134 0.934296 0.251
4 33.93 0.179 0.931175 0.334
10 13.572 0.448 0.920213 0.825
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the difference in the kinetic parameters. Hence, a better
understanding and accurate estimation of the kinetics of
methane decomposition reaction is needed to accurately
predict the methane conversion and hydrogen production.
Otherwise, it leads to the wrong design specications and
estimations.
Fig. 7 shows the effects of carbon seeding and no seeding on
solar hydrogen reactor performance by assuming the plug ow
andmixedowreactormodel forwiderangeofresidencetimes.
From this study, it is seen thatwhen there is nocarbonparticles
seedingwithmethane feed, higher residence time is required in
order to achieve the same methane conversion as in the case
where carbon particles are seeded into the reactor. At lower
temperatures, the necessary residence time is almost ve
orders of magnitude higher and it decreases by the increase in
reaction temperature. This is basically due to the increase in
reaction rate with temperature. It is observed that higher the
temperature, higher the rate constant. Once higher reaction
rate is observed, it leads tomore decomposition ofmethane. By
comparing the plots, we can see that mixed ow reactor
requires higher residence time than the plug ow reactor.
Figs. 8 and 9 show methane conversion and hydrogen
production at selected operating conditions and reactor
geometry using different kinetics found in literature. It can be
observed that methane conversion is always higher when
carbon particles are used as catalyst. Trommer et al. [13] states
that the reason for increased methane conversion is because
the carbon particles provide larger specic surface for
reactions and more efcient radiation heat transfer to the
reaction site, which increases the frequency factor by six
orders of magnitude. Furthermore, carbon seeding has
a signicant effect on the methane conversion and hydrogen
production even at lower residence time as well, which can be
seen in Fig. 7.
As for the methane conversion with no carbon particle
seeding, there is a difference in methane conversion and
hydrogen production found in literature. The reason for this is
mainly because of the difference in kinetic parameters
obtained by the Wyss et al. [29] and Rodat et al. [28]. Kinetic
data, such as reaction mechanism, activation energies, rate
constants and reaction orders for solar methane decomposi-
tion, must be correlated well with the experiments, because;
the optimum operating temperature for maximum chemical
conversion is determined from the kinetic calculations.
Therefore, kinetic data is very important in reactor design,
scale up and optimization [54].
As explained in the thermodynamics and kinetic study
sections, mole fraction of methane in the feed gas has an
impact on methane conversion and hydrogen production.
Fig. 10 shows this fact using Trommer et al. [13] kinetics for
chosen reactor geometry. As it is seen in the gure, conversion
increases with the decrease in methane mole fraction in the
feed gas. For smaller residence time, methane composition in
the feed gas has signicant effect on the conversion.Whenwe
compare the effect of methane mole fraction vs. residence
time on the conversion, we see that the effect of methane
Table 4 (continued )
T k vCH4;0 s FCH4;0 XCH4 FH2
2200 114 652.5 1 135.72 0.045 0.948455 0.085
2 67.86 0.090 0.942357 0.169
3 45.24 0.134 0.938462 0.252
4 33.93 0.179 0.935539 0.335
10 13.572 0.448 0.925272 0.829
2300 166 122.6 1 135.72 0.045 0.951447 0.085
2 67.86 0.090 0.945704 0.170
3 45.24 0.134 0.942034 0.253
4 33.93 0.179 0.939281 0.337
10 13.572 0.448 0.929611 0.833
a b
Fig. 7 Effect of carbon particle feeding.
i n t e r n a t i o n a l j o u rn a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 4 4 8 4 4 4 9 5 4491
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mole fraction in the feed gas is negligible compared to the
effect of residence time.
3.3. Solar reactor design methodology for homogenousmethane cracking
In this section, we present a reactor design methodology for
solar cracking of methane. Previous parametric study shows
that a good understanding of the thermodynamics and
chemical kinetics of the process is prerequisite for reactor
design. Next step is to develop models relating the chemistry
of our reaction to the conservation of mass. Subsequent steps
can be listed as follows:
(1) Estimate the methane conversion and hydrogen produc-
tion from thermodynamics for various temperature,
pressure and inert gas amount present in the methane
feed.
(2) Find kinetics data either experimentally or obtain it from
the literature.
(3) Estimate the total throughput of the feed gas going to
process or the amount of hydrogen production.
(4) Assume the contacting pattern of the methane either by
plug owormixed ow, and estimate the residence time to
nd the required reactor volume for the given operating
conditions.
Kinetics data is found by running experiment at constant
temperature, and then, concentration of the reactant species
orproductsaremeasuredandplottedasa functionof time.The
concentration dependent kinetic parameter is determined
either by using the integral or the differential method. Same
experiment is repeated for the same concentration at different
temperatures. The temperature dependent kinetic parameters
are found by tting the reaction rate with the experimentally
obtained concentration data in the Arrhenius form. If the
reaction is elementary, rate expression follows the stoichi-
ometry, hence rate vs. concentration relationship is directly
found from the stoichiometric equation. If the reaction is non-
elementary, assume the reaction kinetic mechanism and
derive the rate vs. concentration relationship. The above
experimental procedure is repeated to nd out the kinetics of
the reaction.
Once the kinetics of the reaction are available, reactor
volume for the given operating conditions for plug ow and
mixed ow can be estimated for homogenous thermal
decomposition of methane as follows. The general form of
rate expression is found from
rCH4 dCdt
k CnCH4 where k k0exp Ea8:31 T
(11)
whereas the performance equation for plug ow is obtained
from
VFCH4;0
sCCH4;0
VyCH4;0CCH4;0
Z XCH40
dXCH4rCH4
(12)
On the other hand, the performance equation for mixed
ow is found from
VFCH4;0
sCCH4;0
VyCH4;0CCH4;0
XCH4rCH4(13)
Fig. 8 Methane conversion estimated from the kinetics
found in literature.
Fig. 9 Hydrogen production estimated from the kinetics
found in literature.
Fig. 10 Effect of methane feed composition on methane
conversion.
i n t e r n a t i on a l j o u r n a l o f h y d r o g e n en e r g y 3 5 ( 2 0 1 0 ) 4 4 8 4 4 4 9 54492
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Therefore, the volume of the reactor is determined from
V (volumetric feed ow rate of gas) (s). For example,assuming that the methane decomposition occurs as a rst
order reaction, [1,4], then the rate expression is written as
follows:
rCH4 kCCH4 kCCH4;01 XCH4 1 aXCH4
(14)
where by denition expansion factor is
a Change in number of moles for complete conversionTotal moles fed [30,52].Estimation of expansion factor from the reaction stoichi-
ometry and inert gas presence in the methane feed is given
below.
Inertgas
CH4 (g) / C (s) 2H2 (g) Totalmoles
At t 0 (in moles) x y 0 0 x yAt t s (in moles) x 0 2y x 2y
a Nts Nt0=Nt0 x 2y x yx y y
x y YCH4;0mole fraction of methane in the feed gas
The reactor volume calculation for plug ow reactor
assumption is made by substituting equation (14) in equation
(12).
s 1 aln1 XCH4 aXCH4k
(15)
Alternatively, the reactor volume can be calculated for
mixed ow reactor by substituting Equation (14) in Equation
(13), which gives Equation (16).
s VyCH4;0
V$CCH4;0FCH4;0
XCH4 1 aXCH4 k$1 XCH4
(16)
4. Conclusions
We have presented the thermodynamics of methane decom-
position reaction and given a parametric study showing the
effects of temperature, pressure, and initial inert gas compo-
sition presence in the methane feeding gas on methane
conversion. Thermodynamic results show that methane
conversions and hydrogen production decrease with
increasing pressure. On the other hand, inert gas presence in
the feed gas increases the methane conversion. For our
chosen reactor geometry, we used the kinetics found in liter-
ature for methane feed with carbon particles and methane
feed with no carbon particles. It was observed that there are
differences in experimental conversions and theoretical
conversions obtained by different research groups. Results
show that higher conversions are obtained when the carbon
particles laden with methane. Higher residence time is
required to achieve the same conversion under the same
operating conditions for methane decomposition in the case
of methane feed with no carbon particles. The kinetic study
also shows that the methane conversion increases with
decrease in the methane mole fraction in the feed gas. Finally
we presented a reactor design methodology for homogenous
methane decomposition.
Nomenclature
CCH4;0 Methane feed concentration, mol/m3
Ea Activation energy, J/mol
FCH4;0 Methane feed rate, mol/min
FH2 Hydrogen molar ow rate, mol/min
k Kinetic constant, s1
k0 Frequency factor, s1
K Equilibrium constant
ln Liters at normal conditions of temperature and
pressure
n Order of reactionPP0
Pressure ratio
rCH4 Methane reaction rate, mol/m3 s
T Temperature, K
V Volume of the reactor, l
yCH4;0 Methane volumetric feed rate, l/min
XCH4 Methane conversion
y Mole fraction
yCH4 Mole fraction of methane
yCH4;0 Mole fraction of methane in feed
yH2 Mole fraction of hydrogen
yinerts Mole fraction of inert gases
Greek letters
3 Reaction coordinate
h0 Initial total number of moles of inert, methane and
hydrogen, mol
hH2;0 Initial hydrogen moles, mol
hCH4;0 Initial methane moles, mol
a Expansion factor
s Residence time of methane, s
nCH4 Methane stoichiometric coefcient
nC Carbon stoichiometric coefcient
nH2 Hydrogen stoichiometric coefcient
Abbreviations
MFR Mixed ow reactor
PFR Plug ow reactor
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