step-by-step methodology of solar reactor design for emission-free generation of hydrogen

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

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:

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 4485

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


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.


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.


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


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


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.


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.


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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step-by-step methodology of solar reactor design for emission-free generation of hydrogen

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