laminar stangnant flow.mexico.2008

8/8/2019 Laminar Stangnant Flow.mexico.2008.

1/8

Theoretical analysis of the direct decomposition of methane gas in a laminar stagnation-point ow:CO2 -free production of hydrogen

O. Bautista a , F. Me ndez b ,*, C. Trevinoca Seccio n de Estudios de Posgrado e Investigacio n-IPN, Me xico, D.F., 02550, Mexicob Facultad de Ingenier a, UNAM, Me xico, D.F., 04510, MexicocFacultad de Ciencias, UNAM, 04510, Me xico, D.F., Mexico

a r t i c l e i n f o

Article history:Received 20 September 2007Received in revised form10 June 2008Accepted 26 September 2008Available online 12 November 2008

Keywords:Thermal decomposition

MethaneHydrogen productionEndothermic reactionSurface coverage

a b s t r a c t

In this work, a theoretical analysis is developed to predict the decomposition temperatureof methane gas, CH 4 , in a planar stagnation-point ow over a catalytic carbon surface.Hydrogen is produced (without CO 2 as a byproduct) by means of a heterogeneous reactionmechanism, which is modeled with ve heterogeneous reactions, including adsorption anddesorption reactions. The mass species, momentum, and energy conservation equationsfor the gas phase are solved, taking into account that the temperature of decomposition ischaracterized by the Damko hler number. Therefore, the critical temperature conditions forthe catalytic thermal decomposition are found by using a high activation energy analysisfor the desorption kinetics of the adsorbed hydrogen component, H s. Specically, thenumerical estimations show that, for increasing values of the velocity gradient associatedwith the stagnation ow, the temperature of decomposition grows, depending on thesurface coverages of the product species. 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights

reserved.

1. Introduction

Today, it is well known that hydrogen fuel, the combustion of which produces only water vapor, could be a feasible energyresource for the future. The direct decomposition of somehydrocarbons to generate hydrogen by using carbon catalystsis a viable alternative to the conventional steam reforming processes. Methane is a preferred source of hydrogen becauseof its high ratio of hydrogen to carbon and its abundantsupply. The traditional hydrogen production methods includemethane steam reforming (MSR) and partial oxidation of methane (POM) [1], both of which are accompanied byproduction of the greenhouse gas CO 2 , which needs to bereduced. However, non-catalytic methane decomposition

requires high temperatures (15002000 K) in order to obtainreasonable quantities of hydrogen. An alternative method forhydrogen production is the direct thermal decomposition of methane (TDM),which produces no further byproductsexceptvaluable black carbon and low endothermicity (compared toMSR). The TDM process decomposes natural gas (NG) ina high-temperature solar chemical reactor [1,2]. When feeding the reactor with NG, the overall reaction is equivalent toCH4 / 2H2 Csolid . This process results in two products: a H 2-rich gas fuel and high-value carbon black material (CB). TheTDM occurs at temperatures above 700 C and in the absenceof oxygen.

Since the pioneering works of Muradov [3,4] and Suelveset al. [5] identifying the carbon-based catalytic decomposition

* Corresponding author . Tel.: 52 55 56228103; fax: 52 55 56228106.E-mail address: [email protected] (F. Mendez).

Av a i l ab l e a t www.sc i enced i r ec t . com

j ou r na l home page : w w w. e l s e v i e r. c o m / l o c a t e / h e

0360-3199/$ see front matter 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.ijhydene.2008.09.060

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 3 ( 2 0 0 8 ) 7 4 1 9 7 4 2 6
mailto:[email protected]://www.elsevier.com/locate/hehttp://www.elsevier.com/locate/hemailto:[email protected]


2/8

of methane for hydrogen production, a signicant number of experimental and quasi-analytical studies of TDM using various carbon catalysts in packed-bed or uidized-bed reac-tors have been published. However, most of these authors[69] have only reported experimental data for the thermaldecomposition of methane using different types of reactors.Recently, these works have been extended to consider specialeffects, such as theinuence of theprimary particle size ofthecarbon catalyst, that can improve the thermocatalyticdecomposition of the methane in a uidized-bed reactor [10],the kinetics of methane decomposition in a xed bed reactor[11], and the catalyst deactivation [12]. The activity, activationenergy and reaction order of different particle sizes of carbon[13] were analyzed to improve the overall hydrogen produc-tion process. Similar processes of hydrogen production using carbonaceous catalysts were reported on recently [14,15]. Atthe same time, new theoretical methods and predictions inthe specialized literature are missing. Only a few theoreticaland fundamental studies have been conducted. Therefore, inthe present work, we study theoretically the conversion of methane gas to obtain hydrogen gas without CO 2 , using a simple analytical model that takes into account thefollowingfact: in order to accelerate the TDMunder laboratoryconditions, it is necessary to elevate NGs temperature toa level suitable for decomposition ( ! 700 C). However, weshould emphasize that the present theoretical predictionsmust be completed and compared with experimental results.From a fundamental point of view and to our knowledge, this

kind of theoretical analysisofTDMof theCH4 gason a catalyticsurface in a laminar stagnation ow has not been performed.

Therefore, we develop in this work a theoretical model topredict the decomposition temperature of methane gas ina stagnation-point ow conguration. In general, there areimportant differences between combustion and TDM, such asthe presence of reactions involving oxygenated species incombustion and the absence of these reactions in TDM.Nevertheless, there are some common reactions andprocesses; thus, we adopt some steps of the kinetic schemeinvestigated by Deutschmann et al. [16], retaining thosereactions that permit only the decomposition of methane anddeposition of black carbon on the catalysts.

2. Theoretical formulation

2.1. Gas-phase governing equations

In Fig. 1, we show the typical model, the coordinate systemand a sketch of the laminar stagnation-point ow congura-tion. Gaseous methane with a concentration denoted by Y CH4 Nows with a velocity gradient a and temperature TN ,perpendicular to a catalytic at plate of nite thickness h. Weassume that the material of the at plate is composed of a carbon catalyst. The plate temperature is maintained ata uniform value of Tw , slightly greater than TN , in order toinduce the thermal decomposition of the methane. In

Nomenclature

a velocity gradient, adsorption reactionc p specic heatd desorption reactionDi molecular diffusion coefcient of the species i f dimensionless stream functionh thickness of the at platek j reaction ratesm mass of the species i p partial pressure of the species iPr Prandtl number of the methane gas, nr c p=lqr heat for the endothermic reaction on the surface

of the at plateS j sticking probability or accommodation coefcientt physical timeT temperatureTN temperature of the methane gas far from the at

plateT

wtemperature of the at plate

u, v longitudinal and transverse velocitiesW i molecular weight of the species iW molecular weight of the mixturex, y Cartesian coordinatesY i concentration of the species iyi nondimensional concentration of the species iZw rate of collisions

Greek letters

a dimensionless parameterb dimensionless parameterD nondimensional Damko hler numberDTD characteristic Damko hler number to dene the

decomposition temperature3 nondimensional activation energy parameter,

RTN =E5dg nondimensional parameterG surface molar concentration4 nondimensional temperature, Eq. (38)F nondimensional temperature, Eq. (26)h nondimensional transverse coordinate for the gas

phasel thermal conductivitym dynamic viscosityn kinematics coefcient of viscosityr densityqCH3 surface coverage of the component CH 3qCH2 surface coverage of the component CH 2qCH surface coverage of the component CHqH surface coverage of the component HqC surface coverage of the component CqV surface coverage of empty sitess dimensionless timeu surface reaction rate

Subscriptsw conditions at the at plateN denotes conditions far from the plate



3/8

addition, we assume that this process only occurs on thesurface of the catalytic material. Therefore, homogeneousreactions for thegas phase are not taken into account, and thestagnation-point boundary layer governing equations for thegas phase (assumed to be frozen) are the following:vr u

v x vr v

v y 0; (1)

r uv uv x r v

v uv y

v

v ym

v uv y r N mN a; (2)

r c p uv Tv x v

v Tv y

v

v yl

v Tv y ; (3)

and

r uv Y iv x r v

v Y iv y

v

v yr Di

v Y iv y ;

(4)

for i CH4 and the reaction products. Here, u and v are thelongitudinal and transverse components of the velocity eld,respectively, while x and y represent the longitudinal andtransverse axes to the at plate. In addition, T and Y i are thetemperature and the concentration of the species i. Thedensity, viscosity, specic heat at constant pressure, andthermal conductivity of the gas phase are given by r , m, c p and

l , respectively. Di is the molecular diffusion coefcient of thespecies i. The associated boundary conditions are thefollowing:

u v v Y CH4

v y u W CH4r DCH4

v Tv y

u qrl 0 for y 0; (5)

u ax T TN Y i Y iN 0 for y/ N : (6)Here, W i is the molecular weight of the species i; qr is the heatnecessary for the endothermic surface reaction per mole of methane,consideringtheoverallreactionCH 4/ Csolid 2H2;u is the surface reaction rate given in units of moles of methane consumed per unit time and unit surface area of thecatalytic plate.

2.2. Heterogeneous reaction model

The heterogeneous reaction mechanism proposed by thethermal decomposition of methane follows the basic ideassuggested by the simplied model of Reinke et al. [17].Furthermore, the reaction steps and specic values of the rateparameters for the present model were taken directly fromthe reaction mechanism developedby Deutschmann et al. [16]and are shown in Table 1 .

The kinetic model is represented by ve heterogeneousreactions. The reactions nished with a and d representadsorption and desorption, respectively. Here, Ct( s) denotesa free site on the surface of the catalytic plate. All surfacereactions are assumed to be of the Langmuir Hinshelwoodtype. The adsorption kinetics are given by a sticking proba-bility, S j, or accommodation coefcient, which represents theportion of the collisions with the surface that successfullyleads to adsorption. The rate of collisions, Zw , can becomputed using the classical kinetic theory, withZw

p=

ffiffiffiffiffiffiffiffiffiffiffiffiffi2p mkTp , where p and m are the partial pressure and

the mass of the species involved and k is the Boltzmannconstant ( k 1.38 1023 J/K). However, the kinetic desorptionis well represented by an Arrhenius law with high activationenergy for the adsorbed species, and the corresponding concentrations can be represented by the surface coverage qidened by the ratio of the number of sites occupied by surfacespecies i to the total number of available sites. The fractionalcoverage of each species is determined by writing differentialbalances on all surface species. For the stationary case, thedifferential equations then become a set of coupled algebraicequations. For the adsorbed species, the quasi-steady gov-erning equations are then given by

dqCH3dt k1aq2V k2qCH3 qV 0; (7)

dqCH2dt k2qCH3 qV k3qCH2 qV 0; (8)

dqCHdt k3qCH2 qV k4qCHqV 0; (9)

dqHdt 2k1aq

2V k5a q2V k5dq2H 0; (10)

dqCdt k1aq

2V; (11)

and

qV qCH3 qCH2 qCH qC qH 1: (12)Here, qV denotes the surface coverage of empty or vacant sites.In addition, we assume by Eq. (11) that the carbon deposits

Table 1 Heterogeneous reaction model

No. Reaction S A (mol cms) E (kJ/mol)

1a CH4 2Cts/ CH3 H 0.01 *** 2012 CH3 1Cts/ CH2 H *** 3.7E21 203 CH2 1Cts/ CHH *** 3.7E21 204 CHs 1Cts/ Cs Hs *** 3.7E21 205

a,d

H2 2Cts%

H H 0.046 3.7E21 77.8

Stream of CH 4

Externally heated catalytic plate

x

y

8 8 8 8T Y U =ax V =-ay

Fig. 1 Schematic of the physical model, showing thestagnation-point ow conguration.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 3 ( 2 0 0 8 ) 7 4 1 9 7 4 2 6 7421


4/8

onto the carbon catalyst. All reaction rates in Eqs. (7)(11)arein s 1 units. In this sense, the reaction rates given in Table 1can be transformed to the appropriate units by taking

k1a SCH4 pY CH4wW GW 3=2CH4 ffiffiffiffiffiffiffiffiffiffiffiffi2p RTp

; k5a SH2 pY H2wW

GW 3=2H2 ffiffiffiffiffiffiffiffiffiffiffiffi2p RTp (13)

kr GArexp Er=RT for r 2; 3; 4; 5d; (14)where G is the surface molar concentration in mol/cm 2 andcorresponds to the surface site density ( w 1015 sites/cm 2)divided by the Avogadro number, Av 6.022831023molecules/cm 2 , and R is the universal gas constant. Y i are theconcentrations close to the catalytic surface and are to beobtained after solving the coupled gas equations with thegoverning equations for the surface coverage of the adsorbedspecies.

From Eqs. (7) to (12), we nd that the surface coverage of product species is related to qV, as well as to the temperature,through the relationships

qCH3 k1a

k2qV; (15)

qCH2 k1ak3

qV; (16)

qCH k1ak4

qV; (17)

qH bq V; (18)

dqCd s k1a q

2V; (19)

where s represents the nondimensional time given by

s t

a b2=k1a

; (20)

with a 1 k1a1=k2 1=k3 1=k4w 1, b 2k1a k5a=k5d1=2.

Recognizing that k1a=k2 ( 1, k1a=k3 ( 1 and k1a =k4 ( 1, theconservation relationship (12) can be rewritten, in a rstapproximation, as

qC a bqV 1; (21)and the solution of Eqs. (15)(19)allows us to write qCH3 , qCH2 ,qCH, qH and qC as functions of the nondimensional time s , theparameters a , b and the reaction rates in the next form:

qC s

1 s; (22)

qH b

1 b1 s ; (23)

qCH k1ak4

1

1 b1 s ; qCH2

k1ak3

1

1 b1 s ; (24)

qCH3 k1ak2

1

1 b1 s ; and qV

1

1 b1 s : (25)

Substituting Eq. (21) for qV in Eq. (19), we obtaindqC=d s k1a1 qC

2, which can be integrated to obtain Eq.(22). The other Eqs. (23) and (24), are algebraically derived. InFig. 2, we show the corresponding values of the surface

coverage for each product species as a function of thetemperature for a given time, Eqs. (22)(25).

2.3. Gas-phase nondimensional governing equations

For the gas phase, a stream function j x; yis introduced tosatisfy the mass-conservation equation (Eq. (1)): r u v j =v yand r v v j =v x. We also dene the following nondimen-sional variables:

f jxffiffiffiffiffiffiffiffiffiffiffiffiffiffir N mN ap ; h ffiffiffiffiffiffiffiffiffiffi ffiar N mNr Z

y

0r x; y0dy0;

F c pW CH4T TN

qr; Y CH4 Y CH4 : (26)

The resulting nondimensional governing equations nowtake the form

d3 f dh3 f

d2 f dh2

r Nr

d f dh

2

0; (27)

d2Y dh2 ScCH4 f

dY dh 0; (28)

andd2Fdh2 Pr f

dFdh 0; (29)

where Pr is the Prandtl number of the gaseousmixture,Pr mc p=l and Sc i is the Schmidt number of thespecies, Sc i m=r Di. The nondimensional boundary condi-tions are then given by

f d f dh

dY idh G Lei

dFdh G 0 at h 0; (30)

d f dh 1 F Y i Y iN 0 for h / N ; (31)

where

400 600 800 1000 1200 1400 1600 1800

10 -1

10 -2

10 -3

10 -4

10 -5

10 -6

10 -7

10 -8

10 -9

10 -10

10 -11

10 -12

10 -13

10 -14

10 0

C

H

V

CH 3

CH 2

CH

T

= 1e-15

Fig. 2 Surface coverage for the species involved in theTDM.



5/8

Lei SciPr ; G

W CH4 Pr u

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir N mN ap (32)

and the rst parameter represents the Lewis number. Thereaction rate, u , which can be obtained from Eqs. (7) to (9),represents the consumption of the methane gas at the surface of the at plate. By denition, reaction 1a of Table 1 for the methane gas is

dissociative, and the frequency for the consumption of this species isgiven by k1aq2V. Therefore, the product of k1a q

2VG represents the

number of moles of methane gas which are consumed at the surfaceof the catalytic plate. Substituting Eq. (25) for qV in the above rela-tionship, we obtain

u k1a q2VG k1a G

1 b21 s

2$ (33)

The above equation is readily derived.

2.4. Asymptotic solution

From Eq. (10), we obtain the relationship between qV and qH

given byqV K5qH; (34)where K5 is a function mainly of the temperature and given byK5 1=b . Fig. 3shows the valuesof theheterogeneous reactionrates k j as functions of the inverse of the temperature, 1000/ T.The slowest rate of all corresponds to the desorption reactionof the adsorbed atomic hydrogen, k5d . It is important to notethat, in Fig. 3, the cases of k2 , k3 and k4 are indistinguishable.However, the rate plays an essential role in determining thethermal decomposition condition. Fig. 2 shows the evolutionof the surface coverage of the surface species as a function of temperature (Eqs. (20)(25)), assuming that the reactantconsumption is negligible, that is, Y iw

Y iN . The surface

coverage of H sis almost unity for temperature T 1000 K.The surface coverages of H and V are the most important,neglecting allother contributions of Eq. (12), thatis, qH qVx 1.In addition, in Fig. 2, the distributions of the transition speciesCH, CH2 and CH 3 follow a similar behavior. However, forvalues of qHw 1, we obtain from Eq. (34) that qVw K5. In thesame gure, it can be noted that the surface coverage of C is

very small compared with the others. The chemical reaction isthen governed by the adsorption of methane as well theadsorptiondesorption kinetics of hydrogen. From Eq. (34), weobtain an equation for qV:

qV K5 K25 OK35; for K5 1=b2/ 0; (35)

and

qH 1 K5 K25 OK35: (36)Threfore, the reaction rate can be approximated by

u k1a GK5

1 s 2; (37)

where we use the leading-order term in qV. Due tothe fact thatk5d has a large activation energy (desorption of H s), thesurface reaction rate is strongly dependent on temperature.The surface chemical reaction produces vacant sites that arerapidly occupied by fresh adsorbed species. Additional freesites are obtained when the newly generated adsorbedproduct of the surface reaction is rapidly desorbed. This

process nally leads to a thermal runaway, which character-izes the catalytic thermal decomposition process.In Eq. (37), it is shown that the reaction rate depends on

the adsorption kinetics of methane and on the desorptionkinetics of hydrogen, which depends strongly on tempera-ture. To generate the thermal decomposition conditions, it isenough to consider a temperature increase due to theenergy absorbed in the endothermic reaction of the orderTw TN w RTN =E5d . Therefore; it is convenient to denea new variable of order unity for the nondimensionaltemperature as

4 E5dqr

c pW CH4 RT2NF w 1: (38)

With this new variable, the nondimensional governing equa-tions take the form

d3 f dh 3 f

d2 f dh2 1 34

d f dh

2

0; (39)

d2yidh2 Sci f

dyidh 0; (40)

d24dh2 Pr f

d4dh 0; (41)

with the boundary conditions

f

d f

dh dyi

dh D exp4 w1 s

2 ;

d4dh

D exp4 w1 s

2 0 at h 0;d f dh 1 4 yi yiN 0 for h / N ;

(42)

where

yi Y i

3 Leiqr

c pW CH4 TN(43)

and

D qr

3c pTNPr

ffiffiffiffiffiffiffiffiffiffiffiffir N mN ap k1a GK5N 1 s

2; (44)

where K5N is K5 computed with T

TN . For large activation

energy of the desorption reaction for the methane,

0.5 1.0 1.5 2.0 2.5

10 16

10 14

10 12

1010

10 8

10 6

10 4

10 2

10 0

10 -2

10 -4

10 -6

k j ( 1 / s e c

)

1000/T

k1ak2k3k4k5ak5d

Fig. 3 Rate constants, k i (sL 1 ), as a function of the walltemperature (1000/ T ).



6/8

3 RTN =E5d / 0, the temperature variation close to thethermal decomposition condition is very small; thus, in therst approximation, both adsorption reactions can beassumed to be temperature independent. The Damko hlernumber for the surface reactions is expressed as D. With thelimit 3/ 0, the solution to Eqs. (39)(42) can be found else-where [18]:

dyidh h0

0:57 Sc2=5i yiN yiw

D exp4 w1 s

2 ; (45)

d4dh h0

0:57 Pr2=54 w D exp4 w1 s

2 : (46)

The rst equation takes into account reactant consumption.From Eq. (46) we can obtain the critical conditions for thethermal catalytic decomposition of methane as

DTD 0:57 Pr2=5

exp11 s

2: (47)

From Eq. (45), the reactant concentration at the wall, atthermal decomposition conditions, is given by

Y iw Y iN 3 Le3=5i c pW CH4 TN

qr: (48)

In the above relationship, it is very important to note that, inthe rst approximation, the methane consumption can beneglected to obtain the critical endothermic conditions for thetemperature decomposition. Therefore, the mass diffusion inthe boundary layer is important after reaching decompositionconditions.

3. Results

All results plotted in Figs. (2)(4)and the additional Figs. (5)(7)given in this section were obtained with the following valuesfor the parameters: qr 89,750 J/mol, E5d 201 kJ/mol. Theabove data were taken directly from Muradov et al. [10].Although the Prandtl number is dependent on temperature,

we choose an average value for it, and it is given by Pr 0.72,taken directly from Ref. [19]. For the density r N , we assume anideal-gas behavior for the methane gas. For the viscosity mNand specic heat c p of the methane gas, we use the following correlations: mN 1:34 105TN =293

0:87 and c p 19:895:024 102TN 1:269 105T2N 11:01 109 T3N , taken fromRefs. [20] and [21], respectively. The condition for the TDMgiven by Eq. (47), along with the denition of the Damko hlernumber, Eq. (44), represents the parametric dependenceon the TDM. The Damko hler number for this condition isgiven by

DTD qr

c pTNE5d

RTNPr

ffiffiffiffiffiffiffiffiffiffiffir N mN ap G2A5dexp E5dRTN

2 g 0:57 Pr2=5

exp11 s

2:

(49)

where the dimensionless methane-conversion parameter isdened as

0 5 10 15 20 25 30850

900

950

1000

1050

1100

1150

1200

T

( K )

a (1/s)

= 1.667, = 5 = 1.668, = 5 = 1.667, = 8 = 1.668, = 8

Fig. 4 Decomposition temperature as a function of thegradient of velocity for the stagnation-point ow for twodifferent values of the parameter G and of the parameter g .

3 4 5 6 7 8 91130

1140

1150

1160

1170

1180

1190

T (

K )

a = 16seg -1, = 1.66x(10) -8 mol/cm 2

Fig. 5 Decomposition temperature as a function of theconversion parameter g .

0.1 1 10

0.1

1

10

m H 2

/ m C

Fig. 6 Ratio of the hydrogen to the carbon produced in theprocess of TDM.



7/8

g SH2 Y H2w W

3=2CH4

SCH4 Y CH4w W 3=2H2

; (50)

and represents a measure of the conversion process for themethane gas. Taking into account that the parameters SH2 ,W H2 , SCH4 and W CH4 are xed, the ratio given by Y H2w =Y CH4wdetermines the conversion rate. Therefore,the temperature of decomposition for the methane gas can be obtained from Eq.(49) for different values of the parameters. In order to obtainthis temperature, we note that it is highly dependent on theactivation energy of reaction 5 d (Table 1 ) and the ratio of the adsorption rates of the components H 2 and CH 4 given bythe dimensionless parameter g . Fig. 4 shows the decomposi-tion temperature, TN , as a function of the velocity gradient of the stagnation-point ow, a , for two different values of theparameter G and two different values of the parameter g . It isclear from this gure that the analysis predicts correctly thetrends, both quantitatively and qualitatively, according tothe technical literature [1,2,68]. Similarly, in Fig. 5we presentthe decomposition temperature as a function of the conver-sion parameter g , with a 16 s1 and G 1.66 108 mol/m 2 .From this gure, we can see that, for increasing values of g ,the decomposition temperature is also increased, a state thatqualitatively corresponds to the typical experimental datareported previously. For instance, Lee et al. [2] obtainedexperimentally that, during the decomposition process, themethane conversion always increases for larger values of thedecomposition temperature. Therefore, our theoreticalpredictions are in accordance with the above experimentalresultsat least qualitatively, recognizing that both approachesuse different physical models. Finally, Fig. 6shows the ratio of mH2 =mC as a function of the nondimensional time, where mH2and mC are the mass of hydrogen and carbon produced in theprocess, showing qualitatively that the hydrogen produceddecreases as the time increases, causing a decreasing ef-ciency for the catalytic plate, because the carbon produced inthe reaction is deposited on the surface of the catalytic plate.Finally, in Fig. 7, we show the corresponding velocity and

temperature proles for the gaseous phase, taking intoaccount that, in the rst approximation, the critical conditionto nd the decomposition temperature based on the methaneconsumption is negligible; therefore, the methane concen-tration remains uniform.

4. Conclusions

We have developed a theoretical model to predict the criticaltemperature of decomposition of methane into H 2 and valu-able carbon. The above formulation reduces the problem tothe solution of a set of non-linear equations. Since the solu-tion procedure does not require integration of any differentialequations, theset of non-linear equations that emerges can besolved with a standard numerical routine, thereby reducing considerably the required computation time. The formulationis also advantageous for investigation of surface kinetics. Asa concluding remark, it should be emphasized that ourformulations are applicable only when the stream gastemperature on the catalytic surface is sufciently high andnear to the TDM.

Acknowledgments

O. Bautista acknowledges DGAPA of UNAM for supporting thiswork.

Appendix ASupplemental material

Supplementary information for this manuscript can bedownloaded at doi: 10.1016/j.ijhydene.2008.09.060 .

r e f e r e n c e s

[1] Steinberg M. Fossil fuel decarbonization technology formitigating global warming. Int J Hydrogen Energy 1999;24:7717.

[2] Lee K, Han GY, Yoon KJ. Thermocatalytic hydrogenproduction from the methane in a uidized bed withactivated carbon catalyst. Catal Today 2004;9395:816.

[3] Muradov N. CO2-free production of hydrogen by catalyticpyrolysis of hydrocarbons. Energy Fuels 1998;12:418.

[4] Muradov N. Catalysis of methane decomposition overelemental carbon. Catal Commun 2001;2:8994.

[5] Moliner R, Suelves I, Lazaro M, Moreno O. Thermocatalyticdecomposition of methane over activated carbons: inuenceof textural properties and surface chemistry. Int J HydrogenEnergy 2005;30:293300.

[6] Abanades S, Flamant G. Production of hydrogen by thermalmethane splitting in a nozzle-type laboratory-scale solarreactor. Int J Hydrogen Energy 2005;30:84353.

[7] Hirsch D, Steinfeld A. Radiative transfer in a solar chemicalreactor for the co-production of hydrogen and carbon bythermal decomposition of methane. Chem Eng Sci 2004;59:57718.

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

df/d

Fig. 7 Velocity and temperature proles in the gaseousregion.

http://dx.doi.org/doi:10.1016/j.ijhydene.2008.09.060http://dx.doi.org/doi:10.1016/j.ijhydene.2008.09.060


8/8

[8] Dunker A, Ortmann JP. Kinetic modeling of hydrogenproduction by thermal decomposition of methane. Int JHydrogen Energy 2006;31:198998.

[9] Abanades S, Flamant G. Solar hydrogen production from thethermal splitting of methane in a high temperature solarchemical reactor. Sol Energy 2006;80:132132.

[10] Muradov N, Chen Z, Smith F. Fossil hydrogen with reducedCO2 emission: modeling thermocatalytic decomposition of methane in a uidized bed of carbon particles. Int J HydrogenEnergy 2005;30:114958.

[11] Bai Z, Chen H, Li W, Li B. Hydrogen production by methanedecomposition over coal char. Int J Hydrogen Energy 2006;31:899905.

[12] Pinilla JL, Suelves I, Utrilla R, Galvez ME, Lazaro MJ, Moliner R.Hydrogen production by thermo-catalytic decomposition of methane: regeneration of active carbons using CO 2 . J PowerSources 2007;169:1039.

[13] Ryu BH, Lee SY, Lee DH, Han GY, Lee T-J, Yoo KJ. Catalyticcharacteristic of various rubber-reinforced carbon blacks indecomposition of methane for hydrogen production. CatalToday 2007;123:3039.

[14] Suelves I, Lazaro MJ, Moliner R, Pinilla JL, Cubero H.Hydrogen production by methane decarbonization:carbonaceous catalysts. Int J Hydrogen Energy 2007;32:33206.

[15] Pinilla JL, Suelves I, Lazaro MJ, Moliner R. Kinetic study of the thermal decomposition of methane using carbonaceouscatalysts. Chem Eng J 2008;138:3016.

[16] Deutschmann O, Schmidt R, Behrendt F, Warnatz J. Twenty-sixth symposium (international) on combustion, TheCombustion Institute; 1996. p. 1747.

[17] Reinke M, Mantzaras J, Shaeren R. High-pressure catalyticcombustion of methane over platinum: in situ experimentsand detailed numerical predictions. Combust Flame 2004;136:21740.

[18] Trevin o C. Gas-phase ignition of premixed fuel by catalyticbodies in stagnation ow. Combust Sci Technol 1983;30:213.

[19] Kays WM, Crawford ME, Weigand B. MP for convective heatand mass transfer. Bernhard Weigand: McGraw-Hill; 2004.

[20] White FW. Fluid mechanics. McGraw-Hill; 2003.[21] Kyle BG. Chemical and process thermodynamics. Englewood

Cliffs: Prentice-Hall; 1984.


laminar stangnant flow.mexico.2008

Documents