Heterogeneous Reactor Modeling for Simulation of Catalytic Oxidation

*Corresponding author. Tel.: #90-212-263-15-40; fax: #90-212-2872460.

E-mail address: [email protected] (Z. I0 lsen OG nsan).

Chemical Engineering Science 56 (2001) 641}649

Heterogeneous reactor modeling for simulation of catalytic oxidationand steam reforming of methane

A. K. Avcm!, D. L. Trimm", Z. I0 lsen OG nsan!,*!Department of Chemical Engineering, Bog\ azic7 i University, 80815 Bebek, Istanbul, Turkey

"School of Chemical Engineering and Industrial Chemistry, University of New South Wales, Sydney 2052, Australia

Abstract

An autothermal, dual catalyst, "xed-bed reaction system proposed for hydrogen production from methane is mathematicallyinvestigated using di!erent catalyst bed con"gurations and feed ratios. Consecutive placement or physical mixture of the oxidationand reforming catalysts, Pt/d}Al

2O

3and Ni/MgO}Al

2O

3, respectively, are the two con"gurations of interest. Reactor operation at

di!erent feed ratios is analyzed for both catalyst bed con"gurations on laboratory scale and industrial scale via a series of simulationsby using one-dimensional heterogeneous "xed-bed reactor model. The type of heterogeneous components implemented into themodel is decided by checking related criteria. Hydrogen production is predicted to be higher when the catalysts are in a physicallymixed state as well as at low methane-to-oxygen and high steam-to-methane ratios, which are in agreement with the experimentalresults reported for a bench scale integral reactor. The optimum operating conditions for obtaining maximum hydrogen productionare also investigated. ( 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Autothermal operation; Dual catalyst; Fixed-bed reactor; Methane oxidation; Methane steam reforming; Reactor simulation

1. Introduction

In recent years, hydrogen has become a widely usedfeedstock in the chemical, petroleum re"ning and pet-rochemical industries. Hydrotreating and hydrocrackingprocesses, synthesis gas applications such as productionof ammonia and methanol, Fischer}Tropsch synthesisand the manufacture of chemicals having speci"c enduses such as pharmaceuticals are areas in which hydro-gen is employed (Furimsky, 1998; Pena, Gomez &Fierro, 1996). In addition, hydrogen is expected to be anenergy source in the future since it o!ers several environ-mental and economic advantages when compared toother fuels (Jamal & Wyszynski, 1994; Rosen, 1991).

Steam reforming of light hydrocarbons (C1}C

3) run

on nickel catalysts is the most widely employed route forhydrogen production due to its simple construction, op-eration and well-established technology (Armor, 1999;Pena et al., 1996; Rosen, 1991). On the other hand, thedemand for considerable energy input resulting from the

high endothermicity of the reforming reactions and theexistence of catalyst deactivation turn out to be the majordrawbacks of catalytic steam reforming (Rostrup-Niel-sen, 1984; Trimm, 1999).

Catalytic partial oxidation of methane, which is mildlyexothermic (*H0"!35.7 kJ/mol), gives a lower syn-thesis gas ratio (H

2:CO"2:1) (Hickman & Schmidt,

1993). Therefore, it is more suitable for use in processessuch as Fischer}Tropsch synthesis and methanol produc-tion. Direct methane cracking, carbon dioxide reformingof methane, use of membrane reactors and of "xed-bedreactors with reversed #ow in steam reforming, ther-mochemical and photocatalytic water splitting are someof the alternative techniques for hydrogen production.

In a recently proposed reaction system using integralmicroreactors, the endothermic heat and part of thesteam required for methane steam reforming are bal-anced by exothermic methane oxidation in the presenceof two di!erent catalysts, Pt/d}Al

2O

3for total oxidation

and Ni/MgO}Al2O

3for steam reforming (Ma & Trimm,

1996; Ma, Trimm & Jiang, 1996). Increased hydrogenselectivities can thus be attained in autothermal opera-tion. Moreover, the presence of two di!erent catalystsintroduces operational #exibility, i.e. the reaction systemcan be adjusted in an object-oriented manner. For

0009-2509/01/$ - see front matter ( 2001 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 2 7 1 - 2

instance, the synthesis gas ratio may be adjusted fora speci"c end use such as Fischer}Tropsch synthesis.

This work is a computational investigation of thee!ects of catalyst bed con"guration and molar feed ratioson the product distributions achieved in the dual-catalystautothermal operation mentioned above. For this pur-pose, a series of reactor simulations are performed forbench scale and industrial scale reactors by using one-dimensional heterogeneous reactor model. The operatingconditions that will lead to maximum hydrogen yieldsare also evaluated.

2. Description of the reaction system

The reaction system is an adiabatic "xed-bed reactorin which Pt and Ni catalysts are packed in several con"g-urations. During autothermal operation, oxidation,reforming and various side reactions exist within thereactor. Total oxidation of methane in the presence of airis catalyzed by the Pt/d}Al

2O

3catalyst and provides the

exothermic heat to the system:

CH4#2O

2PCO

2#2H

2O, *Ho"!802.3 kJ/mol.

(1)

The rate expression for reaction (1) is given by Ma et al.(1996):

!r1"

k1K

1PCH4

JK2PO2

(1#K1PCH4

#JK2PO2

)2. (1H)

A large fraction of the endothermic heat is consumed bythe steam reforming reactions:

CH4#H

2OHCO#3H

2, *Ho"206.2 kJ/mol, (2)

CH4#2H

2OHCO

2#4H

2, *Ho"165.0 kJ/mol. (3)

The rate expressions for the steam reforming reactionsthat run on Ni/MgO}Al

2O

3(Eq. (2*)) and Ni/MgAl

2O

4(Eq. (2@)) are given as follows (Ma, 1995; Xu & Froment,1989a):

!r2"

k2K

AK

BPCH4

PH2O

P3@2H2

(1#KA(P

CH4/P1@2

H2)#K

B(P

H2O/P

H2))2

, (2H)

!r2"

k2(P

CH4PH2O

!(PCO

P3H2

/K@2))

P5@2H2

(1#KCO

PCO

#KH2

PH2#K

CH4PCH4

#KH2O

(PH2O

/PH2

))2,

(2@)

!r3"

k3(P

CH4P2H2O

!(PCO

P4H2

/K@3))

P7@2H2

(1#KCO

PCO

#KH2

PH2

#KCH4

PCH4

#KH2O

(PH2O

/PH2

))2.

(3H)

Note that two alternative rate expressions (Eqs. (2*) and(2@)) are given for reaction (2).

Water}gas shift and methane cracking are consideredas side reactions running on the Ni/MgO}Al

2O

3cata-

lyst:

CO#H2OHCO

2#H

2, *Ho"!41.2 kJ/mol, (4)

CH4HC#2H

2, *Ho"74.9 kJ/mol. (5)

The corresponding rate expressions for reactions (4) and(5) are (Kuvshinov, Mogilnykh & Kuvshinov, 1998; Xu& Froment, 1989a):

!r4"

k4(P

COPH2O

!(PCO2

PH2

/K@4))

PH2

(1#KCO

PCO

#KH2

PH2

#KCH4

PCH4

#KH2O

(PH2O

/PH2

))2,

(4H)

!r5"

k5(P

CH4!(P2

H2/K@

5))

(1#KHP0.5

H2)n

. (5H)

The temperature dependence of the LHHW-type rate lawparameters in these rate expressions have been takenfrom the references cited.

3. Simulation of autothermal operation in 5xed-bedreactors

Various con"gurations of the two catalysts,Pt/d}Al

2O

3and Ni/MgO}Al

2O

3, present within the

reactor are possible. Experimental data reported showthat a change in the catalyst bed arrangement results indi!erent product distributions (Ma & Trimm, 1996). Twodi!erent bed arrangements are studied in this work. Thecon"gurations of interest are the consecutive dual bedwhere Pt/d}Al

2O

3is placed in the upstream of the reac-

tor followed by Ni/MgO}Al2O

3, and the mixed bed

which involves a physical mixture of the two catalysts. Inthe simulation of autothermal operation in dual-bedscheme, steam reforming and other side reactions areassumed to be consecutive to methane oxidation whilethe simultaneous occurrence of reactions (1}5) are con-sidered in the mixed-bed scheme.

3.1. Reaction model

A one-dimensional heterogeneous reactor model isused for the simulation of the adiabatic autothermal dualcatalyst operation in "xed-bed reactors. The workingequations are as follows:

Model equations for the bulk yuid:

dFj

d="k

sjam(C

sj!C

j), (6)

d¹

d="

hsam(¹

s!¹)

+jFjcpj

, (7)

642 A. K. Avcn et al. / Chemical Engineering Science 56 (2001) 641}649

dP

d="!

bo

Ac(1!/)o

c

Po

P

¹

¹o

FT

FTo

. (8)

Model equations for the solid:

ksjam(C

sj!C

j)"+

i

gi(l

ij)(!r

ij)s, (9)

hsam(¹

s!¹)"+

i

gi(!*H

i)(!r

i)s. (10)

Boundary conditions:

At="0, Fj"F

jo, ¹"¹

o, P"P

o. (11)

The particle-to-#uid mass and heat transfer coe$cientsin Eqs. (9) and (10), k

sjand h

s, respectively, are evaluated

by using the following correlations (Wakao & Kaguei,1982):

hsD

pjf

"2#[email protected], (12)

ksjD

pD

jm

"2#[email protected]. (13)

The temperature dependencies of physical propertiessuch as viscosity, thermal conductivity, binary and e!ec-tive di!usivities of the species present in the reactionmixture and their mixing rules have been reported(Wakao & Kaguei, 1982; Rase, 1990). The ideal gasapproximation is employed in the evaluation of the den-sity of the gas mixture.

In order to reduce the execution time in the reactorsimulations, heterogeneous terms, i.e. interfacial heat andmass transfer resistances and the intraparticle di!usionlimitations, are not incorporated into the reactor model ifthe criteria given below indicating the degree of hetero-geneity are satis"ed (Fogler, 1999):

Mears' criteria for interfacial mass transfer:

+i(l

ij)(r

ij)o

bD

pn

2ksjC

j

(0.15, (14)

K+

i(!*H

i)(!r

i)o

cD

pEA

2hs¹2R

gK(0.15. (15)

Weisz}Prater criterion for intraparticle diwusion:

+i(l

ij)(r

ij)o

cD2

p4D

eC

sj

;1. (16)

These criteria are the versions modi"ed for the multiplereaction case and give approximate indications of thepertinent heterogeneous phenomenon (Rase, 1990).

3.2. Evaluation of the optimum operating conditions

The optimum operating conditions leading to max-imum hydrogen production are determined via the

simultaneous treatment of the energy balance and reac-tion equilibrium expressions. In formulating the energybalance, it is assumed that equilibrium values are reachedfor all reactions, all the oxygen in the feed is consumedand a steam-to-methane ratio of 3 exists for the steamreforming reaction in order to eliminate carbon forma-tion (Ma, 1995). Heat generated by total methane oxida-tion (q

1) is utilized for vaporizing and heating the water

fed to the system (q2), heating the catalyst bed (q

3) and

the gas mixture that exists after oxidation (q4) as well as

supplying energy to reactions (2}5) (q5) in an adiabatic

system:

q1"q

2#q

3#q

4#q

5. (17)

The explicit forms of the terms in the energy balance,q1}q

5, are as follows:

q1"F

CH4~,1*H

1,673, (18)

q2"F

H2O,oqH2O

, (19)

q3"=

505!-PT

673

cp,#!5!-:45

d¹, (20)

q4"+

j

(Fj`,1

)PT

673

cpj

d¹, (21)

q5"

4+i/1

FCH4~,i

*Hi#F

CO~,5*H

5. (22)

Eq. (17) and the reaction equilibrium expressions aresolved together to obtain the optimum conditions withmaximum hydrogen yield as the system objective.

3.3. Numerical techniques

The temperature dependences of the rate-law para-meters in Eq. (1*) are determined by minimizing the sumof squares of di!erences between the reported andcalculated values. This minimization problem is handledby using the Nelder}Mead simplex algorithm.

Eqs. (6)}(10) with the boundary conditions (11) aresimultaneously solved in MATLABTM. The nonlinearalgebraic Eqs. (9) and (10) are solved in a separate sub-routine by least-squares technique where theGauss}Newton method is employed together witha mixed quadratic and cubic line search procedure. In thesolution of the di!erential Eqs. (6)}(8), combination ofa variable order sti! and a non-sti!ODE solver is foundto give the best performance in terms of yielding thelowest CPU time. Optimum operating conditions areevaluated by employing the same algebraic solver routinethat is used in the solution of Eqs. (9) and (10). Reactorsimulations are conducted on an IBM Net"nity 7000M10 workstation.

A. K. Avcn et al. / Chemical Engineering Science 56 (2001) 641}649 643

Tab

le1

Oper

atin

gco

nditio

nsan

dre

acto

rda

ta

Ben

ch-s

cale

reac

tor

(Ma

&Trim

m,19

96)

Indu

strial

-sca

lere

acto

r(X

u&

Fro

men

t,19

89b)

Dual

-bed

sche

me

Mix

ed-b

edsc

hem

eD

ual

-bed

sche

me

Mix

ed-b

edsc

hem

e

¹o

(K)

640}

665

800

815

800

PT

o(a

tm)

2.5

2.9

28.6

28.6

FCH

4,0

(km

ol/h)

2.2]

10~4

1.7]

10~4

62.2

44.4

=505!-(k

g)2]

10~4(

Pt/d}

Al 2

O3)#

3]10

~4(

Ni/M

gO}A

l 2O

3)

5]10

~4(

Pt/

d}A

l 2O

3#

Ni/M

gO}A

l 2O

3)

53.2

(Pt/d}

Al 2

O3)#

79.8

(Ni/M

gAl 2

O4)

133

(Pt/

d}A

l 2O

3#

Ni/M

gAl 2

O4)

d r(m

)1.

3]10

~3

1.01

6]10

~1

d p(m

)3.

4]10

~4

1.33

5]10

~2

4. Results and discussion

In order to test the reactor model, simulations areinitially conducted at di!erent feed ratios and catalystbed con"gurations for bench scale integral reactors andcompared with the experimental results reported by Maand Trimm (1996). Autothermal operation is then ana-lyzed under the same conditions in hypothetical indus-trial reactors whose dimensions are determined by scale-up and by using the industrial "xed-bed reactor dataavailable (Xu & Froment, 1989b). The ratio of the cata-lyst weight to the initial methane molar #ow rate is usedas the scale-up parameter. The operating conditions andreactor data used in the simulations are given in Table 1.

4.1. Bench scale simulations

Comparison of simulation outputs and their experi-mental counterparts for dual- and mixed-bed schemesare given in Tables 2 and 3, respectively.

When the product distributions obtained in the experi-ments and simulations are compared with each other, itis observed that the mixed-bed scheme gives higher hy-drogen yields. Presence of the catalysts in the physicallymixed state enhances heat and mass transfer character-istics, i.e. reduces the degree of heterogeneity of the reac-tion system, which is also con"rmed by the relatively lowvalues of the LHS of the criteria given by Eqs. (14)}(16) inSection 3.1.

The status of the criteria given in Section 3.1 is taken asa measure in the implementation of the heterogeneouscomponents into the reactor model. In both catalyst bedcon"gurations, it is observed that the interfacial heattransfer resistance is signi"cant during the entire opera-tion (LHS (15)'0.15). On the other hand, interfacialmass transfer resistance is observed to be important attemperatures higher than ca. 1100 K. Intraparticle di!u-sion limitations are neglected, i.e. e!ectiveness factorvalues are taken as unity due to the presence of smallcatalyst particles.

Each simulation of the dual-bed scheme is composedof two sub-simulations: one for the Pt bed where onlymethane oxidation is assumed to occur, the other for theNi/MgO bed where reactions (2)}(5) are considered toproceed. The bed temperature reaches to its maximumvalue at the bed interface where endothermic steamreforming reactions become signi"cant. Experimentallydetermined maximum bed temperatures in dual-bed op-eration are less than 900 K (Table 2). Therefore, theinterfacial mass transfer is neglected and only externalheat transfer is considered as the heterogeneous compon-ent in both "rst and second sub-simulations. A singlesimulation is conducted for each run in the mixed-bedcon"guration where reactions (1)}(5) are assumed to pro-ceed in a simultaneous fashion. The experimental valuesof maximum bed temperatures are less than 1010 K


Table 2Experimental results vs. bench scale simulation outputs in dual-bed scheme

Feed conditions (Ma & Trimm, 1996) Experimental results (Ma & Trimm, 1996) Simulation outputs

CH4/O

2H

2O/CH

4GHSV (h~1) x

CH4yH2

(L) yCO

(L) ¹.!9

(K) xCH4

yH2

(L) yCO

(L) ¹.!9

(K)

3.53 0.88 37600 16.2 8.8 0 790 11.0 31.6 0.4 7903.53 1.75 47700 15.0 10.1 0 781 13.1 39.8 0.4 7822.98 1.75 50600 20.7 17.3 0 831 19.3 52.2 0.3 8272.98 2.34 57500 19.9 17.3 0 823 20.9 58.0 0.5 8222.51 1.75 59000 28.7 29.0 0 873 29.0 67.5 0.7 875

Table 3Experimental results vs. bench scale simulation outputs in mixed-bed scheme

Feed conditions (Ma & Trimm, 1996) Experimental results (Ma & Trimm, 1996) Simulation outputs

CH4/O

2H

2O/CH

4GHSV (h~1) x

CH4yH2

! yCO

! ¹.!9

(K) xCH4

yH2

! yCO

! ¹.!9

(K)

2.24 1.17 37600 39.5 47.8 6.3 839 43.8 98.6 12.3 8431.89 1.17 41100 53.3 74.9 11.7 888 53.9 125.7 24.1 9021.89 1.56 44500 53.8 76.4 12.5 889 46.9 129.3 23.6 8901.89 2.34 51300 54.9 82.9 9.9 851 31.0 129.7 20.0 8691.55 1.56 49500 69.1 105.7 15.0 931 55.4 151.5 37.7 9431.55 2.34 56000 70.1 107.1 19.6 908 40.5 153.6 31.9 9131.35 2.34 60000 83.6 119.5 30.3 953 48.7 178.6 48.7 9661.16 2.34 65000 91.7 120.6 35.9 1007 55.0 195.6 64.6 1009

!Product yield: moles of product obtained/100 moles of methane fed.

(Table 3). This leads to the implementation of interfacialheat transfer into the reactor model only. The heterogen-eous characteristics of these reaction systems are alsocon"rmed by checking the related criteria (Eqs. (14)}(15)).

For both catalyst bed con"gurations, it is observed inthe experiments and simulations that, at constant steam-to-methane ratio, a decrease in the methane-to-oxygenratio results in higher hydrogen yields and elevated max-imum bed temperatures. Since the molar #ow rate ofmethane is constant in all runs, any decrease in themethane to oxygen ratio, i.e. any increase in the molar#ow rate of oxygen in the feed will lead to the combustionof more methane which will increase the amount ofenergy generated by total oxidation and hence the bedtemperatures. Higher bed temperatures will facilitateendothermic steam reforming reactions and result inhigher hydrogen yields. In addition, at constant meth-ane-to-oxygen ratio, an increase in the initial molar #owrate of steam lowers the maximum bed temperature. Itcan be concluded that steam facilitates heat transferbetween the two beds.

In both catalyst bed con"gurations, the maximum bedtemperatures obtained from simulations are close to theexperimental ones, whereas predicted hydrogen and car-bon monoxide yields seem to be positively deviating in allruns (Tables 2 and 3). One possible explanation is the

absence of the following side reaction in the reactormodel that removes hydrogen and carbon monoxidefrom the reaction medium:

CO#H2HC#H

2O, *Ho"!135.6 kJ/mol. (23)

The change in the Gibbs free energy of the above reactionis negative at temperatures less than ca. 950 K, indicatingits signi"cance in existing reaction conditions (Tables2 and 3). Hence, simulated H

2and CO yields may

approach experimental ones if this reaction wereimplemented into the model equations.

The methane conversion levels are predicted to belower than the experimental values at low methane-to-oxygen and high steam-to-methane ratios in mixed-bedcon"guration (runs 4}8 in Table 3). It seems that excesssteam inhibits the steam reforming reaction in the simu-lations, which is not observed in the experiments. Thisdi!erence may be due to the lower performance of thekinetic expressions in case of high amount of steam andoxygen, which appears to be a limitation for this model inlarger scale simulations.

Pressure drop is observed to be negligible in both bedschemes. Maximum values are obtained to be 0.063 and0.031 atm for the bench scale dual- and mixed-bed con-"gurations, respectively.


Fig. 1. Temperature pro"les obtained in industrial scale reactor withdual-bed con"guration.

Fig. 2. Temperature pro"les obtained in industrial scale reactor withmixed-bed con"guration.

4.2. Industrial scale simulations

In order to predict characteristics of dual catalystautothermal operation on an industrial scale, a set ofsimulations are performed in hypothetical larger scaletubular reactors with the catalyst bed con"gurations ofinterest. Since steam is fed instead of liquid water into thereactors, the maximum bed temperatures obtained inindustrial scale simulations are higher than ones given inTables 2 and 3. As a result, in dual-bed operation, criteria(14), (15) indicated the existence of interfacial mass andheat transfer in Pt bed, both of which are considered inthe "rst subsimulation. Criterion (14) indicated the im-portance of interface mass transfer resistance only at thebed interfacial, in an incremental layer of steam reform-ing catalyst. Therefore, interfacial heat transfer is the onlyexternal heterogeneous component considered in second-ary subsimulations. Similarly, only external heat transferis considered in simulating the industrial scale reactorwith mixed-bed con"guration in which the local exist-ence of external mass transfer is neglected.

Apart from the above external "lm resistances, in-traparticle di!usion limitations are taken into accountdue to the presence of larger catalyst particles (LHS(16)'1). For this purpose, e!ectiveness factors for reac-tions (1)}(5) are taken from the literature (De Groote& Froment, 1996). Although the results obtainedby using constant e!ectiveness factors are approximate,operating characteristics of the industrial scale reactorcan be identi"ed due to the similarity of the operatingconditions given.

Molar feed ratios given in Tables 2 and 3 are employedin the industrial scale simulations. Bed temperature andproduct yield trends obtained for di!erent runs are sim-ilar to the bench scale simulations. Hydrogen yields arebetween 107 and 139 in the dual bed and 122 and 218 inthe mixed-bed con"gurations. The temperature and typi-cal molar #ow rate pro"les for di!erent bed con"gura-tions are given in Figs. 1}4.

The bed temperatures obtained in dual-bed scheme aregreater than those calculated for mixed-bed con"gura-tion. This is due to the complete consumption of oxygenin the feed, which allows total oxidation to proceed untilcompletion and raise temperatures up to ca. 1600 K(Fig. 1).

Dual-bed simulation results shown in Fig. 1 indicatethat the temperature in the bed rises "rst and then re-mains constant at a certain value, which is a typicaltemperature pro"le for methane oxidation whereasa peak is observed in temperature pro"les obtained inmixed-bed simulations of Fig. 2. The sharp temperaturefall at the dual-bed interface is because of the high en-dothermicity of the reforming reactions running onNi/MgO catalyst, whose existence is con"rmed bya sharp increase in hydrogen #ow rate in Fig. 4. Theincrease in the methane #ow rate and the decrease in the

hydrogen #ow rate after the maximum bed temperaturelocation in Figs. 3 and 4 indicate the occurrence ofreverse reactions (2), (3) and (5). Water}gas shift reactionseems to be important in the determination of CO andCO

2distribution in both the dual-bed and the mixed-

bed schemes.The shift in the locations of the maximum bed temper-

atures in Figs. 1 and 2 is due to the increase in the totalmolar #ow rates at the reactor inlet where methane #owis kept constant. It is worth noting that the maximumpressure drop is estimated to be ca. 1 atm in larger scalereactor simulations.


Fig. 3. Product distribution obtained in industrial scale reactor withmixed-bed con"guration (CH

4/O

2"2.24, H

2O/CH

4"1.17).

Fig. 4. Product distribution obtained in industrial scale reactor withdual-bed con"guration (CH

4/O

2"3.53, H

2O/CH

4"0.88).

Table 4Investigation of the optimum operating conditions

CH4/O

2H

2O/CH

4¹

.!9(K) y

H2!

2.09 1.81 773 1.441.62 1.47 873 2.111.52 1.33 936 2.221.43 1.27 973 2.201.33 1.15 1073 2.09

!Hydrogen yield: moles of H2

produced/moles of CH4

fed.

Several operating conditions such as di!erent molarfeed ratios are investigated thermodynamically for theirhydrogen yield values by the simultaneous solution ofEq. (17) and reaction equilibrium expressions. Results aregiven in Table 4.

It was mentioned that decrease in methane-to-oxygenratio in the feedstock leads to a rise in the maximum bedtemperature, and hence hydrogen production, due to theendothermic character of the reforming reactions. Inmathematical analysis, this trend is observed to increase

up to a certain point where the hydrogen yield reachesa maximum value and then starts to decrease (Table 4).Most of the methane in the feedstock is consumed byoxidation, the bed temperatures increase, limitedamounts of methane are left for the reforming reactions,and hence hydrogen is formed when the methane-to-oxygen ratio in the feed is low. At the other extreme,the e$ciencies of the reforming reactions are low due tothe insu$cient temperature rise provided by oxidation.Therefore, the presence of a maximum in H

2yield is

theoretically expected. Since the H2O/CH

4molar ratio

for steam reforming is kept constant at 3 as mentioned inSection 3.2, the H

2O/CH

4in the feed is decreased to-

gether with the feed CH4/O

2molar ratio, considering

that low CH4/O

2will lead to higher H

2O formation.

Operating conditions leading to maximum hydrogenyield constitute an optimum set. By employing theseresults, approximate operating conditions for increasedhydrogen output can be determined for industrial scaleoperation.

5. Conclusions

Autothermal hydrogen production in the presence oftwo di!erent catalyst is mathematically investigated bya series of simulations conducted for bench scale andhypothetical industrial scale reactors. Pt/d}Al

2O

3and

Ni/MgO}Al2O

3catalyzing total methane oxidation and

steam reforming, respectively, are either placed consecut-ively (dual bed) or packed in the form of a physicalmixture (mixed bed). A one-dimensional heterogeneousreactor model is used for the simulations. Heterogeneouscomponents describing heat and mass transfer resist-ances are incorporated into the simulations after check-ing the values of related criteria, and this greatly reducesthe computation time. Mixed-bed con"guration is ob-served to exhibit better performance when comparedwith dual-bed scheme in both reactor dimensions.Enhanced heat and mass transfer characteristics arebelieved to facilitate hydrogen production in mixed-bedscheme. Larger scale and bench scale operations possess


the same external transport characteristics except thatthe interfacial mass transfer resistance is considered inaddition to the external heat transfer resistance in simu-lating the Pt bed in industrial scale dual-bed operation.In both catalyst bed con"gurations, intraparticle di!u-sion limitations are signi"cant in industrial scale opera-tion. Prediction of a maximum hydrogen yield indicatesthe presence of an optimum set of operating conditions.

Notation

am

exterior surface area per unit mass of catalyst,m2/kg cat

cpj

heat capacity of j, kJ/kgKC

jbulk #uid concentration of j, kmol/m3

Csj

surface concentration of j, kmol/m3

Dp

particle diameter, mD

ee!ective di!usivity inside catalyst, m2/h

Djm

di!usivity of j into a mixture m, m2/hEA

activation energy, kJ/kmolFj

molar #ow rate of j, kmol/hFj~,i

amount of j consumed in reaction i, kmol/hFj`,i

amount of j remaining after reaction i, kmol/hFT

total molar #ow rate, kmol/hFTo

total molar #ow rate at reactor inlet, kmol/hhs

particle-to-#uid heat transfer coe$cient, kJ/m2h Kksj

particle-to-#uid mass transfer coe$cient of j, m/hki

speci"c reaction rate of reaction iK

jadsorption equilibrium constant of j, atm~1

K@i

equilibrium constant of reaction in reaction orderPj

partial pressure of j, atmPT

total pressure, atmPTo

total pressure at reactor inlet, atmPr Prandtl numberqH2O

Energy required to vaporize water in thefeed, kJ/kmol

!ri

rate of reaction i, kmol/kg cat hRe Reynolds numberR

ggas constant, kJ/kmolK

Sc Schmidt number¹ temperature, K¹

.!9maximum bed temperature, K

¹o

inlet temperature, K¹

ssurface temperature, K

= catalyst weight, kg catxCH4

methane conversionyj

yield of j

Greek letters

b0

parameter in the pressure drop equation*H

iheat of reaction i, kJ/kmol

/ void fraction of the catalyst bed

gi

e!ectiveness factor for reaction ijf

thermal conductivity of the bulk #uid, kJ/mhKkf

viscosity of the bulk #uid, kg/mhlij

stoichiometric coe$cient of j in reaction iob

catalyst bed density, kg/m3

of

density of the bulk #uid, kg/m3

oc

solid density of the catalyst, kg/m3

Subscripts

f bulk #uidi reaction numberj component indexo reactor inlets surface conditions¹ total quantity

Acknowledgements

Financial support was provided by Bog\ azic7 i Univer-sity through project DPT-97KI20640.

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