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CFD modeling of hydrogen production using steam reformingof methane in monolith reactors: Surface or volume-basereaction model?

Mohammad Irani*, Asghar Alizadehdakhel, Ali Nakhaei Pour, Nasibeh Hoseini,Morteza Adinehnia

Research Institute of Petroleum Industry (RIPI), West Blvd., Near Azadi Sports Complex, Tehran, Iran

a r t i c l e i n f o

Article history:

Received 2 August 2011

Received in revised form

4 September 2011

Accepted 8 September 2011

Available online 6 October 2011

Keyword:

Monolith reactor

CFD

Steam reforming

Surface-based rate

Volume-based rate

* Corresponding author. Tel.: þ98 21 4825240E-mail addresses: mohammadirani@yaho

0360-3199/$ e see front matter Copyright ªdoi:10.1016/j.ijhydene.2011.09.030

a b s t r a c t

In the present work, two approaches for reaction modeling in monolith reactors were taken

into account and compared to each other. In the first approach, the reactions are assumed

to take place on the wall surfaces, while penetration and reaction of chemical species

inside a thin layer near the walls are of essential concern in the second approach. Exper-

iments of Steam Methane Reforming (SMR) were carried out in a Bench-scale monolith

reactor. A single-channel was considered and two axi-symmetric CFD models were

developed for modeling. General kinetic models for SMR and WatereGas-Shift (WGS)

reaction rates based on LangmuireHinshelwood type were employed. Comparisons

between modeling results and experimental data showed that despite its ease of imple-

mentation, the first approach (surface reactions) exhibits better results both in generality

and accuracy. It was realized that uncertainties in obtaining the effective diffusion coef-

ficients in the volumetric approach may cause a variation up to 16% in the prediction of

reaction conversion.

Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

reserved.

1. Introduction Reforming of Methane (SMR) which converts methane and

Nowadays, environmental impacts of greenhouse gas pollut-

ants emitted from combustion of fossil fuels on one hand, and

legal regulations against production of air pollutants (Euro IV)

on the other hand, have constantly increased the necessity of

using clean fuels. Hydrogen is one of the cleanest fuels which

can replace fossil fuels. In addition there are a variety of appli-

cations for hydrogen in industry such as: fuel cells, green cars,

metal production and fabrication, Petroleum recovery and

refinery, chemical processing, power generation, etc. The afor-

ementioned applications made Hydrogen a strategic product.

The most famous process for hydrogen production is Steam

3; fax: þ98 21 44739716.o.com, Iranim@ripi.ir (M2011, Hydrogen Energy P

other hydrocarbons present in natural gas into hydrogen in

large industrial plants. Research is ongoing to develop small-

scale SMR technology to enable the development of distrib-

uted hydrogen production [1,2]. Modeling and optimizing is an

essential to attain this goal [3e7]. Monolith catalysts are widely

used inmany applications particularly for their high geometric

surface area, low pressure drop and good mechanical strength

anddurability [8]. Inaddition,utilizingmonolithic reactorshave

significant advantages over conventional reactors such as

reduced capital cost, smaller footprints and potentially easier

transportation [1,9e11]. These advantages can be particularly

valuablewhen considering the exploration of remote resources

. Irani).ublications, LLC. Published by Elsevier Ltd. All rights reserved.

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 en e r g y 3 6 ( 2 0 1 1 ) 1 5 6 0 2e1 5 6 1 0 15603

suchasoffshore reservoirs ofnatural gas [12] (likeSiri andmany

other fields in Iran).

Iran’sprovednatural gas reservesareabout1045.7� 10^12 cu

ft (29,610 km3) or about 15.8% ofworld’s total reserves, ofwhich

33%areasassociatedgasand67% is innonassociatedgasfields.

It has the world’s second largest reserves after Russia [13].

Therefore there is a huge potential for hydrogen production. In

order to realize this potential, Research Institute of Petroleum

Industry, National Iranian Oil Company (RIPI-NIOC) carried out

a wide range of experimental and modeling investigations in

this area. In the present study, hydrogenproduction in a bench-

scale SMR monolith reactor was investigated. Two different

approaches were presented in the literature for implementing

reaction rates in monolith reactor models, namely surface

approach and volumetric approach. In the first approach, the

diffusion into the thin catalytic layers (washcoat) inmodelingof

monolithic reactors is neglected and the reactions are assumed

to takeplaceat the surfaceof thewashcoat.Case studies for this

approach include steam methane reforming [14], steam

reforming of methanol [15e17], ethanol steam reforming [18]

and autothermal reforming of n-hexadecane [19]. Hartmann

et al. [20,21] studied hydrogen production by catalytic partial

oxidation of iso-octane at varying flow rate and fuel/oxygen

ratio. They proposed that the effect of diffusion into the wash-

coat on the reaction rate can be treated by adding an effective-

ness factor into the boundary conditions. However, in their

model, they assumed the effectiveness factor to be unity due to

the thinness of the washco at layer.

In the volumetric approach, diffusion of species in the

washcoat is taken into account. Oxidation reactions of mobile

exhaust gas in a catalytic monolith were studied by Zygour-

akis [22]. He proposed that the diffusional resistance of the

catalytic layer is significant in spite of its thinness and it is

important for both the hydrogen and hydrocarbon oxidation

reactions. Hayes and Kolaczkowski [23] studied catalytic

oxidation in monolith reactors. Their numerical and experi-

mental results showed that at typical monolith reactor oper-

ating temperatures, diffusion in the catalyst washcoat is likely

to be important and the effectiveness factors can become

quite low (less than 0.1), especially if the corners of the square

monolith contain most of the catalyst, which increases the

characteristic length in the Thiele modulus.

Massing et al. [24] studied the catalytic conversion of pro-

pene and demonstrated that diffusional limitations within the

washcoat limit the propene conversion. Stutz and Poulikakos

[25] investigated diffusion and reaction inside the washcoat of

a monolithic reformer. In their work, production of syngas by

partial oxidation of methane was modeled and the effect of

washcoat thickness on the process was investigated. Mlade-

nov et al. [26] compared 18 different numerical models for

a honeycomb-type automotive catalytic converter operated

under direct oxidation conditions. They summarized thatmass

transfer in such catalytic converters atmoderate temperatures

can be governed by relatively simple flow field models (plug-

flowwithmass-transfer coefficient and2dcylindricalboundary

layer equations) but requiremore sophisticatedmodels for the

descriptionofdiffusion in thewashcoat.These researchers also

commented that mass-transfer coefficients improve the accu-

racy of the plug-flow solution. However, they have to be used

with caution since they are based on empirical correlations.

In the present study, the surface and volumetric

approaches were used to model SMR in a single-channel

monolith reactor. The obtained results from each model

were compared with experimental data. In addition, a sensi-

tivity analysis was carried out to identify the effect of uncer-

tainties in determining porosity, dparticle, tortuosity and

washcoat thickness and consequently, effective diffusivities

of chemical species in the washcoat on the obtained results

from volumetric approach.

2. Process description

A schematic view of the experimental setup is shown in Fig. 1.

The reactor is fed with amixture of methane andwater vapor.

The flow rates of CH4, supplied from compressed gas cylinders

was adjusted by a calibrated mass flow controller (MFC-

BROOKS 5850�). The flux of liquid water to the vaporizer was

electronically controlled by a Bronkhorst Hi-Tec liquid-flow.

The N2 and H2 lines were utilized only for catalyst regenera-

tion. An illustration of the utilized reactor is displayed in Fig. 2.

It was designed and installed by RIPI-NIOC in 2010 [27]. The

washcoatedmonolithwithNi/Al2O3 catalysts were placed into

the quartz cylinder and sealed by glass wool. There was

a heating jacket around themonolithic reactor through which

the heat of reaction was provided (constant temperature at

reactor walls). The products were identified and quantified

using a gas chromatograph (Varian, GC3800, column type:

SUPELCO 13821). Gas products were cooled by a condenser

prior to entering GC. The GCwas connected to a computer and

the measured values were analyzed. The experiments were

carried out at different reactor temperatures. The inlet H2O/

CH4 molar ratio was fixed at 3 and the operating pressure was

atmospheric in all cases.

3. Mathematical model

In this study, uniform inlet conditions were ensured. There-

fore all channels of monolith behave essentially alike and one

representative channel to be analyzed will suffice. In order to

model the problem, five sets of equations should be solved;

continuity equation, momentum balance, energy and species

transport equations. Themass conservation,momentum, and

total enthalpy equations, may be expressed as follows,

respectively:

V:ð n/ rÞ ¼ 0 (1)

V:ðr n/ n/ Þ ¼ �VPþ V:½mðV n

/ þ V n/ TÞ� þ rgþ S (2)

V:ð n/ ðrHþ PÞÞ þ V:

Xni¼1

hiji

!¼ �V:ðqÞ þ SR (3)

V:ð n/ Ci � DiVCiÞ ¼ Ri r ¼ PMRT

m ¼ mðT;YÞ Y ¼ Y1;Y2;.;Yn

Where, r representsmixture density, n/

is velocity vector, m is

the mixture viscosity, H and hi are total enthalpy and enthalpy

of species, respectively and Ci stands for concentration of

Fig. 1 e Schematic view of the experimental setup.

i n t e rn a t i o n 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 6 ( 2 0 1 1 ) 1 5 6 0 2e1 5 6 1 015604

chemical species. P is the static pressure and SR is the heat of

reaction.

Fluent 6.2.16 CFD software was used and an axi-symmetric

model was employed for each of the two approaches. The

finite volume method was used to discretize the partial differ-

ential equations of the model. The SIMPLEC algorithm was

employed for pressureevelocity coupling [28]. An optimum

number of grids were used for each model regarding the solu-

tion accuracy andCPU time. The 2Dgeometriesweremeshed in

such a way that grid density in zones with the highest velocity

andspecies concentrationgradientswere increased. Formodel I

Fig. 2 e The employed

(surfaceapproach), thesizeofgridsdecreasesbymovingtoward

the walls in radial direction. In addition, the grids in reactor

entrancewere refined. Formodel II (volumetric approach)avery

fine mesh was applied near gas-phase/washcoat interface in

order to resolve the high species concentration gradients. A

view of each model including the employed boundary condi-

tions and surface meshes are pictured in Fig. 3. In all cases, the

numerical computations were considered to be converged

when the scaled residuals of the different variables were lower

than 10�4 for continuity andmomentumequations and 10�7 for

the other variables. Mass-flow-inlet and pressure-outlet

monolith reactor.

Fig. 3 e Boundary conditions and the employed meshes

inside the reactor.

Table 2 e Reaction rate parameters [29,30].

K1 ¼ 10266:76 � expð�26830=Tþ 30:114ÞK2 ¼ expð4400=T� 4:036Þk1 ¼ 9:49e16 � expð�240100=ð8:314 � TÞÞk2 ¼ 4:39e04 � expð�67130=ð8:314 � TÞÞk3 ¼ 2:29e16 � expð�243900=ð8:314 � TÞÞkCH4 ¼ 6:65e� 6 � expð38280=ð8:314 � TÞÞkCO ¼ 8:23e� 7 � expð70650=ð8:314 � TÞÞkH2O ¼ 1:77e5 � expð�88680=ð8:314 � TÞÞkH2 ¼ 8:23e� 22 � expð82900=ð8:314 � TÞÞDEN ¼ 1þ KCOPCO þ KH2PH2 þ KCH4PCH4 þ KH2OPH2O=PH2

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 en e r g y 3 6 ( 2 0 1 1 ) 1 5 6 0 2e1 5 6 1 0 15605

boundary conditions were used for reactor inlet and outlet,

respectively. Ideal gas law was employed for calculation of gas

density. No-slip condition was employed for the reactor walls.

The mathematical expressions used in the two presented

models in order to predict the chemical reactions inside the

reactor are discussed in the next following sections.

3.1. Approach (I): surface-based reaction rate

In this model, it was assumed that the reactions took place at

the reactor walls. This model ignores the effect of washcoat

thickness, porosity and diffusion in pores because of the small

thickness of washcoat. Therefore, the effect of mass transfer

limitation on reactant conversion in catalyst zone is neglec-

ted. The published chemical rates are expressed in kgmol/

(kgcat.s) [29,30]. If multiplied by loading of the catalyst,

Fwashcoat, it will come to surface based reaction rate (si) that is

implemented in the CFD code:

Si ¼ ri � Fwashcoat½ ¼ �kgmolkgcat:s

� kgcatm2

¼ kgmolm2:s

(4)

The value ofmeasured Fwashcoat was 0.04 kg/m2 .The surface

based catalytic reaction is used as source term in right hand of

species continuity equation (Eq. (4)). In this case, the monolith

walls considered as sources of products and sinks of reac-

tants. It implies that the gas-phase species mass flux which is

Table 1 e Reactions stoichiometries.

Reaction stoichiometry Num.

CH4 þH2O4COþ 3H2 1

COþH2O4CO2 þH2 2

CH4 þ 2H2O4CO2 þ 4H2 3

produced by catalytic reaction at gas-phase/washcoat inter-

face equals to the flux of species into the reactor from the

walls:

MiSi ¼ ��Jir þ ryiV�

i ¼ 1;.Ng (5)

3.2. Approach (II): volume-based reaction rate

In this model, the reactions were assumed to take place in

a porous zone of catalyst with 0.07 mm thickness. A source

term was added into the momentum equation of the porous

region:

S ¼ �0@X2

j¼1

Dijmvj þX2j¼1

Cij12rjvjvj

1A (6)

This source term cause a pressure drop proportional to the

fluid velocity in the particular direction. The momentum

source term is composed of two parts: a viscous loss term

(Darcy, the first term on the right-hand side of Eq. (2)) and an

inertial loss term (the second term on the right-hand side of

Eq. (6)). jvj is the magnitude of the velocity and D and C are

prescribed matrices [28]. The reactants diffuse into the reac-

tion (porous) zone and the products moves in the counter-

current radial direction. Diffusive mass flux in the porous

zone was calculated using the following equation:

Ji ¼ �rWi

WDM;eff;iVXi (7)

Here DM;eff;i is the equivalent Fick’s diffusion coefficient which

consists of two terms: DKnud;i and DM,i:

Fig. 4 e Distribution of H2, CH4, CO, H2O and CO2 along the

reactor (Model - I).

0.5

1

1.5

2

2.5

3

3.5

0 0.01 0.02 0.03

Position(m)

Den

sity

(kg/

m3)

00.020.040.060.080.10.120.140.160.18

Vel

city

(m/s

)

Fig. 5 e - Density and velocity profiles along with reactor

(Model - I).

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5

radial distance, mm

H2

mol

e fr

acti

on

x=0.1 mm x=0.6 mm x=1 mm

x=5 mm x=9 mm x=10 mm

Fig. 7 e H2 mole fraction at 6 locations (Model - I).

i n t e rn a t i o n 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 6 ( 2 0 1 1 ) 1 5 6 0 2e1 5 6 1 015606

1DM;eff;i

¼ s3

�1

DM;iþ 1Dkdud;i

�(8)

Dkdud;i ¼ dpore

3

ffiffiffiffiffiffiffiffiffi8RTpMi

s(9)

dpore ¼ dparticle

�ð1� 3Þ�1=3�1

�(10)

s ¼ 3=�1� ð1� 3Þ2=3

�(11)

DM,i andDKnud,i aremixture diffusion and Knudsen diffusion

coefficients. Also R is the universal gas constant, 3is porosity,

T is the gas temperature and s is tortuosity that represents the

deviation of the washcoat pore length from the ideal cylinder

[31,32].

Despite of case 1, the catalytic reaction rate does not

appear as wall boundary condition but it is considered as

a volumetric source term in right hand side of species

conservation equation in reaction zone (catalyst). In order to

describe catalytic reaction rate in kmol/m3.s, the surface

exposed to reaction per unit volume of washcoat should be

calculated:

Fig. 6 e Contours of H2 mo

Pwashcoat ¼ surfaceexposed to reactionwashcoatvolume

¼ 2prinh

p�h��r2out� r2in� (12)

Here, rin is inner diameter and rout, the outer diameter of

washcoat and h is the monolith’s height. By multiplying

Pwashcoat by Si, the reaction rate based on catalyst volume Vi is

obtained:

Vi ¼ Si � Pwashcoat½ ¼ �kmolm2:s

�m2

m3¼ kmol

m3:s(13)

This term is used as reaction source in Eq. (4) in approach II.

3.3. The kinetic models describing the catalytic reactions

The reaction rates of SMR on Ni catalyst reported by Xu and

Froment [29] are adopted in this study. The species which

exist as reactant and products in SMR consist of: CO, H2, CO,

le fraction (Model - I).

Fig. 8 e Distribution of H2, CH4, CO, H2O and CO2 along the

reactor (Model - II).

65

70

75

80

85

90

95

100

923 973 1023 1073 1123

Temperature(K)

%C

H4

C

onve

rsio

n

Experiment Model - I Model - II

Fig. 10 e Comparison of CH4 conversions between Model-1,

Model-2 and experiments.

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 en e r g y 3 6 ( 2 0 1 1 ) 1 5 6 0 2e1 5 6 1 0 15607

CO2, H2O and CH4. The dominant SMR catalytic chemical

reactions [30] are listed in Table 1.

The corresponding rate equations for SMR reactions

Riðmol=hr:grcatÞ are expressed as:

R1 ¼

k1

p2:5H2

pCH4

pH2O � p3H2pCO

K1

!

ðDENÞ2 (14)

R2 ¼k2

pH2

�pCOpH2O � pH2

pCO2

K2

�ðDENÞ2 (15)

R3 ¼

k3

p2:5H2

pCH4

p2H2O

� p3H2pCO2

K1K2

!

ðDENÞ2 (16)

Reaction rates for the formation of CO and CO2 and

consumption of CH4 are as follows:

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6

radial distance, mm

H2

mol

efr

acti

on

x=0.1 mm x= 1 mm x=10 mm

x=25 mm x=30 mm

Fig. 9 e H2 mole fraction at 5 locations (Model - II).

RCO ¼ R1 � R2

RCO2¼ R2 þ R3

RCH4¼ R1 þ R3

(17)

The kinetic parameters of Eq. 14e16 are given in Table 2

[29,30].

4. Results and discussion

The predicted distribution of the products and reactants along

the reactor axis using approach (I) is illustrated in Fig. 4. The

figure shows exponential changes in the mass fractions of

reactants and products along the reactor axis. In addition,

almost 95% of the changes occur at a distance of 9 mm from

the entrance. The predicted velocity and density fields are

shown in Fig. 5. It is observed that lower density of the prod-

ucts, especially hydrogen, (in comparison to the reactants)

causes the fluid density to decline along the reactor. Conse-

quently, the fluid velocity increases along the reactor so that

the mass continuity is conserved.

Hydrogen is themain product of SMR process. The contour

plot of hydrogen mole fraction inside the reactor is given in

Fig. 6. Higher concentrations of hydrogen are observed near

the reactor walls where it is produced. However, the radial

gradient of hydrogen concentration descends along the

reactor due to convectional and diffusional mass transfer and

0.54

0.57

0.6

0.63

0.66

0.69

900 950 1000 1050 1100

Temperature K

Hyd

roge

n Y

ield

model (I) model (II) exp

Fig. 11 e Comparison of H2 yield between Model-I, Model-II

and experiments.

Table 3 e Comparisons between the two models and experimental results.

Model 1 Model 2 Experiment Model 1 error (%) Model 2 error (%)

H2 selectivity (T ¼ 700 �C)a 71.26 51.83 73.78 3.4155598 29.7506099

H2 selectivity (T ¼ 750 �C) 75.65 55.37 77.81 2.7759928 28.8394808

H2 selectivity (T ¼ 800 �C) 78.1 58.36 79.11 1.2767033 26.229301

a Selectivity H2 ¼ ðFH2 ;outlet=ðFH2 ;outlet þ FH2O;outletÞ � 100Þ

i n t e rn a t i o n 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 6 ( 2 0 1 1 ) 1 5 6 0 2e1 5 6 1 015608

lower rate of hydrogen production in the frontier regions. The

profile of hydrogen concentration becomes uniform at

a distance of 9 mm from the entrance. This observation is

expressed more precisely in Fig. 7 wherein the radial profiles

of hydrogen mole fraction at six axial locations along the

reactor are plotted. Figs. 6 and 7 reveal that the major varia-

tions in concentrations of reactants and products occur in the

first 9 mm of the reactor. Therefore, the effective length of the

monolithic reactor is about 9mm. It’s noteworthy that usually

longer length of reactors is employed in order to extend the

overhaul time of the reactor. In other words, when catalysts in

the first part of reactor are deactivated, the catalyst in the

remaining length will convert the reactants to products.

The predicted distribution of the products and reactants

along the reactor using approach (II) is given in Fig. 8. The

figure shows that the steep concentration gradient in the

reactor entrance predicted frommodel I (Fig. 4) is smoothed in

the currentmodel. It can be explained by the controlling effect

of diffusion into/from the porous layer that is considered in

model II. This figure shows that there are considerable chan-

ges in the concentrations at the reactor output. Therefore

according to the predictions of this model, the effective length

of the reactor is longer than 3 cm. Radial distribution of

hydrogen plotted in Fig. 9 confirms this point by showing that

there is still a significant difference between the concentra-

tions in the lengths of 25 and 30 mm.

The product gas species from experiments were measured

by GC (Fig. 1). A comparison between experimental and pre-

dicted values of methane conversion at different reactor

temperatures is given in Fig. 10. This figure shows that the

predicted conversions of approach (I) at all the examined

temperatures are more accurate than that of approach (II).

It can be explained by the fact that due to low diffusion

coefficient in the washcoat, the species can only diffuse to

a limited thickness of it. Therefore, the available volume of the

porous zone for chemical reactions is smaller than the total

volume ofwashcoat. Thus the conversions of the reactions are

underestimated in this model. On the other hand, by consid-

ering the fact that the residence time of gas species inside the

Table 4 e Effective diffusion coefficients of species.

Species Effective diffusion coefficient (m2/s)

Base case Case2 Case3

H2 5.9113E-08 5.9113E-7 5.9113E-09

CH4 2.3857E-08 2.3857E-7 2.3857E-09

CO 1.7919E-08 1.7919E-7 1.7919E-09

CO2 1.5936E-08 1.5936E-7 1.5936E-09

H2O 2.3857E-08 2.3857E-7 2.3857E-09

reactor is in the order of milliseconds [10], it can be realized

that the species don’t have enough opportunity to diffuse into

the porous washcoat. There is no such diffusion limitation for

approach (I) and thismodel predicts higher conversionswhich

are in better agreements with experimental results.

The comparison of predicted and experimental values of

hydrogen yield (Fig. 11) shows similar results and the predic-

tions of approach (I) are better than those of approach (II) for

all examined reactor temperatures. Hydrogen yield is defined

as:

YieldH2¼ �FH2 ;outlet=

�2� FCH4 ;inlet þ FH2O;inlet

�� 100�

(18)

Where, FH2, outlet at outlet, FCH4, inlet and FH2O, inlet are molar

flow of methane and water at inlet. The experimental and

predicted values of hydrogen selectivity are compared in

Table 3. The values in this table show that the error values for

approach (I) are less than 5%, while for approach (II) it is more

than 30%. Above discussion testifies that predictions of

approach (I) is more accurate than those of approach (II).

Another weakness of approach (II) is the uncertainty in the

value of effective diffusion coefficient of the gas species inside

the washcoat. The empirical correlations for calculating

effective diffusion coefficient are particularly functions of

porosity of washcoat, dparticle and washcoat thickness. Gener-

ally, a combination of scanning electron microscopy (SEM),

energy-dispersive spectroscopy (EDS) X-ray mapping, light

microscopy, and digital image processing are used to obtain

these parameters [33,34]. However, the reported Deff may vary

up to one order of magnitude [31,35]. In the present work,

a sensitivity analysis was performed to determine how this

uncertainty in the value of the effective diffusion coefficient

can affect the predictions of approach (II). Eq. (11) was used for

estimating the effective diffusion coefficient [23,36]. The

porosity of the washcoat layer, a, was measured to be approx-

imately0.4 [32]. Thepore sizewascalculatedusing the theoryof

granular media from correlation 9 [33]. The particle size was

assumed to be dparticle ¼ 50 nm [37] which will result

dpore ¼ 10 nm. Also the tortuosity was calculated using correla-

tion 10. Using the mentioned parameters and correlation 11,

the effective diffusivity of all species were calculated and

Table 5 e CH4 conversion of three studied cases forsensitivity analysis.

Case % CH4 conversion

Base case 87.3

Case 2 92.84

Case3 76.4

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 en e r g y 3 6 ( 2 0 1 1 ) 1 5 6 0 2e1 5 6 1 0 15609

mentioned as the base case in Table 4. For cases 2 and 3, the

diffusion coefficients were assumed to be ten times and one-

tenth of the base corresponding effective diffusion coeffi-

cients, respectively.

Simulations were done using approach (II) for the same

conditions and different values of effective diffusion coeffi-

cients. The results of these three cases are compared in Table

5. Results of this table reveal that the uncertainty in deter-

mining effective diffusion coefficients might cause a variation

of about 16% in the prediction of conversion.

5. Conclusion

The current study presents two approaches for numerical

modeling and implementation of reaction rates in simulation

of heat andmass transfer inmonolithic reactors. The chemical

conversion on the Ni-catalyst is modeled using general kinetic

models for SMR and WatereGas-Shift (WGS) reaction rates

based on LangmuireHinshelwood type. Monolithic reactor

was simulated using the two aforementioned approaches

under steady-state condition. The results of two approaches

were compared to corresponding experimental data and

a comprehensive evaluation was carried out. The results

showed that the predictions of surface-based approach are

more accurate than those of volume-based approach. The

volume-based model underestimates the conversion of reac-

tions. Small values of effective diffusion coefficient in porous

washcoat layer and low residence timeare themain reasons of

discrepancy betweenvolume-based approach and experiment

results. Also there is uncertainty in obtaining the effective

diffusion coefficients which affects the prediction of reaction

conversion. A sensitivity analysiswas performed to determine

theeffect of thisuncertainty onconversion. Itwas realized that

it brings about a variation up to 16% in the prediction of reac-

tion conversion. In total, despite of its ease of implementation,

the first approach (surface reactions) gives better results both

in generality and accuracy.

r e f e r e n c e s

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Glossary

P: Pressure, barg: gravity acceleration, m s-2

v: velocity, m s-1

H: Total enthalpy, kJ kg-1 s-1

h: Enthalpy of species, kJ kg-1 s-1

j: Mass flux, kg m-2 s-1

q: Heat flux, kJ m-2 s-1

S: Momentum source term, kg m-2 s-2

Dij: Diffusivity coefficient m-2 s-1

Di,eff: Effective diffusivity coefficient m�2 s�1

Ci: Concentration, kmol m3

Z: Compressibility FactorT: Temperature, Kf: fugacity, barki: Kinetic Constant, mol s�1 gr�1 bar�1

Ei: Activation Energy, kJ kmol�1

Fi: Molar flow of species i, mol s�1

dpore: Pore diameter, mR: Global Gas Factor, kJ kmol�1 K�1

Mi: Molecular Weight, kg kmol�1

V: Volume, m3

xi: mass fractionD: Total Diffusivity Coefficient, m2 s�1

km: Thermal Conductivity, kJ m�1 K�1

Greek Lettersr: Density, kg m�3

m: Viscosity, kg m�1 s�1

4i: Fugacity coefficients: Tortuosity3: Porosity

Subscripti: species numberj: second species numberm: mixture