simulaciones numericas detalladas de reactores de lechofijo catalitico

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Detailed numerical simulations of catalytic xed-bed reactors:Heterogeneous dry reforming of methane

Gregor D. Wehinger n, Thomas Eppinger, Matthias Kraume

Chemical and Process Engineering, Technische Universitt Berlin, Fraunhoferstr. 33-36, 10587 Berlin, Germany

H I G H L I G H T S

Fully 3D CFD modeling of randomly packed catalytic xed-bed reactor.

CFD model combines complex geometry with detailed kinetics of DRM. Meshing recommendations are given due to grid sensitivity studies. Determination of regions with catalyst deactivation by surface-adsorbed carbon.

a r t i c l e i n f o

Article history:

Received 23 May 2014Received in revised form2 September 2014Accepted 4 September 2014Available online 7 October 2014

Keywords:

CFDCatalysisDry reforming of methaneFixed-bed reactorsModeling

a b s t r a c t

Highly endothermic (or exothermic) heterogeneous catalytic reactions are performed commonly inxed-bed reactors with small tube-to-particle-diameter ratios N both in industrial and lab-scaleapplications. For these reactor congurations conventional plug ow models and pseudo-homogeneous kinetic models fail. An adequate modeling can be carried out with full computationaluid dynamics (CFD) in combination with detailed reaction mechanisms. In this study, a full three-dimensional xed-bed reactor for the catalytic dry reforming of methane (DRM) over rhodium wassimulated with a detailed reaction mechanism. The bed consists of 113 spherical solid particles in whichthermal conductivity was considered. Two different Reynolds numbers were investigated, i.e., 35 and

700. The simulated DRM xed-bed reactor demonstrates the strong interaction between chemicalkinetics and transport of momentum, heat and mass. The observed velocity, temperature and specieselds are characterized by their three-dimensional behavior and interactions highlighting theircomplexity and discrepancy from lumped model predictions. In addition, the reaction mechanismdetermines regions with catalyst deactivation by carbon deposition. This study demonstrates theadvantages of modeling heterogeneous catalytic xed-bed reactors with small N fully in three-dimensional in combination with detailed reaction mechanisms. Finally, this modeling approach reducesdependencies on empiricism for the calculation of multiscale reaction devices.

&2014 Elsevier Ltd. All rights reserved.

1. Introduction

The atmospheric concentration of greenhouse gases, i.e.,carbon dioxide (CO2), nitrous oxide (NO), methane (CH4) andchlorouorocarbons (CFCs), has increased dramatically duringthe last decades (Hartmann et al., 2013). These anthropogenicemissions have risen a global concern over the current technolo-gical practices. Hence, the eld of interest involves CH4 and CO2disposal, utilization and removal, as well as the effect of thesegases in the atmosphere (Mikkelsen et al., 2010; Centi andPerathoner, 2009; Hunt et al., 2010; Papadopoulou et al., 2012;

Balat and z, 2007). However, the general engineering interest liesin processes in which CH4and CO2react to synthesis gas or syngas,i.e., COH2. On one hand syngas can be used to produce liquidfuels via the FischerTropsch reaction; a review given in Dry(2002). On the other hand syngas can be utilized in chemicalenergy transmission systems (Wang et al., 1996).

Dry reforming of methane (DRM) is such a process in whichCH4and CO2react to syngas:

CH4CO22H22CO; H 260 kJ=mol 1

This highly endothermic process is performed at temperatures of7001000 1C. One of the largest obstacles for the industrial use ofDRM is coke formation, which quickly leads to a deactivation of thecatalyst (Chen et al., 2001; Ginsburg et al., 2005; Guo et al., 2007).

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/ces

Chemical Engineering Science

http://dx.doi.org/10.1016/j.ces.2014.09.0070009-2509/&2014 Elsevier Ltd. All rights reserved.

n Corresponding author. Tel.: 49 30 314 28733; fax: 49 30 314 21134.E-mail address:[email protected](G.D. Wehinger).

Chemical Engineering Science 122 (2015) 197209
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This prospective process has to be carried out with an appropriatecatalyst. In the last decades Nickel-based catalysts and noble metal-supported catalysts (Rh, Ru, Pd, Pt, Ir) have shown encouragingperformances regarding conversion and selectivity (Torniainen et al.,1994; Wang et al., 1996; Guo et al., 2004). Rhodium for example ischaracterized by its low afnity for carbon formation and its highactivity (Rostrup-Nielsen and Hansen, 1993; Bradford and Vannice,1999).

Typical reactor types for endothermic (or exothermic) reactionsare xed beds, foams, multi-channel reactors or uidized-bedreactors. Still today, the most common way to carry out a hetero-geneous catalytic reaction is a xed-bed reactor. Randomly distrib-uted catalytic particles are the simplest type of such a reactor,whereas particle diameters range from 2 to 10 mm (Eigenberger,2008). For the DRM the heat transfer inside the reactor is one of themajor engineering issues. Thus, small reactor tubes are desirable.Additionally, high gas velocities and reasonable pressure dropsconstrain the particle diameter to be quite large. Hence, xed bedswith a small tube-to-particle-diameter ratio 4oNo15are prefer-able. In some lab-scale applications evenNo4 were carried out, e.g.,Leva et al. (1951),Reichelt (1972),Vortmeyer and Winter (1984), andDixon (1997). In all cases, randomly packed beds are characterized byinhomogeneous structures. Especially for small Nthe inhomogene-ities become dominant resulting in signicant wall effects, local backows and large axial as well as radial gradients. Consequently,conventional descriptions, based on plug ow and pseudo-homogeneous kinetics, are questionable for these xed-bed cong-urations (Bey and Eigenberger, 1997; Dixon, 1997; Bauer and Adler,2003; Freund et al., 2005; Grf et al., 2014). The strong interplaybetween velocity, temperature and species distribution makes thexed-bed reactor a very interesting and likewise challenging devicefor chemical engineers. It includes several time and length scales. Themultiscale modeling, or rst-principles approach (Dudukovic, 2009),pursues to describe entirely the system by theory of the actualphenomena, i.e., elementary reaction steps at the catalyst surface anda detailed characterization of the uid ow. As a consequence, anadequate description of catalytic xed-beds should include the

rigorous modeling with full computational uid dynamics (CFD) inthe interstitial regions as well as in the solid in combination withdetailed chemical reaction models (also called the micro-kinetics).

In recent years, several authors have simulated spatiallyresolved xed-bed reactors accounting for radial, axial and cir-cumferential proles (Dixon and Nijemeisland, 2001; Guardo et al.,2005; Ookawara et al., 2007; Bai et al., 2009; Eppinger et al., 2011;Behnam et al., 2013). However, only few have coupled the uiddynamics of xed-beds with catalytic reactions (Kuroki et al.,2009; Taskin et al., 2010; Dixon et al., 2012). That means thealready complex equation system will be extended by speciesconservation equations. Several authors used pseudo-homo-geneous kinetics in combination with detailed uid dynamics,due to the small number of reaction equations. However, these

kinetics are often limited to a certain range of process parametersand could therefore not be applied to otherow regimes or reactortypes (Salciccioli et al., 2011). Especially the species developmentinside xed-bed reactors are often insufcient reproduced withsuch kinetics in contrast to the exit concentrations, which wasrecently demonstrated byKorup et al. (2011). AsWehinger et al.(2014) concluded spatially resolved uid dynamics must becombined with reliable kinetics, i.e., detailed reaction mechan-isms. Several detailed methane reforming kinetics over rhodiumwere published validated over an operating range relevant toindustrial applications and claimed to be thermodynamicallyconsistent (Hickman and Schmidt, 1993; Mhadeshwar andVlachos, 2005; Maestri et al., 2008, 2009; McGuire et al., 2011;Kahle et al., 2013). Finally, the combination of a rst-principle

approach at different scales, i.e., detailed reaction mechanism at the

catalyst scale and full NavierStokes equations at the reactor scale,helps to obtain a fundamental understanding of chemical reactors.

In this study, we investigated spatially resolved heterogeneouscatalysis of the dry reforming of methane over rhodium in a xed-bed reactor in terms of combining full CFD simulations with adetailed reaction mechanism from McGuire et al. (2011). Acatalytic xed-bed reactor with spherical solid particles and asmall tube-to-particle-diameter ratio (N4) was numerically

simulated. The aim of the study was rstly to obtain a betterunderstanding of the strong interactions between catalytic reac-tions and the surroundingow in xed-bed reactors. Secondly, weinvestigated the feasibility to model catalytic xed-bed reactors inan adequate multiscale way.

2. Simulating heterogeneousxed-bed reactors

2.1. Modeling chemically reactiveow

2.1.1. Governing equations

For the simulations in this study, full three-dimensional gov-erning equations were applied. The conservation of total mass,momentum inx-,y-,z-directions, mass of species and energy leadsto the solution for velocity, pressure, temperature and speciesconcentration in the calculation domain. A laminar problem withEinstein convention can be written as follows.

Conservation of mass:

tvi

xi 0 2

where is the mass density, t is the time, xi are the Cartesiancoordinates and viare the velocity components.

Conservation of momentum:

vit

vivj

xjp

xiijxj

gi 3

The stress tensorijis written as follows:

ij vixj

vjxi

23

ijvkxk

4

where is the mixture viscosity and ij is the Kronecker delta,which is unity for i j, else zero.

Conservation of species i:

Yi

t

vjYi

xjji;j

xj 0 for i 1;; Ng 5

with mass fraction Yi mi=mof species i and total mass m. Ngisthe number of gas phase species. The components ji;j of thediffusion mass ux are described by the mixture-average formula-tion:

ji;j YiXiD

Mi

Xixj

DT

iT

T

xj 6

where DiM is the effective diffusivity between species i and the

remaining mixture.Xirepresents the molar fraction of species i. Miis the molecular weight of species i and Tis the temperature. Thebinary diffusion coefcients Di are obtained through polynomialts. The molar fractionXican be written as

Xi 1

Ng

j 1YjMj

YiMi

7

Conservation of energy in terms of specic enthalpy h is asfollows:

h

t

vjh

xj

jq;j

xj

p

t

vjp

xj

jkvj

xk

Sh 8

G.D. Wehinger et al. / Chemical Engineering Science 122 (2015) 197209198


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whereShis the heat source. Diffusive heat transport jq;j is given bythe following:

jq;j T

xj

Ng

i 1hiji;j 9

with thermal conductivity of the mixture and mixture specicenthalpy h

h

Ng

i 1YihiT 10

as a function of temperature h i hiT.Ideal gas was assumed connecting pressure, temperature and

density to close the governing equations:

p RT

Ngi 1XiMi

11

Additionally, NASA polynomial functions were applied to deriveheat capacities cp;i.

2.1.2. Modeling turbulence

With the help of the particle Reynolds number Rep the ow inxed-bed reactors can be characterized as follows:

Repvindp

12

For Rep4300 the ow behaves highly unsteady, chaotic andqualitatively resembling turbulent, cf. Zikowska and Zikowski(1988). Consequently, such ow congurations were modeledwith the Reynolds-averaged turbulence approximation (RANS).The solution variables are split into mean components vi anductuating components v0i . They are then integrated over aninterval of time much larger than the small-scale uctuations.The turbulence momentum equation can then be written as

v i t

xjvivjv

0iv

0j

p

xiijxj

gi 13

The Reynolds stresses v0

iv0

j

have to be put in terms of theaveraged ow quantities to close the system of equations. In ourcase we used the realizable k model, developed byShih et al.(1995), in combination with a two-layer all-y wall treatmentdriven by shear (Wolfshtein, 1969), cf. manual of STAR-CCM(CD-adapco, 2014).

2.1.3. CFD and heterogeneous chemical reactions

The chemical reactions at the catalytic surface are coupled viaboundary conditions with the species distribution equation (5).Under steady-state conditions gas-phase molecules of speciesi, which are produced/consumed at the catalytic surface bydesorption/adsorption, have to diffuse from/to the catalyst(Deutschmann, 2008):

n! ji!

Rheti 14

with the outward-pointing unit vector normal to the surface n!

and the diffusion mass ux ji!

as in Eq. (6). The heterogeneousreaction term Ri

het is given by

Rheti Fcat=geoMi _si 15

whereMiis the molar weight, _siis the molar net production rate ofgas-phase species i and Fcat=geo is the ratio of catalytic active areaAcatalyticto geometric area Ageometric

Fcat=geoAcatalytic=Ageometric 16

In all the simulations the mean-eld approximation wasapplied to model the surface reactions. The assumption is that

adsorbates are randomly distributed on the surface, which is

interpreted as being uniform, cf. Deutschmann (2008) and Keeet al. (2003). The molar net production _si can be written in thefollowing form:

_si Ks

k 1

ikkfk Ng Ns

j 1c0

jk

j 17

where Ks is the number of surface reactions, cj are the speciesconcentrations, in mol/m2 for the adsorbed speciesNsand in mol/

m3

for the gas phase species Ng, respectively. In addition, thesurface coverage takes into account the surface site density (mol/m2), representing the maximum number of species that canadsorb on a unit surface area. Furthermore, a coordinate numberiexpresses the number of surface sites which are covered by thisspecies:

i cii 1

18

the time-dependent variation ofi can be written as

it

_sii

19

Under steady-state conditions the left side of Eq. (19)will be zero.The reaction rate expression can be modied by the concentration,or coverage, of some surface species:

kfk AkTk exp

EakRT

Ns

i 1iki exp

ikiRT

20

with two extra coverage parameters,ikand ik. The term includ-ing ik indicates the modication of the surface rate expressionproportional to any arbitrary power of a surface species concen-tration.ikrepresents a modication of the activation energy as afunction of coverage.

The occurrence of adsorption reactions results in a modicationof the conventional rate coefcient by referencing sticking coef-cientsSi

kads

fk

S0i

ffiffiffiffiffiffiffiffiffiffiffiffiRT

2Mi

s 21

with Si0 as the initial (uncovered surface) sticking coefcient and

Nsj 10

jk is the sum of all the surface reactant's stoichiometriccoefcients, cf.Kee et al. (2003)and Deutschmann (2008).

Additionally, the operator splitting algorithm was implemen-ted. The algorithm decouples the general species transport equa-tion, due to the different time scales of the ow eld and thechemical reactions. The time integration of the chemical state(species mass fractions and enthalpy) was performed in two steps.For the rst step, only the species source terms were taken intoaccount for the integration of a time interval. For the second, theoweld was integrated over a time interval without the chemicalsource terms, cf.Ren and Pope (2008).

All simulations were realized with the simulation softwareSTAR-CCM version 9.02.005 byCD-adapco (2014). The equation

system for the surface species was solved by DARS, an add-insolver for chemical reactions for STAR-CCM . The computationaltime was high due to the mesh size and chemical reaction steps.The laminar case with a 3.2 million cell mesh (M3) ran for 35,000iterations which yielded in a total CPU time of 1:7 107 s or196 days on a Intel Xeon 3.07 GHz CPU. The turbulent case with a3.6 million cell mesh (M5) ran for 9000 iterations, i.e., 9 :3 106 sor 107 days. However, the simulations were performed on severalparallel CPUs, which reduced the computational time signicantly.

2.2. Detailed reaction mechanism

As already mentioned detailed uid dynamics call for detailedreaction mechanisms. Still today, in many CFD simulations Lang-

muir

Hinshelwood

Hougon

Watson (LHHW) models are applied.

G.D. Wehinger et al. / Chemical Engineering Science 122 (2015) 197209 199


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However, the fundamental mechanism described by LHHW mod-els can be elusive and the physical signicance of parameters canbe seriously questionable, cf.Salciccioli et al. (2011)andWehingeret al. (2014). Taking the strong interactions between the differenttransport quantities into account an erroneous kinetics willdirectly lead to misleading predictions. Therefore, it is recom-mended only to use reliable kinetics for detailed uid dynamicssimulations.

In this study a detailed reaction mechanism, seeTable 1, was

implemented published byMcGuire et al. (2011)for the DRM over

rhodium supported strontium-substituted hexaaluminate. Thiskinetic model describes elementary-like processes occurring atthe catalytic surface with the mean-eld approximation distin-guishing between adsorption, surface reaction and desorption. Themechanism was originally developed for the catalytic partialoxidation of iso-octane on rhodium published byHartmann et al.(2010). Several kinetic parameters were then modied to describethe DRM adequately. The surface reaction mechanism consists

of 42 irreversible elementary reactions including 12 surface-adsorbed species and 6 gas-phase species, as well as reactionsinvolving HCOn. In Table 1the asterisk represents a surface site orsurface adsorbed species. The detailed DRM mechanism waspreviously validated by a three-dimensional calculation of theexperiments which were carried out in a stagnation ow reactor,cf.Wehinger et al. (2014).

2.3. Generation of random packings and meshing

The scheme of the spherical xed-bed reactor is shown inFig. 1. Inaddition to the xed bed an upstream and downstream region wasgenerated to minimize the inuence of the boundary conditions. Thegeometric quantities of the reactor are the following: catalytic bedheight H40 mm, reactor diameter D16.2 mm, sphere diameter dP4.09 mm, which leads to a tube-to-particle-diameter ratioN D=dP 3:96. The reactor contains 113 spheres, which were packedrandomly. This leads to a specic particle area a AP;total=VReactor of784 m2/m3. The geometric generation of the randomly packed bed wascarried out with a discrete element method (DEM) and is described indetail elsewhere (Eppinger et al., 2011; Zobel et al., 2012). In the DEMsimulation the tube was lled up with particles. When all particles weresettled, the geometric information of the particle centroids wasextracted. This information was then used to build up the desiredpacked-bed.

A polyhedral grid was chosen to mesh the solid particles and thegas phase. Additionally, prism layers were introduced at the interfacebetweenuid and solid phases. In the meshing process the particleswere attened locally at particlewall contact-points and particle

particle contact-points to avoid bad cell qualities, see Fig. 2. Besidesattening the spheres at contact points, several other methods exist,

Table 1

Detailed surface mechanism for the dry reforming of methane, from McGuire et al.(2011).

No. Reaction A (a) E(kJ/mol)

1 H2 n n - Hn Hn 1:0 10 2b 0.0

2 O2 n n- On On 1:0 10 2b 0.0

3 CH4 n- CH4

n

8:0 10 3b 0.0

4 H2O n- H2O

n

1:0 10

3b 0.0

5 CO2 n- CO2

n

4:8 10 2b 0.0

6 CO n- COn 5:0 10 1b 0.0

7 Hn Hn- H2 n n 3:0 1021 77.8

8 On On- O2 n n 1:3 1022 355.2

n

O 280c

9 H2On- H2O

n

3:0 1013 45.0

10 COn- CO n 3:5 1013 133.4

n

CO 15c

11 CO2n- CO2

n

4:1 1011 18.0

12 CH4n- CH4

n

1:9 1014 25.1

13 Hn On- OHn n 5:0 1022 83.7

14 OHn n- Hn On 3:0 1020 37.7

15 Hn OHn- H2On n 3:0 1020 33.5

16 H2On n- Hn OHn 5:0 1022 106.4

17 OHn

OHn-

H2On

On

3:0 1021

100.818 H2O

n On- OHn OHn 3:0 1021 171.8

19 Cn O - COn n 5:2 1023 97.9

20 COn n- Cn On 2:5 1021 169.0

21 COn On- CO2n n 5:5 1018 121.6

22 CO2n n- COn On 3:0 1021 171.8

23 COn Hn- HCOn n 5:0 1019 108.9

24 HCOn n- COn Hn 3:7 1021 0.0

n

CO 50c

25 HCOn n- CHn On 3:7 1024 59.5

26 CHn On- HCOn n 3:7 1021 167.5

27 CH4n n- CH3

n Hn 3:7 1021 61.0

28 CH3n Hn- CH4

n n 3:7 1021 51.0

29 CH3n n- CH2

n Hn 3:7 1024 103.0

30 CH2n Hn- CH3

n n 3:7 1023 44.1

31 CH2n n- CHn Hn 3:7 1024 100.032 CHn Hn- CH2

n n 3:7 1021 68.0

33 CHn n- Cn Hn 3:7 1021 21.0

34 Cn Hn- CHn n 3:7 1021 172.8

35 CH4n On- CH3

n OHn 1:7 1024 80.34

36 CH3n OHn- CH4

n On 3:7 1021 24.27

37 CH3n On- CH2

n OHn 3:7 1024 120.31

38 CH2n OHn- CH3

n On 3:7 1021 15.06

39 CH2n On- CHn OHn 3:7 1024 114.5

40 CHn OHn- CH2n On 3:7 1021 36.82

41 CHn On- Cn OHn 3:7 1021 30.13

42 Cn OHn- CHn On 3:7 1021 136.0

Surface site density 2:72 10 9 mol/cm2.a Arrhenius parameters for rate constants. Units: pre-exponential factor A for

unimolecular reactions (s1

), for bimolecular reactions (cm2

mol1

s1

).b Initial sticking coefcientSi

0 ().c Coverage dependent activation energy in Eq. (20). For more information see

e.g.,Kee et al. (2003).

Spheres

dp= 4.09 mm

Flow direction

Inlet

Outlet

Upstream

hu= 1/4 H

Fixed-bed

H= 40 mm

Downstream

hd= 1/2 H

Reactor diameter

D= 16.2 mm

Fig. 1. Scheme of the spherical xed-bed reactor.



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as discussed in Dixon et al. (2013). In all the simulations theboundary layer thickness BL was resolved with two or three prismlayers. BL was approximated with a correlation for the stagnationpoint for spheres (Dhole et al., 2006):

BLdp

1:13 Re 0:5p 22

In addition, as recommended byDixon et al. (2013), the dimension-less cellwall distance y was kept to approx. 0.52.0. For theinvestigated cases the velocity boundary layer (BL) thickness was

smaller than the temperature BL and the concentration BL. ThePrandtl number Pr was of the same order of magnitude as theSchmidt numberSc. The inuence of the mesh size was investigatedby means of mesh renement, see Table 2. The base size is acharacteristic dimension of the mesh model, to which all other meshdimensions refer. It can be interpreted as a scaling factor of the meshresulting in the total number of cells (CD-adapco, 2014).

2.4. Boundary conditions

The conditions at the inlet were the following: feed gascomposition xin;CO2=xin;CH4=xin;N2 0:20=0:10=0:70, inlet velocityvin;1 0:886 m=s or vin;2 17:72 m=s. The corresponding particleReynolds numbers were Rep 35; 700 calculated with a mean

dynamic viscosity gas;973 K 9:504 10 5

m2=s and the particle

diameter dp 4:09 mm. On the catalytic surface the detailedmechanism of the DRM was implemented, see Table 1. Likewiseas in the experiments by McGuire et al. (2011) processes in thepores were treated as instantaneous diffusion resulting in anenlarged catalytic active areaFcat=geo 90 in Eq.(15). Furthermore,a constant reactor-wall temperature and inlet temperatureTwall Tinlet 973 K was chosen. The reactor was in steady-stateoperation at ambient pressure, which is indicated by the pressure

outlet pout 1 bar. The spheres were treated as solid particles withconjugate heat transfer that means the temperature of the solidwas not constant. The solid density cat was set to 2214 kg/m

3,specic heat cp;cat 850 J/(kg K) and thermal conductivitycat 12:6 W/(m K), as reported in Schwiedernoch et al. (2003)for alumina monolith including porosity.

3. Results and discussion

3.1. Porosity

The local porosity as a function of dimensionless walldistance was obtained by averaging the local porosity distribu-tion in terms of height and circumference over 40 cylindricalplanes of different radii inside the xed bed. The rst and the lastlayer of particles were not taken into account to avoid edge effects.InFig. 3the porosity of the computer-generated bed is comparedwith experimental data fromMueller (1992)and a more generalequation fromde Klerk (2003):

r 2:14r2 2:53r1 if zr0:637

r 0:29 exp 0:6r cos 2:3r0:16

0:15 exp 0:9r if z40:637 23

The rst peak of the porosity 1 occurs at the wall 0, wherespheres touch the wall in contact points. The second peak at 1can be reproduced by the simulation. In the center of the bed, 2,experimental values are higher than for the virtual bed. The mini-

mum values of the experiments are lower than the computer-generated packing and they occur at smaller wall distances. Themore general equation fromde Klerk (2003)is valid for a wide rangeofNand therefore not too accurate to compare with the simulatedcase with N 4. However, the trend is comparable. The reason forthe discrepancy between simulation and experiments is the loosepacking structure, as it can be seen inFig. 1, and the low height-to-radius ratio of the computer-generated bed H=D 2:47 in compar-ison with the experiments fromMueller (1992),H=D 7:84. Conse-quently, inhomogeneities are more dominant toward the averagedresults. For loose packings the porosity is generally higher than formore dense packings, except for the center of the bed. That means in

Fig. 2. Section ofxed-bed reactor meshing (A) mesh M3 for Rep 35 and (B) meshM5 for Rep 700. Gas phase polyhedral mesh in gray and solid sphere polyhedralmesh in dark. Flattening is visible between the particles.

Table 2

Characteristics for the investigated meshes.

Mesh Prism layerthickness (mm)

No. oflayers

Base size(mm)

Total no. ofcells [106]

No. solidcells [106]

Laminar Re35M1 0.19 2 8 0.6 0.11M2 0.19 2 4 2.6 0.65M3 0.19 2 3 3.2 0.67

Turbulent Re700

M4 0.0427 2 4 2.8 0.66M5 0.0427 2 3 3.5 0.67M6 0.0427 2 2 10.5 3.38

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2

= (R-r)/dp(-)

Computer-generated packing

Mueller (1992)

de Klerk (2003)

Fig. 3. Comparison of porosity as a function of dimensionless wall distance R r=dp between computer-generated packing and experimental measure-ments fromMueller (1992)averaged over the reactor height and a general equation

fromde Klerk (2003).



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the simulation the channeling in the center is not as severe as in theexperiments. Such packing effects have a great inuence on the localporosity and, therefore, on the uid behavior, e.g., pressure drop andvelocity distribution. The overall porosity in the computer-generatedbed accounts to 0.5, whereas in Mueller's experiments a globalporosity of 0.47 was measured. That highlights the loose packingstructure of the simulated bed. Surface roughness and lling speedinuence the packing density. Mueller (1992) for example used

plexiglas polished spheres to obtain radial porosity distributions. Incontrary, porous spheres, which have a rougher surface, would havea looser packing density. Nonetheless, Eppinger et al. (2011) andZobel et al. (2012)demonstrated good accuracy between simulatedand experimental packed-bed quantities, i.e., local porosity andpressure drop, with the same DEM-bed generation procedure. Thatgives us condence that this method can be used for simulatingheterogeneous catalytic packed-beds. However, lling speed andsurface roughness should be aligned with an industrial relevant case.

3.2. Pressure drop

The pressure drop in a xed-bed reactor is often a crucialparameter, since it designates the necessary energy for pumps andcompressors. The Ergun equation (Ergun, 1952) describes thepressure drop adequately for innite packed beds:

p 150

Rep

12

3 1:75

1

3

!H

dp v2in 24

However, it shows discrepancies when conning walls inuence theoweld, i.e., for smallD=dp ratios. Several authors highlighted thatthe effect is Reynolds number dependent. Therefore, Eisfeld andSchnitzlein (2001) adapted Reichelt's equation (Reichelt, 1972)paying special attention to tube-to-particle-diameter ratios D=dp,

for spherical particles reading

p 154 A2w

Rep

12

3

AwBw

1

3

!H

dp v2in 25

with the mean void fraction and coefcients AwandBw:

Aw 1 2

3 D=dp 1 26

Bw 1:15 dp

D

20:87

" #227

InFig. 4andTable 3, the pressure drop as a function of particleReynolds numbers is given for the CFD simulations with andwithout catalytic reactions for T973 K and calculated with Eqs.(24) and (25). The temperature decreases due to endothermicreactions when DRM takes place, hence gas properties change.Therefore, the denition of the Reynolds number is not explicit.The Eisfeld equation as well as the Ergun equation was calculatedfor two different reference temperatures, i.e., 873 K and 973 K,with a feed gas mixture composition, resulting in differentviscosities and densities. For low N, the Ergun equation under-estimates the pressure drop for low Rep and overestimates the

pressure drop for turbulent regimes, which was demonstrated asearly asReichelt (1972). As it can be seen, the simulated pressuredrops are between the Ergun and Eisfeld equation for 873 K, i.e.,lower pressure for equivalent Rep. It has to be kept in mind thatthe simulated bed has a low H/D ratio. Eisfeld's equation wasdeveloped for much larger xed-beds. The low pressure drop inthe simulated bed might result from the loose packing and the lowH/Dratio leading to wall channeling and strong effects of the edgezones of the bed, respectively. Several groups have validated theirsimulations with pressure drop predictions and found goodagreement especially for low Re, e.g., Guardo et al. (2005) andFreund et al. (2005). Concerning pressure drop grid independenceis reached with mesh renement M2 in the laminar case, seeTable 3. For the turbulent case, the pressure drop increases with

mesh renement. Though the deviation between smallest andlargest mesh is less than 5%. As it can be concluded, the simulatedpressure drops are in reasonable accuracy with predictions fromthe literature even in the turbulent regime. However, localquantities provide more information about mesh dependence.Therefore, in Figs. 9 and 10 velocity, temperature and speciesproles are compared at three different positions for the investi-gated meshes and discussed in the following chapters. The threelines, i.e., in the stagnation zone above one of the rst spheres, in achannel between a sphere and the wall, and in the interstitial areabetween two spheres, are highlighted inFig. 8.

3.3. Velocity distribution

Fig. 5shows the specic velocity distributionj v!j=vinon a planecut through the xed bed for Rep 35 M3 and Rep 700 M5.

10

100

1000

10000

10 100 1000

Pressure

dropp

(Pa

)

Particle Reynolds number ReP= vindP/

Eisfeld Eq.

Ergun Eq.

Simulation w/o reactions

Simulation w reactions

T= 973 K

T= 873 K

Fig. 4. Pressure drop over particle Reynolds number. Comparison between simula-tion (meshes M3 and M5) and Eqs. (24) and (25),respectively.

Table 3

Results of investigated meshes for laminar and turbulent cases.

Mesh No. pw=o;chem: (Pa) pw;chem: (Pa) y () XCH4 (%) XCO2 (%) YCO(%) YH2(%) YH2O (%) COn () Cn ()

Laminar Re 35M1 34.7 33.2 32.7 19.8 28.1 27.5 1.5 0.512 0.098M2 37.9 36.5 35.2 21.9 29.7 28.7 2.2 0.534 0.058M3 37.9 36.5 35.4 22.1 29.9 28.8 2.2 0.535 0.056

Turbulent Re700M4 4218 4120 0.59 11.1 8.4 5.0 5.7 0.3 0.346 0.009M5 4220 4124 0.59 10.9 8.2 5.0 5.7 0.3 0.346 0.009M6 4400 4300 0.65 11.6 8.9 5.0 5.7 0.3 0.343 0.008



7/13

The ow direction is from top to bottom. In both cases the oweld around the particles is highly three-dimensional. Axial as wellas radial differences occurs. Several different kinds of character-istic zones can be noticed: stagnation zones in front of particles,wake and eddying behind particles, acceleration in void regions,deceleration and channeling, especially in the near wall region.The highest specic velocities jv

!j=vin 7 are found for the ow

eld of Rep 35, seeFig. 5(A). Thus, in the turbulent ow regime,Fig. 5(B), the non-axial velocity components must be larger thanfor the quasi-laminar ow. InFig. 6besides the spheres cells withzero or negative velocities are illustrated. For Rep 700 theseregions are larger than for the laminar case. The ow is highlycharacterized by back ow regions and non-axial velocitycomponents.

The local articial axial specic velocityvz=vinas a functionof dimensionless wall distance for different particle Reynoldsnumbers is presented in Fig. 7. It follows the local porosity inFig. 3. High velocities are found in regions with high void fraction.Close to the reactor wall the velocity decreases due to theboundary layer and no-slip condition at the wall. The highestarticial velocities are in the range of 2.02.5, which was alsoobserved in experiments (Giese et al., 1998). The largest differ-ences in the articial axial velocities for different particle Reynoldsnumbers are found in the region close to the wall and in regionswith high void fractions. The different thicknesses of boundarylayers for laminar and turbulent regimes can be clearly seen.Additionally, the diagram highlights that in the turbulent regimeradial and circumferential velocity components contribute to a

more leveled velocity distribution. It should be noted that back-

ow regions are not detected, due to averaging of the axialvelocities. Consequently, taking into consideration only two-dimensional velocity distributions can be misleading.

InFigs. 9and10(a), (e) and (i), the specic velocity proles areshown for the different meshes at three positions. The boundarylayer in the stagnation zone (a) is well resolved by all meshes.However, the ow eld differs from single sphere proles due todisturbance by other spheres, cf. Fig. 8. The channeling betweenthe wall and a sphere is shown inFigs. 9 and 10(e), i.e., position 2.For the laminar case a parabolic velocity prole occurs with aspecic velocity of approx. 6. The peak is moved to the sphere'sside. For the turbulent case a typical prole is shown with a steepgradient near the surfaces and a attened center with approx.v=vin 4:5. Position 3 (i) represents the area between two spheres,which is highly inuenced by the surrounding ow eld. Twovelocity peaks can be recognized located near the surfaces. Theow decelerates in the center due to a recirculation zone further

upstream. In the laminar case the velocity increases smoothly,

Fig. 5. Specic velocity distribution j v!

j=vin on a plane cut through the xed bed.(A) for Rep 35 M3 and (B) for Rep 700 M5.

Fig. 6. Backow regions, i.e., cells with negative velocities. (A) for Rep 35 and(B) for Rep 700.

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2

(vz

())/vin

(-)

= ( R-r)/dp(-)

Rep= 35Rep= 700

Fig. 7. Articial axial specic velocityvz=vin as a function of dimensionless walldistance for different Reynolds numbers.



8/13

whereas it shows a steep rise for the turbulent case. InFig. 9(a) thecalculated velocities from mesh 1 are slightly different than formesh M2 and M3. On the contrary, the meshes M2 and M3 showalmost identical results in the laminar case. For higher Reynoldsnumbers, only at position 3 the meshes show different velocitieswith mesh renement. Here, the minimum velocity decreases inthe center with a ner mesh.

Finally, Fig. 11 shows the frequency of y values for meshesM4M6. As it can be seen, most of the cells are small enough thaty o1:5. Hence, velocity boundary layers are well resolved.

3.4. Temperature distribution

The temperature distribution in the xed bed, i.e., gas phase andsolid particles, is shown inFig. 12. The inlet temperature and the walltemperature are set constant to 973 K. Due to the endothermicreactions the temperature inside the bed decreases. Again, strongaxial and radial temperature differences up to approx. 80 K occur.Low Reynolds numbers result in large residence times. Hence, inFig. 12(A) the overall temperature is lower than inFig. 12(B). In (A), acold spot appears after approx. half of the reactor length, whereas in(B) the temperature in the center decreases constantly. This is due tothe shorter residence time which moves the cold spot out of the bed.InFig. 12(B) the hot ow reaches deep inside the xed bed, whereasfor Rep 35 the ow cools down immediately. The solid particles canbe detected easily due to their almost constant temperature, which is

caused by the high thermal conductivity. As a result of channeling

in the near wall region, the thermal penetration into the bed isdeclined. Again, the transport property temperature shows highlythree-dimensional behavior.

InFigs. 9and10(b), (f) and (j), temperature proles are shownfor the different meshes at the three positions. At position 1 thetemperature decreases from the inlet to the sphere's surface due toendothermic reactions. However, for Rep 35 it is lower than forthe turbulent case. At position 2, i.e., between wall and sphere, the

temperature decreases from the constant wall temperatureT973K to the specic surface temperature, which is inuencedrstly bythe surrounding ow and secondly by the surface reactions. In thelaminar case the temperature decreases almost linearly from thewall to the surface. For the higher Reynolds number boundarylayers can be noticed near both surfaces, which are of the order ofmagnitude of the velocity boundary layers. Finally, between thespheres at position 3 (j) the temperature eld is highly inuencedby the ow eld. In the laminar case the temperature decreasesfrom the outside to the center. Therefore, the left surface in (j) iscooler than the right side. Again, an almost linear prole is shownalthough the recirculation zone brings cooler gas. For Rep 700the endothermic reactions cool down the surface, whereas hot gaspasses this position. The recirculation zone is larger than for lowerReynolds. Hence, the temperature decreases strongly in the center.

3.5. Surface adsorbed species

As mentioned before, catalyst deactivation through carbondeposition is one of the major draw backs of the DRM. It has tobe noticed that in reality coke formation takes place includingmany carbonaceous atomic layers. However, the present reactionmechanism only accounts for monolayer carbon on the surface.Consequently, the model determines the regions where cokingtakes place rather than the amount of coke. InFig. 13surface sitefractions of adsorbed carbon and some streamlines are illustratedfor different Reynolds numbers. As it can be seen, the carbondeposition is not only dependent on the Reynolds number but isdue to the interactions between velocity, temperature and gascomposition. In Fig. 13(A) several regions of spheres are totallyblocked by carbon mainly in the center of the inlet region of thebed. Hence, the catalyst is deactivated resulting in declined orstopped production of syngas. In Fig. 13(B) almost no carbon isadsorbed. Catalyst deactivation by carbon deposition for DRMespecially in the inlet regions ofxed beds was recently observedexperimentally and numerically by Kahle et al. (2013). Fig. 13highlights the advantage of this type of reaction mechanism forDRM that can contribute to identify conditions and regions wheredeactivation of the catalyst is likely to occur. In addition, Fig. 14shows radially and circumferentially averaged surface site frac-tions of the adsorbed species Cn, COn, Hn and RHn. For the laminarcase (A), surface adsorbed carbon monoxide (COn) becomes themost abundant reaction intermediate (MARI) after approx. 10 mm

in the xed-bed. Adsorbed carbon is only dominant in theentrance of the reactor, whereas Hn occurs on less than 1% of thesurface sites. For the turbulent case (B), COn is again the MARI. Dueto the lower residence time, its surface fraction is lower, too. C n

and Hn are found on less 2% on the surface. These two guresillustrate that the DRM is kinetically limited. However, it has to bekept in mind that the two cases are not under iso-conversion.Therefore, a true comparison of location and quantity of surfaceadsorbed species cannot be undertaken.

3.6. Gas phase species distribution

Radially and circumferentially averaged mole fractions of reac-

tants and products as well as temperature are shown in Fig. 15

Position

1

Position

2

Position

3

Fig. 8. Velocity magnitude contours for Rep 35 and positions for the mesh

validation.



9/13

over the reactor length for different particle Reynolds numbers.

Catalytic conversion can be noticed and beside the main productsH2and CO also water is formed. Water is the result of the reversewatergas shift (WGS) reaction, CO2H2COH2O. Undercommon DRM reforming conditions WGS is extremely rapid(Rostrup-Nielsen and Hansen, 1993). For larger residence timesmore hydrogen and carbon monoxide are produced. It becomesclear that both reactors are economically not feasible, because onlyfew syngas is formed.

However, the DRM kinetics is highly inuenced by the reactortemperature and likewise inuences it. This is strongly demon-strated inFig. 16, where the mole fraction of H2 and surface sitefraction of carbon on a plane cut are shown. The strong interplaybetween velocity and temperature distribution and the resultingreactions can be seen. The low temperature and blockage of the

catalyst leads to a weak hydrogen production in the bed center in

Fig. 16(A). Whereas in stagnation zones, e.g., between spheres, the

production is high due to high residence time and low convection.Rows three and four in Figs. 9 and 10show mole fractions of

CO2, CH4and CO in the gas phase and at surfaces. For the laminarcase, at position 1 no syngas is produced due to complete catalystblockage by Cn. On the contrary, for higher Reynolds numbers, COis produced and a boundary layer larger than the temperature BLcan be recognized, cf. Fig 10(d). At positions 2 and 3 the molefractions of methane and carbon dioxide decrease at the catalyticsurfaces, while syngas is produced. In the laminar case, mesh M1shows lower conversion than M2 and M3. This could be due to thelower discretization of the surface. Consequently, the velocityeldas well as the temperature eld is affected. The meshes for theturbulent case show in general similar species proles.

ComparingFigs. 9, 10, 15 and 16it becomes clear that averaged

proles can be illusive, due to the fact that they neglect the radial

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4

Spec

ificve

loc

ityv/vin

[-]

Distance from surface [mm]

920

930

940

950

960

970

980

0 1 2 3 4

T

empera

ture

[K]


0

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4

M

olefrac

tion

[-]


CO2

CH4

0

0.01

0.02

0.03

0.04

0.05

0 1 2 3 4

Mo

lefrac

tion

CO

[-]


0

1

2

3

4

5

6

7

8

9

0 0.5 1 1.5 2

Radial distance surface to

wall [mm]

WallWall

900

910

920

930

940

950

960

970

980

0 0.5 1 1.5 2

Tem

pera

ture

[K]

Wall

0

0.05

0.1

0.15

0.2

0 0.5 1 1.5 2

Mo

lefrac

tion

[-]

Wall

CO2

CH4

0

0.01

0.02

0.03

0.04

0.05

0 0.5 1 1.5 2

Mo

le

frac

tion

CO

[-]

Wall

0

1

2

3

4

5

6

0 0.5 1 1.5 2

Radial distance between surfaces

[mm]

890

895

900

905

910

0 0.5 1 1.5 2

Tempera

ture

[K]

0

0.05

0.1

0.15

0.2

0 0.5 1 1.5 2

Mo

lefrac

tion

[-]

CO2

CH4

0

0.01

0.02

0.03

0.04

0.05

0 0.5 1 1.5 2

Mo

lefractio

nCO

[-]


[mm]


[mm]


[mm]

Spec

ific

ve

loc

ityv/vin

[-]

Spec

ificve

loc

ityv/vin

[-]


wall [mm]


wall [mm]


wall [mm]

Fig. 9. Results of mesh renement for laminar case Rep 35. Specic velocity for (A) position 1, (E) position 2, and (I) position 3. Temperature for (B) position 1, (F) position 2,(J) position 3. Mole fractions CO2and CH4for (C) position 1, (G) position 2, and (K) position 3. Mole fractions CO for (D) position 1, (H) position 2, and (L) position 3.



10/13

and circumferential differences, e.g., boundary layers, of speciesconcentrations.

4. Conclusion

Highly endothermic (or exothermic) heterogeneous catalyticreactions are performed mostly in xed-bed reactors with smalltube-to-particle-diameter ratios N. Inhomogeneities in the bedstructure are dominant especially for small N. This results in

signicant wall effects, local back ows and large axial and radial

gradients. For these reactor congurations conventional plug owmodels and pseudo-homogeneous kinetic models fail. An ade-quate modeling can be carried out with full CFD and detailedreaction mechanisms.

In this study, a fully three-dimensional xed-bed lab-scale reactorfor the catalytic dry reforming of methane was simulated. A DEM-method was applied to generate a randomly packed bed. Themeshing method takes into account boundary layers and particleparticle contact-points. The detailed DRM reaction mechanismdistinguishes between adsorption, surface reaction and desorption.

The bed consists of 113 spherical solid particles with applied

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4


940

945

950

955

960

965

970

975

980

0 1 2 3 4

Tem

pera

ture

[K]


0

0.05

0.1

0.15

0.2

0.25

0 0.2 0.4 0.6 0.8 1

Mole

frac

tion

[-]


CO2

CH4

0

0.002

0.004

0.006

0.008

0.01

0.012

0 0.2 0.4 0.6 0.8 1

Mo

lefrac

tion

CO

[-]


0

1

2

3

4

5

6

7

0 0.5 1 1.5 2


wall [mm]

Wall

930

940

950

960

970

980

0 0.5 1 1.5 2

Tempera

ture

[K]

Wall

0

0.05

0.1

0.15

0.2

0 0.5 1 1.5 2

Mo

lefrac

tio

n[-]

Wall

CO2

CH4

0

0.002

0.004

0.006

0.008

0.01

0.012

0 0.5 1 1.5 2

Mo

lefrac

tion

CO

[-]

Wall

0

1

2

3

4

5

6

0 0.5 1 1.5 2

Radial distance betweensurfaces [mm]

930

935

940

945

950

0 0.5 1 1.5 2

Tempera

ture

[K]

0

0.05

0.1

0.15

0.2

0 0.5 1 1.5 2

Mo

lefrac

tion

[-]

CO2

CH4

0

0.005

0.01

0.015

0.02

0 0.5 1 1.5 2

Mo

lefrac

tion

CO

[-]





wall [mm]


wall [mm]


wall [mm]

Spec

ific

ve

loc

ityv/vin

[-]

Spec

ificve

locity

v/vin

[-]

Spec

ificve

loc

ityv/vin

[-]

Fig. 10. Results of mesh renement for turbulent case Rep

700. Specic velocity for (A) position 1, (E) position 2, and (I) position 3. Temperature for (B) position 1,(F) position 2, and (J) position 3. Mole fractions CO2and CH4 for (C) position 1, (G) position 2, and (K) position 3. Mole fractions CO for (D) position 1, (H) position 2, and(L) position 3.



11/13

conjugate heat transfer. Two different Reynolds numbers wereinvestigated, i.e., Rep 35 and 700. Although the bed dimensionsare not large scale important ndings can be derived. The DRM xedbed reactor demonstrates the strong interactions between chemicalkinetics and transport of momentum, heat and mass. The observedvelocity, temperature and species elds are characterized by their

three-dimensional behavior and interactions highlighting their com-plexity and discrepancy from lumped model predictions. Addition-ally, the reaction mechanism can detect regions where coking takesplace with the help of surface adsorbed carbon. We recommendmeshes with most of the near wall cells being small enough thaty o1:5. This could be achieved by using two prism layers with atotal thickness calculated by Eq.(22). Meshes with approx. 3 milliontotal cells show grid independent results for laminarows. However,

turbulent ows need ner meshes.

0

0.01

0.02

0.03

0.04

0.05

0.06

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Frequency

[-]

y+[-]

M4, 2.8M cells

M5, 3.5M cells

M6, 10M cellss

Fig. 11. Frequency distribution over dimensionless wall distance y for differentmeshes.

Fig. 12. Temperature distribution on a plane cut through the xed bed. (A) forRep 35 mesh M3 and (B) for Rep 700 mesh M5.

Fig. 13. Catalyst deactivation through carbon deposition on the surface. (A) for Rep 35 mesh M3 and (B) for Rep 700 mesh M5.

0

0.2

0.4

0.6

0.8

1

0

0.005

0.01

Surfaces

ite

frac

tion

[-]

Surfaces

ite

frac

tion

H*[-]

Rh*

C*

CO*

H* Rep= 35

0

0.20.4

0.6

0.8

1

0 0.01 0.02 0.03 0.040

0.01

Reactor length z [m]

Rh*

C*

CO*

H*

Rep= 700

0.005

Fig. 14. Mean surface site fractions of Rhn, COn and Cn over reactor length. (A) forRep 35 mesh M3 and (B) for Rep 700 mesh M5.

0

0.050.1

0.15

0.2

0.25

880

900920

940

960

980

Mo

lefrac

tion

[-]

Tempera

ture

[K]

Reacting zone

CH4

CO2

H2

CO

H2O

Temp.

Rep= 35

0

0.05

0.1

0.15

0.2

0.25

-0.01 0 0.01 0.03 0.05880

900

920

940

960

980

Reactor length z [m]

Rep= 700

CH4

CO2

COH2

H2O

Temp.

Fig. 15. Mean mole fractions and mean temperature over reactor length. (A) forRep 35 mesh M3 and (B) for Rep 700 mesh M5.



12/13

The computational time of such detailed simulations is high,i.e., several days on a cluster. Consequently, they are too expensiveand not practical for routine design of a xed-bed reactor. How-ever, they are capable to support fundamental understanding ofthe transport phenomena and kinetics. Therefore, such simula-tions can contribute to determine optimal reactor conditions. Forthe next step, the model should be validated with spatiallyresolved experimental data in a way recently carried out by theHorn group, cf. Horn et al. (2010),Korup et al. (2011), and Geskeet al. (2013), or by the Paul Scherrer Institute in Switzerland (Boscoand Vogel, 2006).

This study demonstrates the advantages of modeling hetero-geneous catalytic xed-bed reactors with small N fully three-dimensional in combination with reliable detailed reactionmechanisms. In that way, resolved simulations can contribute to

a better understanding and therefore better choice of multiscalechemical reactors. Finally, this modeling approach reduces depen-dencies on empiricism for the calculation of multiscale reactiondevices.

Nomenclature

Latin letters

a specic particle area (m2/m3)Ak pre-exponential factor (s

1 or m2/mol s)c species concentration (mol/m3 or mol/m2)cp specic heat capacity (J/kg K)dp particle diameter (m)

D tube diameter (m)Di binary diffusion coefcient (m2/s)

Ea activation energy (kJ/mol)Fcat=geo ratio of catalytic active area to geometric area ()

h specic enthalpy (J/kg)H bed height (m)ji diffusion mass ux (kg/m

2 s)jq diffusion heat transport (W/m

2)k turbulent kinetic energy (J/kg s)k reaction rate constant (s1 or m2/mol s)m mass (kg)Mi molar weight of species i (kg/mol)N tube-to-particle-diameter ratio ()Ng number of gas phase species ()

p pressure (Pa)

Pr Prandtl numberPrcp= ()

r radial coordinate (m)R ideal gas constant (J/K mol)Ri production rate of speciesi (kg/m

3 s)Rep particle Reynolds number Rep vindp=()_s molar net production rate (mol/m3 s)Sc Schmidt numberSc =D ()Si sticking coefcient ()Sh heat source (W/m

3)t time (s)T temperature (K)vin supercial velocity (m/s)vi mean velocity componentsv0i uctuating velocity componentsxi coordinate ini direction (m)Xi molar fraction of speciesi()y dimensionless distance from wall ()Yi mass fraction of speciesi ()

Greek letters

surface site density (mol/m2)BL boundary layer thickness (m)ij Kronecker delta () parameter for modied activation energy porosity () turbulent dissipation rate (J/kg s) surface coverage () thermal conductivity (W/m K) dynamic viscosity (Pa s)

parameter for modied surface rate expression kinematic viscosity (m2/s) dimensionless wall distance R r=dp () uid density (kg/m3) coordinate number () stress tensor (N)

Acknowledgments

This study is part of the Cluster of Excellence UnifyingConcepts in Catalysis (Unicat) (Exc 314), which is coordinated

by the Technische Universitt Berlin. The authors would like to

Fig. 16. Hydrogen production and surface adsorbed carbon on a plane cut through the xed bed. (A) for Rep 35 mesh M3 and (B) for Rep 700 mesh M5.



13/13

thank the Deutsche Forschungsgemeinschaft DFG within theframework of the German Initiative of Excellence for nancialsupport.

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