1-s2.0-S0009250905007748-main

Chemical Engineering Science 61 (2006) 16021616www.elsevier.com/locate/ces

Modelling of packed bed membrane reactors for autothermal production ofultrapure hydrogen

T.P. Tiemersma, C.S. Patil, M. van Sint Annaland, J.A.M. KuipersFundamentals of Chemical Reaction Engineering Group, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE,

Enschede, The Netherlands

Received 26 August 2005; received in revised form 4 October 2005; accepted 4 October 2005Available online 14 November 2005

Abstract

The conceptual feasibility of a packed bed membrane reactor for the autothermal reforming (ATR) of methane for the production of ultrapurehydrogen was investigated. By integrating H2 permselective Pd-based membranes under autothermal conditions, a high degree of processintegration and intensification can be accomplished which is particularly interesting for small scale H2 production units. A two-dimensionalpseudo-homogeneous packed bed membrane reactor model was developed that solves the continuity and momentum equations and the componentmass and energy balances. In adiabatic operation, autothermal operation can be achieved; however, large axial temperature excursions wereseen at the reactor inlet, which are disadvantageous for membrane life and catalyst performance. Different operation modes, such as coolingthe reactor wall with sweep gas or distributive feeding of O2 along the reactor length to moderate the temperature profile, are evaluated.The concentration polarisation because of the selective hydrogen removal along the membrane length was found to become significant withincreasing membrane permeability thereby constraining the reactor design. To decrease the negative effects of mass transfer limitations to themembrane wall, a small membrane tube diameter needs to be selected. For a relatively small ratio of the membrane tube diameter to the particlediameter, the porosity profile needs to be taken into account to prevent overestimation of the H2 removal rate. It is concluded that autothermalproduction of H2 in a PBMR is feasible, provided that the membranes are positioned outside the inlet region with large temperature gradients. 2005 Elsevier Ltd. All rights reserved.

Keywords: Modelling; Membranes; Packed bed; Chemical reactors; Hydrogen; Autothermal operation

1. Introduction

Production of ultra pure hydrogen for use in downstreampolymer electrolyte membrane fuel cells (PEMFC) for small ormedium scale applications is gaining increasing interest in re-cent years. On increasing scale, fuel cells are applied in the auto-motive industry and for distributive power generation, becauseof the high energy efficiency of the combination of an elec-tromotor with hydrogen powered fuel cells (overall efficiency3846%) compared to the overall internal combustion engineefficiency (1030%) (Witjens, 2004). For small scale applica-tions (< 250 kW) in transportation or household power supply(Carrette et al., 2001) the main advantages of the PEMFC over

Corresponding author. Tel.: +31 53 489 4478; fax: +31 53 489 2882.E-mail addresses: [email protected],

[email protected] (M.v. Sint Annaland).

0009-2509/$ - see front matter 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2005.10.004

the other types of fuel cells are its compactness, high energydensity, quick start-up and response time and low operatingtemperature. However, ultra pure hydrogen (< 10 ppm CO) isrequired because of the sensitivity of the anode catalyst in thePEMFC to CO poisoning. A PEMFC can be powered directlyby hydrogen or by hydrogen that is produced on site from asuitable hydrocarbon feedstock such as gasoline, natural gasand methanol (Gallucci et al., 2004; Hoang and Chan, 2004).Use of pure hydrogen as the energy carrier requires an expen-sive hydrogen-fuelling network leading to high costs in the fueldelivery system. Moreover, the low volumetric energy densityof hydrogen at ambient conditions makes hydrogen storage un-economical. Therefore, on site hydrogen generation from a hy-drocarbon feedstock is preferred.

Hydrogen is traditionally produced via multiple reactionsteps as a primary product from steam reforming of hydrocar-bons such as methane, naphtha oil or methanol (Bharadwaj and

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T.P. Tiemersma et al. / Chemical Engineering Science 61 (2006) 16021616 1603

Schmidt, 1995; Rostrup-Nielsen, 1984, 2002). On an industrialscale, most of the hydrogen is currently produced by steamreforming of natural gas. With classical steam reforming ofmethane (SRM) high hydrogen yields can be achieved, how-ever, at the expense of costly high temperature heat exchangeequipments and complex energy integration between a largenumber of process units, including reformer, high and low tem-perature shift reactors (HTS and LTS) and a preferential oxida-tion reactor (PrOX). Moreover, often a pressure swing adsorp-tion (PSA) unit is used to achieve the desired hydrogen purity.For the production of ultra pure hydrogen for small scale appli-cations, this route is not preferred because of the large numberof process units and the associated uneconomical downscal-ing. A high degree of process integration and process intensi-fication can be accomplished by integrating hydrogen perms-elective membranes (Adris et al., 1991; Kikuchi, 1995) in thesteam reformer. Via the integration of hydrogen permselec-tive membranes, the number of process units can be decreasedand the total required reactor volume can be reduced, whilehigher methane conversion and hydrogen yields beyond ther-modynamic equilibrium limitations can be achieved, at lowertemperatures and with higher overall energy efficiencies.

Steam reforming is a highly endothermic process at elevatedtemperatures and requires costly external high temperature heatexchange equipment or expensive non-adiabatic reactors in or-der to supply the required reaction energy, which is very en-ergy inefficient for small scale applications and adds to thecomplexity of the system (Hoang and Chan, 2004; Lattner andHarold, 2004). Autothermal operation with maximum hydro-gen yields without external or internal heat exchange can beaccomplished through a combination of steam reforming andpartial oxidation. By co-feeding air or pure oxygen, part of themethane is oxidised, which generates the required reaction en-ergy for the steam reforming in situ. This process is known asautothermal reforming (ATR). Use of air as the oxidant for the(partial) oxidation will dilute the products with nitrogen, whichincreases the required reactor volume and hydrogen membranesurface area. Moreover, in view of the ever-increasing environ-mental restrictions, the production of hydrogen from naturalgas or lower hydrocarbons for use in fuel cells should ideally berealised without carbon dioxide emissions. The costly carbondioxide sequestration due to the dilution of the products withnitrogen can be avoided by using pure oxygen instead of air asthe oxidant in the oxy-steam reforming process. Depending onthe type and scale of the application, pure oxygentypicallyobtained via expensive cryogenic air separationor air will beused. Although overall autothermal operation can be achievedby combining the steam reforming with the (partial) oxidationof methane, large temperature excursions close to the reactorinlet have been observed in a conventional fixed bed reactor forATR (Ioannides and Verykios, 1998) attributed to the higher re-action rate of methane oxidation compared to the SRM. Theseobservations have also been supported by modelling studiesof partial oxidation and reforming reactions of methane (DeGroote and Froment, 1996; De Smet et al., 2001). Integrationof Pd based hydrogen permselective membranes in a packedbed membrane reactor for the ATR of methane should, there-

fore, be carried out with careful consideration of the thermal-mechanical stability of these membranes. In this study, the con-ceptual feasibility of packed bed membrane reactors (PBMR)for ATR of methane is investigated by means of detailed reac-tor simulations. To the authors knowledge the application ofPBMRs for the ATR of methane has not yet been investigated.

Many studies concerning the modelling of PBMRs have em-ployed 1-dimensional (1D) reactor models. With these 1D mod-els, the enhancement of the reactor performance via insertionof hydrogen permselective membranes has been demonstratedfor dehydrogenation reactions, especially the dehydrogenationof ethylbenzene (Assabumrungrat et al., 2002; Basile et al.,2001; Itoh, 1987), but also for the SRM. For the SRM, Barbieriand Di Maio (1997) have demonstrated the benefits of integrat-ing hydrogen permselective membranes with an isothermal andisobaric 1D reactor model, while Kim et al. (1999) have used a1D non-adiabatic model, also accounting for the axial pressuredrop. In these 1D models, radial gradients in the temperatureand concentrations are neglected and plug flow conditions areassumed. Simulation studies of PBMRs for the dehydrogena-tion of ethylbenzene and cyclohexane have already shown thenecessity of accounting for radial non-uniformities, especiallybecause of the removal of hydrogen via the membranes and es-pecially when employing membranes with a high permeability(Fukuhara and Igarashi, 2003; Itoh et al., 1994; Koukou et al.,1997; Krten, 2003; Mondal and Ilias, 2001).

In this paper, the feasibility of integrating Pd-based mem-branes in an autothermal methane steam reformer for theproduction of ultra pure hydrogen is investigated by meansof detailed reactor simulations. A two-dimensional, pseudo-homogeneous reactor model has been developed to calculatethe axial and radial temperature and concentration profilesin the PBMR. The extent of temperature excursions close tothe inlet of the reactor is investigated and different options tomoderate these temperature peaks to prolong membrane tubelife are evaluated, viz. cooling with sweep gas and stagedoxygen injection. Furthermore, it is investigated whether andto what extent mass and heat transfer limitations affect theperformance of the PBMR. To avoid the detrimental effects ofradial mass transfer limitations in PBMRs, often a very smallmembrane tube diameter needs to be selected. In a PBMRwith relatively large particles relative to the membrane tubediameter, a bypass flow can emerge near the membrane wall.Hydrogen is selectively withdrawn in this region of increasedbed porosity and increased axial velocity reducing the contacttime of the gas mixture in the catalyst bed near the membranewall. In order to evaluate the extent of this effect, the descrip-tion of the two-dimensional flow field is included in the PBMRmodel, following Krten et al. (2003).

2. Reactor model

The packed bed membrane reactor studied, consists of a tubu-lar, steel supported Pd-Ag membrane filled with a reformingcatalyst, as schematically depicted in Fig. 1. Hydrogen is selec-tively withdrawn to the shell side either via a (reactive) sweepgas or by applying a vacuum. In this study the shell side was

1604 T.P. Tiemersma et al. / Chemical Engineering Science 61 (2006) 16021616

Fig. 1. Schematic of the packed bed membrane reactor.

assumed to be at vacuum, maximising the driving force for H2permeation.

In this reactor configuration, the specific membrane area andthe volume of the catalyst bed are linked via the tube diameter.The minimum tube diameter will be determined by the mini-mum acceptable particle size with which intraparticle diffusionlimitations can be avoided as much as possible, while the pres-sure drop over the catalyst bed is kept within acceptable limits.If it is considered necessary to increase the required specificmembrane area relative to the catalyst inventory, i.e., in case themembrane permeability is low compared to the catalyst activ-ity (Bernstein and Lund, 1993), different reactor configurationscould be devised. For example, the membrane tubes could beinserted in a catalyst bed and the hydrogen extracted throughthe inside of the membrane tubes. In this case, the pitch be-tween the membrane tubes should be selected small enoughto avoid mass transfer limitations from the catalyst bed to themembrane tubes. In this paper, the (standard) configuration of amembrane tube filled with spherical catalyst particles has beenselected to study the feasibility of the PBMR for autothermal

Table 1Total continuity and momentum balance equations

Continuity equationgt

+ (gu)= 0

Total momentum balance equationt

(gu)+ (guu)=p gu (g)+ ggFriction coefficient Newtonian fluid

= 150 (1 )2

3g

gd2p

+ 1.75 1 3

|u|dp

g =(g 2

3g

)( u)I g[(u)+ (u)T ]

where |u| =u2r + u2z Porosity profile (Hunt and Tien, 1990)

g =Mgp

RT g(ideal gas) (r)= 0 + (1 0) exp

(6R r

dp

)

Boundary conditions Packed Bed (PB) and Packed Bed Membrane Reactor (PBMR)

Center (r = 0) uzr

r=0

= 0 ur |r=0 = 0

Inlet (z= 0) urz

z=0

= 0 uz|z=0 = m

g

Outlet (z= L) urz

z=L

= 0 p|z=L = p0PB PBMR

Wall (r = R) uz|r=R = 0 ur |r=R = 0 uz|r=R = 0, ur |r=R =JH2H2

methane steam reforming and to investigate the extent and theinfluence of mass transfer limitations from the catalyst bed tothe membrane. Nevertheless, the results could also qualitativelybe used for different reactor configurations by comparing thecharacteristic length scale for radial dispersion, e.g. tube diam-eter vs. tube pitch.

2.1. Model description

A pseudo-homogeneous, two-dimensional reactor modelwas developed consisting of the total gas-phase continuity andNavierStokes equations augmented with gas-phase compo-nent mass balances and the overall energy balance. The modelis based on standard dispersion model (SDM) that describes thegas phase mass and energy transport as convective flow withsuperimposed radial and axial dispersion. The model equationsin two-dimensional axisymmetrical cylindrical-coordinatesand the boundary conditions have been listed in Tables 1and 2. The following assumptions have been made in thismodel:

The particle size is sufficiently small so that both intra-particle mass and heat transfer limitations (see Section 2.1.4)and external mass and heat transfer limitations from the gasbulk to the catalyst surface can be neglected.

Homogeneous gas phase reactions are neglected in view ofthe relatively low temperatures.

The gas bulk can be described as an ideal Newtonian fluid.The most important constitutive equations for the reaction ki-netics, membrane flux and axial and radial dispersion coeffi-cients will be discussed in the next sections.


Table 2Mass and energy balances

Component mass balancet

(gi )= (gui )+ (gDi i )+ Sr,i with Di =[Dr,i

00

Dz,i

]where source terms equals: Sr,i = (1 )sMi

nrj=1

ij rj for i = 1, 2, . . . , ncEnergy balance

(gcp,g + (1 )scp,s )Tt

=cp,g (guT )+ ( T )+ Sh with =[

r0

0z

]where source terms equals: Sh = (1 )s

nrj=1

rjHj for j = 1, 2, . . . , nrBoundary conditionsPosition Mass balance Energy balance

Center (r = 0) ir

r=0

= 0 Tr

r=0

= 0

Adiabatic Cooled wall

PB:ir

r=R

= 0 Tr

r=R

= 0 T |r=R = TwallWall (r = R) PBMR: JH2 = urH2 |r=R

ir

r=R

= 0 i = H2

Inlet (z= 0) (Dz,ig)iz

z=0

+ (uzgi )|z=0 Tz

z=0

+ (uzgcp,gT )|z=0=m,i/Areactor =cp,gT0m/Areactor

Outlet (z= L) iz

z=L

= 0 Tz

z=L

= 0

2.1.1. Reaction kineticsThe ATR reaction kinetics expressions have been taken from

an experimental study on SRM by Numaguchi and Kikuchi(1988) on a 8.7 wt% Ni/Al2O3 catalyst at 520% methane con-versions in a continuous integrated bed reactor. Kinetic equa-tions from Trimm and Lam (1980) are used to describe thecombustion of methane in a packed bed reactor. This expres-sion was determined with experiments on a Pt/Al2O3 catalystand has been corrected for a Ni catalyst by De Smet et al.(2001). Details for the reaction kinetics expressions are given inTable 3.

2.1.2. Membrane fluxPermeation of hydrogen through a dense palladium mem-

brane occurs via a solutiondiffusion mechanism, where the gasmolecules dissolve in the membrane surface at the high (partial)pressure side and desorb at the side with the low partial pres-sure (Mondal and Ilias, 2001). A power law equation is used todescribe the overall permeation rate of hydrogen through themembrane, which is displayed in Table 4.

2.1.3. Dispersion of mass and heatThe effective radial and axial dispersion coefficients are as-

sumed to consist of contributions due to molecular diffusionand turbulent mixing (Krten, 2003) and are listed in Table 5.For the contribution of molecular diffusion, an effective diffu-sion coefficient calculated with Wilke equation is used (Taylorand Krishna, 1993). The contribution due to turbulent mixing

is expressed as a function of the local velocity and the Pcletnumber using the correlations proposed by Schlnder and Tsot-sas and accounting for the porosity profile (Schlnder and Tsot-sas, 1988). For a more detailed discussion on these constitutiveequations, the reader is referred to the work of Krten (2003).

2.1.4. Intraparticle diffusion limitationsThe absence of intraparticle mass transfer limitations was

checked by calculating overall effectiveness factors for both thecombustion and steam reforming reactions in a separate mod-elling study. Micro level mass and energy balances summarisedin Table 6 are solved to calculate the intraparticle concentra-tion and temperature profiles using the kinetic rate expressionsgiven by Numaguchi and Kikuchi (1988) for steam reformingand Trimm and Lam (1980) for methane combustion. The re-actor inlet conditions were selected, because the reaction ratesare expected to be maximum at the inlet conditions. The over-all effectiveness factor for a reaction is defined as the ratio ofthe integrated reaction rates over the radius of the particle andthe reaction rate at bulk phase conditions.

= r=Rpr=0 rj (r,i,local) 4r2 drrj (Rp,i,bulk) 43R3p

.

In Fig. 2 the overall effectiveness factor for the methane com-bustion and steam reforming are plotted as a function of thecatalyst particle diameter for two different bulk temperatures atbulk feed conditions corresponding to autothermal feed ratiosat these respective temperatures.


Table 3Kinetic rate expressions for methane combustion (Trimm and Lam, 1980) and water-gas shift and steam reforming (Numaguchi and Kikuchi, 1988)

Reactions Rate equations

CH4 + 2O2 CO2 + 2H2OH 0298 =802 kJ/mol r1 =

k1apCH4pO2

(1 +KOXCH4pCH4 +KOXO2

pO2 )2+ k1bpCH4pO2

(1 +KOXCH4pCH4 +KOXO2

pO2 )

CH4 + H2OCO + 3H2H 0298 = 206 kJ/mol r2 =

k2(pCH4pH2O p3H2pCO/Keq,2)p1.596H2O

CO + H2OCO2 + H2H 0298 =41 kJ/mol r3 =

k3(pCOpH2O pH2pCO2/Keq,3)pH2O

Kinetic rate constant Adsorption constant Equilibrium constant

ki = Ai exp(Ea,i

RT

)KOXi

=K0i

exp

[H 0i

RT

]Keq,i = exp

[GiRT

]

Unit Ai Ea,i (kJ/mol) Unit K0i

Hi (kJ/mol)

Rate and adsorption parameters

k1a mol bar2 kg1cat s1 8.11 105 86 KoxCH4 bar

1 1.26 101 27.3k1b mol bar

2 kg1cat s1 6.82 105 86 KoxO2 bar1 7.87 107 92.8

k2 mol bar0.404 kg1cat s1 2.62 105 106.9

k3 mol bar2 kg1cat s1 2.45 102 54.5

Table 4Membrane flux equation and parameters for Pd-Ag membrane (Roy, 1998)

JH2 =QPd

dmem(p

nmemH2,tube

pnmemH2,shell) with QPd =QPd,0 exp(Eact,Pd

RT

)

Membrane parameters Value Unit

QPd,0 1.7 1010 mol m1 s1 Pa0.72Eact,Pd 6.17 103 J mol1dmem 4.5 106 mnmem 0.72

Table 5Constitutive equations for the effective radial and axial dispersion coefficients for mass and energy (Krten, 2003; Schlnder and Tsotsas, 1988; Zehner andSchlnder, 1970)

Effective dispersion of mass Effective dispersion of energy

Radial

Dr,i =(1 1 )Dm

i+ udp

Pef (Dt /dp)rg

= bed,0g

+ PexKf (Dt /dp)

= bed,0g

+ Pex8

= (1 1 )Dmi+ udp

8

Axial

Dz,i =(1 1 )Dm

i+ udp

2

zg

= bed,0g

+ PexKf (Dt /dp)

= bed,0g

+ Pex2

bed,0g

=(1 1 ) (1 + radg

)+1

2

1 gcat

B

1 gcat

B

(1 g

catB

)2 ln catgB B + 1

2 B + 1

1 gcat

B

+ 1g

rad+ g

cat

with rad = 0.232rad

1

(T

100

)2dp Pex =

usupgcp,gg

XF

B = C(

1

)10/9C = 1.4 with XF = 1.15 for spherical particles


Table 6Model equations for the micro model describing intra-particle profiles

Boundary conditions

r = 0 (centre) r = R (surface)Mass balanceit

= 1r2

r

(r2Di,eff

ir

)+ cats

nrj=1

rj,iMiir

r=0

= 0 i |r=R = i,bulk

Energy balance

cp,catTt

= 1r2

r

(r2cat

Tr

)+ cats

nrj=1

rj,iHr,jTr

r=0

= 0 T |r=R = Tbulk

Fig. 2. Overall effectiveness factors for methane combustion (MC) and steamreforming (SRM) as function of the catalyst particle diameter for two differentbulk temperatures.

From Fig. 2, it can be inferred that a particle size between0.5 and 1.0 mm is sufficient in achieving a high utilisation ofthe catalyst particle for SRM. The decrease in the effectivenessfactor at higher temperatures is more pronounced for the highlyexothermic methane combustion reaction compared to steamreforming reaction. The larger dependency of the combustionreaction on temperature is also reflected in the intra-particletemperature profiles depicted in Fig. 3.

For a larger catalyst particle most of the combustion takesplace in a shell close to the catalyst surface, while the reformingreaction zone extends more towards the centre of the catalystparticle, which results in a lower core temperature for largerparticles (see Fig. 3). Based on these calculations, a particlediameter of 500 m was selected in this study, such that theeffects of intra-particle mass transfer limitations can be ignored.Using an even smaller particle size (< 500 m) would lead toan unacceptably large pressure drop over the reactor.

2.2. Numerical solution strategy

Although the physical properties (especially density andviscosity) are determined by the local composition and

Fig. 3. Temperature profiles inside the catalyst particle for different particlesizes for a bulk gas temperature of 873 K.

temperature, which are affected by the chemical reactions andthe membrane permeation fluxes, the component mass bal-ances and the energy balance were solved sequentially afterhaving solved the flow model i.e., the total continuity andNavierStokes equations. Since only the steady state profilesare of interest here, this decoupling is possible and desirable be-cause of the large differences in time scales on which the flowphenomena and chemical reactions take place. Furthermore, thedecoupling has the clear advantage that different time steps andscales can be used, speeding up the calculations enormously(Krten et al., 2004).

The total continuity and NavierStokes equations (seeTable 1) are solved with a finite difference technique on astaggered computational mesh using a first order time dis-cretisation and implicit treatment of the pressure gradient andlinearised implicit treatment of the drag force. The implicittreatment of the pressure gradient term requires solution of apressure correction equation (Poisson equation) derived fromthe mass defect of the gas phase continuity equation. Theconvection terms have been discretised using a second or-der accurate Barton scheme (Goldschmidt, 2001), while thedispersion terms have been discretised with standard second-order finite-difference representations. Each new time step of


the computational scheme starts with the calculation of thedensity field from the old pressure and concentration field datausing the ideal gas law. Subsequently, the velocity field is cal-culated using the discretised momentum equations, followedby the calculation of the new pressure field using the pressurecorrection equation. Then, the density field is updated usingthe equation of state, and the iteration loop is repeated untilall variables have converged. The component mass and energybalances (see Table 2) have also been solved with a finitedifference technique employing the same computational meshas used in the flow model. The convection terms have beenevaluated with Bartons scheme and the dispersion terms havebeen discretised with standard second order central differencerepresentations. The discretised component mass and energybalances were solved with the alternating direction implicit(ADI) method where a full time step is calculated via two halftime steps treating the transport in the radial direction implicitand in the axial direction explicit in the first half time stepand vice versa in the next half time step. The advantage ofusing ADI over other techniques is that it provides a fast andunconditionally stable solution of the mathematic problem,which allows the use of a large time step when solving thecomponent mass and energy balances (Krten et al., 2004).

3. Autothermal reforming in a packed bed membranereactor

The feasibility of performing ATR of methane in a PBMR hasbeen investigated by considering two limiting cases: isother-mal and adiabatic operation mode. The isothermal operationmode reflects the ideal situation where the energy consump-tion by the reforming reaction is locally exactly balanced bythe heat produced by the combustion reaction and water gasshift. With this case the effect of H2 removal the methane con-version and outlet composition is studied. An isothermal reac-tor is the most ideal mode of operation, because the constanttemperature along the Pd-membrane wall is advantageous formembrane life and stability. Subsequently, the temperature pro-files in an adiabatic reactor are investigated in order to assesswhether the membranes can withstand the resulting temperaturegradients. It will be shown that in the adiabatic mode, unac-ceptably high temperature gradients will emerge, necessitatingthe exploration of different operation modes, viz. wall-cooledoperation and staged O2 injection.

Table 7Operating conditions and reactor dimensions of the base case

Parameter Value Parameter Value

Temperature (C) 600 (m3g m3bed) 0.43Operating pressure (Pa) 1.013 105 s (kg m3) 2000m (kg s1) 1 105 dp (m) 500 106O2 : CH4 (dimensionless) 0.379:1 Dt (m) 0.01H2O : CH4 (dimensionless) 1.621:1 Lt m 0.6

3.1. Base case

The operating conditions and reactor dimensions for the basecase have been listed in Table 7 . For the base case, constantporosity was assumed. The effect of the radial porosity profileis investigated in Section 4.3. The minimum tube length isdetermined by the amount of hydrogen that needs to be removedat a given feed flow rate (assuming sufficient catalytic activityin the selected reactor volume). Optimally, the separation factorS of hydrogen defined as,

S = mH2,separatedmH2,separated +mH2,reactor exhaust

(1)

should be about 8090% because of the trade-off in the reactorvolume and membrane efficiency. Removing 99% of the hy-drogen results in inefficient use of the membrane, because alarge part of the membrane is used to remove a small amountof the produced hydrogen towards the end of the reactor. Thefeed composition is selected such that there is no net energyproduction or consumption when all the methane is convertedand hydrogen is extracted (based on thermodynamic calcula-tions under adiabatic conditions), 20% excess steam has beenused to enhance the CH4 conversion and to reduce the CO con-tent in the reactor exhaust (Patil et al., 2005). For the base casea grid independent solution was obtained with 200 axial by 12radial grid cells.

3.1.1. Isothermal operationSimulations with the packed bed reactor model revealed that

the production of hydrogen is limited by the thermodynamicequilibria, and calculations with the isothermal PBMR modelshow that indeed the thermodynamic equilibria are shifted tofavour hydrogen production (see Fig. 4 ). Under these isother-mal conditions and relative low membrane permeation fluxes,the methane conversion is restricted by the rate of H2 removalvia the membrane and radial concentration gradients are verysmall (see Fig. 5 ).

In Fig. 6 the corresponding velocity profiles in the isother-mal PBMR are displayed. The radial velocity profile showsa nearly linear increase towards the membrane due to the se-lective removal of hydrogen. At the reactor inlet the axial ve-locity increases due to the high steam reforming reaction rate,which results in a net production of moles. Further down-stream the axial velocity decreased because of the hydrogenextraction.


Fig. 4. Methane conversion in the PB and PBMR for the isothermal operationmode (base case).

Fig. 5. Radial profile of the H2 weight fraction for the isothermal operationmode (base case).

One of the advantages of the PBMR is that the CO concentra-tion in the reactor outlet is significantly reduced. This is shownin Fig. 7, where the axial profiles of the mixing-cup weightfractions of CH4, CO and H2 are displayed. In the PBMR, theweight fraction of CO starts to decrease quite rapidly towardsthe end of the reactor, which can be attributed to the WGS re-action due to the removal of H2. The steam partial pressureis decreasing continuously along the reactor length, which re-sults in decreasing reforming reaction rate. Because this pro-cess proceeds via non-stoichiometric reactions resulting in anet formation of molecules, the reactor pressure will influencethe performance. For a packed bed reactor, operation at higherpressures leads to a decrease in the CH4 conversion due to un-favourable thermodynamics, as quantified in Fig. 8.

On the other hand, for a PBMR the methane conversion in-creases at higher pressures, reaching 100% at 2 bar. Moreover,at higher pressures, nearly all CO can be removed from the

(a)

(b)

Fig. 6. (a) Radial and (b) axial velocity profiles for the isothermal operationmode (base case).

reactor exhaust, which means that the WGS reaction reachescompletion. This is advantageous, since it makes a separateunit for CO removal redundant and CO2 can be easily capturedfrom the reactor exhaust. An additional advantage is that com-plete conversion of CO at the reactor outlet is accompaniedby an increased H2 production. At increased pressure com-plete conversion of CH4 and CO can be achieved, indicatingthat the maximum amount of H2 that can be produced, is in-deed removed via the membrane. At atmospheric conditions,the separation factor of H2 equals approximately 95%, whileat 3 bar the separation factor becomes 100%. In the base case,the hydrogen production rate is completely determined by themembrane permeation flux. Typically, higher membrane fluxesmay lead to a situation where mass transfer towards the mem-brane may affect the separation factor and thereby the reactorperformance. This will be investigated in Section 4.1.


Fig. 7. Axial profiles of the mixing-cup weight fractions (base case).

3

2

1

mol

H2

per

mol

CH

4 fe

d

1 2 3Pressure [bar]

MaximumPBMRPB

Fig. 8. Comparison of PB and PBMR at different reactor pressures.

3.1.2. Adiabatic operationThe isothermal operation mode represents an idealised situ-

ation where the endothermic and exothermic reactions are lo-cally exactly balanced. Actual operation of the PBMR withouta sweep gas will approach adiabatic operation without energyexchange via the membrane. The feasibility of adiabatic oper-ation is assessed and the effect on the reactor performance isstudied. The base case was again used with a grid size of 400axial cells and 12 radial cells and a grid independent solutionwas obtained. Because of the imbalance in the heat generatedduring the combustion reactions and the heat consumed in thereforming reaction, a large temperature peak at the reactor en-trance is observed, as depicted in Fig. 9.

It can be seen that in the packed bed reactor thermodynamicequilibrium is already reached very close to the reactor inlet.The very small decrease in the reactor temperature (10 C) to-wards the exit because of the pressure drop of approximately0.17 bar can hardly be seen. In the PBMR, the decreasing tem-

1100

1000

900

800

T [

K]

0.0 0.2 0.4 0.6 0.8 1.0z/L

PBMR

PB

Fig. 9. Axial temperature profiles in a PB and a PBMR.

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.20.0

CO

sel

ectiv

ity [

-]

0.0 1.0z/L

3

2

1

0

H2

/ CH

4 re

acte

d [-

]

Fig. 10. The CO selectivity and H2 yield in a PB and PBMR for the adiabaticmode.

perature towards the end of the reactor is the result of the on-going SRM/WGS reaction because of the continuing hydrogenextraction compared to the isothermal operation mode. The hy-drogen separation factor has increased because of the increasedmembrane permeability at the temperature peak in the first partof the reactor.

The effect of the membrane on the reactor performance forthe adiabatic reactor mode is shown in Fig. 10. At overallmethane conversion of nearly 96% the H2 removal amountsapproximately 95% of the theoretical maximum (3.24 mol H2per mol CH4). As in the isothermal mode, the CO selectivitystrongly decreases along the reactor. The selectivity towardsCO in the reactor exhaust is still 8%, which can be decreasedfurther only with a longer membrane tube. At the entrance ofthe adiabatic reactor the high temperature peak will cause mem-brane instabilities due to evaporation of the dense metal layer.These large temperature gradients along the membrane wall aredetrimental for membrane operation.


1100

1000

1050

950

900

T [

K]

Radial direction Axial d

irection

Fig. 11. 2D temperature distribution in the PBMR for cooled membrane wallat 873 K (operating conditions listed in Table 7).

3.2. Wall-cooled operation

Simulations in adiabatic mode of operation showed largetemperature gradients along the reactor length. Because of therelatively faster methane combustion reaction rates compared tothe reforming reaction rate, a temperature overshoot of almost200300 K over a length less than 1 cm results. It is essentialthat this temperature peak is moderated so that the temperatureat the membrane wall remains below a limit determined by themembrane stability. By cooling/heating the reactor wall with ahigh sweep gas rate, the membrane wall could be maintainedat a constant temperature. The effect of a constant membranewall temperature on the overall reactor performance has beeninvestigated.

If the membrane wall temperature is to be maintained ata constant value of 873 K large radial temperature gradientsarise, as shown in Fig. 11, particularly at the inlet of the reac-tor because of the faster MC reaction rate compared to SRM.These large temperature gradients are undesirable from a cat-alyst stability point of view. The reactor performance in termsof methane combustion, H2 yield and CO selectivity in theexhaust are comparable to the isothermal operation mode, be-cause the hydrogen permeation was comparable in these cases.Nevertheless, the simulation results show that the large temper-ature gradients cannot be avoided, not even with an infinitelyhigh sweep gas rate.

3.3. Staged oxygen feed

By distributing the oxygen feed along the length instead ofco-feeding with CH4, the large axial temperature gradients canbe minimised. It was chosen to demonstrate the effect of adistributed feed of oxygen by dividing the PBMR into stages.Alternatively the oxygen could be distributively fed to the cat-

1000

950

900

850

800

750

700

Tem

pera

ture

[K

]

0.0 0.1 0.2 0.3 0.4 0.5 0.6L [m]

isothermal

3 stages10 stages

Fig. 12. Temperature profiles in a PBMR with staged oxygen feed.

alyst via a porous membrane (e.g. via a shell and tube typeconfiguration), but the operating conditions should be set suchthat counter-diffusion of reactants and products to the perme-ate side is avoided. The overall oxygen to methane ratio is stillbased on the autothermal conditions, but in this case oxygen isdistributed in equal amounts over a number of stages.

In Fig. 12, the axial temperature profile in the PBMR with 3and 10 stages are compared with the isothermal and adiabaticoperation modes. Indeed, the extent of the temperature excur-sion can be decreased somewhat when using staged oxygenfeeding (axial temperature peak is 1058 K for adiabatic, 985 Kfor 3 stages and 889 K for 10 stages). Just after the temperatureexcursion, a large decrease in temperature is observed. Due tothe decreased oxygen concentration, the reforming reaction be-comes more dominant leading to a decrease in the temperature.This effect increases with an increasing number of stages. Withan infinite number of stages, which resembles feeding oxygenwith a porous membrane, this will eventually lead to a linearlyincreasing temperature along the reactor length. Although theextent of temperature excursions can be decreased with thestaged oxygen feeding, the significantly lower average reactortemperature has consequences for the overall methane conver-sion and thus the hydrogen production, because of the lowermembrane permeabilities at lower temperatures (see Fig. 13).

The overall hydrogen production for the case with 10 stagesis 23% less than the isothermal mode of operation and 21%less than adiabatic operation mode. To overcome this issue andachieve a higher methane conversion, the oxygen should not bedistributed linearly. Distributing the oxygen feed in exponen-tially decreasing amounts might give improvements. Neverthe-less, in a view of reactor construction, staged feeding of oxygenmakes the design of a small scale reactor much more complexand large axial temperature gradients at the reactor inlet can-not be avoided. Moreover, the overall reactor efficiency dropsdue to energy losses between the stages and due to mixing ofreaction products with (cold) oxygen. Concluding, in a PBMRfor ATR of methane, large temperature gradients near the re-actor inlet will always prevail, unless a novel catalyst can be


1.0

0.8

0.6

0.4

0.2

0.0

CH

4 co

nver

sion

[-]

0.0 0.2 0.4 0.6L [m]

isothermal

3 stages10 stages

Fig. 13. CH4 conversion in a PBMR with staged oxygen feed.

invented with a lower activity for methane combustion relativeto methane steam reforming. To avoid large temperature gra-dients over the membrane, the membrane should not be placedat the first section of the reactor inlet.

4. Influence of mass transfer limitations

4.1. Effect of membrane flux

Radial concentration profiles are not very pronounced withcurrently available membrane fluxes (in adiabatic mode of oper-ation). However, with the further development and optimisationof the membranes, higher membrane fluxes will become possi-ble in near future. Whether concentration polarisation will oc-cur with increased permeability was investigated numerically.Simulation results where the membrane permeability was in-creased with a factor of 2 and 4, corresponding to H2 fluxesthat may be achieved within a couple of years based on presentH2 membrane research (Pex et al., 2004) are shown in Figs. 14and 15.

Obviously, the reactor performance is strongly enhancedwhen the membrane permeability is increased. By doublingthe permeability, hydrogen extraction can be increased from94% to more than 99% at almost 100% methane conversionand almost 0% CO concentration.

However, the enhanced transport of hydrogen also causessignificant concentration polarisation, as depicted in Fig. 15. Athigher permeability the relative difference in H2 weight frac-tion between the centre and the membrane wall increases from8% to approximately 30% at quadrupled permeability, indicat-ing that at higher membrane permeabilities indeed mass trans-port limitations to the membrane wall will negatively affect thereactor performance resulting in an increased H2 slip throughthe reactor exhaust.

Fig. 14. CO selectivity and H2 separation factor for varying membranepermeability.

Fig. 15. Relative H2 weight fraction profiles at changing membrane perme-ability.

4.2. Effect of reactor diameter

Although increased membrane permeability results in com-plete removal of all produced H2 at total conversion of methane,high flux membranes lead to more pronounced radial concen-tration profiles. The concentration polarisation can be decreasedby decreasing the reactor diameter. Under isothermal condi-tions, the effect of the reactor diameter on the radial concentra-tion profiles was investigated for a case where the permeabil-ity was four times higher when compared to the expression inTable 4. The reactor length was kept at 0.6 m and the inlet massvelocity was changed for these three cases to have a constantinlet velocity.

Fig. 16a depicts the relative decrease of H2 weight fractionrelative to the centreline weight fraction in the PBMR at amethane conversion of approximately 75%. With a large tubediameter, radial concentration gradients indeed become morepronounced reflecting into higher mass transfer limitations


Dt = 0.005 m

Dt = 0.010 m

Dt = 0.020 m

Dt = 0.005 m

Dt = 0.010 m

Dt = 0.020 m

(a)

(b)

Fig. 16. (a) Radial profile of the relative H2 weight fraction at 75% methaneconversion and (b) axial profiles of the CO selectivity and H2 yield fordifferent tube diameters, for isothermal operation mode.

towards the membrane wall. As shown in Fig. 16b, the COselectivity and H2 yield profiles along the reactor length alsobecome worse when selecting a larger reactor diameter. Forefficient utilisation of the expensive membrane, a small mem-brane tube diameter needs to be selected.

4.3. Effect of the porosity profile

To avoid the negative effects of concentration polarisation, asmall membrane tube diameter needs to be selected. Althoughconcentration polarisation is less pronounced for the case withDt of 0.005 m with the currently used particle diameter of500 m as shown in Fig. 16a, a bypass flow near the membranewall might emerge due to increased porosity, which can havesignificant influence on the reactor performance. Simulationswere performed where the effect of the porosity profile on thevelocity profile was taken into account.

Fig. 17shows the radial profiles of the axial velocity at threedifferent axial locations in the reactor, showing indeed a largedifference in the axial velocity when accounting for the radialporosity profile compared to the radial distribution of the ax-ial velocity for the constant porosity case shown in Fig. 6b.

Fig. 17. Axial velocity profiles accounting for the porosity distribution(Dt = 0.005 m).

(b)

(a)

Fig. 18. (a) Effect of the porosity distribution on H2 yield and flux in aPBMR and (b) radial profiles of the relative H2 weight fractions at 40% CH4conversion under isothermal conditions (Dt = 0.005 m, dp = 0.0005 m).

Because of the increased porosity near the membrane wall, by-passing will occur at this location, which results in a morethan three times smaller velocity in the core of the reactor. Theincreased axial velocity near the membrane wall causes an


increase in convective transport, but also influences the axialand radial dispersion coefficients which depend on the local ve-locity and porosity in the packed bed. The effect of the porosityprofile on the reactor performance is shown in Fig. 18.

It can be seen that despite the large effect on the axial ve-locity profile, the effects on the overall performance are rela-tively small for the currently used particle diameter of 0.5 mm.However, the flux profiles are affected because of the decreasedH2 weight fractions at the membrane wall, which has conse-quences for the amount of H2 that can be removed per unit re-actor length. Approximately 5.3% additional length is neededto remove of 2.5107 kg H2/s because of the porosity profile.

This effect becomes even more pronounced for a larger par-ticle diameter (under the assumption that intra-particle limita-tions are still absent). In Fig. 18b the relative H2 weight frac-tions compared to the centreline of the bed at a CH4 conversionof 40% are displayed and it is shown that because of the poros-ity distribution, the relative difference in H2 weight fractionsbetween the membrane wall and the reactor core is increased.This is caused by an increase in the axial velocity near themembrane wall, but also by a lower H2 production rate due tothe lower amount of catalyst at this location because of the in-creased porosity. Concluding it is important to account for theporosity distribution in the modelling of a PBMR, especiallyfor the case of a relatively large particle diameter compared tothe membrane tube diameter and high membrane permeability.

5. Conclusions

The conceptual feasibility of a PBMR for the ATR ofmethane was investigated by a detailed numerical simulationstudy using a 2D reactor model, evaluating different modes ofoperation. It was shown that the use of a hydrogen permse-lective membrane shifts the thermodynamic equilibrium con-straints, enhances hydrogen production and decreases the COconcentration in the reactor exhaust. Contrary to the conven-tional packed bed reactors, higher reactor pressures increasethe methane conversion and the total removal rate of hydro-gen. Simulations for the PBMR with a currently commer-cially available membrane revealed that radial concentrationgradients are small. Although high energy efficiency can beachieved with the autothermal process in a PBMR, large un-desired temperature gradients along the reactor were observedin the adiabatic mode of operation, which are detrimental forthe membrane stability. With cooling of the membrane witha high sweep gas rate, temperature gradients along the mem-brane can be avoided but decreased the hydrogen removal rateand increased the CO concentration in the reactor exhaust,while large temperature gradients in the catalyst bed were noteliminated. Alternatively, distributed feeding of oxygen wasexplored to moderate the axial temperature gradients. Despitethe fact that the extent of temperature excursions at the reac-tor inlet was decreased, a large temperature gradient near thereactor inlet could not be avoided due to decreased methanecombustion at the inlet because of the staged feeding. Due tothe significantly lower average reactor temperature, the reactorperformance in terms of methane conversion and hydrogen pro-

duction was worse. The major disadvantage of this operationmode is that staged feeding of oxygen gives a complex reactordesign and moreover a loss in energy efficiency between thestages. At higher membrane permeability the effect of concen-tration polarisation on the reactor performance becomes morepronounced, which justifies the use of 2D modelling to pre-vent overestimation of the total hydrogen removal rate. Masstransfer limitations towards the reactor wall become more pro-nounced when accounting for the radial porosity distribution,which is particularly important for small reactor diameters toachieve a high specific membrane surface area and relativelylarge particle diameters (to avoid a large pressure drop). Thisresearch has proved that the production of H2 by means ofATR of methane in a PBMR is feasible, and that H2 permse-lective membranes can be utilised to shift the thermodynamicequilibrium to favour a higher H2 production and lower COconcentration in the reactor exhaust. However, the membraneshould be positioned outside the inlet region, where too hightemperatures (detrimental to membrane life) prevail.

Notation

Ai Arrhenius pre-exponential factor, unit depends onreaction

cp heat capacity, J/kg/Kdmem membrane thickness, mdp particle diameter, mDi,eff effective diffusion coefficient, m2/sDr radial dispersion coefficient, m2/sDt tube diameter, mDz axial dispersion coefficient, m2/sEa,i activation energy for reaction i, J/molEact,Pd activation energy for the Pd membrane, J/molg gravitational constant, 9.81 m/s2

i, j radial and axial grid location, dimensionlessJH2 hydrogen flux, kg/m

2/sk0 reaction rate constant, unit depends on reactionKeq equilibrium constant, unit depends on AiKOXi van t Hoff adsorption equilibrium constant, 1/barK Pclt number for heat, dimensionlessL length of reactor, mm number of moles, molM molecular mass, kg/moln time step, dimensionlessnm pressure exponent for the Pd membrane, dimen-

sionlessp pressure, barQPd permeability of the Pd membrane, mol/m/Pa0.72

QPd,0 pre-exponential factor for permeability of the Pdmembrane, mol/m/Pa0.72

r radial coordinate, mrj reaction rate of reaction j, mol/kgcat/sR gas constant, 8.314 J/mol/KRp particle radius,mSh source/sink term for heat balance, J/m3/s


Sr source/sink term for mass balance, kg/m3/st time, sT temperature, Ku mixture velocity, m/sur radial velocity, m/suz axial velocity, m/sXF shape factor, dimensionless

Greek letters

friction factor, dimensionlessHj reaction enthalpy of reaction j, kJ/molr radial grid size, mt time step, sx grid size in direction x, mz axial grid size, m porosity, dimensionless

effectiveness factor, dimensionless thermal conductivity, W/m/Kg gas shear viscosity, kg/m/s stoichiometric coefficient for reaction, dimension-

less density, kg/m3

g stress tensor, kg/m/sm mass flow, kg/sm mass flux, kg/m2/s weight fraction, dimensionless

Subscripts

bed, 0 bed under zero flow conditionsbulk bulk conditionscat catalystg gas phasei ith componentm molecular contributionnc number of componentsnew new valuenr number of reactionsr radialrad radiations solid phaset turbulent contributionz axial

Acknowledgements

The authors would like to acknowledge the financial supportoffered by Shell Global Solutions International and the Dutchministries of Economic Affairs (EZ/Senter) and EnvironmentalAffairs (VROM).

References

Adris, A.M., Elnashaie, S.S.E.H., Hughes, R., 1991. Fluidized bed membranereactor for the steam reforming of methane. Canadian Journal of ChemicalEngineering 69 (5), 1061.

Assabumrungrat, S., Suksomboon, K., Praserthdam, P., Tagawa, T., Goto, S.,2002. Simulation of a palladium membrane reactor for dehydrogenation ofethylbenzene. Journal of Chemical Engineering of Japan 35 (3), 263273.

Barbieri, G., Di Maio, F.P., 1997. Simulation of the methane steam re-formingprocess in a catalytic pd-membrane reactor. Industrial and EngineeringChemistry Research 36 (6), 21212127.

Basile, A., Paturzo, L., Lagana, F., 2001. The partial oxidation of methaneto syngas in a palladium membrane reactor: Simulation and experimentalstudies. Catalysis Today 67 (13), 6575.

Bernstein, L.A., Lund, C.R.F., 1993. Membrane reactors for catalytic seriesand series-parallel reactions. Journal of Membrane Science 77 (23), 155.

Bharadwaj, S.S., Schmidt, L.D., 1995. Catalytic partial oxidation of naturalgas to syngas. Fuel Processing Technology 42 (23), 109.

Carrette, C., Friedrich, K.A., Stimming, U., 2001. Fuel cellsfundamentalsand applications. Fuel Cells 1 (1), 539.

De Groote, A.M., Froment, G.F., 1996. Simulation of the catalytic partialoxidation of methane to synthesis gas. Applied Catalysis A 138 (2), 245.

De Smet, C.R.H., de Croon, M.H.J.M., Berger, R.J., Marin, G.B., Schouten,J.C., 2001. Design of adiabatic fixed-bed reactors for the partial oxidationof methane to synthesis gas. Application to production of methanol andhydrogen-for-fuel-cells. Chemical Engineering Science 56 (16), 48494861.

Fukuhara, C., Igarashi, A., 2003. Two-dimensional simulation of a membranereactor for dehydrogenation of ethylbenzene, considering heat and masstransfer. Journal of Chemical Engineering of Japan 36 (5), 530539.

Gallucci, F., Paturzo, L., Basile, A., 2004. Hydrogen recovery from methanolsteam reforming in a dense membrane reactor: simulation study. Industrialand Engineering Chemistry Research 43 (10), 2420.

Goldschmidt, M., 2001. Hydrodynamic modelling of fluidised bed spraygranulation. Thesis, University of Twente, Enschede.

Hoang, D.L., Chan, S.H., 2004. Modeling of a catalytic autothermal methanereformer for fuel cell applications. Applied Catalysis A 268 (12),207216.

Ioannides, T., Verykios, X.E., 1998. Development of a novel heat-integratedwall reactor for the partial oxidation of methane to synthesis gas. CatalysisToday 46 (23), 71.

Itoh, N., 1987. Membrane reactor using palladium. A.I.Ch.E. Journal 33 (9),15761578.

Itoh, N., Xu, W.-C., Haraya, K., 1994. Radial mixing diffusion of hydrogenin a packed-bed type of palladium membrane reactor. Industrial andEngineering Chemistry Research 33 (2), 197202.

Kikuchi, E., 1995. Palladium/ceramic membranes for selective hydrogenpermeation and their application to membrane reactor. Catalysis Today 25(34), 333.

Kim, J.-H., Choi, B.-S., Yi, J., 1999. Modified simulation of methane steamreforming in pd-membrane/packed-bed type reactor. Journal of ChemicalEngineering of Japan 32 (6), 760769.

Koukou, M.K., Chaloulou, G., Papayannakos, N., Markatos, N.C., 1997.Mathematical modelling of the performance of non-isothermal membranereactors. International Journal of Heat and Mass Transfer 40 (10),24072417.

Krten, U., 2003. Modeling of packed bed membrane reactors: impact ofoxygen distribution on conversion and selectivity in partial oxidationsystems. Thesis, University of Twente, Enschede.

Krten, U., Van Sint Annaland, M., Kuipers, J.A.M., 2004. Oxygendistribution in packed-bed membrane reactors for partial oxidations: effectof the radial porosity profiles on the product selectivity. Industrial andEngineering Chemistry Research 43 (16), 4753.

Lattner, J.R., Harold, M.P., 2004. Comparison of conventional and membranereactor fuel processors for hydrocarbon-based pem fuel cell systems.International Journal of Hydrogen Energy 29 (4), 393.

Mondal, A.M., Ilias, S., 2001. Dehydrogenation of cyclohexane in apalladium-ceramic membrane reactor by equilibrium shift. SeparationScience and Technology 36 (56), 11011116.

Numaguchi, T., Kikuchi, K., 1988. Intrinsic kinetics and design simulationin a complex reaction network; steam-methane reforming. ChemicalEngineering Science 43 (8), 22952301.

Patil, C.S., Sint Annaland, M.v., Kuipers, J.A.M., 2005. Design of a novelautothermal membrane-assisted fluidized-bed reactor for the production ofultrapure hydrogen from methane. Industrial and Engineering ChemistryResearch.


Pex, P.P.A.C., Delft, A.C.v., Correia, L.A., Veen, H.M.v., Jansen, D.,Dijkstra, J.W., 2004. Membranes for hydrogen production with CO2capture. Seventh International Conference on Green House Gas ControlTechnologies (GHGT-7), Vancouver, Canada.

Rostrup-Nielsen, J.R. (Ed.), 1984. Catalytic Steam Reforming, vol. 5.Springer, Berlin.

Rostrup-Nielsen, J.R., 2002. Syngas in Perspective. Elsevier Science B.V.,Kruger Park.

Roy, S., 1998. Fluidized bed steam methane reforming with high-fluxmembranes and oxygen input. Thesis, The University of Calgary, Calgary.

Schlnder, E.U., Tsotsas, E., 1988. Wrmebertragung in festbetten,

durchmischten schttgtern und wirbelschichten. Georg Thieme Verlag,Stuttgart.

Taylor, R., Krishna, R., 1993. Multicomponent Mass Transfer. Wiley, NewYork.

Trimm, D.L., Lam, C.W., 1980. The combustion of methane onplatinum-alumina fibre catalystsi. Chemical Engineering Science 35,14051413.

Witjens, L.C., 2004. Synthesis and characterization of pd/ag membranes forhydrogen separation. Ph.D. Thesis, University of Utrecht, The Netherlands.

Zehner, P., Schlnder, E.U., 1970. Wrmeleitfhigkeit von schttungen beimssigen temperaturen. Chem-Ing-Tech 42 (14), 41.

Modelling of packed bed membrane reactors for autothermal production of ultrapure hydrogenIntroductionReactor modelModel descriptionReaction kineticsMembrane fluxDispersion of mass and heatIntraparticle diffusion limitations

Numerical solution strategy

Autothermal reforming in a packed bed membrane reactorBase caseIsothermal operationAdiabatic operation

Wall-cooled operationStaged oxygen feed

Influence of mass transfer limitationsEffect of membrane fluxEffect of reactor diameterEffect of the porosity profile

ConclusionsAcknowledgementsReferences