Chemical Engineering Science 66 (2011) 2356–2367

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Chemical Engineering Science

0009-25

doi:10.1

n Corr

Faculda

465 Pornn Cor

E-m

mmade

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

Experimental and modeling studies on the low-temperature water-gas shiftreaction in a dense Pd–Ag packed-bed membrane reactor

Diogo Mendes a, Sandra Sa a, Silvano Tosti b, Jose M. Sousa a,c,n, Luis M. Madeira a,nn, Adelio Mendes a

a LEPAE, Departamento de Engenharia Quımica, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugalb ENEA, Unit �a Tecnica Fusione, C.R. ENEA Frascati, Via E. Fermi 45, Frascati (RM) I-00044, Italyc Departamento de Quımica, Escola de Ciencias da Vida e do Ambiente, Universidade de Tras-os-Montes e Alto Douro, Apartado 1013, 5001-801 Vila-Real Codex, Portugal

a r t i c l e i n f o

Article history:

Received 30 July 2010

Received in revised form

24 December 2010

Accepted 17 February 2011Available online 24 February 2011

Keywords:

Low-temperature water-gas shift reaction

Pd–Ag membrane reactor

Modeling

Simulation

Pure hydrogen

CO conversion

09/$ - see front matter & 2011 Elsevier Ltd. A

016/j.ces.2011.02.035

esponding author at: LEPAE, Departamen

de de Engenharia, Universidade do Porto, R

to, Portugal.

responding author. Tel.: +351 225081519.

ail addresses: jmsousa@fe.up.pt (J.M. Sousa),

ira@fe.up.pt (L.M. Madeira).

a b s t r a c t

In this work, an experimental and modeling study is described, focusing on the performance of a Pd–Ag

membrane reactor recently proposed and suitable for the production of ultra-pure hydrogen. A packed-

bed membrane reactor (MR) with a ‘‘finger-like’’ membrane configuration has been used for carrying

out the water-gas shift reaction (WGS) in the region of low temperature operation using a simulated

reformate feed.

The experiments were performed under a broad range of operating conditions of temperature

(200–300 1C) and space velocity (1200–10,800 LN kgcat�1 h�1); the effect of feed pressure (1–2 bar)

was also analyzed, as well as the operating mode at the permeate side: vacuum (30 mbar) or sweep gas

(1.0 bar; nitrogen at 1 LN min�1). A one-dimensional, isothermal and steady-state model is proposed,

which assumes axially dispersed plug flow pattern and pressure drop in the retentate side and plug

flow with constant pressure in the permeate side. An innovative composed kinetic model was also used

to describe the catalytic activity of the catalyst for the WGS reaction. In general, the simulation results

showed a good agreement to the experimental data, in terms of carbon monoxide conversion and

hydrogen recovery (and also outlet retentate composition) using only two fitting parameters related to

the decline of H2 permeability due to the presence of CO. Both simulation and experimental runs

showed that the MR achieves high performances, for some operating conditions clearly above the

maximum limit for conventional packed bed reactors. The performance reached is particularly relevant

when hydrogen is recovered via sweep gas mode (a high sweep flow rate was employed), because a

lower partial pressure could be reached than using vacuum pumping. In the first case, almost complete

CO conversion and H2 recovery could be reached.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Humanity is facing one of its biggest challenges: the effect ofgreenhouse-gas emissions on climate change. One of the maincontributors for the increased global warming is the carbon dioxide.The increase of CO2 concentration in the atmosphere is mainlycaused by human activities, as a consequence of the large use offossil fuels. In this sense, serious attention is being given to CO2

abatement (Aresta and Dibenedetto, 2007; Perinline et al., 2008).Polymer electrolyte membrane fuel cells (PEMFCs) represent

one of the most promising technologies to effectively reduce CO2

ll rights reserved.

to de Engenharia Quımica,

ua Dr. Roberto Frias, 4200-

emissions. These devices are electrochemical membrane reactorsthat combine hydrogen (the fuel) and oxygen (from air) toproduce electrical power in an efficient way, exhausting justwater vapour (Barbir, 2005). However, strict hydrogen fuelspecifications are required for low temperature PEMFC enginevehicles and therefore ultra-pure hydrogen must be delivered(limit of CO content depends on the temperature and devicesused, typically in the range from r0.2 ppm (ISO, 2008) till10 ppm (Zhang, 2008; Srinivasan, 2006)).

From the point of view of the hydrogen fuel processor, suchtask may be achieved integrating a hydrogen permselectivemembrane, like a Pd–Ag one, into a water-gas shift (WGS) reactor.The goal of this process is to reduce the CO content in thehydrogen streams according to the following chemical reaction:COþH2O 2 CO2þH2. In order to produce high-purity hydrogenat the highest possible CO conversion and reaction rate, two-stageadiabatic WGS converters are typically used in industrial practice.Since each reactor operates in different temperatures range,

Fig. 1. View of the Pd–Ag membrane tube (geometrical characteristics of the

membrane section: 10 mm I.D., 50 mm thick and 50 mm of length).

D. Mendes et al. / Chemical Engineering Science 66 (2011) 2356–2367 2357

distinctive commercial catalysts are used: a Fe-based catalyst forthe high temperature stage (320–360 1C) and Cu-based materialsfor the low temperature operating stage (190–250 1C) (Ratnasamyand Wagner, 2009). The membrane can then be placed on theouter surface of the catalytic bed and withdraw hydrogen con-tinuously from the reaction zone (retentate side). As hydrogenpermeates through the membrane, the chemical equilibrium ofthe WGS reaction is shifted towards the reaction products side,according to Le Chatelier’s principle, thereby increasing thecarbon monoxide conversion. Increasing the driving force forhydrogen permeation (difference between the hydrogen partialpressure values in the retentate and permeate sides), the conver-sion enhancement should also, in principle, increase. If thepermeate side is under vacuum, nearly pure hydrogen can becollected from this chamber (as long as the membrane used isonly permeable towards H2). Another alternative which in prin-ciple also allows increasing the driving force is using steam or aninert as sweep gas, thereby increasing the hydrogen flux, but afurther separation unit is necessary to produce pure hydrogen.

The gas stream leaving the reactor from the retentate side iscomposed predominantly by carbon dioxide, with small amountsof hydrogen and water vapour. Further condensation of the steamleaves a stream more concentrated in CO2, which may be recycledinto useful products (Olah et al., 2006) or may be compressed andstored. In this case, the operating costs may be reduced.

Several authors have developed mathematical models withvarious level of complexity reporting the advantages of using Pd-alloy membrane reactors (MRs) for the WGS reaction. Most ofthem are steady-state and one-dimensional (Adrover et al., 2009;Basile et al., 2001; Brunetti et al., 2007; Criscuoli et al., 2000;Gosiewski et al., 2010), but two-dimensional including axial andradial gradients are also reported (Markatos et al., 2005).Isothermal MR operation is generally assumed, but a few otherworks include also energy balances, allowing to simulate non-isothermal operation, adiabatic or non-adiabatic (Adrover et al.,2009; Brunetti et al., 2007). However, very few studies criticallycompare the proposed models with experimental results. More-over, such comparisons are mostly based only in terms ofconversion (or conversion enhancement over the thermodynamicvalue) and take into account data reported in the open literaturewith respect to membrane properties and kinetic reaction rates,most of the times obtained for very specific conditions, some-times different from those employed in the simulations.

One of the first works that combined experimental results andmathematical modeling was performed by Uemiya et al. (1991).These authors conducted the WGS reaction at 1 bar and 400 1C usinga commercial iron–chromium oxide catalyst placed inside a 20 mm-thick Pd membrane supported on porous glass tube. A simplestream of CO and H2O was fed into the MR and argon supplied tothe permeation side, counter-currently, to sweep the permeatedhydrogen. To validate the experimental results, the authors devel-oped a model based on simple assumptions, namely isobaric andisothermal operation conditions and plug-flow pattern for bothretentate and permeate sides, but whose results agreed well withthe experimental data. A similar mathematical model was alsodeveloped by Criscuoli et al. (2000) for a Pd-supported membranereactor using a typical reformate gas mixture for the WGS reactionand kinetic data taken from literature. Also here the model fittedwell the experimental results.

The main objective of the present study was to develop asimplified model and critically compare it with the experimentalresults obtained in a self-supported membrane, conceived especiallyfor the production of ultra-pure hydrogen. Experiments in a broadrange of operation conditions were carried out in a compact Pd–Agmembrane reactor, which arrangement was recently proposedby Tosti et al. (2006) and Mendes et al. (2010b), packed with a

low-temperature WGS CuO/ZnO/Al2O3 catalyst. This Pd–Ag alloymembrane shows both high permeability and selectivity towardshydrogen (Tosti et al., 2006), being suitable to carry out the WGSreaction. The innovative kinetic equation used in the model wasdependent on the temperature operation range, according to pre-vious experiments obtained by the authors (see Section 2.2.2). Themodel was validated in terms of CO conversion, retentate composi-tion and hydrogen recovery for the temperature, feed space velocityand feed pressure ranges considered. In addition, the model wasused to simulate the performance of the Pd–Ag WGS MR in terms ofCO conversion and H2 recovery in a wide range of the parametricspace described by Damkohler’s number (Da, ratio between thereaction rate at the reference temperature and the feed flow rate(Froment and Bischoff, 1990)) and a parametric contact time(G, ratio between the characteristic feed flow time and the char-acteristic permeation time for the reference component (Sousa et al.,2001)) (cf. Section 3.2). These two parameters describe generally thepossible operation conditions to be used in the reactor, allowingthus to define the optimal operating regions in terms of COconversion and H2 recovery.

2. Experimental

2.1. Palladium–silver membrane tube

The Pd–Ag permeator tube has been produced by cold-rollingand diffusion welding of an annealed commercial metal foil(75 wt% of Pd and 25 wt% of Ag, from Johnson Matthey) accordingto a previously described technique (Tosti and Bettinali, 2004;Tosti et al., 2001). This provided a self-supported 50 mm thickPd-based membrane tube with a diameter large enough (10 mm)to allow hosting the catalyst inside it (in opposition to otherscommercially available membranes with very low diameter—

capillary tubes). In order to give the required mechanical stiffnessand to guarantee the tightness with the membrane module, astainless steel VCRs connection and a steel plug were brazed atthe ends of the membrane tube, as shown in Fig. 1.

The permeator tube was assembled inside the membranemodule in a finger-like configuration, which allows the elonga-tion/contraction of the membrane following thermal and hydro-gen permeation cycles. In this way, mechanical stress is avoidedand a long lifetime for the membrane is expected (Tosti et al.,2006). The WGS catalyst was packed in the bore side and thepermeated hydrogen was collected in the shell side. The config-uration of the single-tube MR used is shown in Fig. 2.

2.2. Experimental set-up

The experimental apparatus used for carrying out the WGSreaction, as well as for evaluating the membrane separation

Fig. 2. Scheme of the Pd–Ag MR (sweep gas flowing counter-currently).

D. Mendes et al. / Chemical Engineering Science 66 (2011) 2356–23672358

properties, is divided into three sections, namely, (i) the feedsection, consisting of gas cylinders and pressure regulators, massflow controllers (Bronkhorst Hi-Tec, model F201) and a ControllerEvaporator Mixer (CEM, Bronkhorst) unit to provide the desiredwater vapour flow rate (streams are heated before the reactorinlet to avoid condensation of water and to pre-heat the reactionmixture), (ii) the reactor section, consisting of an oven (Memmert,type UNE200—maximum operating temperature of 300 1C) forheating the membrane reactor, two pressure gauges (Druck, ref.4010, 7 and 5 bar, respectively), two back-pressure regulators(Swagelok) for controlling the pressure, a condenser and adiaphragm vacuum pump (Thomas Instruments, ref.: 7011-0069), and (iii) the analysis section, which consists of two flow-meters (Bronkhorst Hi-Tec, model F201) to separately measurethe retentate and permeate streams and a gas chromatograph(Dani 1000 GC) to analyze the retentate dry gas composition.Further details concerning the set-up and analysis method can befound elsewhere (Mendes et al., 2009).

2.2.1. Hydrogen permeation and WGS reaction tests

Pure hydrogen permeation tests were performed at temperaturesin the range 200–300 1C, pressures in the range 1.1–2.5 bar and flowrates in the range 50–190 mLN min�1. The H2 feed gas flowed alongthe inner side of the membrane and the permeating stream flowrate was measured on the shell side at atmospheric pressure with amass flow meter after steady state had been achieved (approxi-mately 1 h), at the desired temperature. Neither sweep gas norvacuum was used. Pressures in the two sides of the membrane tubewere monitored via pressure transducers. Frequently, the selectivityof the membrane was obtained against nitrogen. When pressurized

nitrogen was introduced in the retentate chamber and the moduleclosed, no decline in the pressure was noticed after 8 h, confirmingthe full hydrogen permeation selectivity of the Pd–Ag membrane.Besides, no change in the membrane performance was noticedduring the experimental campaign. This is in line with a previouswork by Tosti et al. (2006), who observed the complete hydrogenselectivity and durability of these permeators in long-term tests(1 year).

As shown in Fig. 2, the MR considered in this work is a tube-and-shell configuration system. The WGS reaction was performedin the temperature range 200–300 1C by packing 1.5 g of acommercial CuO/ZnO/Al2O3 catalyst, supplied by REB Researchand Consulting, in the bore side of the inner tube/membrane ofthe finger-like membrane reactor—cf. Fig. 2. As shown in Fig. 2,the catalyst was loaded only in the bed section where there is themembrane. Prior to the reaction runs, the WGS catalyst wasactivated in situ with a mixed gas flow of H2/N2. Details about thecatalyst pre-treatment (reduction) are described elsewhere(Mendes et al., 2009).

The reaction tests were carried out using the following feedgas composition: 4.7% CO, 34.8% H2O, 28.7% H2, 10.2% CO2 andbalanced in N2, which simulates a reformate feed coming from atypical autothermal reforming of either ethanol (Salemme et al.,2010) or liquid hydrocarbons (Pasel et al., 2004). The H2O/COratio used was 7.4. This is a high value, leading in practice to asignificant energy consumption (required for water demineraliza-tion and vaporization). However, it is in the range employed byindustrial packed-bed reactors, where excess of steam is used tofavor the thermodynamic equilibrium shift. Besides, the feed gascomposition used herein is equal to that employed for determin-ing the reaction kinetics (Mendes et al., 2010a).

D. Mendes et al. / Chemical Engineering Science 66 (2011) 2356–2367 2359

The reaction pressure (that is, the pressure in the lumen sideof the membrane) and the feed flow rate were varied in the range1–2 bar and 30–270 mLN min�1, respectively. As the driving forcefor H2 permeation through the membrane is the differencebetween the partial pressures on both sides of the Pd–Agmembrane, the permeation flux increases by reducing the hydro-gen permeate pressure. This can be achieved by decreasing thetotal permeate pressure (pure hydrogen) or using sweep gas.Thus, two operating modes were studied: (i) hydrogen wasrecovered in the shell side by vacuum pumping (shell sidepressure�30 mbar), and (ii) an inert gas (N2, 1 LN min�1) wasfed into the shell side flowing counter-currently (cf. Fig. 2). In thiscase, a sufficient length of the sweep gas pipe was inserted insidethe oven in a spiral form to ensure pre-heating until the desiredtemperature. Additionally, and to simulate the performance of apacked bed reactor (PBR from now on) for posterior comparisonwith the MR operation, the permeate chamber was closed and thesteady-state data were recorded.

Different parameters affecting the catalytic reaction and themembrane operation were studied, namely the feed flow rate, thereaction temperature, the feed pressure and the operation mode(permeate side under vacuum or with sweep gas flowing counter-currently). Such effects have been evaluated in terms of thecarbon monoxide conversion (XCO) and hydrogen recovery(ReH2

) at steady-state conditions. Both quantities were calculatedaccording to Eqs. (1) and (2), respectively:

XCO ¼ 1�uR,outpR,out

CO

uR,inpR,inCO

ð1Þ

ReH2¼

uP,outpP,outH2

uR,outpR,outH2þuP,outpP,out

H2

ð2Þ

where u is the interstitial velocity and p is the partial pressure.The superscripts R and P stand for retentate and permeatechambers, respectively, and in and out means inlet and outlet ofthe reactor, respectively.

2.2.2. WGS reaction kinetics

The WGS kinetics and mechanisms over the above-mentionedcatalysts (Fe-based for the higher temperatures and Cu-based forthe lower temperatures) have been studied in the past by manyauthors (Ayastuy et al., 2005; Koryabkina et al., 2003). However, itis very controversial if the predominant reaction mechanism forCu-based materials is the redox or the associative (Langmuir–Hinshelwood type) one. On the other hand, the predominantreaction mechanism for Fe-based systems is much less contro-versial, being the redox mechanism the most accepted. In thiswork, it was used a commercial CuO/ZnO/Al2O3 catalyst (suppliedby REB Research and Consulting). Previous experiments with thesame catalyst showed a good relation between activity andstability for the WGS reaction in the entire range of temperaturestested (150–300 1C) (Mendes et al., 2009). Experimental runs tocollect intrinsic kinetic data with this catalyst were then carriedout in a packed bed reactor, in the temperature range 180–300 1C.According to preliminary studies (Mendes et al., 2010a), twodifferent kinetic models were proposed. For temperaturesbetween 180 and 200 1C, the associative mechanism showed thebest fitting, while the redox pathway showed the best agreementin the range 215–300 1C, according to Eqs. (3) and (4) below.

For the lower temperatures range—LT (180–200 1C):

RLT ¼kLT pCOpH2O�pCO2

pH2=Ke

� �1þP

iKa,LTi pi

� �2ð3Þ

For the higher temperatures range—HT (215–300 1C):

RHT ¼kHT pCOpH2O�pCO2

pH2=Ke

� �pCO 1þKa,HT

CO2pCO2

=pCO

� � ð4Þ

where i refers to the i-th component, R stands for the localreaction rate, k is the forward rate constant, Ke is the thermo-dynamic equilibrium constant and Ka is the equilibrium adsorp-tion constant of each species. In the membrane reactor, thepressure of each species is the one at the retentate side. Thesetwo kinetic models were used in the present work to describe thecatalytic activity of the catalyst for the WGS reaction carried outin the Pd–Ag membrane reactor.

The temperature dependence for the reaction rate and for theadsorption equilibrium constants is described by the Arrheniusand van’t Hoff laws, Eqs. (5) and (6), respectively:

k¼ k0 exp �Ek

RT

� �ð5Þ

Kai ¼ Ka,0

i exp �DHa

i

RT

� �ð6Þ

where k0 is the pre-exponential factor of the reaction rateconstant, Ek is the activation energy for the WGS reaction, R isthe gas constant, T is the absolute temperature, Ka,0 refers to thepre-exponential equilibrium adsorption constant, and Ha standsfor the enthalpy of adsorption.

Finally, the temperature dependence of the thermodynamicequilibrium constant is described by Eq. (7) (Moe, 1962):

Ke ¼ exp4577:8

T�4:33

� �ð7Þ

The parameters k0, Ek, Ka,0i , and DHa

i were determined for eachtemperature range (LT and HT) through the fitting of the experi-mental data and are shown in Table 1. In addition to the meanestimated values are also given the fitting error associated to eachparameter, assuming t-student distribution and for 95% confi-dence level, and computed using the 10 best fittings.

Analyzing the parameters for the LT regime, it can be inferredthat, under the operating condition used in this work, theadsorption of CO and H2O at the catalyst surface is much lowerthan the adsorption of CO2 and H2. In this way, the kineticequation considered in the simulation calculations performedalong this study was simplified to:

RLT ¼kLT pCOpH2O�pCO2

pH2=Ke

� �1þKa,LT

CO2pCO2þKa,LT

H2pH2

� �2ð3aÞ

3. Membrane reactor model

3.1. Development of the model

The catalytic membrane reactor considered in this study hasthe general features described above. The pseudo-homogeneous1-D model proposed for describing this reactor is based on thefollowing main assumptions:

�

Steady-state and isothermal operation. � Axially dispersed plug-flow pattern in the retentate side with

pressure drop described by Ergun equation.

� Negligible mass and heat-transfer resistances. � Ideal plug-flow pattern in the permeate side with no

pressure drop.

� Ideal gas behavior.

Table 1Calculated parameters for mechanistic-derived rate equations. Fitting errors of parameters are for 95% confidence level (Mendes et al., 2010a).

Parameter T¼180–200 1C (LT) T¼215–300 1C (HT)

k0 (for temperatures 180-2001C�mol g�1cat h�1 Pa�2;

for temperatures 215-3001C�mol g�1cat h�1 Pa�1)

1.18870.000 1.841�10�370.210�10�3

Ek (kJ mol�1) 36.65870.000 6.71070.399

Ka,0CO ðPa�1

Þ 2.283�10�2470.000�10�24

Ka,0H2OðPa�1

Þ 1.957�10�2870.000�10�28

Ka,0CO2ðPa�1

Þ 5.419�10�470.002�10�4 6.343�10�170.727�10�1a

Ka,0H2ðPa�1

Þ 2.349�10�470.000�10�4

DHaCOðkJ mol�1

Þ �45.99670.158

DHaH2 OðkJ mol�1

Þ �79.96370.172

DHaCO2ðkJ mol�1

Þ �16.47470.009 �19.45970.402

DHaH2ðkJ mol�1

Þ �13.27970.192

a This value is dimensionless.

D. Mendes et al. / Chemical Engineering Science 66 (2011) 2356–23672360

The assumption of isothermal operation in a reactor dependson the extent of the reaction heat compared to the heat loss/gainthrough the reactor walls. In low-scale (laboratory) reactors, likethe one considered in the present study, this hypothesis isacceptable, due to the high ratio between heat transfer area andthe reaction volume or when the consumption or release of heatis low. However, this condition may not be true when higherprocess scales are used (Adrover et al., 2009).

The axial and radial dispersion inside the reactor may have alarge effect on the predicted conversion (Koukou et al., 1996).However, radial concentration gradients should be negligiblewhen the permeation flux is comparatively lower than theconvective flux (Tiemersma et al., 2006). Therefore, we consideredin the present model only axial dispersion.

The governing equations for the retentate (reaction) andpermeation sides are as follows:

Retentate side—Partial mass balance:

d

dzuRpR

i

� ��

d

dzDaxPR d

dz

pRi

PR

� �� �þ

2prm

ebARRTJi�

Wcat

ebVRRTniR¼ 0 ð8Þ

Total mass balance:

d

dzðuRPRÞþ

2prm

ebARRTX

i

Ji�Wcat

ebVRRTX

i

niR¼ 0 ð9Þ

Pressure drop:

dPR

dzþ150

mgð1�ebÞ2

ðebÞ3ðdpÞ

2uRþ1:75

rgð1�ebÞ

dpðebÞ3

uR9uR9¼ 0 ð10Þ

Boundary conditions:Danckwerts boundary conditions for retentate side (Froment

and Bischoff, 1990):

z¼ 0:d

dz

pRi

PR

� �¼�

uR

ebDax

pR,ini �pR

i

� �PR

,

uR � uR,in ¼uF

eband PR ¼ PR,in ¼ PF ð11Þ

z¼ ‘:d

dz

pRi

PR

� �¼ 0 ð12Þ

where z is the axial coordinate, ‘ is the reactor length, P is thetotal pressure, Dax is the effective axial dispersion coefficient, rm isthe internal radius of the membrane, AR is the cross-sectional areaof the retentate chamber, VR is the volume of the reactionchamber, eb is the void fraction of the catalyst bed, J is the fluxthrough the membrane, Wcat is the mass of catalyst bed, and dp isthe catalyst particle diameter. vi is the stoichiometric coefficientof species i, taken negative for the reactants, positive for the

reaction products, and null for components that do not take partin the reaction.

The viscosity of the gas mixture, mg, was obtained by the Wilkemethod (Poling et al., 2004). The respective density, rg, wascalculated by the virial equation, with the coefficients takenfrom Smith et al. (1996). The variation of the effective axialdispersion coefficient, Dax, for the range of conditions tested wasnegligible (Perry and Green, 1999); so, the average value of5.40�10�5 m2 s�1 was used.

Permeate side—Partial mass balance:

d

dzuPpP

i

� �þ f

2prm

APRTJi ¼ 0 ð13Þ

Total mass balance:

PP duP

dzþ f

2prm

APRTX

i

Ji ¼ 0 ð14Þ

Boundary conditions—Vacuum mode:

z¼ 0: uP ¼ 0 and pPi ¼ PP ð15Þ

Sweep gas mode (counter-current operation):

z¼ ‘: pPi ¼ pP,in

i and uP ¼ uP,in ð16Þ

where AP is the cross-sectional area of the permeate chamber andf is defined as �1 or +1 according to the flow (co-current orcounter-current, respectively).

Membrane permeation equation: permeation of hydrogenthrough a dense palladium membrane occurs via a solution-diffusion mechanism (Dittmeyer et al., 2001). Richardson’sequation (based on Sieverts’ law) is typically used to describethe overall permeation rate of hydrogen through the membrane(Basile, 2008) and is used herein. Due to the high membraneradius/membrane thickness ratio, the Pd–Ag membrane isapproached to a flat shape, despite its cylindrical geometry.

The transport properties of the Pd–Ag membrane used in thisinvestigation were previously studied based on single permeationmeasurements (for details, see (Mendes et al., 2010b)). The Pd–Agmembrane showed ideal selectivity towards H2, therefore Ji¼0except for i�H2, Eqs. (8) and (9) and (13) and (14).

The H2 permeating flux through the Pd–Ag membrane isexpressed in terms of Richardson’s equation (Eq. (17)) andcorrected for the temperature using an Arrhenius type depen-dence (Eq. (18)):

JH2ðzÞ ¼

LH2

d

ffiffiffiffiffiffiffiffiffiffiffiffiffipR

H2ðzÞ

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffipP

H2ðzÞ

q� �ð17Þ

D. Mendes et al. / Chemical Engineering Science 66 (2011) 2356–2367 2361

LH2¼ L0

H2exp �

Ep

RT

� �ð18Þ

where LH2is the membrane permeability towards hydrogen, d is

the membrane thickness, Ep is the permeation activation energyand L0

H2is the pre-exponential factor.

Gaseous species such as H2O, CO, CO2, and N2 inevitably co-exist in the WGS reaction process, affecting the hydrogen per-meation of the Pd-based membranes, though without affectingthe H2 selectivity (Barbieri et al., 2008; Unemoto et al., 2007). Inthe present MR model, the hindrance effect due to the presence ofCO was taken into account using an extended equation, pre-viously proposed by Barbieri et al. (2008). By including a correc-tion factor, the authors arrived to a modified equation, namedSieverts–Langmuir formulation:

JH2ðzÞ ¼ 1�c

KpCOpCO

1þKpCOpCO

!LH2

d

" # ffiffiffiffiffiffiffiffiffiffiffiffiffipR

H2ðzÞ

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffipP

H2ðzÞ

q� �ð19Þ

c and KpCO are adjustable parameters and were obtained by fitting

the H2 recovery from the theoretical model to the respectiveexperimental results, as described below (Section 4.1). In thisequation, the term Kp

COpCO=ð1þKpCOpCOÞ defines the fraction of the

membrane surface covered by adsorbed CO. The proportionalitycoefficient, c, accounts for the dimensionless reduction of thepermeable area hindered by CO molecules. This parameterdepends only on the temperature, while Kp

CO depends on thetemperature and CO pressure.

3.2. Dimensionless equations

The model variables were made dimensionless with respect tothe feed conditions (uF), to hydrogen species ðLH2

Þ and to thereactor length ð‘Þ. The reference pressure was considered 100 kPaand the reference temperature 273 K. Changing for dimensionlessvariables and introducing suitable dimensionless parameters,Eqs. (3a)–(16) and (19) become as follows:

RLT� ¼exp gk,LT 1� 1

T�

� �� �p�COp�H2O�

p�CO2

p�H2

Ke

� �1þKa,0,LT

CO2exp �

DHa,LTCO2

RT

� �Pref p�CO2

þKa,0,LTH2

exp �DHa,LT

H2RT

� �Pref p�H2

� �2

ð20Þ

RHT� ¼exp gk,HT 1� 1

T�

� �� �p�COp�H2O�

p�CO2

p�H2

Ke

� �p�CO 1þKa,0,LT

CO2exp �

DHa,LTCO2

RT

� �p�

CO2p�

CO

� � ð21Þ

d

dxuR�pR�

i

� ��

1

Pe

d

dxPR� d

dx

pR�i

PR�

� �� �þGT�J�i �DaT�niR

� ¼ 0 ð22Þ

d

dxðuR�PR�ÞþGT�

Xi

J�i �DaT�X

i

niR� ¼ 0 ð23Þ

dPR�

dxþam�guR�þbr�guR�9uR�9¼ 0 ð24Þ

x¼ 0:1

Pe

d

dx

pR�i

PR�

� �¼ uR,in�

pR�i �pR,in�

i

� �PR�

,

uR� ¼ uR,in� and PR� ¼ PR,in� ð25Þ

x¼ 1:d

dx

pR�i

PR�

� �¼ 0 ð26Þ

d

dxuP�pP�

i

� �þ fGsT�J�i ¼ 0 ð27Þ

d

dxuP�PP�� �

þ fGsT�X

i

J�i ¼ 0 ð28Þ

Vacuum mode:

x¼ 0: pP�i ¼ PP� and uP� ¼ 0 ð29Þ

Counter-current mode:

x¼ 1: pP�i ¼ pP,in�

i and uP� ¼ uP,in� ð30Þ

J�H2ðxÞ ¼ 1�c

KpCOPref pR�

CO

1þKpCOPref pR�

CO

!exp gp 1�

1

T�

� �� �" #

�

ffiffiffiffiffiffiffiffiffiffiffiffiffipR�

H2ðxÞ

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffipP�

H2ðxÞ

q� �ð31Þ

where gk,LT ¼ Ek,LT=RTref , gk,HT ¼ Ek,HT=RTref , gp ¼ Ep=RTref , p�i ¼ pi=

Pref , P� ¼ P=Pref , u� ¼ u=uref , L�H2¼ 1, x¼ z=‘, a¼ 150 ð1�ebÞ

2mref

uref‘=ðebÞ3ðdpÞ

2Pref , b¼ 1:75ð1�ebÞMref ðuref Þ2‘=dpðebÞ

3 RTref , s¼ebAR=AP , Pe¼ ‘uref =Dax, G¼ AmRTref

ffiffiffiffiffiffiffiffiPref

pLref ðTref Þ= eburef AR. The

superscript * stands for dimensionless variables, and the subscriptref stands for reference component or conditions. Pe is the Pecletnumber for mass transfer, G is a dimensionless contact time (ratiobetween the characteristic feed flow time and the characteristicpermeance time of the reference component). The Damkohlernumber (ratio between the reaction rate at the reference tem-perature and the feed flow rate to the reactor) was definedindependently for each of the kinetic models, depending on thetemperature range. For the lower temperature range, Da¼WcatR

Tref kLT ðTref ÞðPref Þ2=eburef AR, while Da¼WcatRTref kHT ðTref ÞPref =eburef

AR for the higher temperature range. The remaining symbols arereported in the nomenclature.

3.3. Numerical solution strategy

To simulate the WGS membrane reactor, it is necessary tosolve Eqs. (22)–(24), and (27) and (28) with the respectiveboundary conditions. These equations were transformed intopseudo-transient ones, by adding a time derivative term to theirright-hand side, avoiding so numerical instability problems(Sousa et al., 2001). The partial differential equations werespatially discretized using the finite volumes method (Sa et al.,2009) and the resulting ODEs were integrated in time by LSODA, apackage written by Petzold and Hindmarsh (1997), until an errorcriterion was achieved (time derivative of each dependent vari-able and for each of the spatial coordinate smaller than1�10�12). All physical properties of the gas mixture (mg andrg) were evaluated at local conditions.

4. Results and discussion

4.1. Dimensional analysis: model validation

In this section, the effect of temperature, feed space velocity andreaction pressure on the performance of the MR operating invacuum and sweep gas modes was studied. Moreover, for all theoperating conditions considered, the catalyst activity (evaluatedbased on CO conversion) and the membrane separation ability(evaluated in terms of H2 recovery) were quantified and the resultscompared with the ones from the proposed model. The experimen-tal conditions and the simulation variables are shown in Table 2.

As described in Section 3.1, c and KpCO are adjustable para-

meters, obtained by fitting the H2 recovery from the theoreticalmodel to the respective experimental results. The adjusted values ofc and Kp

CO were in the ranges 0.6–1.0 and (0.5–1.5)�10�4 Pa�1,respectively, considering the values for all temperatures and flow

Experimental Hydrogen Recovery, ReH2

Sim

ulat

ed H

ydro

gen

Rec

over

y, R

e H2

0.00.0

0.2

0.4

0.6

0.8

1.0

MR - Sweep Gas ModeMR - Vacuum Mode

Experimental CO Conversion, XCO

Sim

ulat

ed C

O C

onve

rsio

n, X

CO

0.75

0.75

0.80

0.85

0.90

0.95

1.00

PBRMR - Vacuum ModeMR - Sweep Gas Mode

0.2 0.4 0.6 0.8 1.0 0.80 0.85 0.90 0.95 1.00

Fig. 3. Parity plots of calculated and experimental results for H2 recovery (A) and CO conversion (B).

200

CO

Con

vers

ion,

XC

O

0.80

0.85

0.90

0.95

1.00

Temperature, T / ºC200

Hyd

roge

n R

ecov

ery,

Re H

2

0.0

0.2

0.4

0.6

0.8

1.0

220 240 260 280 300 220 240 260 280 300

Temperature, T / ºC

Fig. 4. Effect of the reaction temperature and feed gas space velocity on the CO conversion (A) and H2 recovery (B) as a function of the reaction temperature in the MR, operating in

counter-current mode. Qsweep ¼ 1:0 LN min�1, PF ¼ 2:0 bar, and PP ¼ 1:0 bar. Error bars are based on t-student distribution and 95% confidence limit (with 3 replicates).

Table 2Experimental conditions for the Pd–Ag MR runs.

Variable Value/range Variable Value/range

T 200–300 1C rm 0.50 cm

PF 1–2 bar rshell 1.75 cm

PP 0.030–1 bar Ep 10.72 kJ mol�1

Wcat 1.5 g L0H2

5.445�10�8 mol m m�2 s�1 Pa�0.5

GHSV 1200–10,800 LN kgcat�1 h�1 d 50 mm

Qsweep 1000 mLN min�1 dp 300 mm

‘ 5 cm eb 0.40

D. Mendes et al. / Chemical Engineering Science 66 (2011) 2356–23672362

rates. Similar results were reported by Mejdell et al. (2009). Ascan be realized from Fig. 3A, the adherence of the simulatedhydrogen recovery to the experimental results is very good. Thecomparison between the experimental and the calculated resultsfor the CO conversion is shown in Fig. 3B. Again, the model showsa good agreement with the experimental data, with a fewexceptions at the lowest carbon monoxide conversions, obtainedfor temperatures of 200 1C (remember that the model was tunedto fit the hydrogen recovery and the conversion was calculatedthereafter).

Figs. 4 and 5 show the influence of the reaction temperatureand the feed space velocity (feed flow rate) on the MR perfor-mance, either in terms of experimental data or in terms of

simulated results. The thermodynamic equilibrium conversionof CO, Xe, based on the inlet reformate gas composition, is alsoincluded to show the conversion enhancement that is possible toattain with the membrane reactor comparatively to the max-imum value possible to obtain in a packed bed reactor, thethermodynamic equilibrium value. Each figure refers to a differ-ent operation mode for extraction of the permeated hydrogen:sweep gas mode in Fig. 4 (QsweepðN2Þ ¼ 1:0 LN min�1, PP

¼1.0 bar,PF¼2.0 bar) and vacuum mode in Fig. 5 (PP

�30 mbar,PF¼1.1 bar).Globally, both Figs. 4 and 5 show that the model describes

quite well the trend of the CO conversion and H2 recovery as afunction of the temperature, for each feed flow rate. For any of the

Temperature, T / ºC

200

CO

Con

vers

ion,

XC

O

0.70

0.75

0.80

0.85

0.90

0.95

1.00

200

Hyd

roge

n R

ecov

ery,

Re H

2

0.0

0.1

0.2

0.3

0.4

0.5

220 240 260 280 300 220 240 260 280 300Temperature, T / ºC

Fig. 5. Effect of the reaction temperature and feed gas space velocity on the CO conversion (A) and H2 recovery (B) in the MR, operating in vacuum mode. PF ¼ 1:1 bar and

PP � 30 mbar. Error bars are based on t-student distribution and 95% confidence limit (with 3 replicates).

D. Mendes et al. / Chemical Engineering Science 66 (2011) 2356–2367 2363

operating temperatures, both CO conversion and H2 recoveryincrease with the residence time, that is, they decrease with anincrease of the gas hourly space velocity—GHSV (ratio betweentotal feed flow rate and catalyst mass). However, the agreementbetween the experimental conversion of CO and the simulatedvalues for the vacuum operation mode is poorer than for thesweep gas mode operation. This may be related to the difficulty incontrolling accurately the vacuum pressure in the permeate sideof the membrane reactor.

Figs. 4A and 5A also show that the CO conversion attained inthe MR may surpass the thermodynamic equilibrium conversion.This conversion enhancement is achieved at the lower feed flowrates for the lower temperatures, but as the temperatureincreases, such conversion enhancement is attained for higherand higher feed flow rates. For the lower temperatures, thethermodynamic equilibrium conversion of CO is high, due to theexothermal nature of the reaction, but the effective conversion islow, because of the relatively slow reaction rate, and, conse-quently, the amount of H2 produced is also small. Besides, thepermeation of H2 is also not favoured in this temperature region,so the equilibrium shift promoted by the hydrogen removal fromthe reaction medium is small. As a result, such enhancement isachieved only for low feed flow rates (high residence times). Asthe temperature increases, the equilibrium shift promoted by thehydrogen removal from the reaction medium becomes significantfor higher and higher feed flow rates, as a result of two mainfactors. On one hand, the increase of the reaction rate with thetemperature leads to an increase of the CO conversion and,consequently, to a corresponding change of the H2 concentration.On the other hand, the permeation rate increases also with thetemperature, at least in a range of temperatures (see the nextparagraph) leading so to a greater capacity of removing H2 fromthe reaction medium. From the balance of these two factors (andalso because the thermodynamic limit is lower at higher tem-peratures), results that the conversion enhancement is attainedfor increasingly higher feed flow rates. A similar effect has beenrecently reported by Tang et al. (2010), although the membranesand operating temperature ranges are different.

Figs. 4B and 5B show also that H2 recovery may tend to aplateau, for certain operating conditions. This behavior can beinferred from Fig. 4B for low feed flow rates, but it is clearin Fig. 5B for all the feed flow rates. This hydrogen recoveryplateau (or even decrease, if we consider also the simulationresults) is attained for the high temperature region considered inthe study and results from the combined effect of reaction andpermeation rates.

Assuming that only the chemical reaction (no permeation)takes place, the conversion of CO increases with the temperaturein the region below the thermodynamic equilibrium value, for agiven feed flow rate. However, for conversions close to thethermodynamic equilibrium, the CO conversion should decreasewith the temperature since the thermodynamic equilibrium alsodecreases. It can then be concluded that the hydrogen concentra-tion as a function of the temperature reaches a maximum, for agiven feed flow rate. For a membrane reactor, the hydrogen isremoved from the reaction medium as it is being formed. For atemperature range where the retentate hydrogen concentrationincreases due to the chemical reaction, the hydrogen permeationshould also increase since the driving force increases, as well asthe membrane permeability (cf. Eq. (18)). If the hydrogen per-meation increases at a higher rate than its formation, the recoverywould increase with the temperature; otherwise, a decrease inthe recovery should be observed. In addition, after a certainthreshold temperature (normally around 280–300 1C) the hydro-gen production decreases with the temperature. For this region,the membrane permeability increase with temperature might notbe enough to compensate the driving force decrease and, as aresult, the hydrogen permeation would decrease as well as therecovery.

Fig. 6 shows the simulated axial composition profiles in theretentate side for each species (dry basis) in terms of theconcerning molar fraction, for GHSV¼1200 LN kgcat

�1 h�1 and forthe two operating modes of the MR, vacuum and sweep gas, bothwith 2 bar in the feed. The experimental compositions obtained atthe exit of the reactor are also included.

The comparison between the predicted compositions and theexperimental results at the exit of the reactor puts also inevidence the validity of the model (cf. Fig. 6). As it can be realizedfrom Fig. 6, there are clearly two different regions inside thereaction medium. In the first one, for about 10% of the initiallength of the reactor, the molar fraction of CO decreases rapidly,while the molar fraction of H2 increases slightly. Since thereaction temperature is high in both cases (T¼300 1C), thereaction kinetics and H2 permeation are favoured. As the reactioncondition for the feed mixture is far away from the thermody-namic equilibrium condition, the chemical reaction shifts quicklytowards the reaction products, decreasing rapidly the CO con-centration. However, the rate of H2 permeation does not followthe rate of production from the WGS reaction, and thus theconcentration of H2 increases, though slowly. After this initialregion, the shift of the reaction condition towards the reactionproducts depends only on the H2 removal due to permeation.

Fig. 7. Effect of Da and G on the CO conversion (A) and H2 recovery (B) in the MR operating in vacuum mode. T¼300 1C, PF ¼ 1:1 bar and PP � 30 mbar. The white lines

describe the parametric region of the operating conditions used in this work.

x0.2

CO

fra

ctio

n (m

ol/m

ol)

0.00

0.01

0.02

0.03

0.04

H

N

CO

CO

x0.0

H2,

CO

2 an

d N

2 fr

acti

on (

mol

/mol

)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

H

N

CO

CO

0.2 0.4 0.6 0.8 1.0 0.4 0.6 0.8 1.0

Fig. 6. Simulated profiles on the reaction side as a function of the dimensionless reactor length: vacuum mode, PF ¼ 2:0 bar and PP � 30 mbar (A) and sweep gas mode,

PF ¼ 2:0 bar, PP ¼ 1:0 bar and Qsweep¼1.0 LN min�1 (B). Other experimental conditions: T¼300 1C, GHSV¼1200 LN kgcat�1 h�1. Symbols represent the experimental molar

fraction (dry basis) of each species measured at the exit of the reactor.

D. Mendes et al. / Chemical Engineering Science 66 (2011) 2356–23672364

As a consequence, the concentrations for both reactants (waternot presented) decrease slowly and in a more or less linear way.The concentration profiles of CO2 and N2 exhibit an increasingtrend along the reactor axis, because the mixture becomes richerin the non-permeating species and, moreover, CO2 is a reactionproduct. The reactor can then be divided into a region of chemicalcontrol and a region of permeation control, this accounting for thelast nearly 90% of the reactor length, for these operatingconditions.

The membrane reactor can only withstand a pressure differ-ence of about 2 bar. Higher feed pressures can only be applied if asweep gas is used at a pressure such that the pressure thresholddifference (2 bar) is not exceeded. High feed pressures coupledwith high sweep flow rates results in a high H2 partial pressuredifference between the two chambers of the membrane reactor.On the other hand, operating at high feed pressures results in anenhancement of CO conversion as a consequence of the reactionrate increase. Following, lower contents of CO were obtained at

the exit of the retentate chamber when the sweep mode was used(cf. Fig. 6(A) and (B)); the content of H2 also decreased and itsrecovery improved because of the higher driving force for hydro-gen permeation.

4.2. Influence of the Damkohler number and contact time

From the results presented above, it is clear that there areregions where the CO conversion is almost complete, as well asthe H2 recovery is maximum. However, it would be of interest todefine the parametric regions where such variables could beoptimized. In order to do so, it is presented a simulation resultof the CO conversion and H2 recovery as a function of the twomodel dimensionless parameters, Damkohler number (Da) andcontact time (G)—Figs. 7 and 8.

The analysis of the MR operating with vacuum pumping andsweep gas mode is briefly accessed in terms of dimensionlessparameters. The values for c and Kp

CO were assumed to be

Fig. 8. Effect of Da and G on the CO conversion (A) and H2 recovery (B) in the MR operating in sweep gas (counter-currently) mode. T¼300 1C, PF ¼ 2:0 bar, PP ¼ 1:0 bar,

and Qsweep¼1 LN min�1. The white line describes the parametric region of the operating conditions used in this work.

D. Mendes et al. / Chemical Engineering Science 66 (2011) 2356–2367 2365

0.93 and 9.53�10�5 Pa�1, respectively, as reported by Mejdellet al. (2009).

Fig. 7A shows that there is a region in the parametric spacecontact time/Damkohler number where an almost completeconversion of CO can be achieved. This happens for Da4E7and G4E0.4. For lower values of G (keeping the same Damkohler),the CO conversion decreases slightly, but for lower values of Da

(keeping the same contact time) the decrease is abrupt. Fig. 7B, on itturns, shows that the H2 recovery is maximized in the sameparametric region. The maximum value attained for vacuum opera-tion was about 0.93, which is related to the hydrogen partialpressure at the permeate side �30 mbar. For lower values of Gand in the same region of Da, the H2 recovery decreases quickly,with a still high CO conversion. This is a consequence of the quickdecrease of the stage cut, that is, the fraction of H2 in the retentateincreases. Fig. 7B shows again that the H2 recovery is much moresensitive to the contact time than CO conversion.

The experimental results obtained for vacuum mode arepresented in Fig. 7 (white line). As it can be inferred, both COconversion and H2 recovery can be ‘‘improved’’ increasing essen-tially the contact time parameter (that is, decreasing the GHSV).

These results show that, for a given membrane reactor (with afixed amount of catalyst—fixed Damkohler) and operating invacuum mode, the CO conversion is mostly controlled by thefeed flow rate, while the H2 recovery depends also strongly on thehydrogen permeation rate (which depends on the hydrogenpartial pressure at the permeate side and total pressure at feed-side). If the membrane reactor operates in sweep mode and with2 bar in the feed, there is a region of the parametric space contacttime/Damkohler number where it is possible to achieve almost100% of CO conversion with almost 100% of H2 recovery, as shownin Fig. 8.

5. Conclusions

The present study deals with model analysis and experimentalassessment of a self-supported finger-like membrane reactorparticularly conceived for ultra-pure hydrogen production. WGS

reaction runs were carried out on a Pd–Ag MR under a broadrange of operating conditions such as temperature (200–300 1C)and gas hourly space velocity (1200–10,800 LN kgcat

�1 h�1), usingdifferent operating modes (vacuum and sweep gas). The metallicmembrane permeability and the kinetics of the reaction were alsoaccessed experimentally, whose equations were introduced in thephenomenological model. The simulation and experimental car-bon monoxide conversion results showed a suitable agreementfor the MR working in both sweep gas and vacuum operatingmodes. The comparison between the predicted compositions andthe experimental results, at the exit of the reactor, confirm alsothe validity of the proposed MR model. Apart from two fittingparameters (related with the decline of permeability due to thepresence of CO in the reaction mixture), all other model para-meters were determined from independent studies, namely reac-tion kinetics and membrane permeability towards hydrogen.

The model was also used to simulate the performance of theMR in a wide range of the parametric space, described byDamkohler’s number and contact time. This allowed us to definethe optimal operating regions in terms of CO conversion and H2

recovery.

Nomenclature

A cross-sectional area (m2)dp catalyst particle diameter (m2)Dax axial dispersion coefficient (m2 s�1)Da Damkohler numberEk activation energy for the WGS reaction (kJ mol�1)Ep activation energy for hydrogen permeation (kJ mol�1)f variable related with the operation mode (f¼�1 for co-

current; f¼1 for counter-current)Ha enthalpy of adsorption (J mol�1)J flux through the membrane (mol m�2 s�1)k rate constant for the WGS reaction (lower temperature

regime – mol g�1cat h�1 Pa�2; higher temperature regime –

mol g�1cat h�1 Pa�1)

D. Mendes et al. / Chemical Engineering Science 66 (2011) 2356–23672366

k0 pre-exponential factor of the rate constant (lower tem-perature regime – mol g�1

cat h�1 Pa�2; higher temperatureregime – mol g�1

cat h�1 Pa�1)Ke equilibrium constant for the WGS reactionKp

CO equilibrium adsorption constant of CO for Sieverts–Langmuir formulation, adjustable parameter (Eq. (19))(Pa�1)

Kai equilibrium adsorption constant of species i for the

reaction rate equation (lower temperature regime –Pa�1; higher temperature regime – dimensionless)

Ka,0i pre-exponential equilibrium adsorption constant of

species i (lower temperature regime – Pa�1; highertemperature regime – dimensionless)

‘ reactor’s length (m)LH2

hydrogen permeability (mol m m�2 s�1 Pa�0.5)L0

H2pre-exponential factor for hydrogen permeation(mol m m�2 s�1 Pa�0.5)

M molar mass (g mol�1)p partial pressure (Pa or bar)P total pressure (Pa or bar)Pe Peclet number for mass transferr internal radius (m)R ideal gas constant (¼8.314 J mol�1 K�1)R rate of consumption or formation (mol g�1

cat h�1)ReH2

hydrogen recoveryT temperature (K or 1C)u interstitial velocity (m s�1)VR volume of the retentate chamber (m3)Wcat mass of catalyst (g)x dimensionless axial coordinateXCO conversion of carbon monoxideXe thermodynamic equilibrium conversionz axial coordinate (m)

Subscripts

i species involved in the reaction experiments (CO, H2O,CO2, H2, or N2)

ref reference component (H2) or conditions

Superscripts

n dimensionless variablein inlet of the reactork relative to the reaction kineticsm membraneout outlet of the reactorp relative to the H2 permeationF feed-sideP permeate-sideR retentate side

Greek letters

a Ergun equation coefficient (Eq. (24))b Ergun equation coefficient (Eq. (24))d Pd–Ag membrane thickness (m)eb void bed fractiong Arrhenius’ numberG dimensionless contact timemg (dynamic) gas mixture viscosity (kg m�1 s�1)rg gas mixture density (kg m�3)s dimensionless parameter: ratio between the cross-

sectional areas of the retentate and the permeatechambers

ni stoichiometric coefficient of species i in the WGSreaction

C adjustable parameter (Eq. (19))

Acronyms

GHSV gas hourly space velocityHT higher temperature regimeLT lower temperature regimeMR membrane reactorPBR packed-bed reactorPEMFC polymer electrolyte membrane fuel cellWGS water-gas shift

Acknowledgments

Diogo Mendes and Sandra Sa are grateful to the PortugueseFoundation for Science and Technology (FCT) for their doctoralGrants (Ref. nos. SFRH/BD/22463/2005 and SFRH/BD/30385/2006,respectively). The authors also acknowledge financing from FCTthrough the projects PTDC/EQU/ERQ/66045/2006 and PTDC/EQU-EQU/71617/2006.

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