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Journal of Membrane Science 362 (2010) 221–233

Contents lists available at ScienceDirect

Journal of Membrane Science

journa l homepage: www.e lsev ier .com/ locate /memsci

ydrogen permeation in palladium-based membranes inhe presence of carbon monoxide

acopo Catalano, Marco Giacinti Baschetti ∗, Giulio C. Sartiipartimento di Ingegneria Chimica, Mineraria e delle Tecnologie Ambientali (DICMA), Alma Mater Studiorum,niversità di Bologna, via Terracini 28, 40131 Bologna, Italy

r t i c l e i n f o

rticle history:eceived 21 April 2010eceived in revised form 10 June 2010ccepted 26 June 2010vailable online 31 July 2010

a b s t r a c t

A theoretical model is proposed to describe hydrogen permeation in palladium and silver–palladiummembranes in presence of a non-inert gas as CO; it is known indeed that hydrogen flux through palladium-based membranes drastically decreases when H2 is fed in mixtures containing carbon monoxide due to theinteraction of the latter gas with the membrane surface. To model this process, the adsorption step of thewell-known approach suggested by Ward and Dao has been suitably modified, since it must be considered

eywords:ydrogen permeationalladiumalladium–silver membranearbon monoxide adsorption

as a competitive adsorption of the different non-inert molecules on the metal interface. In particular, thecompetitive adsorption of CO and H2 has been examined accounting for the spectrum of informationavailable for CO adsorption on palladium, as well as for hydrogen in palladium and palladium–silveralloys. A validation of the model proposed has been performed through a comparison between severalliterature data and model calculations, over a rather broad range of operating conditions. A quite goodagreement was obtained in the different cases; the model, thus, can be profitably used for predictive

purposes.

. Introduction

Graham’s discovery of hydrogen adsorption in palladiumround 1866 [1], made the Pd–H2 system the first metal–hydrogenystem studied and started a profitable research activity that hased to extensive investigation, recently enhanced by the increasednterest in hydrogen as an energy carrier [2–4]. The high solubil-ty and mobility of hydrogen in the Pd lattice makes palladiumn ideal material for separating hydrogen in a highly pure form2,5,6], which is needed for the direct use of this gas in polymerlectrolyte fuel cells (PEM-FCs), the most promising technologyo obtain clean energy from hydrogen [7]. At present, hydrogens largely produced by steam reforming of methane [5,8,9] and, as aonsequence, palladium-based membranes operating in such sepa-ation processes are exposed to complex gases mixtures comprising2, CO, CO2, H2O, CH4, among other species. Many experimen-

al works have studied the behaviour of these membranes andeveral of them reported a dramatic reduction of the hydrogen

ermeate flux when carbon monoxide was added to the feedtream [10–17]; in that case the hydrogen permeate depletion wasttributed mainly to the reduction of the available dissociation sitesn the metal surface caused by CO adsorption which competes

∗ Corresponding author. Tel.: +39 0512090408; fax: +39 0516347788.E-mail address: marco.giacinti@unibo.it (M. Giacinti Baschetti).

376-7388/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.memsci.2010.06.055

© 2010 Elsevier B.V. All rights reserved.

with that of hydrogen. Despite the many experimental evidencesand the amount of studies presented, the influence of this gas onhydrogen permeation has not yet been modelled rigorously andeffectively, and only very general equations have been proposedin order to account for the effect of CO on the reduction of hydro-gen permeance in Pd-based membranes [14,16]. The aim of thiswork, in order to fill the void still present in the modelling of thissystem, is to propose a quantitative description of the hydrogenpermeation process in the presence of carbon monoxide in the feedstream, following an approach which can be naturally extended toinclude the possible presence of other compounds, also affectingthe H2 permeate fluxes, such as H2S or water vapour. In particular,a modification of the theory based on the sequence of elementaryprocesses proposed by Ward and Dao [18] is considered, by intro-ducing the competitive adsorption on the surface exposed to thefeed gas. The model will be described in its main features and theeffect of different parameters and operating conditions will be dis-cussed. Several permeation data available from the literature andconsidering a broad range of operating conditions will then be con-sidered and compared to the model calculations in order to test itsreliability.

2. Theoretical background

Hydrogen transport through Pd-based membranes is commonlydescribed, in the so called diffusion limited regime, by the cou-

2 mbran

pa(taarob

N

wi

(

fe

baoupKdtaff

N

w1tarh

tmtaaSfti

N

wefp

miaf

22 J. Catalano et al. / Journal of Me

ling of two main processes: (i) adsorption of molecular hydrogennd its dissociation into atoms, at the upstream membrane surfaceH2 → 2H) and, vice versa, association and desorption (2H → H2) athe downstream surface of the Pd-alloy film and (ii) diffusion oftomic hydrogen in the metallic lattice [2,19]. In particular, in thebsence of other gases adsorbing onto the metal surface, when theeaction is fast enough for the diffusion to be the controlling stepf the process, Sieverts’ law holds and the hydrogen flux, NH2 , cane written as [20]:

H2 = PH2 ·(p0.5

H2,ret − p0.5H2,per)

ı

≡ P0H2

· exp(

− Ea

RT

)·

(p0.5H2,ret − p0.5

H2,per)

ı(1)

here R is the universal gas constant, T is absolute temperature, pH2s the hydrogen partial pressure in the retentate (ret) or permeate

per) side, ı is the membrane thickness, P0H2

is the pre-exponential

actor of hydrogen permeability, PH2 , and Ea represents the appar-nt activation energy for hydrogen permeability.

Still remaining under diffusion limited conditions for the mem-rane behaviour, other resistances to the flux may also be presentnd have indeed been considered and modelled in different, morer less detailed ways. For example, different approaches have beensed to describe resistances in the porous support, often present inalladium-based membranes, in which the gas can move throughnudsen diffusion, viscous flow or a combination of the two,epending on the average pore dimensions, or in the gas phase dueo the concentration polarization phenomenon. Such resistancesre frequently considered empirically in a lumped way, by modi-ying the exponent of the pressure dependence in Sieverts’ law asollows [17]:

H2 = P0H2

· exp(

− Ea

RT

)·

(pnH2,ret − pn

H2,per)

ı(2)

here the exponent n is considered to range between 0.5 anddepending on the dominant resistance in the system. Alterna-

ively, such effects can be described through more detailed andppropriate approaches which account for the different additionalesistances for hydrogen flux, and more correctly describe theydrogen permeation process [21,22].

When the additional resistance is due to the presence of con-aminants interacting with the membrane surface, such as carbon

onoxide, the number of modelling works present in the litera-ure becomes definitely lower and in general only a global lumpedpproach has been considered, adapting Eq. (1) by introducingn empirical correction factor in the proportionality coefficient ofieverts’ law. In particular, Wang et al. [14] proposed a correctionactor based on a Langmuir isotherm for the CO coverage, assuminghat H2 needs two sites for the dissociative chemisorption, obtain-ng the following expression for hydrogen flux:

H2 =[

1(1 + c · e�ECO/RT )

]2· P0

H2· exp

(− Ea

RT

)·

(p0.5H2,ret − p0.5

H2,per)

ı(3)

here the term in the square brackets is the correction factor for theffective surface area and �ECO represents the heat of adsorptionor carbon monoxide; the parameter c should depend on the partialressure of CO, albeit in a non-specified way.

Another equation to model the hydrogen flux from H2–COixtures was proposed by Barbieri et al. [16] who followed a sim-

lar approach, considered a Langmuir isotherm with a single sitedsorption for hydrogen for the estimation of the available surfaceraction and, based on a heuristic argument, proposed the following

e Science 362 (2010) 221–233

modification of Sieverts’ law:

NH2 =(

1 − ˛(T)KCOpCO

1 + KCOpCO

)P0

H2· exp

(− Ea

RT

)·

(p0.5H2,ret − p0.5

H2,per)

ı(4)

where pCO represents the carbon monoxide partial pressureat metal interface, while ˛ and KCO are the Langmuir affinityparameters.

Both the approaches above retain the overall driving force forhydrogen flux as the difference of the square roots of hydrogenpartial pressures at the opposite sides of the membrane and mod-ify only hydrogen permeance, as if the effects of CO were presenton both sides of the membrane, while in fact they are only act-ing on the retentate side. The resulting equations thus appears tosome extent justified only when the downstream hydrogen pres-sure is negligibly small. In addition, these approaches are based onSieverts’ law and can obviously be applied only when Eq. (1) holdsfor pure hydrogen permeation, that is only in the diffusion limitedregime, while they cannot describe the desorption limited regimeand cannot be applied to the whole permeation phenomenon ina broad range of operating conditions [16]. In fact, the adjustableparameters of both the above models have been estimated from alimited experimental data set, collected ad hoc by the respectiveauthors, without considering a model validation procedure basedon a comparison with the several available adsorption data in thepresence of carbon monoxide; thus such lumped models representmore the description of a well defined and narrow set of experi-mental data rather than a general model useful for a broad rangeof operating conditions. On the other hand, since the parametersused do not refer to the modelling of any single kinetic step, but tothe process as a whole, they have no stringent and precise physicalmeaning and their extension to different experimental conditions,if possible, is certainly not straightforward.

2.1. General model

A complete and sound theoretical approach, on the contrary,needs to consider the effect of CO on hydrogen permeation bydirectly estimating its influence on the hydrogen adsorption pro-cess which is just one of the steps of the whole permeation process.This can be assessed for example by considering the work of Johans-son et al. [23] which studied in details the sticking probability ofhydrogen, in the presence of carbon monoxide, on several tran-sition metals supported on graphite, and took into account thecompetitive adsorption on the metal surface of the two gases inthe equilibrium coverage.

This kind of approach can be coupled with the descriptionof all the other steps contributing to hydrogen permeation, toderive the actual influence of carbon monoxide on the masstransport resistance of the membrane. To that aim, the fundamen-tal approach originally proposed by Ward and Dao [18] can befollowed, considering the sequence of the relevant elementary pro-cesses contributing to H2 transport in Pd films, and their respectivekinetic expressions, also on the basis of the works by Holleck [2] andby King and Wells [24]. In particular, Ward and Dao [18] consideredthe hydrogen transport as the result of the following series of steps:

1. molecular transport from the bulk gas to the gas layer adjacentto the surface;

2. dissociative adsorption onto the metal surface;3. transition of atomic H from the surface into the bulk metal;

4. atomic diffusion of hydrogen through the bulk metal;5. transition from the bulk metal to the surface at the permeate

side;6. recombinative desorption of hydrogen from the surface;7. gas transport away from the surface to the bulk gas phase.

J. Catalano et al. / Journal of Membrane Science 362 (2010) 221–233 223

Table 1Complete set of rate equations for each kinetic step contributing to hydrogen transport, as reported by Ward and Dao [18] under the simplified assumption that the hydrogenadsorption on the metal surfaces is described by a Langmuir adsorption isotherm, with no competing species.

Specific kinetic step Kinetic equation Eq. no.

Dissociative adsorption radsH = 2 · pH2,i ·

(1

2�kTmH2

)0.5

· S0 · n2S(1 − ϑH,i)

2 (I)

Molecular desorption rdesH = 2 · kd,0 · exp

(− 2ED

RT

)· n2

Sϑ2

H,1 (II)S−B

(ES−B

RT

)b · (xs,

,i) · ˇ0

epfi

fhlϑgsnpqld

bba

(

(i

(

(

olai

TCa

Surface-to-bulk rH = nS · nb · �0 · exp −Solid-state atomic diffusion rdiff

H = D0 · exp(

− EdiffRT

)· n

Bulk-to-surface rB−SH = nS · nb · xs,i · (1 − ϑH

The complete theory associating an explicit kinetic equation toach of the steps listed above can be found in Ref. [18] in the case ofure hydrogen feeds, and the corresponding rate and flux equationsor steps 2–6 are reported in Tables 1 and 2, respectively for moremmediate reference.

To our present aim, the presence of CO in the feed is accountedor by considering the simultaneous competitive chemisorption ofydrogen and CO on the feed side of the membrane surface. That

eads to modified expressions for the hydrogen coverage fractionH and for the fraction of surface sites which are available for hydro-en adsorption, which are quantities used in the rate equations forteps 2 and 3, i.e. Eqs. (I) and (IV) of Table 1. Such effects wereot included in the original work by Ward and Dao, who, however,ointed out that, in the presence of a contaminant, one expectsualitatively (i) a rise in the temperature at which the desorption

imited regime would become the rate controlling step and (ii) aecrease of desorption limited flux.

The competitive adsorption of CO and H2 on palladium muste considered and included in the theoretical framework proposedy Ward and Dao and, to that purpose the following reasonablessumptions are considered for simplicity sake:

(i) mass transport resistance in the external gas phases is negligi-ble;

ii) hydrogen and carbon monoxide follow a competitive Langmuiradsorption;

ii) carbon monoxide adsorption is lumped into a process involv-ing a single palladium active site and is described by a singleeffective adsorption rate;

iv) CO does not disproportionate upon adsorption on the metal sur-face in the temperature range inspected, and only the surfaceof the retentate side is exposed to CO;

v) there is no diffusion of carbon monoxide through thepalladium-based membrane.

The first assumption is considered to focus the attention merelyn the membrane behaviour, and the others are introduced fol-owing a general consensus in order to simplify the mathematicalpproach. In particular for assumption (ii) it can be shown that,n the operative condition of interest, the hydrogen concentration

able 2omplete set of flux equations reported by Ward and Dao [18] in the simplified assumptdsorption isotherm.

Kinetic stage Flux equation

Surface adsorption/desorption processes (upstream surface) NH2 = pH2,i ·(

12�kTmH2

Surface-to-bulk transition (upstream side) NH2 = 12 nS · nb · �0 · ex

Solid-state atomic diffusion NH2 = 12 · D0 · exp

(− E

Bulk-to-surface (downstream side) NH2 = 12 · nS · nb · xs,2 ·

Surface desorption/adsorption processes (downstream surface) NH2 = kd,0 · exp(

− 2EDRT

· ϑH,i(1 − xs,i) (III)1−xs,2)

ı(IV)

· exp(

− EB−SRT

)(V)

calculated in the bulk, as well as the hydrogen flux, do not varysignificantly using the Langmuir adsorption isotherm for hydrogeninvolving two sites, instead of the equation derived from the morecomplete statistical thermodynamic arguments [18]. Assumption(iii) is instead related to the fact that at least two different statesof adsorbed CO are known to exist, i.e. linear and bridge-bondedwith the metal surface, depending on the number of metal atomsbinding the C atom: one for the linear and two for the bridge-bonded species, respectively [25]. In the present case, to minimizethe number of model parameters and in agreement also with theapproach proposed by Johansson et al. [23], the choice has beenmade to describe the carbon monoxide adsorption through a singlerate equation which thus must be regarded as an effective averagebetween the different CO adsorption kinetics actually existing onthe metal surface. As far as hypothesis (iv) is concerned, on the con-trary, we notice that there are no experimental evidences on carbonmonoxide dissociation in polycrystalline Pd films above 500 K [26],nor for Pd (1 1 1) in the range between 300 and 750 K, even if experi-ments performed on silica supported Pd nano-clusters indicate thatCO dissociates above 600 K at 185 mbar [27]. Assumption (v) is aconsequence of the fourth one, given the substantial impossibilityof the CO molecule to diffuse in the lattice due to its dimension.

On the basis of the assumptions above and of the resultsobtained by Johansson et al. [23] on the sticking probability for H2on metal surfaces in the presence of CO, the competitive adsorp-tion of CO and H2 on palladium and Pd-based alloys is describedby considering that atomic hydrogen and CO molecules both com-pete for the same surface active sites. Therefore, the adsorption anddesorption rates of CO per unit area, rads

CO and rdesCO , can be written as:

radsCO = kads

CO · pintCO · (1 − ϑCO − ϑH) · nS (5)

rdesCO = kdes

CO · nS · ϑCO (6)

in which nS represents the overall number of adsorption sites avail-able per unit area, ϑCO and ϑH represent the carbon monoxide and

atomic hydrogen coverage fractions, respectively, (1 − ϑCO − ϑH) isthe fraction of available active sites, kads

CO and kdesCO are the CO adsorp-

tion and desorption rate constants and pintCO is CO partial pressure at

the metal interface. Since there is no CO flux across the membrane,under steady state conditions the adsorption and desorption rates

ion that the hydrogen adsorption on the metal surfaces is described by a Langmuir

Eq. no.)0.5

· S0 · n2S(1 − ϑH,1)2 − kd,0 · exp

(− 2ED

RT

)· n2

SϑH,1

2 (VI)

p(

− ES−BRT

)· ϑH,1(1 − xs,1) − 1

2 nS · nb · xs,1 · (1 − ϑH,1) · ˇ0 · exp(

− EB−SRT

)(VII)

diffRT

)· nb · (xs,1−xs,2)

ı(VIII)

(1 − ϑH,2) · ˇ0 · exp(

− EB−SRT

)− 1

2 · nS · nb · �0 · exp(

− ES−BRT

)· ϑH,2(1 − xs,2) (IX))

· n2SϑH,2

2 − pH2,2 ·(

12�kTmH2

)0.5

· S0 · n2S(1 − ϑH,2)2 (X)

2 mbran

f

ϑ

tta

�

iEao

m

(

oCwTtm

r

wc[

k

itc

smr

r

tba

N

iwt

t

24 J. Catalano et al. / Journal of Me

or CO are identical and thus:

CO = (1 − ϑH) · �CO · pintCO

1 + �CO · pintCO

(7)

The adsorption equilibrium constant, �CO = kadsCO /kdes

CO , is a func-ion of temperature and can be calculated by using statisticalhermodynamics arguments, as reported by Dulaurent et al. [25],s follows:

CO = h3

k · (2� · mCO · k)3/2· 1

T5/2· exp

(Edes

CO − EadsCO

RT

)(8)

n which h is the Planck’s constant, k is the Boltzmann’s constant,desCO and Eads

CO represent the activation energies for CO desorptionnd adsorption, respectively, and mCO is the mass of a CO molecule;f course the heat of CO adsorption is �ECO = Edes

CO − EadsCO .

In view of Eq. (7) the fraction of available active sites of theembrane surface exposed to the CO–H2 mixture is given by:

1 − ϑCO − ϑH) = 1

1 + �CO · pintCO

(1 − ϑH) (9)

Eq. (9) represents the new expression needed for the fractionf available active sites which must be used in the presence ofO, in place of the expression (1 − ϑH) which holds true merelyhen hydrogen is the only species adsorbed onto the metal surface.

hat expression will then be used to obtain the rate of dissocia-ive adsorption of hydrogen over the upstream surface from CO–H2

ixtures as follows:

adsH = 2 · S0 · kads

H · pH2 · n2S · (1 − ϑCO − ϑH)2

= 2 · S0 · kadsH · pH2 · n2

S

(1

1 + �CO · pintCO

)2

(1 − ϑH)2 (10)

here, S0 is the sticking probability of H2, and the rate of adsorptionoefficient, kads

H , has no activation barrier and can be expressed as23]:

adsH = 1

(2� · mH2 · kT)1/2(11)

n which mH2 represents the mass of a H2 molecule. Eq. (10) willhen be used in place of Eq. (I) of Table 1, which holds only for thease in which the only adsorbed gas is hydrogen.

Similarly, in the presence of CO in the feed the kinetic expres-ion for the bulk-to-surface hydrogen transfer rate at the upstreamembrane interface is no longer given by Eq. (V) of Table 1 but

ather by the following equation:

B−SH = nS · nb · xs,i · 1

1 + �CO · pintCO

(1 − ϑH,i) · ˇ0 · exp(

−EB−S

RT

)(12)

Correspondingly, the net flux of molecular hydrogen arriving athe interface exposed to CO is finally calculated as the differenceetween the adsorption and desorption rates, described by Eq. (10)nd by Eq. (II) of Table 1, respectively; one thus obtains:

H2 = pH2,1(2� · mH2 kT)−0.5 · S0 ·(

1

1 + �CO · pintCO

)2

· (1 − ϑH,1)2

− kd,0 · exp(

−2ED

RT

)· n2

S ϑ2H,1 (13)

Eq. (13) represents the net flux of molecular hydrogen reach-

ng the upstream interface, and is of course different from Eq. (VI)

hich was used by Ward and Dao [18] to calculate the H2 flux onhe surface of Pd membranes in the absence of CO.

In parallel, the net hydrogen flux due to the surface-to-bulkransport at the upstream side of the membrane is given by the

e Science 362 (2010) 221–233

difference between the surface-to-bulk term, given by Eq. (III), andthe bulk-to-surface term given by Eq. (12); therefore, in the pres-ence of CO in the feed gas, the net surface-to-bulk transport is nolonger given by Eq. (VII) used by Ward and Dao [18], but is rathergiven by:

NH2 = nS · nb · �0 · exp(

−ES−B

RT

)· ϑH,1(1 − xs,1) − nS · nb · xs,1

·(

1

1 + �CO · pintCO

)(1 − ϑH,1) · ˇ0 · exp

(−EB−S

RT

)(14)

Also in the presence of carbon monoxide the entire sequenceof the elementary kinetic steps which contribute to the hydro-gen flux remains the same as indicated by Ward and Dao [18] inthe absence of CO. The only difference is due to the fact that theupstream surface is endowed with a CO coverage which affectsthe rate of hydrogen adsorption/desorption as well as the rateof hydrogen transfer from surface-to-bulk, at the upstream sideof the membrane. On the other hand, since CO is not presentin the bulk of the metallic film, the kinetic expressions for allother stages, namely diffusion of atomic hydrogen to the permeateside, hydrogen transport bulk-to surface at the permeate side andthe desorption/adsorption stage at the permeate side, all remainexpressed by the same equations which hold true in the case ofpure hydrogen feeds, and thus Eqs. (VIII), (IX) and (X) of Table 2 arevalid also in the present case.

Therefore, the complete model for hydrogen transport throughPd-based membranes in the presence of CO in the feed, and in theabsence of mass transfer resistance in the gas phase, is representedby Eqs. (13) and (14), describing the steps occurring at the feed sideof the membrane, coupled with Eqs. (VIII), (IX) and (X) of Table 2,describing the kinetic steps within the membrane and at the down-stream side of it. The set of five non-linear equations was solvedwith the Newton method in Matlab® programming environment.For model validation the results obtained have been compared withseveral available experimental data, spanning in particular a broadrange of temperature values.

3. Parameters estimation

In order to test the model reliability through comparison of sim-ulation results with available experimental data, all the parametersappearing in the model equations presented above, and reported inTable 1, have been determined on the basis of independent informa-tion for different Ag contents in the palladium-based membranes ina broad temperature interval [2,18,28–33]. The values obtained forPd/Ag alloys, are reported in Table 3, while in the work by Ward andDao [18] they were computed only for pure palladium membranes.

The procedure used to obtain the values of the parametersappearing in the flux equations of Tables 1 and 2 will be presentedfor each kinetic step separately.

3.1. Surface processes

The presence of silver in the system, affects the number of activesites per unit surface, nS, as well as the activation energy of theadsorption for the different species. The value of nS can be esti-mated simply from the alloy composition: since only palladiumatoms allow hydrogen dissociative adsorption or CO adsorption, thenumber of active sites on the surface can be related to the Pd surfaceconcentration, nS,Pd, that depends on palladium bulk concentration,

nb,Pd through the equation [18]:

nS = nS,Pd =n2/3

b,Pd

N1/3AV

(15)

J. Catalano et al. / Journal of Membrane Science 362 (2010) 221–233 225

Table 3Model parameters at several silver contents as calculated in this work or retrieved from the literature data indicated.

xPd a (×1010) nb (×10−5) ns,Pd (×105) ES–B ˇ0 (×10−7) EB–S D0 (×107) �EAb �S̃0H

Ref. [28] Ref. Eq. (16) Ref. Eq. (15) Ref. [31] Ref. [29,30] Ref. [31] Ref. [2] Ref. [2]m molPd m−3 molPd m−2 kJ mol−1 m3 mol−1 s−1 kJ mol−1 m2 s−1 kJ mol−1 J mol−1 K−1

1 3.89 1.13 2.77 52.79 6.78 22.19 2.90 16.75 97.530.9 3.91 1.11 2.56 48.60 6.33 22.19 2.69 23.18 98.79

5534

wtm

n

smqbbwl

n

cntutdohvwWm

Fos

0.8 3.93 1.09 2.34 43.890.7 3.95 1.08 2.12 47.360.6 3.97 1.06 1.90 47.590.5 3.99 1.05 1.66 56.65

here NAV represents the Avogadro’s number; the Pd bulk concen-ration, nb,Pd, is then calculated from the density, �i, and the molar

ass, Mi, of the two metals of the alloy:

b,Pd =(

ωPd

MPd

)�Alloy =

(ωPd

MPd

)(ωPd

�Pd+ 1 − ωPd

�Ag

)−1

(16)

In Eq. (16), in view of the lack of experimental data on alloys den-ities, the simplifying assumption of volume additivity has beenade, which in any event is not expected to crucially affect the

uality of the results nor the temperature dependence of the mem-rane response. A similar procedure is applied to calculate also theulk concentration of silver atoms as well as the sum of the two,hich is the total average concentration of metals atoms in the

attice, nb, so one has:

b =(

ωPd

MPd+ 1 − ωPd

MAg

)(ωPd

�Pd+ 1 − ωPd

�Ag

)−1

(17)

The activation energy of the adsorption and desorption pro-esses can be calculated from experimental data or, when that isot possible, can be taken from the values available in the litera-ure [31–38]. In particular for hydrogen, the adsorption process issually considered to have negligible activation energy [18], whilehe activation energy of desorption, ED, can be estimated from theependence of hydrogen permeate flux on temperature in the des-rption limited regime, as shown for example in Fig. 1. On the other

and, several estimates have already been reported for ED in pre-ious works but they are distributed over a wide range of valuesith no univocal choice [34–36]. For pure palladium, for example,ard and Dao used ED values between 41 and 50 kJ mol−1 to fit theajority of literature data; nevertheless in the literature cited in

ig. 1. Data fitting and model sensitivity analysis versus activation energies for des-rption in a 250 �m Pd–Ag membrane at 14 kPa of pure hydrogen in the retentateide and vacuum in the permeate side [10].

.51 19.47 2.33 28.22 100.46

.26 24.70 2.21 30.69 98.37

.59 26.38 1.50 33.58 102.14

.37 33.50 1.82 29.69 100.88

Ref. [18] values of ED are reported between 15 and 50 kJ mol−1. Inaddition, in the alloys, ED was found to be substantially unaffectedby the presence of Ag in the lattice, through a differential scanningcalorimetry (DSC) analysis performed by Artman and Flanagan [37]who investigated pure palladium as well as Pd–Ag alloys contain-ing 20% by weight of silver, while ED was reduced by the additionof silver in the metal surface, according to a first principle studyperformed by Lovvik and Olsen [38]. Experimental data concern-ing 75% Pd 25% Ag alloy can be found in the work by Nguyen et al.[17], who reported a value of ED = 11.0 kJ mol−1, and in the workof Serra et al. [34] who found ED = 11.5 kJ molH−1. On the otherhand Bhargav and Jackson [33] found a coverage dependent acti-vation energy for hydrogen desorption, with ED ranging from 35 to27 kJ molH−1, when the hydrogen coverage goes from zero to a com-plete hydrogen monolayer. In the present work, the choice has beenmade to consider a constant value of the activation energy for thedesorption of hydrogen, obtained directly form pure hydrogen per-meation experiments in the desorption limited region, wheneverpossible.

For carbon monoxide, instead, the determination of the acti-vation energies for the surface processes is complicated by anon-negligible dependence on CO surface coverage [25,39–42] andby the existence of at least two different families of adsorbed car-bon monoxide molecules, namely linear and bridge-bonded withthe metal surface, as pointed out by the analysis performed inRef. [25]. These two archetypal forms involve different numbersof metal atoms binding to the C atom, namely one atom for thelinear and two atoms for the bridge-bonded species, respectively[40]. Dulaurent et al. [25] found that the heat of adsorption (�ECO =Edes

CO − EadsCO ) of carbon monoxide on pure palladium decreases form

92 to 54 kJ mol−1 and from 168 to 92 kJ mol−1 increasing the COcoverage fraction from zero to one for the linear and the bridge-bonded species, respectively. The decrease of the heat of adsorptionis related to the repulsive interaction between adsorbates [39] aswell as to the fact that, due to the surface heterogeneity, differ-ent adsorption sites are present on the metal surface and thoseassociated to high adsorption energies are usually more reactiveand thus are filled first [40]. In particular, �ECO can be reasonablydescribed by a linear relationship with CO coverage and one canestimate its value, from the analysis of literature data [25,41,42], asabout 125 kJ mol−1 for ϑCO = 0.5, obtained by neglecting the possi-ble effects due to different co-adsorbed molecules. In view of thesefindings, a linear dependence of the heat of adsorption �ECO withCO coverage was used in the following to best fit the experimentalbehaviour of the hydrogen permeated flux H2–CO mixture:

�ECO = aϑCO + b (18)

3.2. Surface-to-bulk transitions

Surface-to-bulk transition involves the hydrogen transfer fromadsorption active sites on the surface to the bulk sites in the latticeand vice versa; the parameters entering the rate equations for thesekinetic steps, Eqs. (14) and (IX), are the activation energies ES–B

2 mbrane Science 362 (2010) 221–233

adthv

wpibEhatdatas

ˇcfmau

ˇ

ftc

plbgasto�tas

3

eptfitgpabca

Table 4Main characteristics of the membranes and experimental operative conditions ofthe literature data analyzed in this work.

Authors Chabot et al. Nguyen et al.

Ref. [10] [17]Silver content by weight 23% 25%Thickness (�m) 250 75, 100, 300

26 J. Catalano et al. / Journal of Me

nd EB–S of the different processes involved, which can be obtainedirectly from experimental data [18], and the pre-exponential fac-ors ˇ0 and �0 related, respectively, to jump frequency of theydrogen atoms from the bulk to the surface of the membrane andice versa.

The activation energy for the bulk-to-surface transition, EB–S,as set equal to the activation energy of metal bulk diffusion, asreviously stated by other authors [18,33], while, ES–B, related to the

nverse process, was calculated following the procedure suggestedy Ward and Dao which estimated its value from the knowledge ofB–S and the heats of absorption (�EAb) and adsorption (�EAd) ofydrogen in palladium following the idea that the sum of the twoctivation energies should be equal to the sum of the two absorp-ion and adsorption heats. The values for latter parameters for theifferent Pd–Ag alloys considered were obtained from the datavailable in the open literature: in particular the heats of absorp-ion found in the Sieverts’ limit were taken from Holleck [2] andre reported in Table 3, while �EAd was considered independent ofilver content and its value was fixed at 38 kJ mol−1 [37].

Following the same argument presented by Ward and Dao [18],0 has been calculated through the value of the atomic diffusionoefficient in the metal lattice considering that the jump frequencyrom the bulk to the surface is similar to that for the diffusion in the

etal lattice, since in both cases the hydrogen atom is jumping frombulk site. By equating the two frequencies it is possible to write,nder conditions of hydrogen coverage approaching zero [18]:

0 = 4D0

a2nb(1 − ϑH)(19)

rom which one can calculate ˇ0, using the proper lattice parame-er, a, as well as the specific pre-exponential factor of the diffusionoefficient, D0 of the silver alloy [28,31].

The pre-exponential factor, �0, depends on the thermodynamicroperties of the metal–hydrogen system. Its value can be calcu-

ated following the same procedure used by Ward and Dao [18],y imposing the validity of Sieverts’ approximation at low hydro-en concentration, in the diffusion limited regime. In this case, it isssumed that the relationship between the jump frequency and theurface-to-bulk rate constant is only dependent on the silver con-ent of the membrane, while it is not influenced by the presencef carbon monoxide on the metal surface; therefore, the value of0 can be calculated once the Sieverts’ constant of the hydrogen inhe alloy under consideration is known. By considering Langmuirdsorption for hydrogen atoms and following the same algebrahown in Ref. [18] the final equation correlating ˇ0 to �0 is:

ˇ0

�0= exp

(−�S̃0

H

R

)· S0.5

0

nS,Pdk0.5d,0 · (2�mH2 kT)0.25

(20)

.3. Atomic diffusion

Extensive studies on the diffusion of hydrogen atoms in sev-ral silver–palladium alloys have already appeared, in which bothre-exponential factor and activation energy can be found as a func-ion of silver content [2,31]. The pre-exponential factors D0 takenrom Ref. [31] and reported in Table 3, for example, have been usedn the calculations performed in this work. The values of Ediff onhe other hand can also be calculated directly from pure hydro-en permeation experiments, by considering the dependence of

ermeability on temperature in the diffusion limited regimes. Thispproach allows to obtain this parameter directly for the mem-ranes of interest giving a more stringent validation of the modelsapabilities; therefore it was preferred to the use of literature datand was applied whenever possible.

Total feed pressure (kPa) 147 101.325CO partial pressure (kPa) 0.29–14 0.50–20Temperature range (K) 373–723 300–773

4. Results and discussion

4.1. Model validation

In spite of a large amount of literature data on the hydrogenpermeation in the presence of carbon monoxide, only few authorsinvestigated experimentally wide ranges of temperature and car-bon monoxide compositions, and in particular the experimentaldata by Chabot et al. [10] and Nguyen et al. [17] appear relevantand have been selected in order to test the accuracy of the modelproposed. The main characteristics of the membranes, as well asthe experimental operative conditions used in Refs. [10,17] havebeen reported in Table 4. In both works the experimental set-up used is gas-resistance free and is characterized by extremelylow hydrogen permeate pressures (the permeate was removed bymeans of a vacuum pump); therefore, the model proposed abovecan be applied by using membrane properties alone, with no needto introduce any other parameter or equation relative to gas phaseor support resistances at the downstream side of the membrane.Finally, pure hydrogen permeation rates were considered also indesorption limited regimes, leading to a more stringent valida-tion of the model proposed: indeed, that allows to determine inan accurate way the activation energy for the hydrogen desorptionin silver–palladium alloys, for which there is some discrepancy, asmentioned before, among the values reported in different works[33–36]. In order to capture the pure hydrogen data by Nguyen et al.and Chabot et al., it is necessary to use values of Edes = 11 kJ molH−1

and Edes = 13.1 kJ molH−1, respectively, where the first value wasdirectly suggested by the authors while the second was calcu-lated using Ward and Dao approach to fit the experimental dataas shown in Fig. 1. Such values are definitely lower than those pro-posed by Bhargav and Jackson [33] for a 23 wt% Ag alloy (between27 and 35 kJ molH−1) while are comparable to experimental valueof 11.5 kJ molH−1 found in 25 wt% Ag membranes by Serra et al. [34].

The experimental hydrogen permeate fluxes by Chabot et al.were collected in a 250 �m silver–palladium (23–77 wt%) tubewithout any ceramic or metallic support, with a constant upstreamhydrogen partial pressure of 14 kPa and in the temperature rangebetween 373 and 723 K. They are reported in Fig. 2, together withthe results of our model calculations, for all gas mixtures consid-ered, containing carbon monoxide at partial pressure between 0.29and 14 kPa. In order to fit the experimental data a linear relationshipbetween the CO heat of adsoprtion and carbon monoxide coveragewas used: the value of 125 kJ mol−1 for ϑCO = 0.5 and a value atzero coverage of 140 kJ mol−1 were used for �ECO, according toRef. [42]. The latter value is actually smaller with respect to themaximum value of about 168 kJ mol−1 reported for ϑCO = 0 in purepalladium [25]; nevertheless it is reasonable to consider a non-negligible reduction of the heat of adsorption of CO when palladiumsilver alloys are used instead of pure palladium [43].

A rather good agreement can be noticed between the exper-imental data and the results of model calculations, in the entireregion of ϑCO ∈ [0, 0.95] represented by the solid curves. Theagreement appears particularly remarkable considering that theactivation energies for diffusion and for hydrogen desorption are

J. Catalano et al. / Journal of Membrane Science 362 (2010) 221–233 227

F2tc

tstrttaotaa

ttcsob

votcabtigvtpotahth(fatm

ig. 2. Comparison between experimental data taken from Ref. [10] collected in50 �m silver palladium membrane with an hydrogen partial pressure on the reten-ate side of 14 kPa at several carbon monoxide partial pressures and results of modelalculations (lines).

aken from the best fit with pure hydrogen experimental data,o that only the heat of adsorption of CO is used to describe allhe curves for different CO compositions; in view of the linearelationship between �ECO and ϑCO, all the experimental dataaken at different carbon monoxide concentrations are satisfac-orily described by the use of just two parameters, that possesscompletely defined physical meaning and can be compared to

ther available literature data; the best fit between model calcula-ions and experimental data, over the entire range of temperaturesnd of CO content in the feed, was obtained by using Eq. (18) with= −30 kJ mol−1 and b = 140 kJ mol−1.

Only at very high carbon monoxide coverage (i.e ϑCO > 0.95)he curves predicted by the model for the H2 permeation flux (dot-ed lines in Fig. 2) deviate from the experimental data. In theseonditions, indeed, the interaction between ad molecules becomesignificantly higher and the dependence of the heat of adsorptionf carbon monoxide on CO coverage is thus increased, and cannote described by a simple linear relationship.

Experimental data taken by Nguyen et al. [17] for a 25/75 sil-er palladium membrane of 100 �m and collected at 1.013 barf total retentate pressure and carbon monoxide composition upo 20 vol.%, are reported in Fig. 3. In order to provide a properomparison with data obtained at different upstream or perme-te pressures, in this case the data are not reported in terms of fluxut rather in terms of the permeability PH2 defined in Eq. (1); evenhough PH2 is the proper quantity to consider in the diffusion lim-ted regime when Sieverts’ law holds, it will be considered also for aeneral comparison between the different behaviours observed byarying the operating conditions as temperature and CO content inhe feed gas. In Ref. [17] an anomalous behaviour of the hydrogenermeability was found in pure H2 experiments, with the presencef a maximum in the permeability curves that was not explained byhe authors. Such a phenomenon has not been observed by otheruthors and cannot be predicted by the simple model proposedere; as a consequence these data have not been considered andhe comparison was limited to pure hydrogen data at temperaturesigher than 550 K (diffusion limited regime) and lower than 450 K

desorption limited regime). By using the same heat of adsorptionor carbon monoxide already obtained from the data by Chabot etl. and reported above, the hydrogen permeate flux calculated fromhe model underestimates the experimental data and for an opti-

al fit the value of coefficient b in Eq. (18) should be 120 kJ mol−1,

Fig. 3. Comparison between experimental data taken from Ref. [17] collected in100 �m silver/palladium (25 wt%/75 wt%) membrane, with 1 atm of total pressurein the retentate side and vacuum on the permeate side, at several carbon monoxideconcentrations and results of model calculations (lines).

while the same slope a = −30 kJ mol−1 is required as for the best fitof the experimental data by Chabot et al.

The difference between the heat of adsorption used to describeall the data by Chabot et al. and by Nguyen et al. cannot beattributed only to the different silver content of the membranesused in the two works, which is indeed too small (i.e. 23 wt% against25 wt%, respectively) to produce a �ECO reduction of about 20%.On the contrary, the motivation for the different values of �ECO

required by the two different sets of data can be associated tothe different behaviour of the two membranes, which showed dif-ferent responses in the process to restore the permeance to purehydrogen experienced before CO adsorption. Indeed, Nguyen etal. [17] observed that CO adsorption on their membrane was eas-ily reversible and the pure hydrogen permeance before and afterthe addition of carbon monoxide attained the same value with noneed of a particular regeneration procedure. On the contrary, themembranes used by Chabot et al. [10] experienced a non-reversiblepoisoning upon CO exposure, and the original permeance of purehydrogen could be restored only by heating the membrane undervacuum or by applying a cleaning process. This fact suggests thatCO adsorption was different for the two membranes and in partic-ular it was stronger in the membranes used by Chabot et al. whichin fact requires a higher value of �ECO to best fit the experimen-tal data. The observed differences may reasonably be attributed tothe fact that different amounts of the two types of adsorbed car-bon monoxide species, linear and bridge-bonded, are present overthe membranes considered in Refs. [10,17], and that can lead to thedifferent �ECO values required to best fit the two different sets ofdata.

Data of Ref. [17] are also useful to investigate the relation-ship between hydrogen permeability and thickness of the metallayer, because membranes with three different thicknesses wereemployed, i.e. 75, 100 and 300 �m. The hydrogen permeability cal-culated for the case of pure hydrogen as well as for binary mixturescontaining also carbon monoxide are reported in Fig. 4. As pointedout by Nguyen et al., it is immediate to notice that in the presenceof CO only slight differences in hydrogen permeability are observed

for different membranes thicknesses, while for pure hydrogen thedecrease in the hydrogen permeability with decreasing tempera-ture is more marked for the thinner membrane. Interestingly thisfeature is correctly predicted by the model without changing theparameters found in the initial fitting of the data. Therefore, the

228 J. Catalano et al. / Journal of Membran

Ftc

aflttp

4

aiCtdin

itowoatpothtfaar

ibua[dsat

)

ig. 4. Calculated hydrogen permeability behaviour for pure hydrogen and mix-ures containing also carbon monoxide for membranes with different thickness andomparison with data from Ref. [17].

pproach used to account for the effects of CO on the hydrogenux is able to catch the qualitative behaviour of the experimentalrend also in this case, and to obtain even a satisfactory quantita-ive agreement with the use of the same values of the two fittingarameters a and b in Eq. (18) for �ECO calculation.

.2. Model analysis and predictions

After model validation we can now analyze different aspectsffecting hydrogen permeation in order to understand their relativemportance at different operating conditions, both with or withoutO in the feed. A sensitivity analysis is thus performed by changinghe relevant model parameters around the values obtained to fit theata reported in Ref. [17], and the expected response of the system

s investigated and discussed, even though experimental data areot directly available for comparison.

The effects of CO in the feed gas on hydrogen permeation haven all cases a clear feature both at higher temperatures and at loweremperatures: at high temperatures, say above 623 K, the presencef CO gives only very minor deviations from pure hydrogen results,hile at lower temperatures a dramatic permeability decrease is

bserved with respect to the pure H2 case. The behaviour observedt high temperature [10,17] is correctly described by the modelhat does not predict any flux depletion in that region due to COresence, as it is clearly shown in Figs. 2–4. At lower temperatures,n the contrary, two different limiting behaviours are clearly dis-inguishable in the absence or in the presence of CO; for the pureydrogen case permeation is controlled at low temperatures byhe desorption process at the permeate side, as already discussedor instance in ref [18], while a much steeper decline of perme-bility is observed in the Arrhenius plot, in presence of even smallmounts of carbon monoxide starting already when the desorptionesistance downstream is still negligibly small.

The model presented accounts for the observed behaviour andndicates that at high temperature the overall kinetics is controlledy diffusion so that surface processes, such those involving COpstream or desorption downstream, do not influence the perme-tion behaviour as actually observed from the experimental data

10,17]. When temperature is decreased, however, the situationrastically changes. For the case of pure hydrogen the change inlope of the permeability in the Arrhenius plot at lower temper-tures marks the switch from the regime controlled by diffusionhrough the membrane and the regime controlled by the desorp-

e Science 362 (2010) 221–233

tion from the downstream surface. In the presence of CO, on thecontrary, one never reaches a desorption limited regime since theeffects of CO adsorption onto the upstream interface result in arelevant resistance dominating the overall kinetics already at tem-peratures where the desorption resistance is still negligible. Thedifferent asymptotic behaviours encountered by decreasing sig-nificantly temperature, in presence or absence of CO, are thusassociated to different rate controlling steps: desorption on the per-meate side for pure hydrogen conditions, adsorption on retentateinterface in the case of H2–CO feeds. From a mathematical point ofview the situation is described by the different asymptotes due tosurface limited regimes in absence and presence of carbon monox-ide. In the first case, the desorption limited flux is obtained by Eq.(X) of Table 2, describing the surface adsorption/desorption pro-cess at the downstream side of the membrane, when the hydrogencoverage is unity:

NH2 = kd,0 · exp(

−2ED

RT

)· nS

2 (21)

which is written in terms of hydrogen permeability recalling Eq.(1):

PH2 = ı · kd,0 · nS2

p0.5H2,ret − p0.5

H2,per

· exp(

−2ED

RT

)(22)

On the other hand, in the presence of CO the limiting valueobserved is obtained when the surface process controlling the per-meation rate is the hydrogen adsorption on the retentate side; inthat case, the asymptotic flux is given by Eq. (13), considering acomplete CO coverage or, equivalently, by setting the hydrogencoverage equal to zero:

NH2 = pH2,1(2� · mH2 kT)−0.5 · S0 · nS2 ·

(1

1 + �CO · pintCO

)2

(23)

The corresponding permeability at low temperatures is thenevaluated by Eq. (1) at each retentate and permeate pressures as:

PH2 = pH2,ret

p0.5H2,ret − p0.5

H2,per

· ı(2� · mH2 kT)−0.5 · S0 · n2S

(1

1 + �CO · pintCO

)2

(24

The use of the permeability defined in Eq. (1), which is consistentwith Sieverts’ law, also outside the region in which the diffusionlimited regime holds allows to compare directly various condi-tions in which the rate controlling steps are different; on the otherhand it introduces a dependence on upstream and downstreampressures, as it is clear in Eqs. (22) and (24), which may appearsomewhat artificial. The maximum limiting values of the perme-abilities are reached when the downstream pressures, pH2,per , iszero. The slope of the asymptotes presented by the experimentaldata varies as a function of CO partial pressure, due to the alreadydiscussed dependence of �ECO on surface coverage, as well as ofmembranes thickness, and both effects are correctly predicted bythe model, as shown in Figs. 2–4.

From the model analysis we can also understand better theeffect of membrane thickness: indeed, for the case of pure hydrogenthe change in slope of the permeability in the Arrhenius plot marksthe switch from the regime controlled by diffusion through themembrane and the regime controlled by the desorption from thedownstream surface, at lower temperatures. The desorption resis-

tance is independent of membrane thickness, while the resistanceto diffusion increases with membrane thickness so that, for thickermembranes the transition takes place at lower temperatures. Inthe presence of CO, on the contrary, one never reaches a desorp-tion limited regime and the temperature at which CO adsorption

J. Catalano et al. / Journal of Membrane Science 362 (2010) 221–233 229

Fspt

sb(

eimrbtmttn

per

itapdtiowFtpeuitsrrc

flux is already decreased due to the desorption resistance.Fig. 6 shows, on the other hand, that hydrogen permeability

in presence of carbon monoxide is substantially unaffected by achange in ED since all the curves collapse on one another, indicating

ig. 5. Model calculated permeability obtained varying the hydrogen partial pres-ure on the permeate side, for a 100 �m Pd/Ag (75/25 wt%) membrane. The insetoints out a difference of 5% in the permeability of pure hydrogen with respect tohe theoretical limit of diffusion limited regime, for Pper of 0 and 1 atm.

tarts dominating the overall kinetics is less dependent on mem-rane thickness due to the higher energy involved in this process�ECO > ED).

The model, therefore, clearly indicates that the addition of CO,ven in very small quantities, substantially changes the relativemportance of the different processes involved in hydrogen per-

eation; when low temperatures are considered, indeed, diffusionesistance becomes negligible and the rate limiting step is offeredy the competitive adsorption of CO and H2 on the retentate side ofhe membrane, rather than by hydrogen desorption from the per-

eate side, as in the pure hydrogen case. In the presence of CO,herefore, the system switches from diffusion resistance to adsorp-ion resistance on retentate side, and the downstream processes doot play a role in determining the permeation rate.

In order to clarify better this point a sensitivity analysis has beenerformed by changing the permeate pressure and the activationnergy of desorption, to study their influence on permeability. Theesults are shown in Figs. 5 and 6, respectively.

Remarkably, Fig. 5 shows that when the permeate pressure isncreased from 0 to 1 atm, for a given feed pressure (2 atm absolute),he permeability of pure hydrogen defined in Eq. (1) experiencesdecrease in the temperature range below 623 K. The change in

ermeate pressure indeed affects the hydrogen coverage at theownstream side of the membrane and changes the relative impor-ance of the desorption step on the whole permeation process: byncreasing Pper the hydrogen coverage increases so that the des-rption resistance at the permeate surface gains importance earlierith respect to diffusion. This fact is apparent also in the inset of

ig. 5, in which the temperature value above which permeation is inhe diffusion limited regime increases with increasing the permeateressure from 0 to 1 atm: in the diffusion limited regime Siev-rts’ law holds and the permeability defined in Eq. (1) is constant,naffected by changes in the operative conditions. With decreas-

ng temperature the other resistances increase their relevance; in

hat case, changes in permeate pressure influence the rate of theurface process at the permeate side of the membrane, making theesistance of this step not negligible, even if not dominating, withespect to that due to diffusion or to the competitive adsorption ofarbon monoxide. In the presence of CO, the resistance associated

Fig. 6. Hydrogen permeability calculated from the model at different activa-tion energies for the hydrogen desorption. Data calculated for a 100 �m Pd/Ag(75/25 wt%) membrane considering an upstream hydrogen partial pressure of 1 barand vacuum in the permeate side.

to the complete adsorption of CO is localized at the upstream inter-face and is not directly affected by the permeate pressure, so thatthe change in the curves describing CO–H2 permeation below 600 Kis actually due to the fact that now the adsorption becomes soonimportant and actually dominant in a temperature range where the

Fig. 7. Comparison between data from Ref. [14] for a 100 �m pure palladium mem-brane at 0.51 bar of hydrogen partial pressure in the retentate side and vacuumapplied in the permeate side and model calculations considering three differentactivation energies for hydrogen desorption. The dashed straight lines indicate themolecular desorption limited fluxes.

230 J. Catalano et al. / Journal of Membrane Science 362 (2010) 221–233

F actionC e; and

tthidtw

atftbwtofibi[irve

ig. 8. Calculated behaviours of hydrogen coverage and atomic hydrogen molar frhabot et al. [10]. (a) H2 coverage at retentate side; (b) H2 coverage at permeate sid

hat in presence of CO the permeation behaviour is quite insensi-ive to variations of this parameter that instead strongly affects pureydrogen permeability in the desorption limited regime; changes

n desorption activation energy can increase the relative weight ofesorption process with respect to diffusion or CO adsorption, buthe system behaviour is insensitive to this parameter, contrary tohat seen for pure H2.

That is particularly interesting because it makes it possible topply the model developed also for experimental data relative onlyo the diffusion limited regime, that are the great majority of thoseound in literature, with no information on the desorption activa-ion energy. For example, we can consider the experimental datay Wang et al. [14] for a 100 �m pure palladium membrane, whichere collected at 0.51 bar of hydrogen partial pressure on the reten-

ate side, while vacuum was applied in the permeate side in orderf 0.1–1 Pa. The carbon monoxide partial pressure upstream wasxed at 0.66 kPa and the temperature inspected was in the rangeetween 400 and 473 K. From the analysis of the experimental data

t is clear that, in the temperature range inspected by Wang et al.

14], there is no slope change in the Arrhenius type plot shownn Fig. 7 and that all permeability data fall in the diffusion limitedegime. The desorption limited curves associated to different acti-ation energies have been drawn in the same Fig. 7, allowing tostimate the upper-limit of ED compatible with the experimental

at the two metallic surfaces at the conditions used in the experimental work by(c) H2 molar fractions at the two sides of the membrane.

data, that is around 38 kJ mol−1; however, the use of lower val-ues for the activation energy ED, i.e. 26, 30 and 34 kJ mol−1, doesnot change substantially the response of the model in the pres-ence of carbon monoxide as it is also shown in the same figure.The agreement of the model results with the experimental data isquite good with the same values of the heat of adsorption for car-bon monoxide found for experimental data by Nguyen et al., thatis using Eq. (18) with a = −30 kJ mol−1 and b = 120 kJ mol−1, whichgive �ECO values definitely closer to the experimental values foundin the literature for this parameter [25,38,39,42], rather than thevalue of 30.7 kJ mol−1 indicated in Ref. [14] using the global lumpedapproach given by Eq. (3).

4.3. Simplified model

The complete model formulated above may appear too elabo-rated and possibly more complex than actually needed to representthe observed behaviour of hydrogen flux in the presence of CO,just as the complete Ward and Dao model is more complex than

required to represent the hydrogen flux in the diffusion controlledregime for pure hydrogen. Therefore, it is worthwhile to try tosimplify the model as far as possible, by removing from the descrip-tion those processes that have lower or negligible impact on theflux measured. The most intuitive approach in this case would be

J. Catalano et al. / Journal of Membrane Science 362 (2010) 221–233 231

F n mont (d) hyt 2ret =

tiwaprbbpptea6w

psstFtmi

ig. 9. Comparison between complete and simplified model at two different carbohe upstream surface; (c) carbon monoxide coverage in the upstream surface; andhick 23% Ag/Pd membrane, with �ECO = 140–30ϑCO kJ mol−1, Edes = 13.1 kJ mol−1, PH

o consider the diffusion limited regime, trying to derive a mod-fied Sieverts’ law accounting for the presence of CO similar to

hat presented already by other authors [14,16]; however suchn approach, albeit very appealing, is impractical for the presenturpose. In fact it is easy to notice that if adsorption equilib-ium holds for hydrogen on the retentate surface, the simultaneousulk-to-surface equilibrium would lead to an equilibrium conditionetween the atomic hydrogen mol fraction xs,1 and the externalartial pressure of hydrogen, thus ruling out all effects due to theresence of CO. In the purely diffusion limited regimes, therefore,here is no substantial influence of CO on hydrogen flux, as it isxpected since the competitive absorption is a surface process, ands it is also confirmed by the experimental data (Figs. 2 and 3 above73 K), which in general show very limited flux reduction in theseorking conditions [10,17].

A more comprehensive analysis of the role of the differentrocesses involved in hydrogen permeation can be made by con-idering the behaviours of hydrogen coverage on the membraneurface and of hydrogen concentration in the bulk as a function of

he partial pressure of carbon monoxide in the feed (Fig. 8). Fromig. 8a it can be seen that the hydrogen coverage at the reten-ate side becomes smaller and smaller by increasing the carbon

onoxide partial pressure upstream; this behaviour indicates thatn the presence of CO the temperature at which the diffusion lim-

oxide partial pressures, for: (a) hydrogen permeate flux; (b) hydrogen coverage indrogen concentration in the sub-surface. The calculations are made for a 250 �m14 kPa, Pper = 1 Pa.

ited regime ceases to be the dominant resistance of the process issubstantially increased, as it was already pointed out by Ward andDao. In the presence of carbon monoxide, however, the flux is notlimited by desorption from the permeate side of the membrane,but, as already shown, by the adsorption step on the retentate side,where the competitive effect of carbon monoxide plays its impor-tant role. That can be confirmed also by analyzing the behaviour ofthe hydrogen coverage at the permeate side, reported in Fig. 8b;in the presence of CO, ϑH does not reach the value of unity asit happens for pure hydrogen in the case of desorption limitedregime (see Eq. (21)); on the contrary, it has a complex trend whichbecomes independent of CO partial pressure when the surface lim-ited regime is reached, that is when the hydrogen coverage at theretentate side approaches zero. From Fig. 8c it can be seen that, atthe same time, also the value of hydrogen mol fraction in bulk pal-ladium at retentate side collapses on that of the permeate side andeventually reaches the value which can be calculated by Sieverts’law, considering the equilibrium with permeate hydrogen partialpressure. More precisely, at the permeate side the hydrogen bulk

concentration never differs substantially from its equilibrium valueso that the kinetics of all the surface and sub-surface processes canbe neglected at the permeate side of the membrane.

By looking at the model behaviour, therefore, the completeapproach can be simplified considering the following conditions:

2 mbran

(

(

uottttrtsflwbd

igapaeprhdImtbrlacpp

5

biditassfadiombw

32 J. Catalano et al. / Journal of Me

(a) the downstream sorption/desorption kinetics are extremelyfast so that actual equilibrium holds for them;

b) also the bulk-to-surface kinetics is extremely fast, sobulk/surface equilibrium conditions are satisfied at the down-stream side of the membrane;

(c) the mol fractions of atomic hydrogen in the membrane bulk aresystematically much smaller than unity;

d) similarly to point (b), the bulk-to-surface kinetics is consideredextremely fast also at the upstream side.

Vice versa, in view of the previous considerations, at thepstream membrane surface equilibrium is considered to holdnly for CO adsorption, and not for hydrogen. The equations ofhe general model, therefore, can be simplified on the basis ofhe assumptions indicated above, leading to a set of three equa-ions instead of five as it was for the complete model. In particularhe system behaviour can be obtained by solving Eq. (13), whichemains unchanged also in the simplified approach, together withhe equilibrium condition for the bulk-to-surface flux at the feedide, which can be obtained from Eq. (14) setting the hydrogenux equal to zero, and the diffusion equation (Eq. (IV) of Table 1)here, due to equilibrium at the permeate side, the value of xs,2 can

e directly calculated through Sieverts’ constant from the value ofownstream hydrogen pressure.

Considering the heat of adsoprtion for the carbon monoxidendependent of CO coverage, the simplified model results in a sin-le implicit equation relating the hydrogen flux to the upstreamnd downstream H2 partial pressures and to the upstream partialressure of CO, while considering �ECO a function of coverage thebove simplifications yield to a set of two equations. The resultingquations, even in the case of �ECO constant, are clearly more com-lex than the simplified heuristic models given in Eqs. (3) and (4),espectively; nonetheless all the parameters entering the modelave a precise physical meaning and a well defined temperatureependence and can be obtained from independent measurements.

n Fig. 9 four parity plots are presented, in which the hydrogen per-eate flux, the hydrogen and carbon monoxide coverage as well as

he hydrogen concentration at the upstream interface of the mem-rane calculated from the simplified model are compared with theesults obtained by using the complete general model; in particu-ar, the parameter optimized on experimental data from Chabot etl. [10] has been used. The maximum deviation observed betweenomplete and simplified model is less than 0.1%, confirming theossibility to adopt the simplified model to describe the hydrogenermeation in the presence of carbon monoxide.

. Conclusions

A model for hydrogen permeation in palladium and palladium-ased membranes is proposed, in the presence of carbon monoxide

n the feed. The well know equations used by Ward and Dao [18] toescribe the whole hydrogen permeation process were modified

n the adsorption step to account for the simultaneous competi-ive adsorption of hydrogen and carbon monoxide molecules. Thedsorption of the carbon monoxide as well as that of hydrogen wereimply described using a Langmuir type adsorption and consideringteady state conditions for co-adsorption. The parameters neededor the calculations are endowed with a precise physical meaningnd were obtained by best fitting the model to the experimentalata available over a rather broad range of experimental conditions,

n particular of temperature and CO partial pressure, for adsorptionn pure palladium, and have been adapted to describe the per-eation in Pd–Ag membranes. The calculated behaviour obtained

y changing temperature, hydrogen and CO partial pressures asell as membrane thickness were compared with available liter-

e Science 362 (2010) 221–233

ature data and showed a good agreement, at all the temperaturesinspected. In this procedure the only fitting parameter used was theheat of adsorption of carbon monoxide, that was allowed to vary inthe range of values experimentally observed for different Pd-basedmembranes.

Acknowledgement

This work was performed with financial support of the ItalianMinistry of University and Research “Contributo del Fondo Inte-grativo Speciale Ricerca FISR DM 17/12/2002-anno 2001” Progetto:Idrogeno puro da gas naturale mediante reforming a conversionetotale ottenuta integrando reazione chimica e separazione a mem-brana.

Nomenclature

Symbolsa lattice parameter [m]c pre-exponential factor for the CO coverage in Eq. (3)D0 pre-exponential factor of the diffusion coefficient

(m2 s−1)Ea apparent activation energy for the hydrogen perme-

ation phenomenon (J mol−1)�EAb heat of absorption of hydrogen in palladium

(J mol−1)�EAd heat of adsorption of hydrogen in palladium

(J mol−1)ES–B activation energy for the surface-to-bulk transition

(J mol−1)EB–S activation energy for the bulk-to-surface transition

(J mol−1)Eads

CO activation energy for CO adsorption on the surface(J mol−1)

EdesCO activation energy for CO adsorption from the surface

(J mol−1)ED activation energy for hydrogen desorption (J mol−1)Ediff activation energy for the atomic diffusion coefficient

(J mol−1)h Planck’s constant (J s)k Boltzmann’s constant (J K−1)KCO Langmuir affinity parameter in Eq. (4)kd,o pre-exponential factor for the molecular desorption

constant (m2 mol−1 s−1)kads

iadsorption constant for species i (Pa−1 s−1)

kdesi

desorption rate constant for species i (m4 mol−2 s−1)mi mass of a molecule of species i (kg mol−1)Mi molecular mass of species i (kg mol−1)n empirical exponent in modified Sieverts’ law Eq. (2)NAV Avogadro’s numbernb Pd bulk concentration in palladium (molPd m−3)nb,Pd Pd bulk concentration in palladium alloys

(molMe m−3)NH2 hydrogen flux (mol m−2 s−1)nS total number of adsorption sites available on the

palladium surface (molPd m−2)nS,Pd total number of adsorption sites available on the

alloy surface (molPd m−2)pi partial pressure of species i (Pa)

P̄H2 hydrogen permeability (mol m−1 s−1 Pa−0.5)R universal gas constant (J mol−1 K−1)rCO adsorption or desorption rates (s−1)S0 hydrogen sticking coefficient

J. Catalano et al. / Journal of Membran

T absolute temperature (K)xs,i H/Pd ratio in bulk metal referred to surface i

Greek symbols˛ parameter in Eq. (4)�ECO heat of adsorption for carbon monoxide (J mol−1)�S̃0

H partial molar entropy of dissolution of hydrogenatoms at infinite dilution (J mol−1 K−1)

ı membrane thickness (m)�CO adsorption coefficient for CO (Pa−1)�0 pre-exponential factor for the surface-to-bulk metal

transition (m3 mol−1 s−1)ϑi coverage of species i�i density of species i (kg m−3)ωi weight fraction of species i

Superscripts and subscriptsads refers to adsorptiondes refers to desorption

R

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per refers to permeate sideret refers to retentate side

eferences

[1] T. Graham, Philos. Trans. Roy. Soc. 156 (1866) 415–431.[2] G.L. Holleck, Diffusion and solubility of hydrogen in palladium and

silver–palladium alloys, in: G. Alefeld, J. Volkl (Eds.), Hydrogen in Metals II,Springer, Berlin, Heidelberg, 1978.

[3] F.A. Lewis, The Palladium Hydrogen System, Academic Press, London,1967.

[4] A. Pisarev, V. Shestakov, R. Hayakawa, Y. Hatano, K. Watanabe, Gas-drivenhydrogen permeation in the surface-limited regime, J. Nucl. Mater. 320 (2003)214–222.

[5] J. Tong, R. Shirai, Y. Kashima, Y. Matsumura, Preparation of a pinhole-free Pd–Agmembrane on a porous metal support for pure hydrogen separation, J. Membr.Sci. 260 (2005) 84–89.

[6] K.S. Rothenberger, A.V. Cugini, B.H. Howard, R.P. Killmeyer, M.V. Ciocco, B.D.Morreale, R.M. Enick, F. Bustamante, I.P. Mardilovich, Y.H. Ma, High pressurehydrogen permeance of porous stainless steel coated with a thin palladiumfilm via electroless plating, J. Membr. Sci. 244 (2004) 55–68.

[7] N. Itoh, T. Akiha, T. Sato, Preparation of thin palladium composite membranetube by a CVD technique and its hydrogen permselectivity, Catal. Today 104(2005) 231–237.

[8] D.A. Pacheco Tanaka, M.A. Llosa Tanco, S. Niwa, Y. Wakui, F. Mizukami, T.Namba, T.M. Suzuki, Preparation of palladium and silver alloy membrane on aporous �-alumina tube via simultaneous electroless plating, J. Membr. Sci. 247(2005) 21–27.

[9] Y. Chen, Y. Wang, H. Xu, G. Xiong, Hydrogen production capacity of membranereformer for methane steam reforming near practical working conditions, J.Membr. Sci. 322 (2008) 453–459.

10] J. Chabot, J. Lecomte, C. Grumet, J. Sannier, Fuel clean-up system. Poisoning ofpalladium–silver membranes by gaseous impurities, Fusion Technol. 14 (1988)614–618.

11] A.B. Antoniazzi, A.A. Haasz, P.C. Stangeby, Effect of adsorbed carbon and sulphuron hydrogen permeation through palladium, J. Nucl. Mater. 162–164 (1989)1065–1070.

12] H. Amandusson, L.-G. Ekedahl, H. Dannetun, The effect of CO and O2 on hydro-gen permeation through a palladium membrane, Appl. Surf. Sci. 153 (2000)259–267.

13] K. Hou, R. Hughes, The effect of external mass transfer, competitive adsorptionand coking on hydrogen permeation through thin Pd/Ag membranes, J. Membr.Sci. 206 (2002) 119–130.

14] D. Wang, T.B. Flanagan, L. Kirk, Shanahan, Permeation of hydrogen through pre-oxidized Pd membranes in the presence and absence of CO, J. Alloys Compd.372 (2004) 158–164.

[

[

e Science 362 (2010) 221–233 233

15] F.C. Gielens, R.J.J. Knibbeler, P.F.J. Duysinx, H.D. Tong, M.A.G. Vorstman, J.T.F.Keurentjes, Influence of steam and carbon dioxide on the hydrogen flux throughthin Pd/Ag and Pd membranes, J. Membr. Sci. 279 (2006) 176–185.

16] G. Barbieri, F. Scura, F. Lentini, G. De Luca, E. Drioli, A novel model equation forthe permeation of hydrogen in mixture with carbon monoxide through Pd–Agmembranes, Sep. Purif. Technol. 61 (2008) 217–224.

17] T.H. Nguyen, S. Mori, M. Suzuki, Hydrogen permeance and the effect of H2Oand CO on the permeability of Pd0.75Ag0.25 membranes under gas-drivenpermeation and plasma-driven permeation, Chem. Eng. J. 155 (2009) 55–61.

18] T.L. Ward, T. Dao, Model of hydrogen permeation behaviour in palladium mem-branes, J. Membr. Sci. 153 (1999) 211–231.

19] A. Sieverts, W. Danz, Solubilities of D2 and H2 in palladium, Z. Physik. Chem.(B) 34 (1936) 158–159.

20] R.E. Buxbaum, A.B. Kinney, Hydrogen transport through tubular membranesof palladium-coated tantalum and niobium, Ind. Eng. Chem. Res. 35 (1996)530–537.

21] A. Caravella, G. Barbieri, E. Drioli, Modelling and simulation of hydrogenpermeation through supported Pd-alloy membranes with a multicomponentapproach, Chem. Eng. Sci. 63 (2008) 2149–2160.

22] J. Catalano, M. Giacinti Baschetti, G.C. Sarti, Influence of the gas phase resistanceon hydrogen flux through thin palladium–silver membranes, J. Membr. Sci. 339(2009) 57–67.

23] M. Johansson, O. Lytken, I. Chorkendorff, The sticking probability for H2 in pres-ence of CO on some transition metals at a hydrogen pressure of 1 bar, Surf. Sci.602 (2008) 1863–1870.

24] D.A. King, M.G. Wells, Reaction mechanism in chemisorption kinetics: nitrogenon the {1 0 0} plane of tungsten, Proc. Roy. Soc. London 339 (1974) 245–269.

25] O. Dulaurent, K. Chandes, C. Bouly, D. Bianchi, Heat of adsorption of carbonmonoxide on a Pd/Al2O3 solid using in situ infrared spectroscopy at high tem-peratures, J. Catal. 188 (1999) 237–251.

26] D.R. Alfonso, Comparative studies of CO and H2O interactions with Pd(1 1 1)surface: a theoretical study of poisoning, Appl. Phys. Lett. 88 (2006),051908–051908-3.

27] E. Ozensoy, B.K. Min, A.K. Santra, D.W. Goodman, CO dissociation at ele-vated pressures on supported Pd nanoclusters, J. Phys. Chem. B 108 (2004)4351–4357.

28] C.-Y. Huang, H.-J. Chiang, J.-C. Huang, S.-R. Sheen, Synthesis of nanocrystallineAg–Pd alloys by chemical reduction method, Nanostruct. Mater. 10 (1998)1393–1400.

29] R.J. Borg, G.J. Dienes, An Introduction to Solid State Diffusion, Academic Press,San Diego, 1988.

30] C. Wert, C. Zener, Interstitial atomic diffusion coefficients, Phys. Rev. 76 (1949)1169–1175.

31] H. Züchner, Untersuchung der Diffusion of Wasserstoff in Pd- und Pd/Ag-Legierungen mit einer Stromstoß-Methode, Z. Naturforsch. Pt. A 25 (1970)1490–1496.

32] J. Behm, K. Christmann, G. Ertl, Adsorption of hydrogen on Pd(1 0 0), Surf. Sci.99 (1980) 320–340.

33] A. Bhargav, G.S. Jackson, Thermokinetic modeling and parameter estimationfor hydrogen permeation through Pd0.77Ag0.23 membranes, Int. J. HydrogenEnergy 34 (2009) 5164–5173.

34] E. Serra, M. Kemali, A. Perujo, D.K. Ross, Hydrogen, Deuterium in Pd-25 Pct Agalloy: permeation, diffusion, solubilization and surface reaction, Metall. Mater.Trans. A 29A (1998) 1023–1028.

35] S. Tosti, A. Basile, G. Chiappetta, C. Rizzello, V. Violante, Pd–Ag membrane reac-tors for water gas shift reaction, Chem. Eng. J. 93 (2003) 23–30.

36] H. Yoshida, S. Konishi, Y. Naruse, Effects of impurities on hydrogen perme-ability through palladium alloy membrane at comparatively high pressure andtemperature, J. Less-Common Met. 89 (1983) 429–436.

37] D. Artman, T.B. Flanagan, Desorption of hydrogen from palladium andpalladium–silver alloys followed by differential scanning calorimetry, Can. J.Chem. 50 (1972) 1321–1324.

38] O.M. Lovvik, R.A. Olsen, Density functional calculations of hydrogen adsorptionon palladium–silver alloy surfaces, J. Chem. Phys. 118 (2003) 3268–3276.

39] M. Myyrylainen, T.T. Rantala, Kinetic Monte Carlo modeling of CO desorptionand adsorption on Pd(1 1 0) surface, Catal. Today 100 (2005) 413–417.

40] D.M. Ruthven, Principles of Adsorption and Adsorption Processes, John Wileyand Sons, New York, 1984.

41] T.M. Duncan, K.W. Zilm, D.M. Hamilton, T.W. Root, Adsorbed states of car-

bon monoxide on dispersed metals: a high-resolution solid-state NMR study,J. Phys. Chem. 93 (1989) 2583–2590.

42] E.H. Voogt, L. Coulier, O.L.J. Gijzeman, J.W. Geus, Adsoprtion of carbon monoxideon Pd(1 1 1) and palladium model catalysts, J. Catal. 169 (1997) 359–364.

43] K. Christmann, G. Ertl, Adsorption of carbon monoxide on silver/palladiumalloys, Surf. Sci. 33 (1972) 254–270.