Chemical Engineering Journal 218 (2013) 394–404

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Chemical Engineering Journal

journal homepage: www.elsevier .com/locate /ce j

Simulation of binary gas separation through multi-tube molecularsieving membranes at high temperatures

1385-8947/$ - see front matter � 2012 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.cej.2012.12.063

⇑ Corresponding author. Tel.: +61 7 3365 6960; fax: +61 7 3365 4199.E-mail address: j.dacosta@uq.edu.au (J.C. Diniz da Costa).

Guozhao Ji a, Guoxiong Wang a, Kamel Hooman b, Suresh Bhatia a, João C. Diniz da Costa a,⇑a The University of Queensland, FIMLab – Films and Inorganic Membrane Laboratory, School of Chemical Engineering, Brisbane, Qld 4072, Australiab The University of Queensland, School of Mechanical and Mining Engineering, Brisbane, Qld 4072, Australia

h i g h l i g h t s

" A model was validated for a multi-tube membrane module for binary gas separation." H2 driving force is greatly affected by process conditions and module design." The radius of the module influences significantly on H2 purity and recovery." Similar counter and co-current flows due to high gas-through-gas diffusion.

a r t i c l e i n f o

Article history:Received 20 September 2012Received in revised form 4 December 2012Accepted 24 December 2012Available online 29 December 2012

Keywords:Binary gas separationHydrogenMolecular sieving membraneMulti-tube module

a b s t r a c t

An experimentally validated theoretical model was developed to investigate the influence of operatingconditions on the performance of a multi-tube membrane module containing cobalt oxide silica (COxS)membranes with molecular sieving properties. The model investigated the separation process for a bin-ary gas mixture consisting of H2 and Ar at 400 �C. Engineering parameters such as feed flow rate, feedpressure, module size and flow configuration were systematically varied in order to optimise the separa-tion performance promoting three main goals: H2 yield, H2 purity and H2 recovery. Changing theseparameters led to different flows and H2 fractions in the feed domain, thus altering the driving forcesfor the preferential permeation of H2. The simulated results suggest that gas separation was greatlyimproved by reducing the module radius which meets all of the three aforementioned optimisation cri-teria. Interestingly, increasing the feed flow rate and feed pressure were found to be beneficial but theformer led to lower H2 recovery whilst the latter did not deliver the same purity when compared to lowerfeed pressure. In addition, two flow configurations, counter-current and co-current, were compared. Itwas observed that the results of counter-current were effectively the same as the co-current. This wasattributed to the high gas-through-gas diffusion for high-temperature membrane operation. Finally,neglecting diffusion effects, or considering advection only, leads to over prediction of H2 permeate molarfraction.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction branes derived from ceramics, silica or metal alloys [2] and zeolites

Hydrogen is widely accepted as a clean energy carrier, particu-larly in fuel cell deployment, whereby reaction with oxygen fromair generates water, an environmentally benign emission. Conven-tional gas separation technologies using organic membranesrequire low temperature operation due to the poor thermo-stability and anti-oxidation properties of polymers. As H2 is oftengenerated at high temperatures by natural gas reforming or coalgasification [1], separation of H2 attracts energy penalties due tothe required cool down of high temperature streams to meet theoperating requirements of polymeric membranes. Inorganic mem-

[3,4] can be employed in high temperature gas separation due totheir thermo-stability and good resistance to chemical attack.Molecular sieving membranes for H2 separation are quite promis-ing due to superior performance at elevated temperatures [5,6],especially those derived from metal oxide silica matrices [7].Therefore, there has been a major concerted effort of the researchcommunity to improve the gas separation performance by primar-ily focusing on membrane synthesis.

However, membrane performance is intrinsically linked to theoperating conditions and design of membrane modules, which playa significant role in gas separation processes. It is well known thathigher driving forces are favourable for the efficient operation ofmembrane systems in most cases. Moreover, operating conditionsand the membrane module design (size and flow configuration)

Nomenclature

A permeable area in a computational cell (m2)C total molar concentration (mol m�3)D Fick diffusivity in gas phase (m2 s�1)Ð Maxwell–Stefan diffusivity in the membrane (m2 s�1)Ði Maxwell–Stefan single gas diffusivity in membrane

(m2 s�1)Ðij Maxwell–Stefan mutual diffusivity describing

interchange between component i and componentj (m2 s�1)

Ðij self exchange coefficient (m2 s�1)dt time stepF flow rate (NL min�1)JH2 permeate flux across membrane of component H2

(mol s�1 m�2)JAr permeate flux across membrane of component Ar

(mol s�1 m�2)K Henry’s constant (mol m�3 Pa�1)l position of the module (m)n the number of elements (m)R gas constant (8.314 J mol�1 K�1)R0 radius of the module (m)rm radius of the membrane (m)r radial coordinateA source term (mol s�1 m�3)T temperature (K)p pressure (Pa)pH2 partial pressure of component H2 (Pa)

pAr partial pressure of component Ar (Pa)Q molar permeate flow rate across membrane (mol s�1)QH2 molar permeate flow rate across membrane of

component H2 (mol s�1)q concentration of adsorbed gas (mol m�3)V computational cell volume (m3)v permeation speed (m s�1)xH2 H2 molar fraction[B] coefficient matrix in Maxwell–Stefan equation[L] inversed matrix of [B][J] matrix of flux across membrane[rp] matrix of pressure gradientFp(n) permeate flow rate at permeate outletXp(n) permeate fraction at permeate outlet

Greek lettersg viscosity (Pa s)l chemical potential (J mol�1)l0 chemical potential in the chosen standard state

(J mol�1)h fractional occupancy of adsorption

SubscriptsH2 hydrogenAr argonPermeate permeate sideRetentate retentate side

G. Ji et al. / Chemical Engineering Journal 218 (2013) 394–404 395

determine the driving force magnitude and its distribution withinthe membrane module. In order to understand the influence of theoperating conditions and module design on gas separation, it isessential to understand the behaviour of gas flow status in tandemwith membrane properties, an area which requires investigation.Literature related to gas separation on this topic is generally lim-ited, whilst the majority of Computational Fluid Dynamic (CFD)investigations have focused on liquid separation [8]. To date, CFDsimulation has been carried out for molecular sieve silica [9,10],Pd [11] and polymeric [12] membranes. These studies showedthe significant benefit of distributed-parameter simulation in mod-elling membrane gas separation processes, thus replacing the aver-aged or ‘‘lumped’’ parameter model.

In this work, we focused on the performance of multi-tubemembrane modules, which are becoming an engineering require-ment for the deployment of gas separation units. Depending uponthe engineering design, membrane modules could be arranged inseries instead of longer single tube lines, mainly attributed to thecurrent limitation of fabricating defect free longer single inorganicmembrane tubes. To address this problem, we have developed amathematical model, as a predictive tool, to investigate the influ-ence of the operating conditions (e.g. feed flow rate, feed pressure,feed fraction) and membrane module design on the gas separationprocess. Furthermore, we built and tested a membrane modulecontaining two COxS tube membranes in line to validate the modeland simulated results under various operating conditions.

2. Model development

The design of the gas separation module investigated in thiswork is depicted in Fig. 1a. Multiple membranes are envisagedfor industrial application, so here we have installed two mem-branes in series to simulate the complexity of multiple mem-

branes. In the gas separation process, the feed gas is introducedfrom the inlet to the shell. The preferentially permeable gas mole-cules diffuse across the membranes to the permeate gas streamwhich is collected at the outlet. The less permeable gas remainsin the shell of the membrane module, and exits via a second outletnamed the retentate gas stream. A binary mixture consisting of H2

and Ar was chosen as feed gas to investigate binary gas separationat high temperature (400 �C) using COxS membranes, due to theirvery low sorption coverage at these testing conditions. Hence, gasadsorption is negligible.

In the membrane module shell, gas molecules move freely, andmass transfer is controlled by gas-through-gas diffusion in the gasphase. More importantly, the mass transfer across the membrane islimited by the diffusion of gas molecules via constrictions consist-ing of apertures or pore sizes in the molecular sieving region(dp < 5 Å), in addition to gas to solid adsorption. In the case of silicaderived membranes, average pore sizes are in the region of 3 Å,thus conferring pore size exclusion for the diffusion of moleculeswith larger kinetic diameters such as CO2, N2 and Ar. However, sil-ica films have amorphous structures characterised by pore size dis-tribution. Hence, larger gas molecules are able to diffuse throughthe small concentrations of large pores. Many of these gases showa reduction of permeance with temperature, attributed to adsorp-tion effects. In order to simulate the gas separation process, themathematical model can be discretised into a large number of sub-domains as illustrated in Fig. 1b. Thus, the mass transfer processesin the gas phase and across the membrane can be described by fi-nite differences. The resulting set of equations can then be solvednumerically.

2.1. Gas phase mass transfer

Gas-through-gas diffusion in the gas phase usually occurs at amuch faster rate than through the membrane, by four orders of

Fig. 1a. The structure of the gas separation module. R0 = 0.05 m, rm = 0.007 m, Lm1 = 0.16 m, Lm1 = 0.16 m and L = 1 m.

Fig. 1b. The simplified and discretised schematic of the gas separation module.

396 G. Ji et al. / Chemical Engineering Journal 218 (2013) 394–404

magnitude [9]. Given this situation, the concentration variation inradial direction (or concentration polarisation phenomena) is veryweak as discussed elsewhere [9–13]. Therefore, we assume therewas negligible concentration variation in the radial direction. Inthis case, we consider the one dimension (1D) transient masstransfer in the axial direction only.

The basic mass balance in the gas phase can be described by thecontinuity equation:

@c@tþ @J@l¼ S ð1Þ

where c is the molar concentration, J the bulk flux, t time, l the posi-tion in the module, and S is the source term which represents themass transfer across the membrane. It must be noted that sourceterm is zero everywhere except at the membrane surface [10]. Inthe membrane feed interface side the source term is negative,whereas it is positive in the permeate interface side.

For component H2 the mass balance is governed by the follow-ing solution conservation equation

@ðcxH2Þ@t

þ @ðJxH2Þ@l

¼ @

@lD@ðcxH2Þ@l

� �þ SH2 ð2Þ

where xH2 is the molar fraction of H2, D the diffusivity of H2 in Arwhich can be estimated from Fuller equation [14], and SH2 is thesource term for permeate H2.

It is important to observe that Eq. (2) contains both the advec-

tion term @ðJxH2Þ@l and the diffusion term @

@l D @ðcxH2Þ@l

� �. In liquid or low

temperature gas separation in small scale modules, advection is farmore intense than diffusion, so diffusion is always omitted in thecomponent mass balance equation [15–20]. As a result, Eq. (2) isreduced to a simpler and less complex simulation as per the fol-lowing equation:

@ðJxH2Þ@l

¼ SH2 ð2aÞ

However, a major principle of chemical engineering design in hereis the recovery of a gas species from a gas mixture at high temper-atures. To take advantage of a high recovery, and likewise stage cut,excessive feed flow is undesirable. In addition, the intrinsic proper-ties of molecular sieve silica membranes shows temperature depen-dent transport, where high separation factors are preferentiallyattained at high temperatures [2,21,22]. At these conditions, advec-tion plays a less dominating role, particularly that gas to gas diffu-sion is very high at high temperature. As a consequence, thediffusion coefficient increases [14,23]. Therefore, diffusion becomesprevalent over advection in this case and Eq. (2) containing the dif-fusion term should be used instead of Eq. (2a).

The relationship between permeate pressure and flow rate isgoverned by Hagen–Poiseuille equation [24]

dpdl¼ �8gFRT

pr4mp

ð3Þ

where p is pressure, g viscosity, F the bulk flow rate, R the gas con-stant, T the temperature and rm is the radius. Eq. (3) is applicable forthe cylindrical tube-like permeate domain of a membrane (Fig. 1b).For the feed domain (also Fig. 1b), the pressure variation is quitesmall [17,18,20,25,26] and takes the following form for an annulusshell

dpdl¼ � 8gFRT

p R20 � r2

m

� �R2

0�r2m

lnðR0=rmÞ � R20 þ r2

m

� �h ip

ð4Þ

The source terms in Eqs. (1) and (2) represent the mass transferbetween feed side and permeate side and are derived from the fol-lowing formulas [27,28]

S ¼ QV¼ JA

Vð5Þ

SH2 ¼QH2

V¼ JH2A

Vð6Þ

G. Ji et al. / Chemical Engineering Journal 218 (2013) 394–404 397

where Q and QH2 are the total permeate flow rate and the hydrogenpermeate flow rate in one computational cell, respectively; JH2 is thehydrogen permeate flux; A is the permeable area in a cell; and V isthe computational cell volume. The source terms are zero if thecomputational cell is not in the permeable region (such as cells 1,2 and 3 in Fig. 1b). The source terms apply (such as cells k � 1, kand k + 1 in Fig. 1b) to the permeable region only.

2.2. Membrane mass transfer

The mass transfer across the membrane for single gas can be de-rived from [29–31]

J ¼ �qÐ1

RTdldz

ð7Þ

where l is the chemical potential which is expressed as [29,32,33]

l � l0 þ RT ln p ð8Þ

Eqs. (7) and (8) may be combined to give

J ¼ �Ðd ln pd ln q

dqdz¼ �Ð

11� h

dqdz

ð9Þ

where h is fractional occupancy of adsorption. In Eq. (9), 11�h is called

thermodynamic factor. At high temperatures, adsorption is veryweak which implies h � 0 and thus 1

1�h � 1. Meanwhile adsorptionfollows Henry’s law, and the adsorbed gas concentration, q, is pro-portional to pressure, p, giving

q ¼ Kp ð10Þ

So the single gas flux across the membrane can be expressed as

J ¼ �ÐKdpdz

ð11Þ

Eq. (11) is mainly suitable for describing single gas transfer acrossthe membrane. If the feed gas is a mixture, the situation is morecomplex. Although some authors still assume the gas permeancein a mixture is the same as pure gas permeance [16,34,35], we tendto believe there is a mutual interaction due to the different gas per-meation speeds. In order to examine this theory, the Maxwell–Ste-fan (MS) equation should be applied to consider this kind ofcounter-exchange [29,36,37]. For a multiple gas system the MSequation gives

�rli ¼ RTXn

j¼1

xjðv i � v jÞ

Ðijþ xnþ1

ðv i � vnþ1ÞÐi;nþ1

!ð12Þ

where vi is the velocity of component i, and the relation betweenmolar flux Ji and vi is given by

Ji ¼ civ i ¼P

RT

� �xiv i ð13Þ

Dij in Eq (12) is Maxwell–Stefan diffusivity describing interchangebetween i and j. x is the molar fraction.

In gas mixture separation systems, the membrane is treated asthe n + 1th component which is motionless, i.e.

vnþ1 ¼ 0 ð14Þ

Combining Eqs. (8), (12), (13), and (14) obtains

� 1RTrpi ¼

Xn

j¼1

xjJi � xiJj

Ðij

þ Ji

Ðið15Þ

Ði is the Maxwell–Stefan diffusivity of single gas i which can beobtained from single gas permeation test. The proper estimationof Ðij remains an issue. The value can be calculated by the empirical

Vignes correlation, adapted to micropore diffusion by Krishna,Wessling and co-workers [38,39]:

Ðij ¼ Ðxiii �Ð

xj

jj ð16Þ

where Ðii and Ðjj are self-exchange coefficient. Since self-exchangecoefficients are rarely available, the assumption that Ðii=Ði � 1 isoften used for membranes with micropores [29,36,37,40–42], lead-ing to

Ðij ¼ Ðxii �Ð

xj

j ð17Þ

Eq. (15) can be cast into matrix form

� 1RT½rp� ¼ ½B�½J� ð18Þ

For H2/Ar binary gas system, the elements of [B] are given byaccording to Eq. (15)

½B� ¼xArÐ12þ 1

Ð1� xH2

Ð12

� xArÐ12

xH2Ð12þ 1

Ð2

" #ð19Þ

where Ð1 is the Maxwell–Stefan diffusivity of H2, and Ð2 is that ofAr. Ð12 is the Maxwell–Stefan interchange diffusivity inside themembrane.

Multiplying both sides of Eq. (18) by [B]�1 we get

½J� ¼ � 1RT½B��1½rp� ð20Þ

If we define another matrix [L] as

½L� ¼ ½B��1 ð21Þ

then the flux of the two species can be obtained from an explicitexpression

JH2 ¼ � 1RT ðL11 � rpH2 þ L12 � rpArÞ

JAr ¼ � 1RT ðL21 � rpH2 þ L22 � rpArÞ

8<: ð22Þ

As both [L] and [rp] are functions of fraction xH2, it is necessary tosolve the fraction xH2 distribution across membrane in advance.

By differentiating Eq. (22) with respect to r, and applying massbalance rule, we obtain

dðr � JH2Þdr

¼ ddr½rðL11 � rpH2 þ L12 � rpArÞ� ¼ 0 ð23Þ

which finally leads to a second order differential equation of xH2 to r

xH2dpdrþ pðrÞdxH2

dr

� �dL11ðxH2Þ

dr� dL12ðxH2Þ

dr

� �þ ðL11ðxH2Þ

� L12ðxH2ÞÞ pðrÞd2xH2

drþ 2

dpðrÞdr

dxH2

dr

!þ dpðrÞ

drdL12ðxH2Þ

dr

þ 1rðL11ðxH2Þ � L12ðxH2ÞÞ xH2

dpðrÞdrþ pðrÞdxH2

dr

� �þ L12ðxH2Þ

dpðrÞdr

� �¼ 0

ð24Þ

According to Eq. (15), dpðrÞdr is constant and p(r) is known as well. Two

boundary conditions for Eq. (24) are available by extracting fromthe iteration results in gas phase.

r ¼ rm;feedinterface; xH2 ¼ xH2;feedinterface ð25Þ

r ¼ rm;feedpermeateinterface; xH2 ¼ xH2;permeateinterface ð26Þ

Thus the molar fraction xH2 distribution across the membrane is de-rived from Eqs. (24)–(26), and permeate flux can be accurately cal-culated by Eq. (22).

Table 1Parameters of experimental operating condition.

Operating conditions Value

Temperature 400 (�C)H2 permeance 3.22 � 10�8 (mol s�1 m�2 Pa�1)Ar permeance 4.99 � 10�10 (mol s�1 m�2 Pa�1)Ro 0.05 (m)rm 0.007 (m)pf 6 (atm)pp 1 (atm)

Table 2Selected feed H2 molar fraction and feed flow rate.

H2 feedfraction (%)

Feed flow rate (mL/mincalibrated at 1 atm)

Symbols inFigs. 3 and 4

99.06 250.65 �

98.81 226.58 j

97.73 142.69 N

94.04 92.89 �70.73 32.43 d

40.94 16.81 +

200

250

L/m

in)

398 G. Ji et al. / Chemical Engineering Journal 218 (2013) 394–404

3. Numerical details and experimental

The model was discretised into n cells as shown in Fig. 1b to ob-tain the numerical variable values throughout the module. Theboundary conditions was set as follows: (i) constant pressure atretentate, (ii) constant pressure at outlet and (iii) constant feed fluxat inlet. At initial state, t = 0, both feed and permeate domains werefilled with Ar only. Upwind scheme was applied to update thevalue of each cell with iteration [43].

The model was compiled in Matlab. The variables were solvedby explicit finite difference solver. Stability of the solver waschecked to prove the numerical scheme was satisfactorily stable.Different combinations of time step and grid size were run by thismodel. Time steps from Dt = 0.001–0.1 s were checked to reachsteady state and they were congruent. Therefore, Dt = 0.1 s wasused in the following cases since it was sufficient to provide accu-rate and quick results. The iteration stopped right after the calcu-lation process reached steady state when the H2 mass balancereached a difference smaller than 1e�5.

A grid independence study in Fig. 2 was performed to determinethe suitable grid size for this model. It showed the H2 fraction pro-file along axial positions with different grid sizes. When the cellnumber reaches n = 40, further increasing the cell number didnot lead to any significant changes of the H2 fraction. Therefore,n = 40 was deemed adequate to provide accurate values fordescribing the physical problem in this work.

In this study, the model equations developed above werenumerically solved under operating conditions similar to thoseused in the experimental work, as listed in Tables 1 and 2. Theexperiments were carried out at 400 �C with various H2 feed frac-tions and feed flow rates. Table 1 presents the basic properties ofsingle gas permeances, module size and system operating pressureused. The typical feed fractions and feed flow rates used in variousexperiments for binary gas mixure separation are listed in Table 2.The experimental permeance of using the membrane module de-scribed in Fig. 1 was measured at 400 �C. Cobalt oxide silica mem-branes were produced by sol–gel synthesis [44] and dip coated onhigh quality supports purchased from the Energy Centre of theNetherlands. The substrate was composed of asymmetric layers,the top layer being derived from c-alumina with an intrinsic poresize distribution �4 nm. The top from c-alumina layer was coatedon a mechanically robust porous a-alumina substrate with the fol-lowing dimensions: length 160 mm, external and internal diame-ters 14 and 10 mm, respectively. Based on molecular probingcharacterisation, the cobalt silica layer had an average pore �3 Å.Single gas permeation was carried out at the dead end mode,where the retentate stream was closed. The binary gas mixturesof H2 and Ar were mixed using MKS mass flow controllers. The per-meate stream pressure was kept constant at 1 atm whilst the

0.36

0.38

0.4

0.42

0.44

0.46

0.48

0.5

0 0.2 0.4 0.6 0.8 1

hydr

ogen

mol

ar fr

actio

n

position of the module

n=10n=20n=40n=60n=80n=100

Fig. 2. The grid independence study of this model. Bold lines on abscissa are theposition of membranes.

retentate pressure was controlled by a backpressure regulator at6 atm. The permeate flow rate was measured by a bubble flow me-ter, and a Shimadzu gas chromatograph was used to analyse thecomposition of the permeate gases in the case of binary gasmixtures.

4. Results and discussion

The simulated permeate flow rates and H2 molar fractionsshown in Figs. 3 and 4 fit very well with the experimental results,thus validating the model developed in this work. The root meansquared errors for the permeate flow rate and H2 molar fractionwere 6.48% and 1.43%, respectively. Based on this good agreement,the model is considered robust permiting its utilisation for furthersimulations into understanding how operational parameters can af-fect gas separation performance and module design optimisation.

In this simulation, the H2 gas separation process is mainly eval-uated by three parameters: H2 yield, H2 purity, and H2 recovery. H2

yield is the flow rate at the permeate outlet multiplied by purityFp(n)�Xp(n). H2 purity is the H2 molar fraction at the permeate

0

50

100

150

0 50 100 150 200 250

mod

elle

d pe

rmea

te fl

ow ra

te (m

experimental permeate flow rate (mL/min)

Fig. 3. Comparison of permeate flow rates obtained from experiments andmodelling.

0.4

0.5

0.6

0.7

0.8

0.9

1

0.4 0.5 0.6 0.7 0.8 0.9 1

mod

elle

d pe

rmea

te H

2fra

ctio

n

experimental permeate H2 fraction

Fig. 4. Comparison of permeate H2 molar fractions results from experiments andmodelling.

G. Ji et al. / Chemical Engineering Journal 218 (2013) 394–404 399

outlet which is sourced from the last element of the permeate H2

fraction array Xp(n). H2 recovery is the H2 yield divided by H2 inputwhich is calculated as Fp(n)�Xp(n)/(feed flow rate times feed H2

fraction). For each of these parameters, the feed flow rate, feedpressure, module size and flow configuration were systematicallyvaried in order to investigate the separation performance.

4.1. Feed flow rate

Fig. 5a shows the simulation results for the H2 molar fractiondistribution in the module for feed flow rates from 0.1 to0.3 NL min�1 where the H2 and Ar feed fractions were equally setat 0.5 each. It is observed that the H2 molar fraction changed alongthe length module. This gives a strong indication that the drivingforce was not constant, varying according to the position of themembrane in the module. The driving force is a function of the to-tal pressure multiplied by the H2 molar fraction in the feed domainminus the permeate domain. As the total pressure was constant,then a reduction in the H2 molar fraction results in a reduction ofthe driving force. In addition the feed flow rate also affects theH2 molar fraction distribution, and consequently the driving force.This can be explained by a mass balance over the two outlets, thepermeate and retentate streams. In the case of low feed flow rate of0.1 NL min�1, the membrane was able to process a relatively great-er proportion of the feed H2 volume. As H2 preferentially perme-ates through the membrane, this causes the Ar fraction toincrease in the module. For this situation, H2 molar fraction re-duces from 0.5 to 0.45 at the inlet, and undergoes a slow rate ofreduction to 0.4 until the end of the module. In the case that theflow rate was increased twofold to 0.2 NL min�1, the membranewas no longer able to process all of the extra feed volume of H2,which was consequently depleted via the retentate stream. Hencethe H2 fraction increased along the module, whislt the Ar fractionreduced.

An interesting observation from the simulated results in Fig. 5ais the small sharp reduction of the H2 fraction distribution rightafter the entrance to the module. This is counter intuitive as onewould expect that the H2 fraction would remain similar to the feedgas concentration. This view is consistent when advection is signif-icant as explained in Eq. (2a). However, further considerationshould be given to the full engineering system. Immediately tothe entrance of the module, the feed gas is discharged from a1 mm diameter tube to a 100 mm diameter module. The difference

in scales here is very significant, and as a result the feed flux is re-duced to 10�4 of its original value. In this case, advection is notstrong enough to warrant a constant H2 fraction profile, particu-larly that high temperature gas to gas diffusion will thus prevailto maintain the chemical potential within the module. This unu-sual behaviour can be further elucidated by comparing the effectsof advection and diffusion. At the entrance to the module, there isno membrane, and therefore there is no gas permeation throughthe membrane (SH2 = 0). Hence, the steady state Eq. (2) is

@ðJxH2Þ@l

¼ @

@lD@ðcxH2Þ@l

� �ð27Þ

Since J = cu, where u is the feed gas velocity, and if c is constant, Eq.(27) can be simplified as

@ðuxH2Þ@l

¼ D@2ðxH2Þ@l2 ð28Þ

By considering the membrane module design in Fig. 1, the finite dif-ference form of Eq. (28) is

uiþ1 � xi � ui � xi�1

Dl¼ D

xiþ1 � 2xi þ xi�1

Dl2 ð29Þ

and the fraction in ith cell is

xi ¼1

uiþ1Dl þ 2D

Dl2xi�1

ui

Dlþ D

Dl2

� �þ xiþ1

D

Dl2

� �ð30Þ

Eq. (30) clearly indicates that the fraction in ith cell xi is affected byits upstream neighbour xi�1 in form of advection ui

Dl and diffusion DDl2

and also downstream neighbour xi+1 in form of diffusion. In the caseof feed flowrate = 0.1 NL min�1, ui

Dl ¼ 0:003 and DDl2¼ 0:091, which

indicates that the diffusion plays a more significant role than advec-tion in governing the H2 fraction. Hence, this argument confirms thesmall sharp change of the H2 fraction at the entrance to the module,in addition to the importance of considering the diffusion effect.

The simulated results of the parameters of interest are dis-played in Fig. 5b–d under operating conditions as listed in Table 1.For each feed flow rate condition, the H2 fraction was gradually in-creased to investigate its effects on the gas separation performanceof the membrane module. It was observed that all three parame-ters increase as a function of the H2 feed fraction. This logicallypoints out that higher H2 feed fraction gives higher H2 yield andH2 purity. However, the H2 recovery curve indicates that H2 yieldincreased faster than feed H2 flow rate.

Increasing the feed flow rate promotes H2 yield and H2 purity,but in this case H2 recovery is compromised. H2 yield shows themost remarkable improvement by increasing the feed flow rate.This can be explained by the H2 fraction distribution inside themodule as depicted in Fig. 5a. When the total pressure is constant,only H2 fraction determines the driving force. Feed flow rate at2 NL min�1 provides a higher H2 fraction throughout the modulethan 1 NL min�1 does. This means that the driving force of H2 ishigher, resulting in higher H2 permeate flow rate across the mem-brane. In the case of a 1 NL min�1 flow rate, the H2 fraction in feedstreams reduced further, thus decreasing the total driving force.The feed flow rate supplies H2 to the feed domain to maintainthe driving force which in turn is affected by the feed flow rate.

H2 recovery is an important production parameter in H2 gasseparation. Fig. 6 shows the H2 yield and recovery as a functionof the feed flow rate. It is observed that H2 yield and recoveryare competing parameters. Increasing the feed flow rate will like-wise increase the H2 yield, though at the expense of decreasedH2 recovery, and vice versa. These results are strongly associatedwith the changes of the H2 molar fraction or driving force in themodule (see Fig. 5a). At high feed flow rate, the driving force ishigher resulting in more H2 permeating through the membrane,

0.35

0.4

0.45

0.5

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(c) (d)Fig. 5. Effect of different feed flow rates: (a) H2 molar fraction distribution inside the module under different feed flow rates with feed pressure = 6 atm, permeatepressure = 1 atm, and feed H2 fraction = 0.5; (b) H2 yield; (c) H2 purity; and (d) H2 recovery. Bold lines on abscissa are the position of membranes.

0.150.20.250.30.350.40.45

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Fig. 6. Trade-off between H2 yield and H2 recovery under conditions: feedpressure = 6 atm; permeate pressure = 1 atm; and feed H2 fraction = 0.5.

400 G. Ji et al. / Chemical Engineering Journal 218 (2013) 394–404

thus increasing the H2 yield. However, as the feed flow rate is high-er, this also translates into a greater volume of H2 being lost via theretentate stream, thus reducing the H2 recovery. Therefore increas-ing the feed flow rate is not an optimal solution to promote H2 sep-aration performance.

4.2. Feed pressure

Membrane separation for gas processes is essentially a pressuredriven process, indicating in principle that high pressure shouldimprove gas flux. Fig. 7a shows the simulation results for the H2

partial pressure distribution in the module with pressure varyingfrom 6 to 18 atm, whilst the feed flow rate 0.2 NL min�1 was keptconstant for H2 and Ar feed fractions of 0.5 each. As the pressureincreases so does the driving force, resulting in higher H2 fluxthrough the membrane. This caused Ar to remain in the modulelonger, which back diffused towards the inlet to maintain thechemical potential in the module. In a similar fashion, if the pres-sure was reduced to 6 atm, the driving force was mainly halved,

resulting in a lower H2 flux through the membrane. In this case,Ar back diffusion was minimal as the H2 molar fraction in the mod-ule was greater.

As can be seen from Fig. 7b and c, H2 yield and recovery in-creased with feed pressure, which is logical as the driving force in-creased whilst the feed flow rate was kept constant. Contrary tothis trend, it was interesting to observe that the H2 purity slightlydecreased (Fig. 7d). This was counterintuitive, because as the pres-sure increases, the flux of the preferentially permeable gas H2

should increase. The explanation of this unexpected trend was clo-sely related to the change in driving force in the membrane module(Fig. 7a). At 18 atm total pressure, the H2 partial pressure reducesfrom 9 atm at the inlet to 6.38 atm at the retentate outlet. As thetotal pressure in the module was constant, this clearly indicatesthat the Ar partial pressure increases from 6 atm at the inlet to11.62 atm at the outlet. In the case of 6 atm total pressure, the vari-ations of H2 and Ar partial pressure are very small along the tube.Hence, at higher total pressures, the driving force of Ar permeationincreased resulting in a slightly greater Ar permeation and conse-quently a reduction in the H2 purity. By the same token, at lowertotal pressures, the variation of the driving forces are not signifi-cant to increase the flux of the less preferentially permeable gasAr, thus accounting for higher H2 purity in the permeate stream.Therefore, these results strongly suggest that elevated total pres-sure is not necessarily a preferred solution to promote separationperformance.

4.3. Module radius

The radius of the module is an important factor in the design ofindustrial membrane separators. This has implications in terms of

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(c) (d)Fig. 7. Effect of different feed pressures: (a) H2 partial pressure distribution inside the module under different feed pressures at feed flow rate = 0.2 NL min�1, permeatepressure = 1 atm, and feed H2 fraction = 0.5; (b) H2 yield; (c) H2 purity; and (d) H2 recovery. Bold lines on abscissa are the position of membranes.

G. Ji et al. / Chemical Engineering Journal 218 (2013) 394–404 401

the size of the unit operation, foot print and capital costs. In thisstudy, the effect of the module radius was investigated by varyingit from 0.03 to 0.05 m for a feed flow rate of 0.2 NL min�1 and amembrane tube radius of 0.007 m. As shown in Fig. 8a, there aretwo important distintic regions. The first region, roughly equiva-lent three quarters of the membrane module from the inlet, showsthat the H2 molar fraction is higher for smaller radius. As the feedflow rate was kept constant, this means that for a smaller radiusthe feed flux of the gases is higher in the feed domain. In a similarfashion, increasing the radius reduces the feed flux. For the secondregion (Fig. 8a), from the third quarter of the module to the reten-tate outlet, the H2 molar fractions tend to converge irrespectivelyof the radius.

These results are quite interesting as they give different trendsto those shown in Fig. 5. Unlikely increasing feed flow and feedpressure which negatively affect H2 recovery and H2 purity, reduc-ing the radius of the module offers beneficial effects. The H2 yield(Fig. 8b) increases strongly suggesting that smaller module radiuscan deliver extra H2 permeate for the same H2 feed input as thefeed flow rate is kept constant. A higher H2 recovery (Fig. 8c) canalso be achieved with smaller module radius, though H2 purity(Fig. 8d) improvements are marginal. Therefore, the radius of mod-ule should be decreased as much as possible to enhance both H2

yield and recovery.It is noteworthy to observe that the drop of H2 molar fraction

immediately to the entrance of the module reduces as the radiusdecreases. As the feed flow rate is kept constant, reducing the ra-dius leads to high molar fluxes (Fig. 8e). Hence, and axial velocityof gases increase and the contribution from advection (Eq. (2)) be-comes more significant over diffusion. This explains the H2 molarfraction profile in Fig. 8a. These results suggest that in the first sec-tion the permeation of H2 through the membrane for the smallermodule radius is higher due to a higher driving force.

4.4. Flow configuration

All of the above simulated results were obtained using a co-current flow configuration. Counter-current flow configuration isalso commonly used in separation processes, particularly thoserelated to liquid processing which is generally the preferred setupto improve separation performance. The model developed in thisstudy can easily be extended to simulate the gas separationthrough membranes with counter-current flow configuration(Fig. 2). To achieve this, the model was run subject to the sameinitial state in which both the feed and permeate sides areassumed to be filled with pure Ar. The boundary conditions aregenerally the same, with a small variation in the permeatedomain only, as the previous dead end is now the outlet and viceversa.

Table 3 summarises the results from the comparative simula-tions of the co- and counter-flow configurations for the COxS mem-brane module. The simulations show that under the sameoperating conditions, co-current flow and counter-current flowgave almost the same results. These findings are in line with thosereported by Murad Chowdhury et al. [17] for gas separation. It wasfound that co-current flow is around half a minute quicker to reachsteady state than counter-current, but the difference is marginalcompared with the total transition time. However, these findingsfor gas separation differ from those for liquid separation [45,46]or room temperature gas separation [16,47–50]. The major differ-ence in gas separation is that the gas-through-gas molecules diffu-sion at high temperature (400 �C) is around five orders ofmagnitude higher than of molecules in liquid-through-liquid diffu-sion. For low diffusivity fluid, the concentration profile is domi-nated by convective flow (left side of Eq. (2)), and counter-current configuration tends to shift permeate fraction lower thusgiving a relative higher driving force [51]. For high diffusivity gas

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(e)Fig. 8. Influence of module radius on membrane performance: (a) H2 molar fraction distribution inside the modules with different radii at feed pressure = 6 atm, permeatepressure = 1 atm, and feed H2 fraction = 0.5, (b) H2 yield, (c) H2 purity, (d) H2 recovery and (e) feed flux distribution along the module. Bold lines on abscissa are the position ofmembranes.

Table 3Comparative simulations of co- and counter-current flow configurations in MSS membrane module.

Operating condition Temperature 400 �C, module radius 0.05 m, feed pressure = 6 atm, permeate pressure = 1 atm, feed flow rate 0.2 NL min�1

Feed H2 fraction 0.2 0.5 0.8Flow configuration Co-current Counter-current Co-current Counter-current Co-current Counter-currentH2 yield (10�3� NL min�1) 3.68 3.68 26.08 26.09 97.07 97.07H2 purity 0.42 0.42 0.84 0.84 0.96 0.96H2 recovery 0.09 0.09 0.26 0.26 0.61 0.61Separation factor 3.03 3.03 6.96 6.96 15.02 15.02Transition time (s) 43965 43984 38701 38729 37786 37818

402 G. Ji et al. / Chemical Engineering Journal 218 (2013) 394–404

at high temperatures, the flow configuration has little effect on thedriving force.

4.5. Diffusion versus advection

The model developed in this work was further tested in terms ofEq. (2) (with diffusion) and Eq. (2a) (without diffusion or advection

only) at steady state conditions. In the Supplementary information,it is shown that our model also fits well the experimental work andmodels presented by Pan [18] (Fig. S1) and Kaldis et al. [20](Fig. S2). Their work also encompassed gas permeation and separa-tion, though at low temperatures, generally below 40 �C. At theseconditions, it is expected that diffusion is less significant in gasseparation. Fig. 9 displays the H2 permeate fraction at 400 �C at this

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Fig. 9. comparison of two models against experimental data of for silica membraneseparation at high temperature (400 �C).

G. Ji et al. / Chemical Engineering Journal 218 (2013) 394–404 403

work, as a function of experimental results versus model results.The model results clearly indicates that if diffusion is not consid-ered (i.e. advection only) at these high temperature conditions,the model over predicts the H2 molar fraction in the permeatestream by 16% at 0.5 H2 molar fraction (also see Table S1 in Supple-mentary information). However, as the experimental permeate H2

molar fraction increases towards 1, both models tend to convergeunder the experimental conditions in this work, as also presentedin Table S1. The convergence associated with high H2 permeatefraction is a direct consequence of increasing the H2 feed flow rate.Therefore, advection becomes significant over diffusion upon con-vergence to high H2 experimental molar fraction.

5. Conclusions

This study presents an experimentally validated model for amulti-tube membrane module operating at 400 �C for binary gasmixture separation. The conditions associated with feed flow rate,pressure, module design and configuration were changed and thenapplied to analyse how and why different operating conditions canaffect gas separation performance. Altering these conditions led tovariations in H2 feed fraction, space velocities, and ultimately dif-ferent driving forces. As a result, gas diffusion is significant imme-diately to the entrance to the module, resulting in a slight drop ofH2 molar fraction profile. This was attributed to preferential per-meation of a high volume of H2 through the membranes which al-lowed for the less permeable Ar gas to remain in the feed side. Inthe case that the feed flow rate increases, advection becomes sig-nificant over diffusion, and the drop in H2 molar fraction at the en-trance to the module is greatly reduced.

Three benchmark parameters were considered: H2 yield, H2

purity and H2 recovery. H2 yield and H2 purity can benefit fromincreasing feed flow rate, but H2 recovery is compromised. Higherfeed pressure only increases H2 yield and H2 recovery, though H2

purity slightly decreases due to the higher Ar driving force. Themost beneficial solution to achieve superior performance is reduc-ing the module radius. By bringing the module shell close to themembrane tube, space velocities increase thus improving H2 yield,purity and recovery. Counter-current flow and co-current flow pro-vide similar result in terms of the three-benchmark indexes. This ismainly attributed to the high gas-through-gas diffusion in the feeddomain at high temperatures. Finally, neglecting diffusion overpredicts the H2 molar fraction in the permeate stream at high tem-perature conditions, though conversion of results occur for high H2

molar fraction values due to high H2 feed flow rate.

Acknowledgements

Guozhao Ji specially thanks for the scholarship provided by theUniversity of Queensland and the China Scholarship Council. Theauthors acknowledge funding support from the Australian Re-search Council (DP110101185).

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.cej.2012.12.063.

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