Fp

LL

a

ARRA

KHMPPPM

1

tvtAtfsofrc

iogrepTs

r

1d

Chemical Engineering Journal 178 (2011) 398– 406

Contents lists available at SciVerse ScienceDirect

Chemical Engineering Journal

jo u r n al hom epage: www.elsev ier .com/ locate /ce j

orced composition cycling of a Pd-membrane reactor for pure hydrogenroduction from the reaction of partial oxidation of methane

emnouer Chibane ∗, Brahim Djellouli, Yacine Benguerbaaboratoire de Génie des Procédés Chimiques (LGPC), Faculté de Technologie, Université Ferhat Abbas, 19000, Sétif, Algeria

r t i c l e i n f o

rticle history:eceived 19 April 2011eceived in revised form 7 October 2011ccepted 16 October 2011

a b s t r a c t

The performance of a Pd-membrane reactor under periodic inlet composition and sweeping gas is theo-retically analyzed in order to improve the pure hydrogen production from the reaction of partial oxidationof methane. This reaction was conducted under low steam to methane ratio and at moderate temperatureand pressure.

The results obtained show that to achieve process intensification is to operate the process in a periodic

eywords:ydrogen productionodulation

eriodic operationd-membrane reactorartial oxidation

way. Therefore, it was found that when the reactor feed is forced by cycling of the feed composition andsweeping gas via a square wave symmetric, the level of methane conversion and hydrogen recovery issignificantly superior to that which was found in the case of steady state conditions.

© 2011 Elsevier B.V. All rights reserved.

ethane

. Introduction

The production of synthesis gas, especially hydrogen is impor-ant for the chemical industry. Because hydrogen is an energyector [1] which can be stored and does not generate any pollu-ants such as carbon dioxide, vast hopes are placed on this vector.ctually, hydrogen energy could find significant applications in the

ransportation sector and distributed power generation, and wouldurther facilitate renewable energy implementation by acting as atorage medium [2]. Because of its high efficiency, the fuel cell isften seen as one of the main drivers for hydrogen as a fuel of theuture [3]. The vast majority of automotive fuel cell applicationsely on PEM fuel cells, which have proven to be highly efficient inonverting hydrogen to power.

A several possible routes including the thermochemical reform-ng techniques can produce hydrogen. The reaction of partialxidation of methane appears as an alternative process for hydro-en production. This technology has been the subject of severalesearches aimed to improve the chemical processes [4–6]. In gen-ral, improved performance is obtained by acting on operatingarameters such as inlet composition, temperature and pressure.herefore, the process can operate in the steady state or in unsteady

tate conditions [7].

In recent years, there has been a good deal of work, whichevealed that unsteady state operation of chemical reactors often

∗ Corresponding author. Tel.: +213 559736695; fax: +213 36925133.E-mail address: clemnouer@yahoo.com (L. Chibane).

385-8947/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.cej.2011.10.042

proves superior to the optimal conventional steady state operation[8–11]. Moreover, other advantages of catalytic reactor operationby composition forcing include increased conversion, improvedselectivity, and reduced catalyst deactivation [8].

A reactor or a separating reactor may be brought into peri-odic operation by cyclically switching an input. A variety of inputsare suited to manipulation. Some of these inputs are flow rate,composition, temperature and pressure [7]. The total pressuremodulation can be used to improve the reactor performance andcan increase the rate of transport. It has been proven that fast peri-odic temperature and pressure variation may increase the reactionrate compared to the stationary temperature conditions [10–12].The periodic operation of chemical membrane reactors used forhydrogen production is a new concept and the amplitude effectshave not been heavily explored in periodically operated mem-brane reactors. Our study aims to enhance the performance of aPd-membrane reactor used for pure hydrogen production from thereaction of partial oxidation of methane. Therefore, a square wave isassumed for forcing the input composition and sweeping gas at lowfrequencies.

2. Mathematical model

2.1. Chemical reaction scheme and kinetics

In this study, the partial oxidation of methane is carried out ina Pd-based membrane reactor where many reactions are takingplace and whose rates depend strongly on the reforming conditions.Only the reactions with significant rates will be considered [13].

L. Chibane et al. / Chemical Engineerin

Nomenclature

A reactor section (m2)D diameter (m)�Ej activation energy (kJ/mol)�Ep hydrogen permeation activation energy (kJ/mol)F molar flow (kmol/h)f frequency (Hz)�H heat of reaction (kJ/mol)I sweeping gas ratioKc

ispecies combustion constants

Ki species adsorption constantsKj equilibrium constantski reaction rate constantL reactor length (m)M molar mass (kg/mol)P pressure (bar)R ideal gas constant (8.314 J/mol K)r reaction rate (k mol/kgcat h)Rm membrane radius (m)rp radius pore (m)t time (s)Q permeation coeficient of hydrogen (mol/m s Pa0.5)Q0 pre-exponential factor (mol/m s Pa0.5)T temperature (K)W catalyst weight (g)X conversionYH2 hydrogen recoveryZ dimensionless reactor length

Indices/subscripts0 reactor inletforced forced conditionsi reaction species ij reaction jp on the permeation sider on the reaction sides at the catalyst particle surfacess steady state conditions

Greek lettersεs porosity of catalyst particleı membrane thickness (m)� effectiveness factor�s catalyst density (kg/m3)� amplitude� stoichiometric coeffecient� period of the square wave�s tortuosity factorω angular frequency (radian/s) dimensionless pellet coordinate

AcronymsO/C oxygen to methane ratioS/C steam to methane ratio

Ti

1PCH4 , PO2 , PH2 , PCO, PH2O, and PCO2 are the partial pressures of

herefore, the process reaction scheme is as follows [14] andncludes the following reactions.

Total combustion of methane:

CH4 + 2O2 ⇔ CO2 + 2H2O �H0 = −802kJ/mol (1)

g Journal 178 (2011) 398– 406 399

2 Steam reforming:

CH4 + H2O ⇔ CO + 3H2 �H0 = +207kJ/mol (2)

3 Water gas shift:

CO + H2O ⇔ CO2 + H2 �H0 = −41.2kJ/mol (3)

4 Steam reforming:

CH4 + 2H2O ⇔ CO2 + 4H2 �H0 = 165kJ/mol (4)

In the current study, the Langmuir–Hinshelwood model [15]was chosen for the reaction of the complete oxidation of methane(reaction (1)). The rate expressions for steam reforming and watergas shift reactions (reactions (2)–(4)) were based on the analysis ofXu and Froment [16]. In this work, Ni/Alumina was assumed as cat-alyst for the partial oxidation of methane. Some kinetic equationsfor the total oxidation of methane (reaction (1)) were reported byTrimm and Lam [17] and Ma et al. [15]. The kinetic expression ofTrimm and Lam was also applied to describe the combustion ofmethane in a packed bed reactor. This expression was determinedwith experiments on a Pt/Al2O3 catalyst and has been corrected fora Ni catalyst by De Smet et al. [18].

The reaction rates rj (j = 1, 2, 3 and 4) of reactions (1)–(4) respec-tively are:

r1 = k1aPCH4 PO2

(1 + KcCH4

PCH4 + KO2 PO2 )2+ k1bPCH4 PO2

1 + KcCH4

PCH4 + KO2 PO2

(5)

r2 =k2/P2.5

H2(PCH4 PH2O − P3

H2PCO/K2)

(1 + KCOPCO + KH2 PH2 + KCH4 PCH4 + KH2OPH2O/PH2 )2(6)

r3 = k3/PH2 (PCOPH2O − PH2 PCO2 /K3)

(1 + KCOPCO + KH2 PH2 + KCH4 PCH4 + KH2OPH2O/PH2 )2(7)

r4 =k4/P3.5

H2(PCH4 P2

H2O − P4H2

PCO2 /K4)

(1 + KCOPCO + KH2 PH2 + KCH4 PCH4 + KH2OPH2O/PH2 )2(8)

where kj (j = 1, 2, 3 and 4) is the reaction rate constant of reaction j,which is defined by Arrhenius equation:

kj = k0,jexp

(−Ej

RT

)(9)

Kj (j = 2, 3 and 4) is the equilibrium constant, which is defined byVan’t Hoff equation:

Kj = K0,jexp

(−�Hj

RT

)(10)

Kci

(i = CH4 and O2) in reaction (1) is the species adsorption constantin the oxidation reaction and defined as:

Kc = Kcexp

(−�Hci

RT

)(11)

The adsorption constants of species (i = CO, H2, CH4 and H2O) inreactions (2)–(4) are defined by the following equation:

Ki = K0,iexp(−�Hi

RT

)(12)

R is the universal gas constant and T is the temperature.

CH4, O2, H2, CO, H2O and CO2, respectively. Kinetic and ther-modynamic parameters used for simulation are summarized inTables 1–3 [19,20].

400 L. Chibane et al. / Chemical Engineering Journal 178 (2011) 398– 406

Table 1Arrhenius kinetic parameters.

Reaction k0,j �Ej (kJ/mol)

1 k0,1a = 8.11 × 105 mol bar−2 kg−1cat s−1 86.0

k0,1b = 6.82 × 105mol bar−2 kg−1cats

−1 86.02 1.17 × 1015 mol bar0.5 kg−1

cat s−1 240.13 5.43 × 105 mol bar−1 kg−1

cat s−1 67.14 2.83 × 1014 mol bar0.5 kg−1

cat s−1 243.9

Table 2Van’t Hoff parameter values for equilibrium constants.

Reaction K0,j �Hj (kJ/mol)

2 5.75 × 1012 bar2 95.413 1.26 × 10−2 −38.564 7.24 × 1010 bar2 179.9

Table 3Van’t Hoff parameter values for species adsorption.

Species K0,i �Hi (kJ/mol)

CH4 (combustion) Kc0,CH4

= 1.26 × 10−1 bar−1 −27.3

O2 (combustion) Kc0,O2

= 7.78 × 10 − 7 bar−1 −92.8

CH4 6.65 × 10−4 bar−1 −38.3−5 −1

2

hTawpttcsNttde

topmot

CO 8.23 × 10 bar −70.7H2 6.12 × 10−9 bar−1 −82.9H2O 1.77 × 105 +88.7

.2. Membrane and reactor description

The membrane used [21] is a dense palladium membrane whichas a thickness of ı = 20 �m and it is only permeable to hydrogen.he reactor studied (Fig. 1) has an internal diameter D = 0.85 cm,nd a length L = 0.4m. According to Hoang and Chan [22] a reactorith a small diameter and a great length (L/D > 25) gives bettererformance in terms of high methane conversion. In this work,he computation data concerning the dimensions of the reactor andhe catalyst were taken from Halabi et al. [19]. The reactor usedonsists of two concentric tubes, the external tube is a stainlessteel tube and the internal one is an inert membrane. The weight ofi/�-Al2O3 catalyst used is W = 11 g. It is regularly arranged inside

he internal tube. The reactants are axially injected inside the innerube through the catalyst. The hydrogen produced by the reactionsiffuses through the membrane into the outside tube where it isvacuated by a sweeping gas.

For the simulation purpose, a mathematical model is developedo investigate the partial oxidation process behavior under periodicperation conditions in a fixed bed membrane reactor to produce

ure hydrogen. The principal difficulty in such reactors is the accu-ulation of the so-called heat wave, which leads to the formation

f regions of very high catalyst temperature [23]. Since the reac-ion is performed under forced composition conditions, the catalyst

Fig. 1. Schematic representation of membrane reactor.

Fig. 2. Schematic of the square wave function.

deactivation is reduced [8] and the periodic operation increasesprocess stability [7]. Furthermore, in order to prevent flame flash-backs and small explosions, O/C ratio between 0.5 and 2 is suitable[24]. In our work, we have used a ratio of O/C equal to 0.5. In gen-eral, the safe control is based on stabilization of all parameters(feed rate of reaction mixture, its composition, feed temperatureand operation pressure). Behavior of such reactor can be identifiedby temperature profile in catalyst bed. Nevertheless, the influenceof pulses is very beneficial; pulses drown any temperature devia-tion, suppress hot spot formation in the bed and improve the safetyoperation of the reactor [25].

Furthermore, the total methane combustion reaction (1) isstrongly exothermal, the steam reforming reactions (2) and (4)are endothermic and the water gas shift reaction (3) is slightlyexothermal. It is known that if an exothermic reaction is occurring,composition forcing modulates the heat release; this modulationcan be exploited to control overheating of a catalyst bed and thushot spot development [26]. Moreover, the hot spot formation dueto the interaction of heat and mass transfer when the reactantmixture has a volatile component present [26]. The most stronglyexothermal reaction of complete oxidation of methane shown inreaction (1) provides most of the heat for the process; this heatis then consumed by the endothermic reforming reactions (2)and (4). Then, there is a hot cycle in which the dominant reac-tion is the combustion of methane, a cold cycle in which the twoendothermic reforming reactions are occurred alternatively or bothreactions occur simultaneously [23,27]. The heat produced in hotcycle could be accumulated owing to the large thermal capacityof the bed and then consumed during cold cycle [23]. Addition-ally, intuitively switching alternatively between O/C and S/C feedmixtures presents itself as a means of ensuring a thermally self-sustaining process [24]. In our case, the square wave function usedfor modulation is symmetric as presented in Fig. 2. Thus, the heat ofreaction is modulated according to the cycle. In this case, the cycleis composed by the hot half cycle (from 0 to �) and the cold halfcycle (from � to 2�). All the inputs alternate regularly and instan-taneously between two levels. Therefore, the times taken for thesignal to rise from the low level to the high level and back again arecalled the rise time and the fall time, respectively, i.e., the inputsare modulated according to the defined square function. The ris-ing and falling edges of the square function (symmetric) ensurethat approximately the process operates at steady state conditions(called quasi steady state conditions) [28,29]. Therefore, we assumethat the integral value of the reaction heat is equal to that the steadystate conditions.

The development of mathematical model is based in the follow-ing assumptions:

- The thermal effect and pressure drop are not taken in account inthis study.

- The catalyst deactivation by coke formation is negligible.

L. Chibane et al. / Chemical Engineerin

Table 4Catalyst properties.

Weight catalyst (g) 11Catalyst density (kg/m3) 1870Pores diameter (m) 30 × 10−10

Particle diameter (m) 2 × 10−3

Porosity of catalyst particle 0.53Tortuosity factor 4

Table 5Reactor dimensions and operating conditions.

Temperature (◦C) 500Reaction pressure zone (bar) 1.50Permeation pressure zone (bar) 1.01Reactor length (m) 0.4Reactor diameter (m) 0.85 × 10−2

Membrane thickness (m) 20 × 10−6

Methane flow rate (kmol/h) 1.07 × 10−4

Steam to methane ratio 0.5

-

-

--

2

whhtooo

df

F

Pt

pf

Q

o

t[

Oxygen to methane ratio 0.5Hydrogen/methane ratio 0.001Sweeping ratio 3

The periodic operation is only imposed for the steam to methaneratio, oxygen to methane ratio and sweeping gas to methane ratio.The square function is used.Under forcing conditions, we suppose that the period of changeof the modulation function is significantly larger than the charac-teristic process time, so the reactor operates under quasi steadystate conditions [28,29].The membrane is only permeable to hydrogen.

The catalyst properties and operating conditions used in the sim-ulation are presented respectively in Tables 4 and 5 [19,21,30].

.3. Hydrogen transport in Pd-membrane

The hydrogen permeation through the palladium membraneith a thickness ı follows a particular mechanism of molecularydrogen dissociation and atomic diffusion form. The quantity ofydrogen permeated depends not only on the membrane proper-ies but it is also a linear function of the driving force [31]. The ratef hydrogen permeation can therefore be expressed as a functionf the difference in the square root of hydrogen partial pressuresn both sides of the membrane.

A permeation law resulting from a mechanism of solution-iffusion allows us to express the term of permeation by theollowing equation [32]:

0CH4

dYH2 = 2�RmdL

ıQ (P0.5

H2,r− P0.5

H2,p) (13)

H2,rand PH2,p

, are the hydrogen partial pressures respectively inhe reaction and permeation sides.

Rm is the membrane radius and F0CH4

is the methane inlet feed.The hydrogen permeation coefficient is a strong function of tem-

erature and can be described by an Arrhenius type of equation, asollows:

= Q0exp

(−�Ep

RT

)(14)

By introducing the dimensionless form (dZ = dL/L) to Eq. (13), webtain the following expression:

dYH2

dZ= 2�RmL

ıF0Q0

(−�Ep

RT

)(P0.5

H2,r− P0.5

H2,p) (15)

CH4

The apparent activation energy is �Ep = 29.73 kJ/mol andhe pre-exponential factor is Q0 = 7.7 × 10−5mol m/(s m2 k Pa0.5)14].

g Journal 178 (2011) 398– 406 401

The hydrogen pressure in the permeation zone PH2,pis defined

by:

PH2,p= YH2 PP

YH2 + I(16)

I is the sweeping gas ratio, which is defined as the ratio of thesweeping gas flow rate (F0

I ) to that of methane at the inlet of thecatalyst bed (F0

CH4).

I = F0I

F0CH4

(17)

2.4. Mass balances

The axial differential mass balance in the gaseous phase is givenfor each component by the expression:

dFi

dL= �A

4∑j=1

�j�ijrj (18)

where A is the reactor cross-section (m2), � is the catalyst density(kg/m3), �ij is the stoichiometric coefficient of component i of reac-tion j and �j (j = 1, 2, 3 and 4) is the effectiveness factor for reaction(1)–(4). �j is defined as the ratio of the observed reaction to thereaction rate calculated at external catalytic surface conditions (orat bulk fluid conditions in absence of external mass transport resis-tance). For this purpose, we define an effectiveness factor �j for acatalyst particle as:

�j =

V∫0

rj(Ps,i)�s(dV/V)

rj(Pri)�s

(19)

rj is the rate of consumption or formation of each species is givenby:

rCH4 = −�1r1 − �2r2 − �4r4 (20)

rO2 = −2�1r1 (21)

rCO2 = �1r1 + �3r3 + �4r4 (22)

rH2O = 2�1r1 − �2r2 − �3r3 − 2�4r4 (23)

rCO = �2r2 − �3r3 (24)

rH2 = +3�2r2 + �3r3 + 4�4r4 (25)

The mass balance relative to the methane can be written as:

dFCH4

dL= �ArCH4 (26)

According to the reactions stoichiometry, the disappearancerate of methane is equal to the sum of its disappearance rates in thefirst, the second and in the fourth reaction. Eq. (26) can be furtherexpressed by the introduction of a dimensionless reactor length Z,dZ = dL/L. Hence, we obtain:

dXCH4

dZ= �LA

F0CH4

(+r1�1 + r2�2 + r4�4) (27)

dXCH4

dZ= W

F0CH4

(+r1�1 + r2�2 + r4�4) (28)

The oxygen disappearance rate can be expressed as follows:

dXO2

dZ= W

F0O2

(+2r1�1) (29)

4 ineerin

g

c

∇

T2

i

N

f

D

c

C

C

O

H

C

H

t

D

D

02 L. Chibane et al. / Chemical Eng

Moreover, the rates of the formations of H2O, CO2 and CO areiven by:

dXH2O

dZ= W

F0CH4

(2r1�1 − r2�2 − r3�3 − 2r4�4) (30)

dXCO2

dZ= W

F0CH4

(r1�1 + r3�3 + r4�4) (31)

dXCO

dZ= W

F0CH4

(r2�2 − r3�3) (32)

Reaction and diffusion in a single symmetrical and isotropicatalyst pellet is described by the following:

Ni =4∑

j=1

�i,jrs,j (33)

he subscript i represents the reaction gas species in reaction j (j = 1,, 3 and 4)

Ni is the flux of the species i, the molar flux from Fickian models given by the following expression:

i = −De,i

RT

dPi

drp(34)

The internal mass transfer resistances are accounted using theollowing expression.

e,i

d2Ps,i

d 2= �sRTr2

P × 10−54∑

j=1

(�i jrs, j) (35)

Then the mass balance in the catalytic solid is given for eachomponent by the following expressions:

H4 : De,CH4

d2Ps,CH4

d 2− �sRTr2

P × 10−5(−r1 − r2 − r4) = 0 (36)

O2 : De,CO2

d2Ps,CO2

d 2− �sRTr2

P × 10−5(+r1 + r3 + r4) = 0 (37)

2 : De,O2

d2Ps,O2

d 2− �sRTr2

P × 10−5(−2r1) = 0 (38)

2O : De,H2O

d2Ps,H2O

d 2− �sRTr2

P × 10−5(+2r1 − r2 − r3 − 2r4) = 0 (39)

O : De,CO

d2Ps,CO

d 2− �sRTr2

P × 10−5(+r2 − r3) = 0 (40)

2 : De,H2

d2Ps,H2

d 2− �sRTr2

P × 10−5(+3r2 + r3 + 4r4) = 0 (41)

, is the dimensionless pellet coordinate.The partial pressures of species H2, CO and H2O are related to

he pressure of CH4, O2 and CO2 by the following relations:

e,H2

d2Ps,H2

d 2= −3De,CH4

d2Ps,CH4

d 2+ De,CO2

d2Ps,CO2

d 2

+2De,O2

d2ps,O2

d 2(42)

e,COd2Ps,CO

d 2= −De,CH4

d2Ps,CO

d 2− De,CO2

d2Ps,CO2

d 2(43)

g Journal 178 (2011) 398– 406

De,H2Od2Ps,H2O

d 2= +De,CH4

d2Ps,CH4

d 2− De,CO2

d2Ps,CO2

d 2

−2De,O2

d2ps,O2

d 2(44)

Integration of the precedent Eqs. (42)–(44), we obtain:

De,H2 (PH2 − Ps,H2 ) = 3De,CH4 (Ps,CH4 − PCH4 ) − De,CO2 (Ps,CO2 − PCO2 )

− 2De,O2 (Ps,O2 − PO2 ) (45)

De,CO(PCO − Ps,CO) = De,CH4 (Ps,CH4 − PCH4 ) + De,CO2 (Ps,CO2 − PCO2 )

(46)

De,H2O(PH2O − Ps,H2O) = −De,CH4 (Ps,CH4 − PCH4 )

+ 2De,O2 (Ps,O2 − PO2 ) + De,CO2 (Ps,CO2 − PCO2 ) (47)

With the boundary conditions:

d2Ps,CH4

d 2=

d2Ps,CO2

d 2=

d2Ps,O2

d 2= 0, at = 0 (48)

Ps,CH4 = PCH4 , Ps,CO2 = PCO2 , Ps,O2 = PO2 at = 1 (49)

It is known that the internal diffusion is not only dependent onthe density of dry matter (directly related to the porosity (εs)), butalso on the tortuosity (�s) of the matrix composed by that dry mat-ter [33]. Because, the tortuosity factor includes both the effect ofaltered diffusion path length as well as changing cross-sectionalareas in constrictions. It is often used to correct the concentrationgradient and expressing the topology of the pore network [34,35].Therefore, the tortuosity factor �s is the simplified and lumped ofmany complexities. Tortuosity factor should have a value of approx-imately

√3 for loose random pore structures, but measured values

of 1.5 up to 10 or more have been reported. Satterfield [36] statesthat many common catalyst materials have a �s ≈ 3–4. In highlyturbulent flow, the contribution of molecular diffusion is usuallynegligible [34]. Thus, using the average value of Knudsen diffusivity,the effective diffusivity would have the form [37,38]:

De,i = 4 εs

3 �s

rp

2

√8RT/�Mi (50)

In the simulation εs = 0.53 is the porosity of catalyst particle,�s = 4 is the tortuosity factor that have been obtained from theliterature [39] and rp is the radius of pores; Mi is the molar mass foreach species i.

2.5. Concept used for modulation

Practically, the unsteady state operation of the reactor that canbe easily achieved by means of a programmable electronic timersconnected to the flow controllers was used to generate squarewaves [24,40]. Furthermore, a single reactor vessel can be usedwith a valving system to change periodically the composition ofthe feed flowing to the reactor. Modulation equipment of this typeis easily fabricated and is inexpensive. Microreactors could be usedthat require just milligram samples of catalyst and provide differ-ential performance [8]. The volumetric flow rates of reactants canbe switched periodically between two values to generate a chain

of step-changes representing a square-wave variation of reactantconcentrations in the reactor feed [8]. In this work, we consider aperiodic reactor operation for the reaction of the partial oxidationof methane given previously. This reaction is characterized by a

ineering Journal 178 (2011) 398– 406 403

mot[apagdsa

iaiap

fωcωmf

f

F

F

F

F

wgihs

tlEitftscaamfto

oo

Table 6Characteristics of the square function.

Amplitude, � 0.1–0.6Period, � (s) 2�

L. Chibane et al. / Chemical Eng

ild exothermicity and a very short residence time on the surfacef the catalyst [41]. In a periodic operation, an input that affectshe system performance is selected for manipulation (modulation)7]. We investigate the concept of using a membrane reactor with

periodic operation to enhance the hydrogen recovery during theartial oxidation of methane. Under the periodic operations, it isssumed that the composition (steam and oxygen) and sweepingas ratio imposed features of a steady component and a time depen-ent component. So, at t = 0, the integral values of molar flow rate ofteam, oxygen and sweeping gas under periodic operations (forced)re equal to those in steady state (ss).

The periodic operation could be conducted with a variety ofnput pulses, such as square, triangular, rectangular, sinusoidal, sawnd noise. In our work, we have chosen the square wave becauset is the most effective [42]. Then, the molar flow rate of steamnd oxygen in reaction side and molar flow rate of sweeping gas inermeate side are varied using a symmetric square wave function.

The cycle is described by a period � = 2�, an amplitude � variedrom 0.1 to 0.6 for each modulated input and an angular frequency. The angular frequency gives the frequency with which phase

hanges in term of usual or ordinary frequency f = 1/�. Then, = 2�/�. The modulation functions at a constant inlet feed ofethane (F0

CH4= constant) can be written using a square function

(t) as follows:

(t) = { (51)

forcedH2O = Fss

H2O + FssH2O�1f (t),

�1∫0

FssH2O�1f (t)dt = 0 (52)

forced = FssO2

+ FssO2

�2f (t),

�2∫0

FssO2

�2f (t)dt = 0 (53)

forcedI = Fss

I + FssI �3f (t),

�3∫0

FssI �3f (t)dt = 0 (54)

So, at t = 0

forced = FssH2O, F forced = Fss

O2and F forced

I = FssI (55)

here �1, �2 and �3 are the running amplitudes for the steam, oxy-en and sweeping gas, respectively. Low frequencies may be usedf the characteristic time of the reactor is constant. On the otherand, high frequencies may force the reactor into a relaxed steadytate condition [7].

�1, �2 and �3 are the periods of change of the modulation func-ion. In this work, it is supposed that these periods are significantlyarger compared to the characteristic times of the reactor [28,29].ven though the operation is periodic, the average reaction times uniquely determined by the steady state behavior of the reac-ion or reactor. The term “quasi steady state” is commonly usedor this mode [8]. All the inputs alternate regularly and instan-aneously between two levels. Therefore, the times taken for theignal to rise from the low level to the high level and back again arealled the rise time and the fall time, respectively, i.e., the inputsre modulated according to the defined square function. The risingnd falling edges of the square function (symmetric) ensure that theode quasi steady state. It should be noted that the large and small

eed rates for each modulated input at given amplitude (from 0.1o 0.6) could be calculated using Eqs. (51)–(54). The characteristics

f the used square function are summarized in Table 6.

The choice of the studied inputs is based on the specific behaviorf the studied reaction. In general, the partial oxidation of methaneperates under O/C ratio equal to 0.5 and typically at low S/C ratio

Frequency, f (Hz) 0.15Angular frequency, ω (radian/s) 1Long of period � (m) 0.22

[19]. The O/C molar ratio appears as the key parameter in thisreaction because it determines and governs the CO formation. Fur-thermore, in order to obtain a better performance (in steady stateconditions) it is appropriate to switch between O/C and S/C ratio[24]. Thus, the effect of these ratios on the variation of methane con-version and hydrogen recovery were studied. In order to improvethe hydrogen pumping, the effect of sweeping gas to methane ratiois also studied.

Since the composition affects the effectiveness factors, and inorder to take into account the effect of cycling, we assume that theeffectiveness factors are variable and are computed. The periodicstate corresponding to oscillations about some given value of thecontrol is compared with the steady state for that control value.

The reactor performance was evaluated through the followingratios (normalized) which are defined respectively as the ratio ofthe methane conversion and hydrogen recovery ratio computedunder forcing conditions (forced) to their ratio under steady stateconditions (ss):

Normalized conversion : ̨ =Xforced

CH4

XssCH4

(56)

Normalized hydrogen recovery : ̌ =Y forced

H2

Y ssH2

(57)

3. Simulation results and discussions

3.1. Solution procedure

The procedure followed to study the partial oxidation ofmethane process at moderate temperature (500 ◦C) consists to thecomputation of the normalized hydrogen recovery and normalizedconversion of methane.

The numerical resolution technique is based on the use ofthe method of Runge–Kutta to solve the mass first order dif-ferential equations [43] (Eqs. (15) and (18)). The effectivenessfactors, unknown at this stage, are calculated by resolving theset of differential equations given by Eqs. (19) and (35). To dothis, the orthogonal collocation method [43] is used to reducethe set of the differential equations to a set of algebraic equa-tions. The resulting nonlinear algebraic equations are solved bythe Marquardt–Levenberg algorithm. In the case of the periodicoperation, the Eqs. (51)–(55) are added.

An analysis of the effect of steam to methane ratio (S/C), oxygento methane ratio (O/C) and sweeping gas ratio (I) under forcing con-ditions was presented by a mathematical model. Those inputs aremodulated periodically around their steady state values (S/C = 0.5,O/C = 0.5 and I = 3). Because of kinetic limitations, we cannot usezero as a value for hydrogen partial pressure because this will giveus infinite kinetics. To overcome this problem, we have to use asmall quantity of hydrogen. In addition, we have used a mixtureof methane and steam (inlet gas) for improved hydrogen yield andreduced carbon monoxide [22].

3.2. Analysis under forcing conditions

In this work, all the periodic operations are conducted at afixed methane flow rate inlet. Without the periodic phenomonon

404 L. Chibane et al. / Chemical Engineerin

Fvt

tl(pipfiiiit

ato

iac01itrmo

ig. 3. Effect of input modulation on the reactor performance: (a) normalized con-ersion, (b) normalized hydrogen recovery (case of forcing of one input and holdinghe remaining two inputs constants).

o methane flow rate inlet, the reaction system has three manipu-ated inputs: steam to methane ratio (S/C), oxygen to methane ratioO/C) and sweeping gas raio (I). Here, those inputs are switchederiodically. The inputs flow in the reactor feed is periodically var-

ed in the form of a square wave function. The strategy followed [8]resents many different periodic operations which are possible: therst manipulation is to force one input and hold the remaining two

nputs constants, the second, two of the inputs are forced while ones held constant, and the third one consists of manipulating all threenputs with two cycles exhibiting changes both in phase while thehird one is 180◦ or � radians out of phase.

In this paper, only the most significant results obtained formplitude range from zero up to 0.6 are presented. It must be notedhat, beyond this value of amplitude (0.6), there is no improvementf reactor performance.

The study begins by the analysis of the effect of modulationnputs separately (Fig. 3a and b). In the case of O/C modulationt a constant S/C ratio and sweeping gas (I), it was found that theonversion of methane increases with amplitude increasing up to.4. The enhancement factor relative to conversion of methane was.13, but under this condition of modulation, there was a decrease

n hydrogen recovery. This behavior can be explained by the fact

hat all methane was reacted with oxygen, and consequently theeforming reactions did not take place. We can conclude that theodulation of O/C ratio is unfavorable for the reaction of partial

xidation of methane for hydrogen production. The negative effect

g Journal 178 (2011) 398– 406

of the O/C ratio may be explained by the fact that feeding O/C at aratio of 0.5 yields complete combustion products.

In a second operation, the S/C ratio was forced keeping thesweeping gas (I) and O/C constant. At a fixed molar methane flowrate, the S/C ratio is varied via the square function. The resultsobtained which are presented in Fig. 3a and b shows the effect ofamplitude modulation on the performance of the reactor. It wasfound that the conversion of methane increases slightly when theamplitude increases. Therefore, there was a low improvement inconversion of methane. The hydrogen recovery exhibits a max-imum at amplitude ranging from 0.3 to 0.4. In this interval ofamplitude, the hydrogen recovery was enhanced by a factor of 1.08.From these results, we can say that the modulation of S/C ratio isfavorable for the improvement of methane conversion but from thepoint of view of hydrogen recovery, there is an optimal amplitude,which gives the maximum of hydrogen recovery. This behavior maybe explained by the fact that the reaction rate corresponding tothe reaction of reforming (reaction (2)) has non-monotonic depen-dence on water partial pressure while the dependence of the globalreaction rate (reaction (3)) on water partial pressure has monotonicfunction. This means that there would be an optimum amplitudeof inlet steam to methane ratio that gives a maximum performancein terms of hydrogen production.

In order to accelerate the hydrogen pumping through the mem-brane, only the sweeping gas was forced. Results obtained (Fig. 3aand b) show that there is an enhancement of hydrogen recov-ery at low amplitudes namely between 0.3 and 0.4, but there isan insignificant improvement of methane conversion. This can beexplained by the fact that the hydrogen produced reacts in theopposite reaction direction. It is apparent that the water gas shiftreaction plays an important role in determining the reactor perfor-mance.

In the second modulation mode, two of the inputs are forcedwhile one is held constant (Fig. 4a and b). The S/C and O/C ratioswere modulated in phase at a constant sweeping gas ratio (I). Itwas found that there was not any enhancement of hydrogen recov-ery but a maximum of methane conversion was obtained at anamplitude of 0.3 corresponding to an enhancement factor of 1.14.

At a fixed S/C ratio, the modulation of O/C ratio and sweeping gas(I) in phase was applied. The results showed that under this con-dition, the enhancement of hydrogen recovery was not significantwhere the maximum, which was obtained for an amplitude of 0.10,yields an enhancement factor equal to 1.03. However, the conver-sion of methane was improved by a factor of 1.14 at an amplitudeof 0.3.

The results obtained in the case of combination between forcingcomposition (S/C) and sweeping gas (I) are shown in Fig. 4a and b.It was found that there is a parallel effect between combinationsof the modulation of these inputs, therefore the improvement inconversion accompanied by an enhancement in hydrogen recov-ery. Both the overage enhancement of conversion and hydrogenrecovery were obtained for the same range of amplitude, whichis between 0.3 and 0.5. The improvement in conversion and inhydrogen recovery can be explained by the pumping effect, whichprovides efficient hydrogen transport phenomenon through themembrane. Then the reaction side was exhausted in hydrogen. Inthis case, hydrogen is more produced in the reaction side, and thepumping is provoked by the difference of pressure between thereaction side and permeation side, and by the modulation effect.The equilibrium was shifted towards the direction of hydrogen pro-duction and the conversion of methane increases consequently. Inthis case, it should be noted that the enhancement factor of con-

version is 1.10 and for hydrogen recovery is ranged from 1.25 to1.31.

To have a global effect on the reactor performance, the threeinputs at all possible periodic operations were varied. The system

L. Chibane et al. / Chemical Engineering Journal 178 (2011) 398– 406 405

Fig. 4. Effect of input modulation on the reactor performance: (a) normalized con-vw

wtiteceaotei

ceeabwrst

omp

Fig. 5. Effect of input modulation on the reactor performance: (a) normalized con-

ersion, (b) normalized hydrogen recovery (case of two of the inputs are forcedhile one is held constant).

as conducted with S/C and O/C ratios being both in phases whilehe sweeping gas being 180◦ out of phase. It was found that vary-ng the sweeping gas cyclically but asymmetrically with respecto S/C and O/C ratios has no positive effect on hydrogen recov-ry, because the hydrogen pumping effect was overturned. Theonversion of methane increases slightly and reaches a maximumnhancement factor of 1.06 at an amplitude ranging between 0.2nd 0.3. The same results concerning the hydrogen recovery werebtained when the S/C ratio was modulated out of phase whilehe O/C ratio and sweeping gas changed in phase. However, a highnhancement factor of conversion of 1.12 is achieved at the samenterval of amplitude (0.2–0.3).

When the periodic operation was running with all inputshanging cyclically in phase, it was found that the maxima ofnhancement factors of methane conversion and hydrogen recov-ry were respectively 1.14 and 1.06 obtained respectively atmplitudes of 0.2–0.3, and 0.1. This enhancement may be explainedy the fact that the concordance shown by the modulation inputshere the S/C and O/C ratios enhance the progress of the reforming

eaction and the oxidation reaction respectively. Furthermore, theweeping gas improves the pumping effect of hydrogen throughhe membrane (Fig. 5a and b).

The hydrogen flux through the palladium membrane dependsn the pressure difference between the reaction side and the per-eation side. The modulation of sweeping gas, that decreases the

artial pressure of hydrogen on the permeation side results in the

version, (b) normalized hydrogen recovery (case of manupilating all the three inputsin phase or with two cycles exhibiting changes both in phase while the third one is180◦ out of phase).

higher hydrogen separation rate and methane conversion. So, themodulation of the sweeping gas ratio is expected to enhance thereactor performance.

When the O/C ratio was varied asymmetrically and S/C ratioand sweeping gas were in phase, it was obtained that the conver-sion of methane decreased with amplitude increasing, but higherenhancement factor (1.38) was obtained for hydrogen recovery(Fig. 5 a and b). It is obvious that the S/C ratio favors the hydro-gen production via the steam reforming reaction and the sweepinggas favors its pumping.

The pumping may eliminate the radial distribution of thehydrogen concentration inside the support pores and keep the per-meation side under a low pressure. So, a relatively high drivingforce of hydrogen permeation through the palladium membrane isobtained.

Therefore, the hydrogen flux through the palladium membranedoes not depend only on the pressure difference between thereaction side and the permeation side but also on the periodicphenomenon.

4. Conclusion

The effect of modulation of inlet composition and sweeping gason the behavior of the reactor is investigated by using a mathe-matical model. This model can predict the average performance of

4 ineerin

tP

saptorstc

teipitat

R

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

[

06 L. Chibane et al. / Chemical Eng

he reaction of the partial oxidation of methane carried out in ad-based membrane reactor under the investigated conditions.

The numerical investigation has shown that the variation of theteam to methane ratio and the sweeping gas ratio via a square waynd with an amplitude ranging between 0.3 and 0.5 can boost theerformance especially in term of pure hydrogen recovery. Underhe investigated conditions, the value of the enhancement factorf hydrogen recovery and conversion of methane achieved wereespectively 1.31 and 1.10 times higher than those found underteady state conditions. Therefore, operating under periodic condi-ions could be favorable regarding average reactor performance inomparison to the steady state operation.

The periodic operation is therefore a useful tool to improvehe reaction performance. It leads to the assessment of the ben-fits of periodic operation of a specific reactor system and thedentification of the ranges of operating conditions where forcederiodic operation is beneficial. This information provides valuable

nsight for planning detailed experimental studies. Indeed, addi-ional experimental research work is required to test overheatingnd reactor stability. Behavior of such reactor can be identified byemperature profile in catalyst bed.

eferences

[1] F. Orecchini, The era of energy vectors, Int. J. Hydrogen Energy 31 (2006)1951–1954.

[2] G.V. Nirmal, B.V. Reddy, M.A. Rosen, Feasibility of an energy conversion systemin Canada involving large-scale integrated hydrogen production using solidfuels, Int. J. Hydrogen Energy 35 (2010) 4788–4807.

[3] M.N. Eisler, Getting power to the people: technological dramaturgy and thequest for the electrochemical engine, Hist. Technol. 25 (2009) 49–68.

[4] A.M. De Groote, G.F. Froment, Simulation of the catalytic partial oxidation ofmethane to synthesis gas, Appl. Catal. 138 (1996) 245–264.

[5] H. Dong, Z. Shao, G. Xiong, J. Tong, S. Sheng, W. Yang, Investigation on POMreaction in a new perovskite membrane reactor, Catal. Today 67 (2001) 3–13.

[6] Z. Rui, K. Zhang, Y. Li, Y.S. Lin, Simulation of methane conversion to syngas in amembrane reactor. Part I: a model including product oxidation, Int. J. HydrogenEnergy 33 (2008) 2246–2253.

[7] T. Aida, P.L. Silveston, Periodic Operation in “Cyclic Separating Reactors”, Black-well Publishing Ltd., 2005.

[8] P.L. Silveston, R.R. Hudgins, A. Renken, Periodic operation of catalytic reactors– introduction and overview, Catal. Today 25 (1995) 91–112.

[9] M. Petkovska, D. Nikolic, A. Markovic, M.A. Seidel, Fast evaluation of periodicoperation of a heterogeneous reactor based on non linear frequency responseanalysis, Chem. Eng. Sci. 65 (2010) 3632–3637.

10] Y. Benguerba, B. Djellouli, Enhancement of the catalytic performances in thecase of a consecutive-parallel reaction scheme, Int. J. Chem. Reactor Eng. 8(2010) A641–A720.

11] Y. Benguerba, B. Djellouli, Enhancement of the catalytic performances undernon-steady state conditions, Chem. Eng. J. 166 (2011) 1090–1094.

12] P.L. Silveston, R.R. Hudgins, Periodic pressure forcing of catalytic reactions,Chem. Eng. Sci. 59 (2004) 4055–4064.

13] S.H. Chan, H.M. Wang, Thermodynamic analysis of natural gas fuel processingfor fuel cell applications, Int. J. Hydrogen Energy 25 (2000) 441–449.

14] A. Basile, L. Paturzo, F. Lagana, The partial oxidation of methane to syngas ina palladium membrane reactor: simulation and experimental studies, Catal.Today 67 (2001) 65–75.

15] L. Ma, D.L. Trimm, C. Jiang, The design and testing of an autothermal reactorfor the conversion of light hydrocarbons to hydrogen – I. The kinetics of thecatalytic oxidation of light hydrocarbons, Appl. Catal. 138 (1996) 275–283.

16] J. Xu, G.F. Froment, Methane steam reforming, methanation and water-gasshift: I. Intrinsic kinetics, AIChE J. 35 (1989) 88–96.

[

[

g Journal 178 (2011) 398– 406

17] D.L. Trimm, C.W. Lam, The combustion of methane on platinum-alumina fibercatalysts-I: kinetics and mechanism, Chem. Eng. Sci. 35 (1980) 1405–1413.

18] C.R.H. De Smet, M.H.J.M. De Croon, R.J. Berger, G.B. Marin, J.C. Schouten, Designof adiabatic fixed-bed reactors for the partial oxidation of methane to synthesisgas. Application to production of methanol and hydrogen-for-fuel-cells, Chem.Eng. Sci. 56 (2001) 4849–4861.

19] M.H. Halabi, M.H.J.M. De Croon, J. Van der Schaaf, P.D. Cobden, J.C. Schouten,Modeling and analysis of autothermal reforming of methane to hydrogen in afixed bed reformer, Chem. Eng. J. 137 (2008) 568–578.

20] D.L. Hoang, S.H. Chan, Modelling of a catalytic autothermal methane reformerfor fuel cell applications, Appl. Catal. 268 (2004) 207–216.

21] J. Shu, B.P.A. Grandjean, S. Kaliaguine, Methane steam reforming in asym-metric Pd and Pd–Ag/porous ss membrane reactors, Appl. Catal. 119 (1994)305–325.

22] D.L. Hoang, S.H. Chan, Effect of reactor dimensions on the performance of anO2 pump integrated partial oxidation reformer: a modeling approach, Int. J.Hydrogen Energy 31 (2006) 1–12.

23] K. Gosiewski, Mathematical simulations of reactors for catalytic conversion ofmethane to syngas with forced concentration cycling, Chem. Eng. Process. 39(2000) 459–469.

24] K.O. Gyamfi, A.A. Adesina, Forced composition cycling of a novel thermallyself-sustaining fluidized-bed reactor for methane reforming, Chem. Eng. Sci.54 (1999) 2575–2583.

25] J. Hanika, V. Jiricn, P. Karnetova, J. Kolena, J. Lederer, D. Skala, V. Stanek, V.Tukac, Trickle bed reactor operation under forced liquid feed rate modulation,CI & CEQ 13 (2007) 192–198.

26] P.L. Silveston, J. Hanika, Challenges for the periodic operation of trickle-bedcatalytic reactors, Chem. Eng. Sci. 57 (2002) 3337–3385.

27] K. Gosiewski, Simulation of non-stationary reactors for the catalytic conversionof methane to synthesis gas, Chem. Eng. Sci. 56 (2001) 1501–1510.

28] V.V. Andreev, Increasing the productivity of a porous catalyst granule withrespect to the target compound for an arbitrary chemical reaction in a non-stationary regime, Mendeleev Commun. 7 (1997) 35–37.

29] V.V. Andreev, Conditions required to maximize the productivity of porous cat-alyst granules with a controlled activity profile, Mendeleev Commun. 8 (1998)77–79.

30] P. Ji, H.J. van der Kooi, J. de Swaan Arnos, Simulation and thermodynamic anal-ysis of conventional and oxygen permeable CPO reactors, Chem. Eng. Sci. 58(2003) 2921–2930.

31] G. Barbieri, A. Brunetti, G. Tricoli, E. Drioli, An innovative configuration of a Pd-based membrane reactor for the production of pure hydrogen: experimentalanalysis of water-gas shift, J. Power Sources 182 (2008) 160–167.

32] F.A.N. Fernandes, A.B. Soares Jr., Methane steam reforming modeling in a pal-ladium membrane reactor, Fuel 85 (2006) 569–573.

33] L.F. Melo, Biofilm physical structure, internal diffusivity and tortuosity, WaterSci. Technol. 52 (2005) 77–84.

34] G.F Froment, K.B. Bischoff, Chemical Reactor Analysis and Design, John Wiley& Sons, Inc., 1979.

35] G.F. Froment, Production of synthesis gas by steam and CO2 reforming of naturalgas, J. Mol. Catal. A: Chem. 163 (2000) 147–156.

36] C.N. Satterfield, Mass Transfer in Heterogeneous Catalysis, MIT Press, Cam-bridge, MA, 1970.

37] M.N. Pedernera, J. Pina, D.O. Borio, Kinetic evaluation of carbon formationin a membrane reactor for methane reforming, Chem. Eng. J. 134 (2007)138–144.

38] B. Krishna, R. Nair, M.P. Harlod, Hydrogen generation in a Pd-membrane fuelprocessor: productivity effects during methanol steam reforming, Chem. Eng.Sci. 61 (2006) 6616–6636.

39] J. Xu, G.F. Froment, Methane steam reforming: II. Diffusional limitations andreactor simulation, AIChE J. 35 (1989) 97–103.

40] A. Ayude, T. Rodriguez, J. Font, A. Fortuny, C. Bengoa, A. Fabregat, F. Stuber,Effect of gas feed flow rate and gas composition modulation on activated carbonperformance in phenol wet air oxidation, Chem. Eng. Sci. 62 (2007) 7351–7358.

41] D.A. Hickman, L.D. Schmidt, Synthesis gas formation by direct oxidation of

methane over Pt monoliths, J. Catal. 138 (1992) 267–282.

42] P.L. Silveston, Composition Modulation of Catalytic Reactors, Gordon andBreach Science Publishers, Amsterdam, 1998.

43] B.A. Finlayson, Nonlinear Analysis in Chemical Engineering, McGraw-Hill, NewYork, 1980.