Consecutive-Parallel Reactions in Nonisothermal …lepabe/publicacoes_restritas/papers/...Consecutive-Parallel Reactions in Nonisothermal Polymeric Catalytic Membrane Reactors Jose

Consecutive-Parallel Reactions in Nonisothermal Polymeric Catalytic MembraneReactors

Jose M. Sousa†,‡ and Adelio Mendes*,‡

Departamento de Quımica, UniVersidade de Tras-os-Montes e Alto Douro, Apartado 202,5001-911 Vila-Real Codex, Portugal, and LEPAEsDepartamento de Engenharia Quımica,Faculdade de Engenharia, UniVersidade do Porto, Rua Roberto Frias, 4200-465 Porto, Portugal

This work reports the development of a nonisothermal and nonadiabatic pseudo-homogeneous model to studya completely back-mixed membrane reactor with a polymeric catalytic membrane, for conducting theconsecutive hydrogenation of propyne to propene and then to propane. The performance of the reactor isanalyzed in terms of the propyne concentration in the permeate stream (the only outlet stream from the reactor),the conversion of propyne and hydrogen, and the selectivity and overall yield to the intermediate productpropene. The operating and system parameters considered are the Thiele modulus, the dimensionless contacttime, the Stanton number, and the effective hydrogen sorption and diffusion coefficients. To define the regionswhere the catalytic membrane reactor may perform better than a conventional reactor, a comparison betweenboth reactors is made. For the range of parameter values considered, the reactor model in this study demonstratesthat the catalytic membrane reactor performs better than the conventional catalytic reactor in some regions ofthe Thiele modulus parametric space, for medium to high Stanton number values and for the total flow-through configuration (total permeation condition). Concerning the effective sorption and diffusion coefficientsof hydrogen, they shall be higher than the ones of the hydrocarbons.

1. IntroductionTheoretically speaking, the combination of a chemical reac-

tion and separation modules in a single processing unitsacatalytic membrane reactorsshould have several advantagesover the conventional arrangement of a chemical reactor follow-ed by a separation unit. Among other advantages that can beexplored in this new configuration,1 two main ones can be identi-fied. In one hand, membrane reactors can be used to increasethe overall conversion above the theoretical thermodynamic valuefor equilibrium-limited reactions, by a selective product removal.2,3On the other hand, a segregated feed of the reactants can beused to improve the selectivity and/or overall yield to an inter-mediate product in complex reactive systems and/or to controlthe reactor temperature, thus improving operation safety.4-7Most of the potential applications for this new technology re-

fer to the ensemble of processes conducted at high temperatures,from 300 to 1000 °C.1,8 As a consequence, only inorganic cera-mic or metallic membranes, able to operate in such harsh condi-tions, can be considered. Nevertheless, beyond the applicationsin the field of biocatalysis,1,9 catalytic polymeric membranescan also be integrated into membrane reactors to be used in spe-cific areas where processes are conducted in mild conditions,namely, in fine chemical synthesis10,11 and partial hydrogenationof alkynes and/or dienes to alkenes,12-14 among others.15-17The focus of this study is on the performance of a catalytic

polymeric membrane reactor, by comparing it with a conven-tional reactor, when conducting a consecutive-parallel reactionsystem given by

Many commercially important chemicals are intermediate

products in consecutive-parallel reactions, which, in this case,is product C. The interest in using catalytic membrane reactorsto study its overall yield and/or selectivity has been increasedamong the scientific community, according to the number anddiversity of papers available on the open literature.1,4,7,18-21Some of such studies focus on the improvements that can beachieved with a distributed feed of a reactant alongside a tubularreactor,4,19,20 while others analyze the impact of a strategy basedin a segregated feed of the reactants on the overall yield to theintermediate (desired) product.7 All these works considerinorganic membranes, catalytic7,18 or inert.4,19-21 They reportmodeling,4,7 experimental,18,21 or both modeling and experi-mental works.19,20Another important class of consecutive-parallel reactions that

have been studied in polymeric catalytic membrane reactors areselective hydrogenations.12-14,22-24 For example, the selectivehydrogenation of impurities such as propyne and propadienein an industrial propene stream is an important reaction in thepetrochemical industry.12,25 As a monomer for the industrialproduction of polypropylene, the purified propene stream shouldcontain <10 ppm of propadiene and <5 ppm of propyne.12 Onthe other hand, typical industrial propene streams produced bysteam cracking contain about 5% of such species,25 which,ideally, should be removed selectively. Among the methodsknown for removal of alkynes and dienes, catalytic hydrogena-tion is the most elegant one. Under adequate conditions, itreduces the content of such species (they may even becompletely removed), avoiding, however, the deeper hydrogena-tion to the correspondent alkane or other possible reactions. Asa result, the overall yield to the olefins may even be improved.Moreover, selective hydrogenation is a relatively simple processto implement, is efficient, and is easy to operate.The main objective of this work is to analyze in which

conditions a catalytic polymeric membrane reactor can takeadvantage of its effective diffusivity and sorption selectivitiesto improve its performance over that obtained in a conventionalreactor, considering the consecutive-parallel hydrogenation

* To whom correspondence should be addressed. Tel.: +351 225081695. Fax: +351 22 5081449. E-mail: [email protected].

† Universidade de Tras-os-Montes e Alto Douro.‡ Universidade do Porto.

Reaction 1: A + Bf C Reaction 2: B + Cf D

2094 Ind. Eng. Chem. Res. 2006, 45, 2094-2107

10.1021/ie050650h CCC: $33.50 © 2006 American Chemical SocietyPublished on Web 02/21/2006

propyne f propene f propane. More specifically, can onelower the concentration of propyne in the outlet stream underlevels obtained using a conventional catalytic reactor? To answerthis question, we developed a comprehensive model of acompletely back-mixed catalytic membrane reactor. The math-ematical model is nonisothermal and nonadiabatic, and it isbased on the model of the solution-diffusion for the transportthrough the membrane. A set of simulation results are thenprovided which illustrate some key points about the use of thismembrane reactor. In addition to the analysis of the concentra-tion of propyne on the permeate stream, also discussed is thepossibility of enhancing the selectivity and overall yield to thedesirable intermediate product (propene) and the conversion ofthe main reactants propyne and hydrogen.In principle, the conversion of propyne and the selectivity to

propene can benefit from a catalytic membrane reactor. Ideally,the concentration of the intermediate desired product (propene)in the reaction medium should be as low as possible, to avoidits hydrogenation to propane. This can be achieved, for example,by enhancing its diffusivity in the membrane and/or loweringits concentration at the catalyst surface. On the other hand, it isimportant to hydrogenate the contaminant propyne to a verylow level. So, its diffusivity should be as low as possible (toincrease its residence time), and the concentration in the reactionmedium should be as high as possible. However, as thehydrocarbons propyne and propene are chemically alike, it isexpected that their diffusivity and sorption coefficients are close.Relative to the remaining reactant, hydrogen, the desirableeffective values for the diffusivity and sorption coefficients aredependent on the reaction considered. On one hand, hydrogenmust react with propyne, to eliminate it. On the other hand, itis important to avoid the hydrogenation of propene. Consideringthat hydrogen has a positive order on both hydrogenations, itsconcentration at the catalyst sites should be high for the firstreaction (hydrogenation of propyne) and low for the secondreaction (hydrogenation of propene). Thus, the desirable valuesfor effective diffusivity and sorption of hydrogen must bebalanced and found from a complete numerical analysis.

2. Development of the Membrane Reactor ModelThe catalytic membrane reactor considered in this study has

the general features of the one depicted in Figure 1. It consistsof retentate and permeate perfectly mixed chambers, separatedby a flat membrane with surface area Am and thickness !. Theperfectly mixed flow pattern assumption considerably simplifiesthe analysis, allowing an easier assessment of the impact of thedifferent diffusivity and sorption selectivities on the reactorperformance. If tubular membranes with plug-flow pattern wereconsidered, the complexities introduced by concentration gra-dients along the length of the membrane would make theanalysis much more complex. The reaction studied is of thetype consecutive-parallel and irreversible, describing the hy-drogenation of propyne,

with A ) propyne, B ) hydrogen, C ) propene, and D )propane.

The model proposed for this reactor is based on the followingadditional main assumptions:(1) steady-state and nonisothermal conditions;(2) negligible film transport resistance for mass and energy;(3) negligible drop in the total pressure for the retentate and

permeate sides;(4) Fickian transport through the membrane thickness;(5) sorption equilibrium between the bulk gas phase and the

membrane surface described by Henry’s law;(6) constant sorption and diffusion coefficients;39-41(7) unitary activity coefficients;(8) homogeneous distribution of the catalytic nanoparticles

throughout the membrane;(9) reaction occurring only on the catalyst surface;(10) concentration of the reaction components on the catalyst

surface and in the surrounding polymer matrix being equal (anyrelationship can be considered in principle, but this onesimplifies the original problem without compromising the mainconclusions). In principle, a change of the sorption coefficientof a given species in the membrane can lead to a change of thecorresponding adsorption coefficient at the catalyst surface.However, we do not consider such an influence. The steady-state mass and energy balance equations are presented in thefollowing sections.2.1. Mass Balance for the Membrane.

where i refers to the ith component and j refers to the jthreaction, D is the effective diffusivity, c is the concentrationinside the membrane (sorbed phase), and z is the spatialcoordinate perpendicular to the membrane surface. " is thestoichiometric coefficient, taken negative for reactants, positivefor reaction products, and null for the components that do nottake part in the reaction. k(T) is the reaction rate constant basedon the conditions inside the membrane (temperature andconcentration). f is the local reaction rate function, which isgiven by the following rate expressions:

The justification for this proposal of rate expressions is providedbelow (Section 3.2).The reaction rate constants are assumed to follow the

Arrhenius’ temperature dependence,

where kj0 and Ej are the preexponential reaction rate constantand the activation energy for reaction j, respectively. R is thegas constant, and the subscript ref refers to the referencecomponent or conditions.2.2. Energy Balance for the Membrane.

Figure 1. Schematic diagram of the catalytic membrane reactor.

Reaction 1: A + Bf C Reaction 2: B + Cf D

Di

d2ci

dz2+∑

j)1

2

"ijkj(T)fj(ci) ) 0 i ) A, B, C, D (1)

f1(ci) ) cAcB i ) A, B, C (2)

f2(ci) ) cB i ) B, C, D (3)

k1(T) ) k10 exp(- E1

RT) ) k1(Tref) exp[- E1R(1T - 1

Tref)] (4)

k2(T) ) k20 exp(- E2

RT) ) k2(Tref) exp[- E2R(1T - 1

Tref)] (5)

#ed2T

dz2+∑

i)1

4 (Cp,i(T)Di

dci

dz ) dTdz +∑j)12

(-!Hjr)kj(T)fj(ci) ) 0

i ) A, B, C, D (6)

Ind. Eng. Chem. Res., Vol. 45, No. 6, 2006 2095

where #e is an effective thermal conductivity that depends onboth thermal conductivities of the solid and sorbed species, !Hris the reaction enthalpy, and Cp is the heat capacity in the sorbedphase.Following the assumption of negligible external transport

limitations at the membrane surface (assumption 2), the bound-ary conditions for the mass and energy balances are7

where the superscripts R and P refer to the retentate andpermeate stream conditions, respectively. S is the sorptioncoefficient, p is the partial pressure in the bulk gas phase, and! is the membrane thickness.2.3. Partial and Total Mass Balances for the Retentate

Side.

where Q is the volumetric flow rate, P is the total pressure, andAm is the membrane surface area. The superscript F refers tothe feed stream conditions.2.4. Energy Balance for the Retentate Side.

The first and second terms of eq 10 account for the enthalpy ofthe gas phase in the feed and retentate streams; the third termaccounts for the enthalpy transported by the species that comein or out of the membrane; the fourth term accounts for theheat exchange by conduction between the bulk gas and themembrane surface; the fifth term accounts for the sorptionenthalpy; and the last term accounts for the heat transfer betweenthe bulk gas and a heat exchanger with a coolant temperatureText. H is the enthalpy for the gas phase, and !Hs is the sorptionenthalpy. Ut,R and At,R are the external overall coefficient andarea of heat transfer, respectively, for the retentate side.2.5. Partial and Total Mass Balances for the Permeate Side.

2.6. Energy Balance for the Permeate Side.

The meaning of the various terms in eq 13 is identical to thecorresponding ones in eq 10.

2.7. Dimensionless Equations. The model variables weremade dimensionless with respect to the feed conditions (QF, PF,and TF), to component A (DA, SA, and Cp,A), and to the membranethickness, !. The external and feed temperatures were consideredto be equal. The reference temperature was set to 298 K.

It seems reasonable to consider that the temperature is uniformfor the entire catalytic membrane reactor, in view of the usuallylow membrane thickness (few hundred microns, normally) andthe perfectly mixed flow pattern assumption for both chambers.According to this hypothesis, the energy balances for theretentate and permeate chambers, eqs 10 and 13, respectively,can be simplified to a single global energy balance, eq 23.

Changing for dimensionless variables and introducing suitabledimensionless parameters, eqs 1-13 become as follows,

where

z ) 0, ci ) SipiR, and T ) TR

z ) !, ci ) SipiP, and T ) TP (7)

QFpiF

RTF)QRpi

R

RTR- AmDi

dcidz |z)0 i ) A, B, C, D (8)

QFPF

RTF)QRPR

RTR- Am∑

i)1

4

Di

dci

dz|z)0

i ) A, B, C, D (9)

∑i)1

4 QFpiF Hi

F

RTF)∑

i)1

4 QRpiR Hi

R

RTR- Am∑

i)1

4

HiDi

dci

dz|z)0

-

Am#edT

dz|z)0

- Am∑i)1

4

(-!His)Di

dci

dz|z)0

+

Ut,RAt,R(TR - Text) i ) A, B, C, D (10)

QPpiP

RTP+ AmDi

dcidz |z)!

) 0 i ) A, B, C, D (11)

QPPP

RTP+ Am∑

i)1

4

Di

dci

dz|z)!

) 0 i ) A, B, C, D (12)

∑i)1

4 QPpiP Hi

P

RTP+ Am∑

i)1

4

HiDi

dci

dz|z)!

+ Am#edT

dz|z)!

+

Am∑i)1

4

(-!His)Di

dci

dz|z)!

+ Ut,PAt,P(TP - Text) ) 0 (13)

Di/d2ci/

d$2+ !2∑

j)1

2

"ij"j(T*)fj(ci/) ) 0 (14)

f1(ci/) ) cA

/ cB/ (15)

f2(ci/) ) cB

/ (16)

k1(T*) ) exp[%(1 - 1/T*)] (17)

k2(T*) ) Rr exp[RE%(1 - 1/T*)] (18)

1

PeH

d2T*

d$2+ (∑

i)1

4

Cp,i/ Di

/dci/

d$ ) dT*d$-

!2&

PeH("1f1 + RH"2f2) ) 0 (19)

$ ) 0, ci/ ) Si

/ piR* and T* ) TR*

$ ) 1, ci/ ) Si

/ piP* and T* ) TP* (20)

QF*piF*

TF*)QR*pi

R*

TR*- "

' + 1Di/ dci

/

d$ |$)0

(21)

QF*PF*

TF*)QR*PR*

TR*-

"

' + 1∑i)14

Di/dci/

d$|

$)0(22)

QF*∑i)1

4

piF* Cp,i

/ - QR*∑i)1

4

piR* Cp,i

/ +

"

' + 1∑i)14

Cp,i/ Di

/dci/

d$ |$)0

TR* +

1

' + 1

"

PeH(dT*d$ |$)0 -

dT*

d$ |$)1) - St(TR* - TF*) ) 0 (23)

QP*piP*

TR*+ "

' + 1Di/ dci

/

d$ |$)1

) 0 (24)

QP*PP*

TR*+

"

' + 1∑i)14

Di/dci/

d$|

$)1) 0 (25)

2096 Ind. Eng. Chem. Res., Vol. 45, No. 6, 2006

! is the Thiele modulus referred to the first reaction and at thereference temperature (ratio between a characteristic intramem-brane diffusion time, for the reference component, and acharacteristic reaction time); " is the dimensionless contact timereferred to species A (ratio between the maximum possible fluxacross the membrane for the reference component, that is,permeation of pure species against null permeate pressure, andits molar feed flow rate); Rr is the ratio of the reaction rateconstants at the reference temperature; % is the Arrhenius’number based on the first reaction; RH is the ratio of the heatsof reaction; RE is the ratio of the activation energies; PeH is themodified heat Peclet number; & is the Prater number based onthe first reaction; ' is the ratio of the reactants’ composition inthe feed stream (referred to the first reaction); and St is theStanton number. The remaining symbols are reported in thenomenclature.The performances of the catalytic membrane reactor (CMR)

and the conventional catalytic reactor (CSTR) are not directlycomparable, as the reactors are different. However, we may statethat a CMR with a nonpermselective membrane and operatingin the total flow-through configuration (total permeation condi-tion) is loosely equivalent to a CSTR. This equivalence isdiscussed below in Section 6.1, where the results of simulatingboth reactors are shown. The dimensionless equations for theCSTR are presented below:

where

Da is the Damkohler number (ratio between the rate of the firstreaction at the reference temperature and the feed flow rate tothe reactor), and B is the adiabatic temperature rise.26 Thesuperscript O refers to the reactor exit conditions.

3. Model Reaction System and Input Parameters

Table 1 summarizes the default values and ranges of theparameters used in the simulations. Some of these values werecalculated from literature data. Others were proposed based onqualitative knowledge of the reactions. In the following sections,we discuss our selection of such values.3.1. Reaction System. The model reaction system simulated

in this work corresponds to the hydrogenation of propyne topropene. The deeper hydrogenation of propene to propane isalso considered, but other possible reactions (oligoisomeriza-tions, for example) are ignored.28 All reaction steps are assumedto be irreversible.283.2. Reaction Kinetics. The simple power-law type kinetics

for the reaction rate equations have been often proposed in theliterature for catalytic reactions. However, these simple kineticequations should be regarded rather as empirical correlationsthat predict the rates of reactions within the range of theexperimental conditions.4,29 For example, some published worksreport that the power-law type rate equations represent theexperimental results better than the Langmuir-Hinshelwood-Hougen-Watson models for the same hydrogenation reactionsas the one considered in the present study, even though theywere carried out in packed-bed reactors (see refs 25, 28, and30 as well as the references therein). Thus, we consider alsopower-law type kinetics in the present study. Although any typeof reaction rate expression can be inserted into the catalyticmembrane reactor model, this formulation considerably simpli-fies the problem, without compromising the main conclusions.We consider that the reaction rate of the first reaction depends

on the concentration of both reactants, propyne and hydrogen,because their concentrations are set to close values in the presentstudy (' ) 1.5). For the second reaction, on the other hand,we consider zero order relative to the hydrocarbon.25 As theconcentration of propene is in very large excess relative to thatof hydrogen and is almost constant during the reaction, weincluded it in the reaction rate constant.25 Additionally, weconsider that the reaction kinetics is kept constant over the entirerange of simulated conditions.4We choose the activation energies based on experimental data,

despite the fact that they show a large scattering.25,28,30-32 Weconsidered E1 ) 50 kJ mol-1 and E2 ) 75 kJ mol-1 (% ! 20,RE ) 1.5). This ratio of activation energies is compatible withthe decrease of the selectivity to the intermediate product withthe increase of the reaction temperature.30 Also, Jackson andKelly33 reported the same qualitative relation of activationenergies in a propyne-to-propene hydrogenation study overplatinum/silica catalysts.For reactions of this type, it is desirable that the ratio between

the rates of the selective and unselective reactions (first andsecond hydrogenations, respectively), that is, the ratio k1(T)f1-

Table 1. List of the Base Set Parameter Values Used in theSimulations

Di/ ) 1 PeH ) 0.05 % ) 20

Si/ ) 1 B ) -9.096 ' ) 1.5Cp,A/ ) 1 " " [0.01 - TPC] RE ) 1.5

Cp,B/ ) 0.469 St " [0.1-100] PP* ) 0.5

Cp,C/ ) 1.054 ! " [10-2 - 103] Rr ) 0.001

Cp,D/ ) 1.214 Da " [10-2 - 105] RH ) 0.753

yAF ) 0.0465 yB

F ) 0.0698 yCF ) 0.8837

ci/ ) ci/Cref, pi

/ ) pi/Pref, P* ) P/Pref, Di/ ) Di/Dref,

Cref ) SrefPref, Q* ) Q/Qref, RE ) E2/E1, Si/ ) Si/Sref,

T* ) T/Tref, RH ) !H2r /!H1

r , Cp,i/ ) Cp,i/Cp,ref,

$ ) z/!, ! ) ![Crefk1(Tref)Dref ]1/2, " )AmRTrefSrefDref

!QrefyAF ,

St )Ut,GAt,GRTrefQrefPrefCp,ref

, ' ) yBF/yA

F , Rr )1Cref

k2(Tref)k1(Tref)

,

PeH )CrefCp,refDref

#e, & )

!H1rCrefDref#eTref

, % ) E1/(RTref)

QF*piF*

TF*-QO*pi

O*

TO*+ Da∑

j)1

2

"ij"j(T*)fj(piO*) ) 0 (26)

QF*PF*

TF*- QO*PO*

TO*- Da("1(T*)f1(pi

O*) +

"2(T*)f2(piO*)) ) 0 (27)

QF*∑i)1

4

piF* Cp,i

/ - QO*∑i)1

4

piO* Cp,i

/ - DaB("1(T*)f1(piO*) +

RH"2(T*)f2(piO*)) - Da(k1(T*)f1(pi

O/)!Cp1* +

k2(T*)f2(piO*)!Cp

2*) - St(TO* - TF*) ) 0 (28)

f1(piO*) ) pA

O* pBO* (29)

f2(piO*) ) pB

O* (30)

!Cp1* ) Cp,C

/ - Cp,B/ - Cp,A

/ (31)

!Cp2* ) Cp,D

/ - Cp,C/ - Cp,B

/ (32)

Da )PrefVRTrefk1(Tref)

Qref, B )

!H1r

TrefCp,ref


(ci)/(k2(T)f2(ci)), should be as high as possible, to improve theselectivity to the intermediate product. From the work by Fajardoet al.,25 we considered a feed partial pressure of 5000 Pa forhydrogen and 95 000 Pa for propene and a temperature of 350K. In these conditions, such a ratio took a value of 18 or 53,depending on the reaction-rate model considered.25 The sameratio was also obtained with data from Godınez et al.,30 leadingto values of #50-70. Thus, based on the feed composition andreference conditions considered in our study, we set the ratioof the reaction rates to 50. From this value, we calculated theratio of the reaction rate constants, Rr, by eqs 2-5, where therate of reaction j is given by kj(T)fj(ci).It should be emphasized that the present work intends to

analyze the possible operating and system conditions where acatalytic polymeric membrane reactor can take advantage ofits effective sorption and diffusivity selectivity to outperform aconventional catalytic reactor. Hence, only the ratios of thereaction rates and activation energies are truly necessary. Achange of the respective values will change the values ofconversion, selectivity, overall yield, and outlet composition.Yet, the influence of the different sorption and diffusionselectivities will be maintained, providing that the same relativetrends of the reaction rates and activation energies are kept.3.3. Membrane Features. We consider in the present work

a hypothetical rubbery membrane filled with a nanosizedcatalyst.14,34-36 The transport of a species through a homoge-neous rubbery membrane can be described by the sorption-diffusion model.34-36 However, when solid particles (metallicclusters or zeolites, for example) are built-in in a rubberymembrane, the transport mechanism becomes more com-plex.35,37,38,42 First, a decrease in the diffusivity due to thediffusion barrier created by the clusters, which act as inorganicfillers, should be considered.35,37,38,42 On the other hand, thecatalyst particles occluded in the membrane affect its overallsorption capacity, that is, the adsorption on the catalyst particlesshould also be considered in addition to the sorption on thepolymeric phase.37,42

To the best of our knowledge, sorption and diffusioncoefficients in a nonporous polymeric catalytic membrane werenot yet determined under the real conditions of sorption/diffusion/reaction. In few cases, only effective sorption anddiffusion or permeation coefficients were reported.13,34-36 Hence,we will also consider effective diffusion and sorption coefficientsfor the reaction species.We consider that all the hydrocarbons have identical effective

diffusion coefficients in the membrane matrix. This assumptionis based on the propene/propane diffusivity selectivities of 1.3(measured by the authors on a PDMS homogeneous membrane)and 1.5 (reported for a polyethylene homogeneous membrane43)and on the difficulty to find data of diffusivities for propyne.Concerning the effective sorption capacity, we also consideredequal values for all hydrocarbons, based on the propene/propaneselectivities of 0.90 (obtained by the authors in PDMS homo-geneous membranes) and of 0.89 (reported for a polyethylenehomogeneous membrane43) and also on the difficulty to finddata of sorption for propyne. Despite the fact that these selectiv-ities are relative to homogeneous polymeric membranes, we con-sider that the presence of the catalyst built-in in the membraneaffects the diffusivity and sorption of all hydrocarbons in thesame way. In fact, Theis et al.44 report a constant propene/propane permselectivity of 1.1 for PDMS membranes, pure andbuilt-in with different amounts of palladium nanoclusters.For hydrogen, we consider an effective diffusivity 10 times

higher than the one for the hydrocarbons, based on a hydrogen/

propane diffusivity selectivity of 11 obtained by the authors ina homogeneous PDMS membrane. We assume also that theinfluence of the catalyst particles on the diffusivity of hydrogenis equivalent to the one considered for the hydrocarbons. Forthe sorption capacity, a hydrogen/propane selectivity of < 1was obtained by the authors and by Merkel45 for a homogeneousPDMS membrane. However, the hydrogen sorption capacity ofa catalytic membrane built-in with palladium catalyst canincrease strongly46,47 (the other components sorb poorly onpalladium). Because we are assuming equal concentration onthe catalyst surface and in the surrounding polymer matrix, wemay consider a wide range of values for the effective sorptioncoefficient of hydrogen. Thus, we consider values higher than,equal to, and lower than the effective sorption coefficient forthe hydrocarbons.3.4. Thermal Parameters. We obtained the heat capacities

and heats of reaction from the literature at the referencetemperature.48 The molar heat capacity of each component isconsidered constant within the range of temperatures andpressures considered and independent of being in the sorbed orgas phases. A more exact dependence of the heat capacity withtemperature could be considered, but this extra complexitywould not change the main conclusions. Moreover, the operatingtemperature of the reactor considered in this study is close tothe reference one.We also considered the sorption enthalpy constant with

temperature. Accordingly, Hi0,s + (-!Hi

s) ) Hi, where Hi0,s and

Hi are the enthalpies of component i in sorbed and gaseousphases, respectively, at the reference temperature.We arbitrated a value for the modified heat Peclet number

in such a way that the temperature change across the membranethickness is small. This is a reasonable assumption, since thethickness of these membranes is normally small (usually lessthan a few hundred microns).The ratio between the Prater number and the modified heat

Peclet number was replaced by the adiabatic temperature rise(already defined in Section 2.7): &/PeH ) !H1

r /(Cp,refTref) ) B.In this way, parameter B directly reflects the heat of the firstreaction. Moreover, this choice eliminates the need to assign avalue to the reference diffusion coefficient (to set the Praternumber).3.5. Feed and Operation Conditions. The feed stream to

the reactor is made up of propyne, propene, and hydrogen. Theratio between concentrations of hydrogen and propyne, ', wasset to 1.5. The concentration of propyne in a mixture of propyneand propene was set to a value of 5%.25 The feed volumetricflow rate was varied over a wide range, by changing thedimensionless contact time parameter. The maximum value forthis parameter is defined by the total permeation condition(TPC), that is, when the retentate volumetric flow rate is zero(total flow-through configuration).

4. Analysis Strategy

As mentioned in the Introduction, it is crucial to determinewhat improvements can be achieved with our hypotheticalmembrane reactor (CMR) when compared with the moreconventional counterpart. “Conventional”, in the context of thiswork, means a catalytic gas-phase reactor with perfectly mixedflow pattern (CSTR) fed with the same stream, with the samereactions taking place at the catalyst surface and described byequivalent kinetic equations.Given the rather large number of parameters that describe a

catalytic membrane reactor, it is impractical to perform acomplete parametric sensitivity analysis. However, the main


objective of this work can be achieved by varying only a fewkey parameters. These include the effective sorption coefficientof hydrogen (all the other sorption and diffusion coefficientsare fixed, as discussed in Section 3.3), the contact time, theThiele modulus, and the Stanton number. The study will focusprimarily on the analysis of the concentration of propyne inthe outlet stream (for a total flow-through configuration),because, as was stated in the Introduction, this is the key variablein an industrial purified propene stream for the production ofpolypropylene. Additionally, we also perform the analysis ofthe selectivity and overall yield to the intermediate propene, aswell as the conversion of propyne and hydrogen.The conversion of a component i in the membrane reactor is

given by

There are different ways to define the selectivity to anintermediate product. In our work, we consider the selectivitydefined as the net moles of C produced per mole of A reacted4(this quantity is also known as relative yield27). For themembrane reactor, it is given by

The overall yield to the species C is defined as the net molesof C produced per mole of A fed. For the membrane reactor, itis given by

A negative value for both (C and YC means that all of species

A (propyne) and part of species C (propene) fed to the reactorare converted in the final reaction product D (propane).

5. Resolution of the Model Equations

The general strategy considered in this work for solving themodel equations is the same that was used before.49 The steady-state eqs 14, 19, 21, 23, and 24 were transformed intopseudotransient ones, while eqs 22 and 25 were solved explicitlyin order to calculate the volumetric flow rate. Equations 14 and19 were subsequently transformed into a set of ordinarydifferential equations in time by a spatial discretization usingorthogonal collocation50 in a transformed mesh with 11 internalcollocation points.49 The time integration routine LSODA51 wasthen used to integrate the resulting set of equations until asteady-state solution was reached. The corresponding equationsof the fixed bed reactor, eqs 26-28, were solved using the samestrategy.

6. Results and Discussion

6.1. Catalytic Membrane Reactor with a NonpermselectiveMembrane. As mentioned in Section 2.7, we may assume thatthe results of the variables under study obtained for theconventional catalytic reactor (CSTR) are loosely equivalentto the ones obtained for the catalytic membrane reactor (CMR)operating at the total permeation condition and with a catalyticmembrane not showing any diffusivity and sorption selectivities.We may conclude that such an equivalence is realized bycomparing the simulation results of the hydrogen conversion(Figure 2), selectivity to propene (Figure 3), and reactortemperature (Figure 4) for both reactors, as a function of theThiele modulus (for the CMR) or the Damkohler number (forthe CSTR) and Stanton number parameters. From this point on,we consider this CMR as the reference reactor, which will benamed throughout the text as “equivalent conventional catalyticreactor” or ECSTR.

Figure 2. Conversion of hydrogen (A) as a function of the Stanton number and Thiele modulus for the catalytic membrane reactor at the total permeationcondition and (B) as a function of the Stanton number and the Damkohler number for the conventional catalytic reactor. The other parameters have thevalues defined in Table 1.

Xi ) 1 -QR*pi

R*/TR* + QP*piP*/TP*

QF*piF*/TF*

(33)

(C )QR*pC

R*/TR* + QP*pCP*/TP* - QF*pC

F*/TF*

QF*pAF*/TF* - (QR*pA

R*/TR* + QP*pAP*/TP*)

(34)

YC )QR*pC

R*/TR* + QP*pCP*/TP* - QF*pC

F*/TF*

QF*pAF*/TF*

) XA(C (35)


The analysis of the results presented in Figures 2-4 for themembrane reactor (left half), as well as the corresponding onesfor the propyne conversion and propene overall yield (not shownhere), allows us to define the most suitable regions for operatingthe membrane reactor. According to the specifications of theoutlet stream in terms of the concentration of propene, it isdesirable to maximize the conversion of propyne and minimizethat of propene, that is, maximize the selectivity to theintermediate product. Therefore, we selected the parametricspace of intermediate-to-high Thiele modulus (10-1000) to

ensure significant reactants conversion and intermediate-to-highStanton number (10-100) values. We selected a minimum valueof 10 for the Stanton number to assess the influence of sometemperature rise in the performance of the reactor. In fact, forthe reaction system considered in this study, an increase in thecatalyst temperature has a detrimental effect on the selectivityof the partial hydrogenation product (see Figures 3 and 4). Thisis typical, for example, in most hydrocarbon partial hydrogena-tion and oxidation systems. This trend is due in part to therelative values of the activation energies. That is, the activation

Figure 3. Selectivity to propene (A) as a function of the Stanton number and the nThiele modulus for the catalytic membrane reactor at the total permeationcondition and (B) as a function of the Stanton number and the Damkohler number for the conventional catalytic reactor. The other parameters have thevalues defined in Table 1.

Figure 4. Temperature of the reactor (A) as a function of the Stanton number and the Thiele modulus for the catalytic membrane reactor at the totalpermeation condition and (B) as a function of the Stanton number and the Damkohler number for the conventional catalytic reactor. The other parametershave the values defined in Table 1.


energy of the species C produced in reaction 1 (propynehydrogenation) is less than the activation energy of the speciesC consumed in reaction 2 (propene hydrogenation). As thereaction temperature increases, the rate of reaction 2 increasesmore than the rate of reaction 1, because of such relativeactivation energies. Anyway, the operating reactor temperatureis not far from the feed temperature in the selected parametricregion.The discontinuities evidenced in Figures 2-4, along the

Stanton number parameter (for the lower values) and along theThiele modulus/Damkohler number (for intermediate values),represent a “jump” from the lower-temperature steady state to

the higher-temperature steady state. This jump occurs becauseof the existence of a region of multiple steady states,27,52 typicalof exothermic reactions. However, the analysis of this operatingregion is out of the scope of the study. Moreover, the Thielemodulus and Stanton number parametric space chosen toperform the analysis is far from the region where multiple steadystates occur.The results shown in Figures 2A-4A were obtained in the

total permeation condition. Nevertheless, a scanning of thedimensionless contact time parameter should also be performed,to identify its optimal operating range. Following this, we showin Figure 5 the propyne conversion (left half) and the reactor

Figure 5. (A) Conversion of propyne and (B) temperature of the reactor as a function of the dimensionless contact time and the Thiele modulus for thecatalytic membrane reactor, with St ) 10. The other parameters have the values defined in Table 1.

Figure 6. Molar fraction of propyne in the (A) retentate and (B) permeate streams as a function of the dimensionless contact time and the Thiele modulusfor the catalytic membrane reactor, with St ) 10. The other parameters have the values defined in Table 1.


temperature (right half) and in Figure 6 the molar fraction ofpropyne in the retentate (left half) and permeate (right half)streams, all as a function of the Thiele modulus and dimension-less contact time and for a medium Stanton number value (St) 10). The results presented previously reveal several features,which are primarily a consequence of one or more of thefollowing three factors:

• Factor I: Influence of the Dimensionless Contact Time.The retentate flow rate decreases with an increase of thedimensionless contact time. Thus, the relative permeant fluxacross the membrane increases according to the balance, directlyaffecting the retentate composition: the concentration of thereaction products increases, while the concentration of the mainreactants (propyne and hydrogen) decreases.• Factor II: Influence of the Catalytic Activity. The

reaction rate depends directly on the Thiele modulus and onthe concentration of the main reactants. Yet, the concentrationof the reactants is also a function of the Thiele modulus, thatis, the reactants are consumed in a rate depending on thecatalytic activity. Thus, the effective change of the reaction rateacross the membrane depends directly on the balance betweenthese two opposite trends. The catalytic activity influences alsothe fraction of the membrane thickness effectively used in thechemical reaction. Because of the increasing depletion of themain reactant hydrogen with the increase of the Thiele modulus,the reaction takes place in an effectively narrower and narrowerfraction of the catalytic membrane. As a consequence, there isan enrichment of the retentate stream in relation to the reactionproducts, with the corresponding depletion of the main reactants.• Factor III: Relative Extension of Reactions 1 and 2. If

the main reactants hydrogen and propyne exist in the reactionmedium in relative excess, that is, if the reaction occurs in akinetic-controlled regime, the extension of each reaction dependsessentially on the kinetic parameters. As the operation regimechanges from kinetic- to diffusion-controlled, the competitionbetween both reactions for the limiting reactant (hydrogen)becomes more and more important. Because of the different

sensitivity of the selective (reaction 1) and unselective (reaction2) reactions concerning the reactants concentration, the resultof such a competition is favorable to the unselective reaction,as its reaction rate depends only on the concentration ofhydrogen, while the selective reaction rate depends on theconcentrations of propyne and hydrogen.Figure 6A shows that the propyne molar fraction in the

retentate stream is a monotonically decreasing function, eitherwith the dimensionless contact time for a fixed Thiele modulusvalue (primarily a consequence of factor I) or with the Thielemodulus value for a fixed dimensionless contact time (primarilya consequence of factor II).Concerning the propyne molar fraction in the permeate

stream, it shows a much more complex dependence on thedimensionless contact time, for a fixed Thiele modulus value(Figure 6B). This dependence is the one expected for the lowerThiele modulus values, due primarily to factor I. That is, adecrease of the main reactants concentration on the retentatestream, for a kinetic-controlled regime, leads to a decrease ofthe driving force accountable for the transport across themembrane and, consequently, to a decrease of its concentrationon the permeate stream. When increasing the Thiele modulusvalue, the propyne concentration in the permeate streamdecreases with the dimensionless contact time until it reaches aminimum, due essentially to factors I and II. After this turningpoint, it increases continuously until the dimensionless contacttime reaches the total permeation condition, now due primarilyto factor III, even though there is also a secondary influence offactors I and II. The influence of factor III extends progressivelyas the Thiele modulus increases, leading to a decrease of theturning point corresponding to the minimum molar fraction ofpropyne.Figure 6B shows also a decreasing trend of the propyne molar

fraction with the Thiele modulus, for a fixed dimensionlesscontact time, until a minimum value. Such behavior is now dueessentially to factor II. The subsequent increase is a consequenceof the increasing importance of factor III. This trend can be

Figure 7. Ratio between the quantities (A) conversion of propyne and hydrogen, (B) molar fraction of propyne in the permeate stream, (C) selectivity topropene, and (D) overall yield to propene in the CMR and in the ECSTR, as a function of the Thiele modulus and for different Stanton number values, forDB/ ) 10 and " corresponding to the total permeation condition. The other parameters have the values defined in Table 1.


also realized in Figure 5A for the total permeation condition.Even though the conversion depends simultaneously on theupstream (retentate) and downstream (permeate) flow rates, theinfluence of the upstream rate is higher. It should be emphasizedthat a nonzero retentate flow rate means that a fraction of thepropyne and hydrogen fed to the reactor is lost, which leads toa decrease of its conversion. The maximum attainable propyneconversion approaches a level that depends on the relative extentof the selective reaction and on the feed composition ratio ('),while for hydrogen, the maximum attainable conversion is 100%(Figure 2A), due essentially to factors II and III.We can see from Figure 6 that the retentate stream is much

richer in propyne than the permeate stream, on one hand, andthat the level of propyne in the retentate or permeate streamschanges considerably. A decision about the conditions to operatethe reactor must be taken based on the specification of the outletstreams.6.2. Catalytic Membrane Reactor with a Permselective

Membrane. To define the membrane characteristics range aswell as the operating conditions where the CMR outperformsthe CSTR, a criterion based on the ratio between the propynemolar fractions in the outlet streams of both reactors (permeatestream for the CMR) will be considered. The performance ofthe CMR improves relative to the ECSTR (equivalent to theCSTR) if, for a certain region of the Thiele modulus-Stantonnumber plane, such a ratio is <1. Additionally, equivalent ratiosfor the selectivity and overall yield to the intermediate productpropene and for the conversion of the main reactants propyneand hydrogen are also presented. In these last cases, themembrane reactor performs better if the respective ratios are>1. The range of the effective values for the dimensionlesssorption and diffusion coefficients considered in the simulationswas stated in Section 3.3.6.2.1. Higher Hydrogen Diffusion Coefficient.We are going

to study in this section the case where the effective diffusioncoefficient of hydrogen is 10 times higher than that of thehydrocarbons, with equal effective sorption coefficients for all

components. In this way, we are analyzing only the influenceof a higher hydrogen diffusion coefficient. Figure 7 shows thesimulation results for this case.Globally, these results show that there is a region on the

Thiele modulus-Stanton number parametric space where theCMR performs better than the ECSTR, in terms of the propynemolar fraction in the outlet stream (Figure 7B). Moreover, theselectivity (Figure 7C) and the overall yield (Figure 7D) to theintermediate product are also improved, in the entire and in partof the parametric region, respectively. These results are theconjoint expression of the above-mentioned factors II and IIIand of factor IV, described next.

• Factor IV: Diffusion Rate of the Main ReactantsHydrogen and Propyne. An increase of the hydrogen diffu-sivity (corresponding to an increase of the respective perme-ability) leads to a faster transport of this component throughthe membrane. As a consequence, the concentration of hydrogendecreases, either in the retentate stream or in the reactionmedium. The global effect of this decrease of the hydrogenconcentration is a decrease of the global reaction rate and anenhancement of the selective reaction (the two reactions showdifferent sensitivities toward a change in the hydrogenconcentrationssee factor III description).A more detailed analysis of Figure 7 reveals several more

features. Let us consider first the region of the lower Thielemodulus values, where the conversion of hydrogen and propyneis lower in the CMR than in the ECSTR (Figure 7A). This trendis due essentially to the influence of factor IV. However, theinfluence of the higher hydrogen diffusion coefficient is moremarked for hydrogen conversion than for propyne conversion(Figure 7A), resulting in a more selective production of theintermediate product propene (Figure 7C). The molar fractionof propyne in the permeate stream is also penalized in thisregion, essentially because of the lower propyne conversion(Figure 7B).By increasing the Thiele modulus, different trends can be

observed. The hydrogen conversion in the CMR increases

Figure 8. Ratio between the quantities (A) conversion of propyne and hydrogen, (B) molar fraction of propyne in the permeate stream, (C) selectivity topropene, and (D) overall yield to propene in the CMR and in the ECSTR, as a function of the Thiele modulus and for different Stanton number values, forDB/ ) 10, SB

/ ) 10, and " corresponding to the total permeation condition. The other parameters have the values defined in Table 1.


continuously until a value equal to the one attained in theECSTR (Figure 7A). This result was expected and can beexplained by the combined influence of factors II and IV. Onthe other hand, the conversion of propyne in the CMR increasesuntil a value higher than the one attained in the ECSTR (Figure7A), for intermediate Thiele modulus values. This evolution isalso a consequence of factors II and IV. Increasing the Thielemodulus more leads to a slow decrease of the conversion ofpropyne, because of the competition between both selective andunselective reactions, as pointed out in factor III. The propynemolar fraction in the outlet stream directly reflects this evolutionof the propyne conversion, Figure 7B.The selectivity to the intermediate product propene is always

improved in the CMR, because the higher hydrogen diffusivityis more detrimental for hydrogen conversion than for propyneconversion, due to factors II and IV. The trend shown in Figure7C results from the balance between the evolution of theconversions of propyne and hydrogen. That is, the relativepropyne conversion grows faster than the relative hydrogenconversion for the lower Thiele modulus values, causing theselectivity to increase. Above a given Thiele modulus value,the relative hydrogen conversion grows faster than the relativepropyne conversion and the selectivity decreases.The minimum propyne molar fraction in the permeate stream

is favored by the lower temperatures (Figure 7B), because theratio of the activation energies favors the unselective reaction,as was already referred in Section 6.1. However, there is a regionwhere the higher temperatures (for the range considered) aremore favorable for the propyne conversion, as can be concludedfrom Figure 7A for the different Stanton number values and,consequently, for the propyne molar fraction in the outlet stream(Figure 7B). This is not an inconsistency, but the effect of factorsII and IV, associated with the increase of both reaction rateswith the temperature. That is, a higher hydrogen diffusioncoefficient leads to a decrease of its concentration inside themembrane (factor IV) and, consequently, to a decrease of the

global reaction rate. This negative effect can be partiallycanceled out by increasing the temperature.As the Thiele modulus approaches its upper limit, the reaction

tends to occur in an infinitesimal fraction of the membranethickness at the retentate surface. In this region, the advantageof the diffusion selectivity of hydrogen vanishes completely.As a result, the CMR has no advantage over the ECSTR when! f ∞.6.2.2. Higher Hydrogen Diffusion and Sorption Coef-

ficients. We are going to study in this section the case whereboth effective diffusion and sorption coefficients of hydrogenare 10 times higher than those of the hydrocarbons. Figure 8shows the simulation results for this case.Globally, these results show that the propyne conversion

reached in the CMR is never penalized in the entire Thielemodulus/Stanton number parametric space. The propyne molarfraction in the outlet stream is also enhanced for the sameparametric region, though more marked for the lower Thielemodulus values. Concerning the selectivity and overall yield tothe intermediate product, they are considerably penalized forthe lower-to-medium Thiele modulus values and slightly favoredin the region of medium-to-high Thiele modulus values.Additionally, the conversion of hydrogen attained in the CMRis improved for the lower-to-medium Thiele modulus values.For the higher Thiele moduli region, the hydrogen conversionreaches the ECSTR value, as in the case discussed in theprevious section. These global trends are a consequence of theconjoint influence of factors II, III, and IV and of factor V,described next.

• Factor V: Sorption Coefficient of the Main ReactantHydrogen. An increase of the hydrogen sorption capacity bythe membrane (corresponding to an increase of the respectivepermeability) leads not only to a faster transport from theretentate to the permeate chambers but also to an increasedintramembrane concentration. Because this last factor is muchmore important than the increase of the permeability, there is

Figure 9. Ratio between the quantities (A) conversion of propyne and hydrogen, (B) molar fraction of propyne in the permeate stream, (C) selectivity topropene, and (D) overall yield to propene in the CMR and in the ECSTR, as a function of the Thiele modulus and for different Stanton number values, forDB/ ) 10, SB

/ ) 0.1, and " corresponding to the total permeation condition. The other parameters have the values defined in Table 1.


an effective improvement of the intramembrane hydrogenconcentration, resulting in an increase of the global reactionrate. The same conclusions are also valid for the case of propyne.If the sorption coefficient decreases, the conclusions arereversed.A more detailed analysis of Figure 8 reveals some features

that deserve a deeper discussion. First of all, the combinationof factors IV and V results in an effective increase of thehydrogen and propyne relative conversion for the lower Thielemoduli region (Figure 8A). On the other hand, the pattern ofthe propyne relative conversion in the intermediate Thielemoduli region shows a more-complex dependence than the onefor the hydrogen relative conversion (Figure 8A), which isreflected in the propyne relative molar fraction in the permeatestream as a function of the Thiele modulus (Figure 8B). Thisbehavior is a consequence of the different importance of factorsIV and V as the Thiele modulus increases. That is, the higherhydrogen sorption coefficient has an important impact in thereactor performance for the kinetic-controlled regime, wherethe change of the main reactants concentration in the reactionmedium is high, on opposition to the small impact of the higherdiffusion coefficient. This enhancement of the hydrogen con-centration favors the unselective reaction more than the selectiveone, as can be observed from eqs 2 and 3. As a result, theenhancement of the hydrogen conversion is higher than the onefor the propyne conversion (Figure 8A). For the same reasons,the selectivity and overall yield are also penalized (Figure 8parts C and D). As the Thiele modulus increases, the influenceof the higher hydrogen sorption coefficient decreases rapidlyuntil it completely vanishes for medium-to-high Thiele modulus,because the main reactants’ concentration becomes very lowand the more important factor is the competition for the limitingreactant (factor III). For this region, the influence of the higherhydrogen diffusion coefficient is dominant, resulting in thepattern of the plot in Figure 8 for this parametric region beingidentical to the one shown in Figure 7.6.2.3. Higher Hydrogen Diffusion and Lower Hydrogen

Sorption Coefficients. In this section, the effective hydrogensorption coefficient is considered to be 10 times lower than thatof the hydrocarbons, while the effective diffusion coefficientsare kept as in the previous sections. Figure 9 shows theconcerning results.Following the conclusions from the previous section, the

lower hydrogen sorption coefficient has a strong penalizinginfluence on the main reactants’ conversion and on the propynemolar fraction in the outlet stream. This occurs only for thelower Thiele modulus values, as expected, and is mainly aconsequence of factor V. The relative selectivity to theintermediate product propene, as well as the relative overallyield, presents some improvement for the lower Thiele modulusregion, because the relative propyne conversion grows fasterthan the relative hydrogen conversion, as was pointed out inSection 6.2.1. As the Thiele modulus increases, the influenceof the lower hydrogen sorption coefficient decreases rapidly untilit completely disappears, for medium-to-high Thiele modulusvalues. As in the previous cases, the more important factor inthis parametric region is the competition for the limiting reactant(factor III), and the results presented in Figure 9 for this regionshow the exclusive influence of the higher hydrogen diffusioncoefficient.It should be emphasized that the membrane considered in

this section is nonpermselective, that is, all the reaction specieshave the same permeability. Nevertheless, the results obtainedin the CMR are different from the ones obtained in the ECSTR

(also with a nonpermselective membrane), because of thedifferent sorption and diffusion coefficients.

7. Conclusions

In the present study, we analyzed the operating and systemconditions where a catalytic polymeric membrane reactor cantake advantage of its diffusivity and sorption selectivities tooutperform a conventional reactor. It was considered a consecu-tive-parallel reaction describing the hydrogenation of propynein a mixture of propyne and propene. We assessed the membranereactor by analyzing the molar fraction of propyne in the outlet(permeate) stream, the conversion of the main reactantshydrogen and propyne, and the selectivity and overall yield tothe intermediate product propene. To make the comparison, weconsidered that the conventional reactor is equivalent to thecatalytic polymeric membrane reactor with equal sorption anddiffusion coefficients for each reaction species and operatingin a flow-through configuration.The simulation results presented in this study demonstrated

that one can exploit the sorption and diffusivity selectivityprovided by the membrane to lower considerably the level ofpropyne in the outlet stream relative to the value attained in aconventional reactor. This occurs when the hydrogen sorptioncapacity is equal to or higher than that of the hydrocarbons andthe hydrogen diffusivity is higher than that of the hydrocarbons.The region of Thiele modulus where there are enhancementsdepends on the relative sorption and diffusion coefficients. Thesimulation results were obtained for an operating region of smalltemperature rise, to favor the propyne conversion and propeneselectivity. Additionally, the simulation results also demonstratedthat both selectivity and overall yield can be improved in thesame parametric region.The model presented in this study considers perfectly mixed

flow pattern in both retentate and permeate chambers. Futurestudies will consider more complex models, closer to the realsystems, as well as the influence of other parameters.

Acknowledgment

The authors acknowledge the research projects POCTI/EQU/32452/99 and POCTI/EQU/44994/2002 funded by FCT. Theyalso would like to acknowledge Prof. Fernao D. Magalhaes forhis valuable contributions on improving the manuscript.

Nomenclature

A ) external area (m2)B ) adiabatic temperature risec ) partial intramembrane concentration (mol m-3)C ) total intramembrane concentration (mol m-3)Cp ) heat capacity (J mol-1 K-1)D ) diffusion coefficient (m2 s-1)Da ) Damkohler numberE ) activation energy (J mol-1)H ) enthalpy (J mol-1)kj0 ) preexponential reaction rate constant for reaction j(m3(2-j) mol-(2-j) s-1)

kj ) reaction rate constant for reaction j (m3(2-j) mol-(2-j) s-1)PeH ) modified heat Peclet numberP ) total pressure (Pa)p ) partial pressure (Pa)Q ) volumetric flow rate (m3 s-1)R ) universal gas constant (J mol-1 K-1))RE ) ratio of the activation energiesRH ) ratio of the heats of reaction


Rr ) ratio of the reaction rate constantsS ) Henry’s sorption coefficient (mol m-3 Pa-1)St ) Stanton numberT ) absolute temperature (K)U ) overall heat transfer coefficient (J m-2 s-1 K-1)X ) conversiony ) molar fractionYC ) overall yield to species Cz ) membrane spatial coordinate (m)

Greek Symbols& ) Prater number based on reaction 1% ) Arrhenius’ number based on reaction 1" ) dimensionless contact time based on species A! ) membrane thickness (m)$ ) dimensionless membrane spatial coordinate" ) dimensionless reaction rate constant#e ) effective thermal conductivity (J m-1 s-1 K-1)" ) stoichiometric coefficient ("A,1 ) -1, "B,1 ) -1, "C,1 ) 1,

"D,1 ) 0, "A,2 ) 0, "B,2 ) -1, "C,2 ) -1, "D,2 ) 1)(C ) selectivity to species C' ) ratio of the reactants composition in the feed stream (basedon reaction 1)

! ) Thiele modulus# ) dimensionless heat generation parameter

Subscriptsi ) component ij ) reaction jref ) reference conditions or component

Superscripts* ) dimensionless variableF ) relative to the feed stream conditionsG ) relative to the entire reactor (Stanton number definition)m ) relative to the membraneO ) relative to the exit conditions (CSTR model equations)P ) relative to the permeate chamber conditionsr ) relative to reactionR ) relative to the retentate chamber conditionss ) relative to the sorbed phase

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ReceiVed for reView June 6, 2005ReVised manuscript receiVed December 7, 2005

Accepted January 24, 2006

IE050650H


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