co-current and countercurrent configurations for a membrane dual type methanol reactor

Research Article

Co-current and Countercurrent Configurationsfor a Membrane Dual Type Methanol Reactor

A dynamic model for a membrane dual-type methanol reactor was developed inthe presence of catalyst deactivation. This reactor is a shell and tube type wherethe first reactor is cooled with cooling water and the second one with feed synth-esis gas. In this reactor system, the wall of the tubes in the gas-cooled reactor iscovered with a palladium-silver membrane which is only permeable to hydrogen.Hydrogen can penetrate from the feed synthesis gas side into the reaction sidedue to the hydrogen partial pressure driving force. Hydrogen permeation throughthe membrane shifts the reaction towards the product side according to the ther-modynamic equilibrium. Moreover, the performance of the reactor was investi-gated when the reaction gas side and feed gas side streams are continuously eitherco-current or countercurrent. Comparison between co-current and countercur-rent mode in terms of temperature, activity, methanol production rate as well aspermeation rate of hydrogen through the membrane shows that the reactor in co-current configuration operates with lower conversion and also lower permeationrate of hydrogen but with longer catalyst life than does the reactor in countercur-rent configuration.

Keywords: Countercurrent mode, Dual-type reactors, Modeling

Received: July 21, 2007; accepted: October 18, 2007

DOI: 10.1002/ceat.200700269

1 Introduction

Methanol is an important multipurpose base chemical, a sim-ple molecule which can be recovered from many resources,predominantly natural gas. The factors affecting the produc-tion rate in an industrial methanol reactor are parameters suchas thermodynamic equilibrium limitations and catalyst deacti-vation [1]. Two zones could be distinguished in the methanolsynthesis reactor with imprecise transition point. The firstzone begins at the reactor entrance and continues to a pointwhere conversion approaches equilibrium. In this zone thekinetics controls the process, increasing temperature improvesthe rate of reaction, which leads to more production of metha-nol. Later on, control of the process switches to equilibriumand, as the temperature increases, the deteriorating effect ofequilibrium conversion emerges and decreases methanol pro-duction. Therefore, one of the key issues in methanol reactorconfiguration is to implement a higher temperature at the en-trance of the reactor for a higher reaction rate and then togradually reduce temperature at the exit of the reactor for in-creasing thermodynamic equilibrium conversion.

Recently, a dual-type reactor system was developed formethanol synthesis. This reactor configuration permits a hightemperature in the first reactor and a low temperature in thesecond one. In this system the water-cooled reactor is com-bined in series with a synthesis gas-cooled reactor. The first re-actor, the isothermal reactor, accomplished partial conversionof the synthesis gas to methanol at higher space velocities andhigher temperatures, as compared to the single-stage synthesisreactor. In the new process design, the coolant temperature ofthe first stage is higher than that of the second stage. This re-sults in a significant size reduction of the water-cooled reactorcompared to conventional processes. The dual-type methanolreactor is an advanced technology for converting natural gas tomethanol at low cost in large quantities. In the dual-type sys-tem, hydrogen is withdrawn from the methanol synthesispurge stream by a pressure swing adsorption (PSA) unit or amembrane unit and recycled to the reactor in order to controlthe stoichiometric number (SN) and avoid wasting hydrogen.

The aim to generate an optimum synthesis gas is character-ized by the stoichiometric number given below:

SN � H2 � CO2

CO � CO2� 2 � 2�1 (1)

In case of need, the stoichiometric number can be adjusted byinjecting hydrogen or carbon dioxide into the raw synthesis gas

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.com

Mohammad Reza

Rahimpour1

Mansooreh Lotfinejad1

1 Department of Chemical andPetroleum Engineering, ShirazUniversity, Shiraz, Iran.

–Correspondence: Prof. M. R. Rahimpour ([email protected]),Department of Chemical and Petroleum Engineering, School ofEngineering, Shiraz University, Shiraz 71345, Iran.

38 Chem. Eng. Technol. 2008, 31, No. 1, 38–57

coming from the reforming reactor. In this case study, the opti-mum synthesis gas composition is achieved by injecting hydro-gen into the methanol synthesis loop [2]. Also, in the reactionsystem the addition of hydrogen to the reacting gas selectivelyleads to a shift of the chemical equilibrium towards the productside, which results in higher conversion of synthesis gas tomethanol [3]. Therefore, hydrogen should be used more than re-action stoichiometry in the methanol synthesis reactor.

One of the key issues of the dual-type methanol reactor con-figuration is the addition of H2 to the reacting gas using amembrane reactor [3]. For this purpose, a membrane type re-actor is chosen as second reactor. The main advantages of amembrane dual-type methanol reactor are: simultaneousmethanol synthesis reaction and diffusion of the reactant, thepossibility of overcoming the limitation imposed by the ther-modynamic equilibrium [3], enhancement of kinetically lim-ited reactions in the first reactor due to the higher feed tem-perature, enhancement of equilibrium limited reactions in thesecond reactor due to a lower temperature and control of thestoichiometric number of the reacting gas along the reactor.

A membrane reactor combines the chemical reaction andmembrane in one system. The application of membrane reac-tion technology in chemical reaction processes now mainlyfocuses on reaction systems containing hydrogen and oxygenand is based on inorganic membranes such as Pd and ceramicmembranes [4]. In many hydrogen related reaction systems,Pd-alloy membranes on a stainless steel support were used asthe hydrogen-permeable membrane [5]. The highest hydrogenpermeability was observed at an alloy composition of 23 wt %silver [6]. Key requirements for the successful development ofpalladium-based membranes are low costs as well as permse-lectivity combined with good mechanical/thermal and long-term stability [7]. These properties make palladium-basedmembranes such as Pd/Ag membranes very attractive for usewith petrochemical gases.

A thin palladium or palladium-based alloy layer is preparedon the surface or inside the pores of porous supports. Manyresearches have developed supports for palladium or palla-dium-based alloy membranes. The materials commerciallyused for porous supports are ceramics, stainless steel and glass.For metallic composites membrane support should be porous,smooth-surfaced, highly permeable, thermally stable and ad-herent to metals [8].

There are a few experimental studies on methanol synthesisin Pd/Ag membrane reactors [3, 4, 6]. This work is aimed atimproving methanol production and reducing catalyst deacti-vation in dual-type methanol reactors. In this new system, thewalls of the tubes in the second reactor are coated with a hy-drogen permselective membrane. The hydrogen partial pres-sure gradient is the driving force for hydrogen permeationfrom the feed synthesis gas to the reacting gas. The advantagesof the concept are discussed in terms of temperature and con-centration profiles as well as catalyst activity profiles along thereactors and the results compared with the performance of aconventional dual-type methanol reactor. This comparison re-veals that the production rate of membrane dual-type metha-nol reactors is greater than that of conventional dual-type typemethanol reactors. Also, the profile of catalyst activity alongthe membrane dual-type reactor system shows that catalyst

activity along the second reactor of the membrane system ismaintained at a higher level than in the second reactor of theconventional system, which permits a longer catalyst life in themembrane dual-type reactor.

Moreover, in the current work the effect of flow type on theperformance of the methanol reactor is studied. There are twotypical modes in the feed synthesis gas flow direction againstthe reacting gas flow in the synthesis gas-cooled reactor of thedual-type methanol reactor: co-current (in parallel flow) andcountercurrent (in counterflow) configuration [9–11]. Here,the performance of the methanol reactor in co-current andcountercurrent configurations is compared in terms of pro-duction rate and catalyst activity. Both reacting gas and feedsynthesis gas side streams are considered continuously in co-current or countercurrent mode under the same operatingconditions. It should be noted that the reactor actually worksin countercurrent configuration. Co-current and countercur-rent modes of flow are compared in terms of temperature andconcentration profiles as well as catalyst activity profiles alongthe reactor. The results show that the countercurrent modegives a higher conversion than the co-current one. Catalyst ac-tivity profiles demonstrate that catalyst activity in co-currentmode is maintained at a higher level than in countercurrentmode, and this permits a longer catalyst life in co-currentmode. Also, the comparison between permeation rate profilesof hydrogen shows a higher rate of hydrogen permeation incountercurrent rather than in co-current mode.

2 Reactor Configurations

2.1 Single-type Methanol Reactor

Fig. 1 shows the schematic diagram of a single-type methanolreactor. This reactor type is basically a vertical shell and tubeheat exchanger. The catalyst is packed in vertical tubes and sur-rounded by the boiling water. The methanol synthesis reac-tions are carried out over a commercial CuO/ZnO/Al2O3 cata-lyst. The heat of exothermic reactions is transferred to theboiling water and steam is produced.

The technical design data of the catalyst pellet and the inputdata of the single-type methanol reactor are summarized inTabs. 1 and 2.


Table 1. Catalyst and reactor specifications.

Parameter Value Unit

qs 1770 [kg m–3]

dp 5.47 � 10–3 [m]

cps 5.0 [kJ kg–1 K–1]

kc 0.004 [W m–1 K–1]

av 626.98 [m2 m–3]es

s0.123 [–]

Number of tubes 2962 [–]

Tube length 7.022 [m]

Chem. Eng. Technol. 2008, 31, No. 1, 38–57 Dual-type reactors 39

2.2 Conventional Dual-type Methanol Reactor

Fig. 2 shows the schematic diagram of a conventional dual-type methanol reactor. This system is mainly based on thedual-type reactor system consisting of a water-cooled and agas-cooled reactor. The synthesis gas is fed to the tubes of thegas-cooled reactor (second reactor). The cold feed synthesisgas for the first reactor is routed through the tubes of the sec-ond reactor in a countercurrent flow with reacting gas andthen heated by the heat of reaction produced in the shell. So,the reacting gas temperature is continuously reduced over thereaction path in the second reactor. The outlet synthesis gasfrom the second reactor is fed to the tubes of the first reactor(water-cooled) and the chemical reaction is initiated by thecatalyst. The heat of reaction is transferred to the cooling water

inside the shell of the reactor. In thisstage, the synthesis gas is partly con-verted to methanol in a water-cooledsingle-type reactor.

The methanol-containing gas leavingthe first reactor is directed into theshell of the second reactor. Finally, theproduct is removed from the down-stream end of the second reactor. Thelarge inlet gas preheater normally re-quired for synthesis by a single water-cooled reactor is replaced by a relative-ly small trim preheater. Temperature inthe second reactor is lower than in thefirst reactor so that the main catalystdeactivation occurs in the first reactor.Therefore, the lower operating temper-ature in the second reactor results in avirtually unlimited catalyst service lifefor the gas-cooled reactor. In addition,reaction control also prolongs the ser-vice life of the catalyst in the water-cooled reactor. If the methanol yields

in the water-cooled reactor decrease as a result of decliningcatalyst activity, the temperature in the inlet section of the gas-cooled reactor will rise, leading to improved reaction kineticsand, hence, an increased yield in the second reactor.

The technical design data of the catalyst pellet and the inputdata of the CDMR are summarized in Tabs. 3 and 4.

2.3 Membrane Dual-type Methanol Reactor inCountercurrent Mode

Fig. 3 shows the schematic diagram of a membrane dual-typemethanol reactor (MDMR) in countercurrent configurationfor methanol synthesis. The methanol synthesis process in themembrane dual-type methanol reactor is similar to that in the


Figure 1. Schematic diagram of a single-type methanol reactor.

Table 2. Input data of reactor.

Feed conditions Value Unit

Composition [mole %]

CH3OH 0.50 [–]

CO2 9.40 [–]

CO 4.60 [–]

H2O 0.04 [–]

H2 65.90 [–]

N2 9.30 [–]

CH4 10.26 [–]

Total molar flow rate per tube 0.64 [mole s–1]

Inlet temperature 503 [K]

Pressure 76.98 [bar]

Table 3. Catalyst and specifications of dual-type methanol reac-tors.

Water-cooled reactor

(first reactor)

Gas-cooled reactor

(second reactor)

Parameter Value Value

D [m] 4.5 5.5

Do [m] 0.0445 0.0254

dp [m] 0.00574 0.00574

av [m2 m–3] 625.7 625.7

es 0.39 0.39

eB 0.39 0.39

Tube length [m] 8 10

Shell side pressure [bar] – 71.2

Tube side pressure [bar] 75 76.98

40 M. R. Rahimpour et al. Chem. Eng. Technol. 2008, 31, No. 1, 38–57

conventional dual-type methanol reactor in countercurrentmode, with the exception that in the membrane system thewalls of the tubes in the second reactor consist of a hydrogenpermselective membrane. The pressure difference between theshell (71.2 bar) and tube (76.98 bar) in the conventional dual-type reactor permits diffusion of hydrogen through the Pd/Ag

membrane layer. On the other hand, inthe new system, the mass and heattransfer process simultaneously occursbetween shell and tube, while in theconventional reactor only a heat trans-fer process occurs between them.

The membrane specifications arelisted in Tab. 5. Also, all specificationsof the first and second reactor in themembrane dual-type system are thesame as of the industrial methanol re-actor listed in Tabs. 3 and 4.

2.4 Membrane Dual-typeMethanol Reactor inCo-current Mode

Fig. 4 shows the schematic diagram ofa membrane dual-stage reactor in co-current configuration for methanolsynthesis. The methanol synthesis pro-cess in co-current mode is similar tothat in countercurrent mode, with theexception that in co-current mode the

synthesis gas flows through the tubes of the second reactor inthe same direction as the reacting gas mixture stream in theshell.

All specifications of the first and second reactor in co-cur-rent mode are the same as of the industrial methanol reactorlisted in Tabs. 3 and 4.


Figure 2. Schematic diagram of a conventional dual-type methanol reactor.

Figure 3. Schematic diagram of a membrane dual-type methanol reactor in countercurrent mode.


3 Mathematical Model

To represent the membrane dual-type methanol reactor sys-tem, the differential conservation of the components equationwas derived for co-current and countercurrent configurations.The main assumptions made for this model are:– Pressure decreases linearly in the axial coordinate.– One-dimensional plug flow in both shell and tube sides– Gas flow is ideal.– The radial diffusion in the catalyst pellet is negligible.– Axial dispersion of heat is negligible compared to convec-

tion.Reaction rate expressions observed in the mathematical

model are explained in Appendix A. Auxiliary correlations in-cluding mass and heat transfer relations are available in Ap-pendix B. Physical properties were calculated under averageoperating conditions. This assumption was made because of apresensitivity analysis that illustrates the effect of physicalproperties on the reactor performance. An element of lengthDz as depicted in Fig. 5 was considered.

3.1 Water-cooled Reactor (First Reactor)

The mass and energy balances for the solid phase are expressedby1):

esct∂yis

∂t� kgi

�yi � yis� � g riqBa i = 1,2,...,N – 1 (2)


Table 4. Input data of reactor.

Feed conditions Value

Composition [mole %]

CO2 8.49

CO 8.68

H2 64.61

CH4 9.47

N2 8.2

H2O 0.1

CH3OH 0.37

Argon 0.24

Inlet temperature [K] 401

Pressure [bar] 76

Table 5. Membrane specifications.


Ri 0.027 [m]

RO 0.027008 [m]

d 0.8 � 10–6 [m]

Figure 4. Schematic diagram of a membrane dual-type methanol reactor in co-current mode.

–1) List of symbols at the end of the paper.


qBcpsdTs

dt� avhf �T � Ts� � qBa

�i�1

Ng ri��DHf �i� (3)

where, yis and Ts are, respectively, the mole fraction and tem-perature of the solid-phase and i represents H2, CO2, CO,CH3OH, and H2O. Argon and methane are inert componentsand g is the effectiveness factor which is calculated by a dustygas model [12].

The following two conservation equations are written forthe fluid phase:

eBct∂yi

∂t� � Ft

Ac

∂yi

∂z� avctkg i

�yis � yi� i = 1,2,...,N – 1 (4)

eBctcpg∂T

∂t� � Ft

Accpg

∂T

∂z� avhf �Ts � T��

pDi

AcUshell�Tshell � T� (5)

where, yi and T are, respectively, the fluid-phase mole fractionand temperature. As can be seen in Fig. 2, the outlet synthesisgas from the second reactor is the inlet synthesis gas to the firstreactor. The boundary conditions are unknown and furtherdetails are explained in the numerical solution.

z = 0; Ft = Fin, yi = yi,in, T = Tin (6)

while, the initial conditions are:

t � 0 � yi � yssi � yis � yss

is � T � Tss �Ts � Tsss � a � 1 (7)

3.2 Gas-cooled Reactor (Second Reactor)

3.2.1 Shell Side (Reaction Side)

Overall mass balance:

eB∂ct

∂t� � 1

Ashell

∂F

∂z

sh

�aH

Ashell�

��P t

H

��

��P sh

H

�� (8)

where, Fsh is the molar flow rate, aH is thehydrogen permeation rate constant,

P tH� P sh

H

are, respectively, the hydrogen partial pres-sure in the tube and reaction sides. Themass and energy balances for the solidphase in the gas-cooled reactor are thesame as in the water-cooled reactor. Thefollowing equations are written for thefluid phase:

eBct∂yi

∂t� � 1

Ashell

∂F shi

∂z� avctkgi�yis � yi��

aH

Ashell�

��P t

H ��P sh

H

��

�i = 1,2,...,N – 1 (9)

eBctcpg∂T

∂t� � 1

AshellCpg

∂�F shT�∂z

� avhf �Ts � T��aH

Ashell�

��Pt

H

��

��P sh

H

��cph�Ttube � T��

pDi

AshellUtube�Ttube � T� (10)

3.2.2 Tube Side (Feed Synthesis Gas Flow)

Overall mass balance:

∂ct

∂t� ±

1

Ac

∂Ft

∂z� aH

Ac�

��P t

H

��

��P s

H��

(11)

where, Ft is the molar flow rate. The mass and energy balanceequations for the fluid phase are given by:

ct∂yi

∂t� ±

1

Ac

∂F ti

∂z� aH

Ac�

��P t

H

��

��P s

H ��

i = 1,2,...,N – 1 (12)

ctcpg

∂Ttube

∂t� ±

1

AcCpg

∂�FtTtube�∂z

� pDi

AcUtube�T � Ttube� (13)

The boundary conditions are as follows:

z = L; yi = yif, T = Tf (14)

When aH is zero, the membrane is not permeable to hydro-gen and the model is used for the conventional dual-typemethanol reactor. It should be noted that Eqs. (1) to (6) canbe used to simulate the single-type methanol reactor. Also, inEqs. (10) to (13), the positive sign is used for the countercur-rent mode and the negative sign for the co-current mode.


Tube side

Fs (

Z+

∆Z)

Ft (

Z)

Shell sideZ+∆Z

Z

Fs (

Z)

Ft (

Z+

∆Z)

2Hj

Tube side

Fs (

Z+

∆Z)

Ft (

Z)

Shell sideZ+∆Z

Z

Fs (

Z)

Ft (

Z+

∆Z)

2Hj

Counter-current mode Co- current mode

Figure 5. Schematic diagram of an elemental volume of a membrane reactor in co-current and countercurrent modes.


3.3 Deactivation Model

Deactivation of catalyst pellets has to be taken into considera-tion. The loss of catalyst activity, which corresponds to the lossof active surface area, is due to thermal sintering in commer-cial low-pressure CuO/ZnO/Al2O3 catalysts. Catalyst life isestimated to be 3–4 years (almost 1400 days) [13]. Among dif-ferent deactivation models, the model proposed by Hankenwas found to fit the data of an industrial methanol synthesisreactor [14]. So, this model was selected as the deactivationmodel of Cu-based methanol catalysts. The deactivation modelis in the following form:

da

dt� �kd exp

�Ed

R

1

T� 1

TR

� �� a5 (15)

where, a is the activity of the catalyst pellet, Kd, Ed and TR aredeactivation parameters as listed in Tab. 6.

3.4 Hydrogen Permeation in Pd/Ag Membrane

The composite membrane used in this study is made of a verythin layer of palladium-silver alloy. The membrane is depositedas a continuous layer on the outer surface of a thermostablesupport. The flux of hydrogen permeating through the Pd/Agmembrane is assumed to follow the half-power pressure law(Sievert’s law), then:

jH � aH��P t

H ��P s

H ��

(16)

Data for the permeation of hydrogen through the Pd/Agmembrane were determined experimentally. In Eqs. (7) to(12), aH is the hydrogen permeation rate constant and definedas [15]:

aH � 2pLP�

lnRo

Ri

� � (17)

where, Ro and Ri stand for the outer and inner radius of thePd/Ag layer. Here, the hydrogen permeability through thePd/Ag layer is determined assuming the Arrhenius law, whichas a function of temperature is as follows [16, 17]:

�P � P0exp�Ep

RT

� �(18)

where the pre-exponential factor P0 above 200 /C is reportedas 6.33 � 10–8 mol m–2s–1Pa–1/2 and the activation energy Ep is

91�270kJ

kmol[16, 17].

4 Numerical Solution

To solve the set of coupled partial differential-algebraic equa-tions of the system, kinetic and deactivation models and alsoauxiliary correlations, a two-step procedure was used consist-ing of a steady-state simulation performed prior to a dynamicsimulation to obtain the initial conditions of the states alongthe reactor.

4.1 Steady State Simulation

Steady-state simulation of the dual-type methanol reactor isperformed by setting all the time-variations of the states tozero and also considering a fresh catalytic bulk with theactivity of unity. This way, the initial conditions for tempera-ture and concentration are determined for the dynamic simu-lation.

To solve the set of nonlinear differential-algebraic equationsat the steady-state model, backward finite difference approxi-mation was applied to the system of ordinary differentialalgebraic equations. The set of nonlinear algebraic equations(NAEs) are a boundary value problem and solved usingthe trial and error method. The water and gas-cooled reactorsare divided into 14 and 16 sections, respectively, and theGauss-Newton method is used to solve the NAEs in eachsection.

The procedure is as follows:As the gas-cooled reactor is a membrane reactor, tempera-

ture (Tin), molar flow rate (Fin) and composition (yi) of thegas flow entering the catalyst bed of the first reactor are un-known.– The values for temperature, molar flow rate and composi-

tion of the gas flow entering the catalyst bed of the first reac-tor are assumed.

– The equations of the first reactor are solved from up todown of the first reactor; for the second reactor, the samepattern is followed.

– The calculated values of temperature, molar flow rate andcomposition of fresh feed gas flow to the second reactor floware compared with the actual values given as input of theproblem.

– This procedure is repeated until the specified terminal val-ues are obtained within a small convergence criterion.As the model is used for the conventional dual-type metha-

nol reactor, the temperature of feed gas to the first reactor isthe only unknown variable.

4.2 Solution of Dynamic Model

The results of the steady-state simulation are used as initialconditions for time integration of the dynamic state equationsin each node through the reactor. The set of dynamic equa-tions consists of simultaneous ordinary and partial differentialequations due to the deactivation model and conservationrules, respectively, as well as algebraic equations due to auxili-


Table 6. Parameters of deactivation model [14].


Kd 0.00439 h–1

Ed 91270 J mol–1

TR 513 K


ary correlations, kinetics and thermodynamics of the reactionsystem. The set of equations were discretized with respect tothe axial and time coordinates of the nodes. After discretiza-tion of the partial differential equations (PDEs) of the nodesof a one-dimensional mesh in the axial direction, a system ofordinary differential equations (ODEs) is obtained for eachnode. One characteristic feature of the system is its stiffness.The stiffness originates from the fact that (i) the dynamics ofthe deactivation of catalyst particles is much faster than that oftemperature and concentration of both phases, (ii) the spatialdiscretization causes stiffness because of local variations in therate of kinetic and transfer processes and, finally, (iii) the rateof the chemical reactions and the deactivation process in thesystem can be very different from each other.

Initially, it was tried to solve the equations by the Runge-Kutta method of different orders, the Euler and modified Eulermethod but, due to the divergence of the numerical solution,application of these methods was abandoned. Instead, a multidimensional Newton method was used and the system of mod-el equations conveniently converged. The process duration wasconsidered to be 1400 operating days. The procedure of theshooting method in the dynamic simulation is the same assteady state solution.

5 Results and Discussion

5.1 Steady State Model Validation

The steady-state model was validated by comparing the modelresults with plant data at time zero for a conventional dual-type reactor (aH = 0) under the design specifications and inputdata listed in Tabs. 3 and 4, respectively. The model results andthe corresponding observed data of the plant are presented inTab. 7. It was observed that the steady-state model performedsatisfactorily well under industrial conditions and the daily ob-served plant data were in good agreement with simulationdata.

5.2 Dynamic Model Validation

To verify the “goodness” of the dynamic model, simulation re-sults were compared with the historical process data of a sin-gle-type reactor under the design specifications and input datalisted in Tabs. 1 and 2, respectively. The predicted results ofproduction rate and the corresponding observed data of theplant are presented in Tab. 8. It was observed that the modelperformed satisfactorily well under industrial conditions anddaily observed plant data were in good agreement with thesimulation data.

A parametric analysis was performed to address the vital is-sues, such as temperature, catalyst activity, methanol molefraction and methanol production rate profiles along the reac-tors. Fig. 6(a) shows the effect of the stoichiometric number(SN) of the synthesis gas on the production rate of methanolfor fresh catalyst. As can be seen, there is an optimum SN atwhich the production rate is maximal. Fig. 6(b) presents theeffect of hydrogen addition on SN for fresh catalyst. In theabove equation, SN depends on the synthesis gas composition.The continuous addition of hydrogen leads to an increase inhydrogen mole percent in the reacting gas, resulting in a higherSN in the reactor. Fig. 6 shows that by adding 225 mol/s ofhydrogen to the gas, an optimum synthesis gas is obtained, re-sulting in maximum production. It should be rememberedthat in the case study, the SN of the synthesis gas withdrawnfrom the reforming reactor is less than two; hence, hydrogeninjection into the system is required.

Figs. 7(a) and (b) show the partial pressure of hydrogen andthe flow rate profiles, respectively, along the membrane dual-type methanol reactor for fresh catalyst. As shown in Fig. 7(a),there is a considerable difference between the hydrogen partialpressure in the reaction (shell side) and the feed synthesis gas


Table 7. Comparison between model results with plant data forfresh catalyst aH = 0.

Product conditions Plant Predicted Error %

Composition

CH3OH 0.106 0.1023 –3.4

CO2 0.0799 0.0764 –4.38

CO 0.0251 0.0228 –9.16

H2O 0.0234 0.0211 –9.82

H2 0.5519 0.5323 –3.55

N2/Ar 0.0968 0.0905 –6.5

CH4 0.114 0.103 –9.64

Temperature (K) 495 489.5 –1.2

Production rate (ton/day) 5200 5078.4 –2.3

Table 8. Comparison between predicted methanol productionrate and plant data.

Time (day) Plant (ton/day) Predicted (ton/day) Error %

0 295.0 308.80 2.93

100 296.5 297.03 0.18

200 302.6 289.10 –4.46

300 284.3 283.09 –0.44

400 277.9 278.19 0.10

500 278.2 274.03 –1.50

600 253.0 270.41 6.88

700 274.0 267.19 –2.48

800 268.1 264.30 –1.65

900 275.5 261.67 –5.02

1000 274.6 259.25 –5.58

1100 262.9 257.02 –2.24

1200 255.2 255.18 –0.05


(tube side) sides. Thus, hydrogen can continuously pass fromthe feed synthesis gas zone into the reacting gas zone. There-fore, the flow rate of the reacting gas should increase along thesecond reactor due to the addition of hydrogen to the reactinggas side, as shown in Fig. 7(a).

Fig. 8(a) shows the temperature profile of the feed synthesisgas along the second reactor of the membrane dual-typemethanol reactor for fresh catalyst. A decreasing trend is ob-served. Fig. 8(b) illustrates the effect of feed gas temperatureon the hydrogen permeation rate. Since hydrogen permeabilityfollows the Arrhenius law according to Eq. (18), increasingtemperature promotes hydrogen permeability. Therefore, a de-creasing trend is identified for the permeation rate profile ofhydrogen along the reactor due to the temperature profile.Hydrogen permeation depends on the hydrogen partial pres-sure square root difference between the reaction zone and thepermeation zone. As shown in Fig. 8(c), the partial pressure

difference of hydrogen increases along the reactor, while thepermeation rate of hydrogen decreases. According to Fig. 8,the effect of reducing temperature overcomes the effect ofincreasing the partial pressure difference of hydrogen on thepermeation rate of hydrogen along the reactor.

Fig. 9 illustrates the profiles of reactor temperature and cat-alyst activity versus time and length for a membrane dual-typemethanol reactor in countercurrent mode. In the first reactor(from the reactor entrance to 8 m), the temperature of the re-acting gas mixture on the first days is higher due to fresh cata-lyst and higher conversion. The rate of reaction heat decreasesduring further operation as the catalyst is deactivated. Since re-action heat is continuously removed by the water coolant, thetemperature of the reacting gas mixture is reduced with timein the first reactor.

In the second reactor (from 8 m to 18 m), catalyst deactiva-tion leads to an increase in methanol concentration gradient


(a) (b)

Figure 6. Effect of (a) stoichiometric number on production rate and (b) hydrogen injection on SN for fresh catalyst.

(a) (b)

Figure 7. Profiles of (a) hydrogen partial pressure and (b) flow rate along the membrane dual-type methanol reactor for fresh catalyst.


along the reactor and therefore reaction heat rises with time.Since the ability of the coolant gas to remove reaction heat isless than that of coolant water, temperature along the secondreactor increases with time, as shown in Fig. 9(a). The localchange of activity along the reactor is due to the local variationof temperature, which consequently affects the catalyst activityof the bed. The minimum activity level is observed near thefirst reactor inlet that is exposed to higher temperatures at anytime. The catalyst in the gas-cooled reactor tends to have alower temperature which improves catalyst activity in this re-actor, as shown in Fig. 9(b). Also, this figure shows that duringoperation time the catalyst is deactivated due to poisoning andmainly due to thermal sintering which is the loss of catalystactive surface area owing to crystallite growth of either thesupport material or the active phase.

Figs. 10(a) and (b) illustrate the coolant temperature andmethanol mole fraction profiles versus time and length,respectively, for a membrane dual-type methanol reactor incountercurrent mode. As can be seen, the temperature of thegas coolant increases along the reactor and during operationtime. Also, the mole fraction of methanol increases along thereactor, while it decreases with time due to catalyst deactiva-tion, as shown in Fig 10(b).

Fig. 11 demonstrates the temperature profiles of the feed gas(coolant-gas) and permeation rate of hydrogen profiles versusoperation time and length of the reactor in countercurrentmode. Fig. 11(a) shows that the temperature of the gas coolantincreases along the reactor and also during operation time. Itshould be remembered that hydrogen permeation follows theArrhenius law. On the other hand, hydrogen permeation is


(a) (b)

(c) (d)

Figure 8. Profiles of (a) feed synthesis gas temperature along the membrane dual-type methanol reactor for fresh catalyst, (b) hydrogenpermeation rate versus temperature, (c) hydrogen partial pressure difference and (d) permeation rate along second reactor.



(a) (b)

Figure 9. Profiles of (a) temperature and (b) catalyst activity versus time and length for a MDMR in countercurrent mode.

(a) (b)

Figure 10. Profiles of (a) coolant temperature and (b) mole fraction of methanol versus time and length for a MDMR in countercurrentmode.

(a) (b)

Figure 11. Profiles of (a) temperature of feed gas and (b) permeation rate of hydrogen versus time and length for a MDMR in countercur-rent mode.


exponentially proportional to temperature, so it increases withtime, as shown in Fig. 11(b).

A comparison of the temperature profiles and productionrate profiles along the conventional and membrane dual-typereactor systems for fresh catalyst are shown in Fig. 12. As illus-trated in Fig. 12(a), the temperature profile in the first reactorof the membrane dual-type reactor is higher than in the con-ventional reactor because the temperature of the feed synthesisgas to the first reactor is higher due to the higher heat gainfrom the reacting gas mixture in the second reactor. Thismeans that the cooling of the reacting gas mixture in the sec-ond reactor is more efficient than in the conventional reactor.Since the reactions in the first reactor are kinetically limited,the higher temperature in the first reactor of the membranedual-type reactor enhances the reaction and production ratecompared to the conventional reactor, as shown in Fig. 12(b).

Fig. 12(a) also shows a lower temperature for the secondrector of the membrane reactor system due to the addition ofhydrogen to the reacting material. Since the membrane reactorconfiguration permits the contact of reaction gases and feedsynthesis gas, heat transfer between the feed synthesis gas andthe reacting gas mixture increases. Also, since the reactions inthe second reactor are equilibrium limited, the lower tempera-ture enhances equilibrium conversion, as shown in Fig. 12(b).Fig. 12 demonstrates that the membrane reactor provides abetter temperature profile along the reactor.

Simulations with a position dependent catalyst activity pro-file were carried out in an attempt to show the reasons for thebetter performance of membrane dual-type reactors comparedto conventional dual-type reactors. Temperature and activityprofiles along the reactors are plotted in Fig. 13 for both typesof systems on the 40th and 800th day of operation. As evidentfrom Figs. 13(a) and (c), the membrane reactor system pro-vides a more favorable temperature profile along the reactorthan the conventional reactor system at different operatingtimes. The lower temperature profile along the second reactorof the membrane dual-type reactor system leads to a lower rateof catalyst deactivation along this reactor. Therefore, the mem-

brane dual-type reactor provides a more favorable catalyst ac-tivity compared with the conventional dual-type reactor, asshown in Figs. 13(b) and (d).

The methanol production rate profiles along the reactors areshown in Fig. 14 for both systems on the 40th and 800th dayof operation. In the first reactor of both systems, the catalyst atthe last part of the reactor tends to maintain high tempera-tures, causing a lower equilibrium conversion, so that themethanol mole fraction approaches an equilibrium value.

The catalyst in the gas-cooled reactor of both systems tendsto have a lower temperature, which improves the equilibriumconstant and catalyst activity and results in a shift of equilibri-um conversion to a higher value, as shown in Figs. 14(a) and(b). The thermodynamic equilibrium becomes favorable atlower temperatures for exothermic systems. The lower temper-ature in the membrane type reactor is one reason for obtainingthe higher production rate in this system at any time of opera-tion, as compared to the conventional system. Therefore, amembrane dual-type reactor provides a superior rate of pro-duction due to the desired close control of reactor temperaturefor efficient utilization of the catalyst, as compared with a con-ventional dual-type reactor.

5.3 Comparison of Co-current and CountercurrentModes in a MDMR

Fig. 15 shows the comparison between the temperature pro-files and production rate profiles along co-current and coun-tercurrent reactor configurations for fresh catalyst. As can beseen in Fig. 15(a), the first reactor operates at higher tempera-ture in countercurrent configuration compared to the co-cur-rent one because the feed synthesis gas to the first reactor ispreheated more effectively in the countercurrent configurationalong the second reactor. As mentioned before, the higher tem-perature in the first reactor is favorable, which leads to betterreaction and production rates in the countercurrent modethan in the co-current one, as illustrated in Fig. 15(b).


(a) (b)

Figure 12. Comparison of (a) temperature and (b) methanol production rate profiles in conventional and membrane dual-type reactorsfor fresh catalyst.



(a) (b)

(c) (d)

Figure 13. Comparison between (a, c) temperature profiles and (b, d) activity profiles in conventional dual-type and membrane dual-typereactor systems on the 40th and 800th day of operation.

(a) (b)

Figure 14. Comparison of methanol production rate profiles along the length of conventional and membrane dual-type reactor systemson the (a) 40th and (b) 800th day of operation.


Fig. 15(a) also shows that the second reactor (from 8 m to17.4 m) operates at lower temperature in co-current modethan in countercurrent mode, while near the reactor outlet itoperates at higher temperature. On the other hand, the rate ofreducing temperature along the countercurrent reactor config-uration is higher than along the co-current one, which resultsin a lower temperature of the gas mixture near the reactor out-let. Since the high temperature in the second reactor is not fa-vorable, the higher temperature near the countercurrent reac-tor outlet leads to a decrease in equilibrium conversion in thisconfiguration, as shown in Fig. 15(b). The net result of Fig. 16indicates that the reactor can operate at suitable temperaturein co-current mode along the reactor except near the reactoroutlet.

Fig. 16 compares the temperature difference profiles andtemperature profiles of the coolant gas along co-current andcountercurrent reactor configurations for fresh catalyst.Fig. 16(a) shows the higher temperature difference betweenfeed gas and reacting gas in the first 3 m of the second reactor(from 8 m to 11 m) for the co-current configuration, whilethe lower difference is observed for lengths > 11 m. Since thetemperature difference is the driving force for heat transferbetween the feed synthesis gas and the reacting gas mixture,the higher temperature difference enhances heat transfer incountercurrent mode. Also, since the reaction heat is used topreheat the cold feed synthesis gas to the first reactor, the high-er heat transfer leads to a higher heat gain from the reactinggas mixture, resulting in a more effective preheating of the feed


(a) (b)

Figure 15. Results of steady simulation in a MDMR for co-current and countercurrent modes: (a) temperature and (b) production rate ofmethanol.

(a) (b)

Figure 16. Results of steady state simulation for co-current and countercurrent modes: (a) temperature difference and (b) coolant tem-perature.


gas to the first reactor in countercurrent mode, as shown inFig. 16(b).

Fig. 17 compares the partial pressure difference profiles andpermeation rate profiles of hydrogen along the second reactorof a membrane dual-type methanol reactor for co-current andcountercurrent configurations for fresh catalyst. Fig. 17(a)shows a higher partial pressure difference of hydrogen alongthe second reactor (from 8 m to 17.4 m) in co-current modein comparison with countercurrent mode, while an inversebehavior is observed near the reactor outlet. Fig. 17(b) showsthe higher permeation rate of hydrogen in the first 5 m of thesecond reactor (from 8 m to 13 m) for the co-current config-uration, while lower permeation is observed for lengths above13 m.

Temperature profiles and activity profiles along the reactorfor both modes of flow on the 40th and 800th day of operationare compared in Fig. 18. Figs. 18(a) and (c) show that the re-sults for temperature profiles are similar in co-current andcountercurrent mode at any time of operation.

The lower temperature in most sections of the co-current re-actor configuration improves catalyst activity, which results ina more efficient use of the catalyst. Therefore, the reactor inco-current mode provides a favorable catalyst activity in com-parison with countercurrent mode, as shown in Figs. 18(b)and (d).

Fig. 19 compares the production rate profiles between co-current and countercurrent flows along the reactor on the 40thand 800th day of operation. It can be seen that the counter-current reactor configuration has a higher production rate atdifferent times of operation due to the greater driving force forheat transfer. The thermodynamic equilibrium becomes favor-able at lower temperatures for exothermic systems and this isone reason for the higher production in countercurrent modein the reactor outlet stream during operation.

Average activity and production rate profiles in the mem-brane dual-type reactor between co-current and countercur-rent flow over a period of 1400 days of operation are comparedin Figs. 20(a) and (b), respectively. Fig. 20(a) shows a higher

activity for the co-current reactor configuration, as comparedwith the countercurrent one. Production rate of methanol inthe countercurrent reactor configuration is higher due to thehigher permeation rate and heat transfer in this mode in com-parison with the co-current one, as shown in Fig. 20(b).

6 Conclusion

The performance of a membrane dual-type reactor system wascompared with a conventional dual-type reactor for methanolsynthesis. A comparison of the temperature profiles of the cata-lyst along the length of both reactor systems shows the extremelyfavorable temperature profile of the catalyst of the membranedual-type reactor system. A favorable temperature profile of thecatalyst along the membrane dual-type reactor system leads tohigher activity along the reactor and results in a longer catalystlife. Also, a favorable temperature profile of the catalyst alongthe reactor plus a high level of catalyst activity in the gas-cooledreactor of the membrane dual-type reactor system result in ahigher production rate in this system. The effect of flow typeon the performance of the membrane dual-type reactor interms of production rate and catalyst activity was investigated.The results show that the rector in co-current configurationoperates at lower temperature in comparison with the counter-current configuration. Due to the favorable temperature pro-file of the catalyst in co-current mode, catalyst activity is main-tained at a higher level than in countercurrent mode, whichresults in a longer catalyst life. Also, the reactor in co-currentconfiguration operates at lower temperature, but the produc-tion rate in this configuration is lower due to the lower heattransfer. Moreover, the countercurrent configuration gives ahigher permeation rate of hydrogen along the second reactorrather than the co-current one. It should be remembered thatthe hydrogen permeation has a positive effect on the produc-tion rate. Therefore, optimization of key parameters such asproduction rate of methanol and catalyst activity can deter-mine which configuration of flow is better for the reactor.


(b)(a)

Figure 17. Profiles of (a) partial pressure difference and (b) permeation rate of hydrogen along the reactor for co-current and countercur-rent modes for fresh catalyst.



(a) (b)

(c) (d)

Figure 18. Profiles of (a, c) temperature and (b, d) activity along the reactor for co-current and countercurrent modes on the 40th and800th day of operation.

(b)(a)

Figure 19. Comparison of (a) mole fraction profiles of methanol along the reactor for co-current and countercurrent modes on the 40thand 800th day of operation.


Appendix A. Reaction Kinetics

A.1 Reaction KineticsIn methanol synthesis, three overall reactions are possible:

hydrogenation of carbon monoxide, hydrogenation of carbondioxide and reverse water-gas shift reaction, which follow as:

CO + 2 H2 � CH3OH DH298 = –90.55kJ

mol(A-1)

CO2 + 3 H2 � CH3OH + H2O DH298 = –49.43kJ

mol(A-2)

CO2 + H2 � CO + H2O DH298 = +41.12kJ

mol(A-3)

Reactions (A-1) to (A-3) are not independent, one is a linearcombination of the others. In the current work, the rate expres-sions were selected from Graaf et al. [18]. The rate equationscombined with the equilibrium rate constants [19] provideenough information about the kinetics of methanol synthesis.The corresponding rate expressions due to the hydrogenation ofCO, CO2 and the reversed water-gas shift reactions are:

r1 � k1KCO�fCOf 3�2H2

� fCH3OH��f 1�2H2 KP1�

�1 � KCOfCO � KCO2fCO2

��f 1�2H2

� �KH2O�K1�2H2

�fH2O(A-4)

r2 � k2KCO2�fCO2f 3�2H2

� fCH3OHfH2O��f 3�2H2

Kp2��1 � KCOfCO � KCO2

fCO2��f 1�2

H2� �KH2O�K1�2

H2�fH2O

(A-5)

r3 � k3KCO2�fCO2

fH2� fH2OfCO�KP3

�1 � KCOfCO � KCO2fCO2

��f 1�2H2

� �KH2O�K1�2H2

�fH2O(A-6)

The reaction rate constants, adsorption equilibrium con-stants and reaction equilibrium constants which occur inthe formulation of kinetic expressions are listed in Tabs. 9to 11.


(a) (b)

Figure 20. Comparison of (a) average activity profiles of catalyst and (b) production rate profiles of hydrogen for co-current and counter-current modes over a period of 1400 days of operating.

Table A-1. Reaction rate constants [18].

k � A exp� B

RT� A B

k1 (4.89 ± 0.29) · 107 –113000 ± 300

k2 (1.09 ± 0.07) · 105 –87500 ± 300

k3 (9.64 ± 7.30) · 1011 –152900 ± 11800

Table A-2. Adsorption equilibrium constants [18].

K � A exp� B

RT� A B

KCO (2.16 ± 0.44) · 10–5 46800 ± 800

KCO2 (7.05 ± 1.39) · 10–7 61700 ± 800

�KH2O�KH21�2� (6.37 ± 2.88) · 10–9 84000 ± 1400

Table A-3. Reaction equilibrium constants [18].

KP � 10�A

T� B� A B

KP1 5139 12.621

KP2 3066 10.592

KP3 –2073 –2.029


Appendix B. Auxiliary Correlations

B.2 Mass Transfer CorrelationsIn the current work, mass transfer coefficients for the com-

ponents were taken from Cusler [20]. These are mass transfercoefficients between the gas phase and the solid phase.

kgi = 1.17 Re–0.42 Sci–0.67 ug · 103 (B-1)

where the Reynolds and Schmidt numbers were defined as:

Re � 2Rpug

l(B-2)

Sci � Dim � 10�4(B-3)

and the diffusivity of component i in the gas mixture is giv-en by [21]:

Dim � 1 � yii�j

yi

Dij

(B-4)

The binary diffusivities are calculated using the Fuller-Schet-ter-Giddins equation reported by Reid and his co-workers[22]. In the following, the Fuller-Schetter-Giddins correlation,vci, Mi are the critical volume and molecular weight of compo-nent i reported in Tab. A-1 [23].

Dij �10�7T3�2

��1

Mi

� 1

Mj

�

P�v3�2ci � v3�2

cj �2(B-5)

Knowing that the diffusion path length along the pores isgreater than the measurable thickness of the pellet, for theeffective diffusivity in the catalyst pore, a correction should beimplemented due to the structure of the catalyst. The correc-tion factor is the ratio of catalyst void fraction to the tortuosityof the catalyst (s).

B.3 Heat Transfer CorrelationsThe overall heat transfer coefficient between the circulating

boiling water of the shell side and the bulk of the gas phase inthe tube side is given by the following correlation:

1

Ushell� 1

hi�

Ai ln�Do

Di

�2pLKw

� Ai

Ao

1

ho(B-6)

where, hi is the heat transfer coefficient between the gas phaseand the reactor wall and obtained by the following correlation[24]:

hi

Cpql

Cpl

K

� �2�3

� 0�458

eB

q udp

l

� ��0�407

(B-7)

where, u is the superficial velocity of gas and the other parame-ters are those of the bulk gas phase; dp is the equivalent catalystdiameter, K is the thermal conductivity of gas, q, l are the den-sity and viscosity of the gas, respectively, and eB is the voidfraction of the catalyst bed.

In Eq. (B-6), ho is the heat transfer coefficient of boilingwater in the shell side and estimated by the following equation[25]:

ho � 7�96�T � Tsat�3� P

Pa�0�4 (B-8)

where, T and P are the temperature and pressure of boilingwater in the shell side, Tsat is the saturated temperature of boil-ing water at the operating pressure of the shell side, and Pa isthe atmospheric pressure. The last term of the above equationwas introduced due to the effect of pressure on the boiling heattransfer coefficient. For the heat transfer coefficient betweenthe bulk gas phase and the solid phase (hf), Eq. (B-7) is applic-able.

Symbols used

a [–] activity of catalystAc [m2] cross sectional area of each tubeAi [m2] inner area of each tubeAo [m2] outside are of each tubeAshell [m2] cross section area of shellav [m2 m–3] specific surface area of catalyst

pelletcPg [J mol–1 k–1] specific heat of the gas at

constant pressurecp,h [J mol–1 k–1] specific heat of the hydrogen at

constant pressurecPs [J mol–1 k–1] specific heat of the catalyst at

constant pressurect [mol m–3] total concentrationDi [m] tube inside diameterDij [m2 s–1] binary diffusion coefficient of

component i in jD i

m [m2 s–1] diffusion coefficient ofcomponent i in the mixture

Do [m] tube outside diameterdp [m] particle diameterEd [J mol–1] activation energy used in the

deactivation modelFsh [mole s–1] total molar flow in shell sideFt [mole s–1] total molar flow per tubefi [bar] partial fugacity of component i


Table B-1. Molecular weight and critical volume of the compo-nents.

Component Mi [g/mol] vci [m3/mol] · 106

CH3OH 32.04 118.0

CO2 44.01 94.0

CO 28.01 18.0

H2O 18.02 56.0

H2 2.02 6.1

CH4 16.04 99.0

N2 28.01 18.5


hf [W m–2 K–1] gas-catalyst heat transfercoefficient

hi [W m–2 K–1] heat transfer coefficient betweenfluid phase and reactor wall

ho [W m–2 K–1] heat transfer coefficient betweencoolant stream and reactorwall

K [W m–2 K–1] conductivity of fluid phaseKd [s–1] deactivation model parameter

constantKi [bar–1] adsorption equilibrium constant

for component iKPi [–] equilibrium constant based

on partial pressure forcomponent i

Kw [W m–1 K–1] thermal conductivity of reactorwall

k1 [mol kg–1 s–1 bar–1/2] reaction rate constant for 1st rateequation

k2 [mol kg–1 s–1 bar–1/2] reaction rate constant for 2nd

rate equationk3 [mol kg–1 s–1 bar–1/2] reaction rate constant for 3rd rate

equationkgi [m s–1] mass transfer coefficient for

component iL [m] length of reactorMi [g mol–1] molecular weight of component iN [–] number of componentsNi [mol s–1 m–2] molar fluxP [bar] total pressurePa [bar] atmospheric pressureP t

H [bar] tube side pressureP sh

H [bar] shell side pressure�P [mol m–1s–1Pa–1/2] permeability of hydrogen

through Pd-Ag layerP0 [mol m–1s–1Pa–1] pre-exponential factor of

hydrogen permeabilityR [J mol–1 K–1] universal gas constantRe [–] Reynolds numberRi [m] inner radius of Pd-Ag layerRo [m] outer radius of Pd-Ag layerri [mol kg–1 s–1] reaction rate of component ir1 [mol kg–1 s–1] rate of reaction for

hydrogenation of COr2 [mol kg–1 s–1] rate of reaction for

hydrogenation of CO2

r3 [mol kg–1 s–1] reversed water-gas shift reactionSci [–] Schmidt number of component iT [K] bulk gas phase temperatureTR [K] reference temperature used in

the deactivation modelTs [K] temperature of solid phaseTsat [K] saturated temperature of boiling

water at operating pressureTshell [K] temperature of coolant stream,

in first reactorTtube [K] temperature of coolant stream,

in second reactort [s] time

Ushell [W m–2 K–1] overall heat transfer coefficientbetween coolant and processstreams

U [m s–1] superficial velocity of fluid phaseug [m s–1] linear velocity of fluid phaseyi [mol mol–1] mole fraction of component i in

the fluid phaseyis [mol mol–1] mole fraction of component i in

the solid phasez [m] axial reactor coordinate

Greek symbols

aH [mol m–1s–1Pa–0.5] hydrogen permeation rateconstant

DHf,i [J mol–1] enthalpy of formation ofcomponent i

DH298 [J mol–1] enthalpy of reaction at 298 °KeB [–] void fraction of catalytic bedes [–] void fraction of catalystl [kg m–1 s–1] viscosity of fluid phasem [–] stoichiometric coefficientmci [cm3 mol–1] critical volume of component iq [kg m–3] density of fluid phaseqB [kg m–3] density of catalytic bedqs [kg m–3] density of catalystg [–] catalyst effectiveness factors [–] tortuosity of catalystX [–] auxiliary variabled [m] thickness of membrane

Superscripts and subscripts

f feed conditionsin inlet conditionsout outlet conditionsk reaction number index (1, 2 or 3)s at catalyst surfacesh shell sidess initial conditions (i.e., steady-state conditions)t tube side

References

[1] M. R. Rahimpour, S. Satar, M. Baniadam, J. Fathikalajahi,Chem. Eng. Technol. 2003, 26 (6), 672.DOI: 10.1002/ceat.200390102

[2] http://www. Freepatentsonline.com/5310506.html[3] M. R. Rahimpour, S. Ghader, Chem. Eng. Proc. 2004, 43, 1181.[4] G. Chen, Q. Yuan, Sep. Purif. Technol. 2004, 34, 227.[5] Y.-M. Lin, M.-H. Rei, Catal. Today 2001, 67, 77.[6] M. R. Rahimpour, S. Ghader, Chem. Eng. Technol. 2003, 26

(8), 902. DOI: 10.1002/ceat.200301717[7] R. Dittmeyer, V. Hollein, K. Daub, J. Mol. Catal., A: Chem.

2001, 173, 135.[8] S.-K. Run, J.-S. Park, S.-H. Kim, S.-H. Cho et al., J. Mem. Sci.

2006, 279, 439.[9] F. Gallucci, A. Basile, Int. J. Hydrogen Energy 2006, 31 (15),

2243.



[10] N. Basile, L. Paturzo, F. Gallucci, Inst. Mem. Technol. 2003,82, 275.

[11] H. Thunman, B. Leckner, Fuel 2003, 82, 275.[12] N. Rezaie, A. Jahanmiri, B. Moghtaderi, M. R. Rahimpour,

Chem. Eng. Proc. 2005, 911.[13] I. Løvik, M. Hillestad, Comp. Chem. Eng. 1998, 22, 707.[14] L. Hanken, Master’s Thesis, The Norwegian University of

Science and Technology, Trondheim 1995.[15] S. Hara, W. C. Xu, K. Sakaki, N. Itoh, Ind. Eng. Chem. Res.

1999, 38, 488.[16] G. Barbieri, F. P. D. Maio, Ind. Eng. Chem. Res. 1997,

36, 2121.[17] G. Shu, B. P. I. Gramdgean, S. Kaliaguine, Appl. Catal. 1994,

119, 305.

[18] G. H. Graaf, H. Scholtens, E. J. Stamhuis, A. A. C. M. Bee-nackers, Chem. Eng. Sci. 1990, 45 (4), 773.

[19] G. H. Graaf, P. J. J. M. Sijtsema, E. J. Stamhuis, G. E. H.Joosten, Chem. Eng. Sci. 1986, 41 (11), 2883.

[20] E. L. Cussler, Diffusion – Mass Transfer in Fluid Systems,Cambridge University Press, Cambridge 1984.

[21] C. R. Wilke, Chem. Eng. Prog. 1949, 45, 218.[22] R. C. Reid, T. K. Sherwood, J. Prausnitz, The Properties of

Gases and Liquids, 3rd ed., McGraw-Hill, New York 1977.[23] F. Hartig, F. J. Keil, Ind. Eng. Chem. Res. 1993, 32, 424.[24] J. M. Smith, Chemical Engineering Kinetics, McGraw-Hill,

New York 1980.[25] J. P. Holman, Heat Transfer, McGraw-Hill, New York 1989.



co-current and countercurrent configurations for a membrane dual type methanol reactor

Documents