enhancement of methanol production in a membrane dual-type reactor

Research Article

Enhancement of Methanol Production in aMembrane Dual-Type Reactor

In this study, a dynamic model for a membrane dual-type methanol reactor wasdeveloped in the presence of long term catalyst deactivation. The proposed modelis used to compare the performance of a membrane dual-type methanol reactorwith a conventional dual-type methanol reactor. A conventional dual-typemethanol reactor is a shell and tube heat exchanger reactor in which the first reac-tor is cooled with cooling water and the second one is cooled with synthesis gas.In a membrane dual-type reactor, the wall of the tubes in the gas-cooled conven-tional reactor is covered with a palladium-silver membrane, which is only perme-able to hydrogen. Hydrogen can penetrate from the feed synthesis gas side intothe reaction side due to the hydrogen partial pressure driving force. Hydrogenpermeation through the membrane shifts the reaction towards the product sideaccording to the thermodynamic equilibrium. The proposed dynamic model wasvalidated against measured daily process data of a methanol plant recorded for aperiod of four years and a good agreement was achieved. The simulation resultsshow that there is a favorable profile of temperature and activity of the membranedual-type reactor relative to single and conventional dual-type reactor systems.Therefore, the performance of methanol reactor systems improves when a mem-brane is used in a conventional dual-type methanol reactor.

Keywords: Catalysts, Dynamic models, Membrane reactors

Received: March 21; 2007; revised: April 22; 2007 accepted: April 27, 2007

DOI: 10.1002/ceat.200700114

1 Introduction

In the methanol synthesis process, synthesis gas (CO2, CO andH2) converts to the methanol in a tubular reactor. The factorsaffecting the production rate in an industrial methanol reactorare parameters such as thermodynamic equilibrium limita-tions and catalyst deactivation. In the case of reversibleexothermic reactions, such as methanol synthesis, selection ofa relatively low temperature permits higher conversion, butthis must be balanced against a slower rate of reaction, whichleads to the requirement of a large amount of catalyst. Up tothe maximum production rate point, increasing temperatureimproves the rate of reaction, which leads to more methanolproduction. Nevertheless, as the temperature increases beyondthis point, the deteriorating effect of equilibrium conversionemerges and decreases methanol production [1]. Thereforeone of the important key issues in methanol reactor configura-

tion is implementing a higher temperature at the entrance ofthe reactor for a higher reaction rate, and then reducing tem-perature gradually towards the exit from of reactor for increas-ing thermodynamic equilibrium conversion.

Recently, a dual-type reactor system instead of a single-typereactor was developed for methanol synthesis. The dual-typemethanol reactor is an advanced technology for convertingnatural gas to methanol at low cost and in large quantities.This reactor configuration permits a high temperature in thefirst reactor and a low temperature in the second reactor. Inthis system, the water-cooled reactor is combined in series witha synthesis gas-cooled reactor. The first reactor, the isothermalreactor, accomplishes partial conversion of the synthesis gas tomethanol at higher space velocities and higher temperaturescompared with the single-type reactor. In this dual-type sys-tem, hydrogen is withdrawn from the methanol synthesispurge stream by a pressure swing adsorption (PSA) unit and isrecycled to the reactor in order to control the stoichiometricnumber and to prevent the wasting of hydrogen. In the reac-tion system, the addition of hydrogen to the reacting gas selec-tively leads to a shift of the chemical equilibrium towards theproduct side, resulting in a higher conversion of synthesis gasto methanol [2].

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.com

Mohammad Reza

Rahimpour1

Mansooreh Lotfinejad1

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

–Correspondence: Associate Professor Dr. M. R. Rahimpour ([email protected]), Department of Chemical and Petroleum Engineering,School of Engineering, Shiraz University, P.O. Box 71345, Shiraz, Iran.

1062 Chem. Eng. Technol. 2007, 30, No. 8, 1062–1076

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 [2]. This leads to higher CO conversion rel-ative to CO2 conversion so that a little water is produced dur-ing the methanol synthesis [2]. It should be noted that waterproduced during methanol synthesis by CO2 hydrogenationgreatly reduces the methanol synthesis rate by suppressing thegas shift reaction [3]. Water produced during methanol syn-thesis from CO2 conversion accelerated the crystallization ofCu and ZnO contained in a CuO/ZnO/Al2O3 catalyst, leadingto its deactivation [3, 4].

The main advantages of a membrane dual-type methanol re-actor are: simultaneous methanol synthesis reaction and diffu-sion of reactant, the possibility of overcoming the limitationimposed by thermodynamic equilibrium [2], enhancement ofkinetics-limited reactions in the first reactor due to the higherfeed temperature, enhancement of equilibrium-limited reac-tions in the second reactor due to a lower temperature, andstoichiometric control of reacting gases in the reactor. A mem-brane reactor is a system or device which combines the chemi-cal reaction and membrane in one system [5].

The application of membrane reaction technology in chemi-cal reaction processes are now mainly focused on reaction sys-tems containing hydrogen and oxygen, and are based on inor-ganic membranes such as Pd and ceramic membranes [5]. Inmany hydrogen-related reaction systems, Pd-alloy membraneson a stainless steel support were used as the hydrogen-perme-able membrane [6]. It is also well known that the use of purepalladium membranes is hindered by the fact that palladiumshows a transition from the a-phase (hydrogen-poor) to the b-phase (hydrogen-rich) at temperatures below 300 °C and pres-sures below 2 MPa, depending on the hydrogen concentrationin the metal. Since the lattice constant of the b-phase is 3 %larger than that of the a-phase, this transition leads to latticestrain and, consequently, after a few cycles, to a distortion ofthe metal lattice [7]. Alloying the palladium, especially withsilver, reduces the critical temperature for this embittermentand leads to an increase in the hydrogen permeability. Thehighest hydrogen permeability was observed at an alloy com-position of 23 wt % silver [8]. Palladium-based membraneshave been used for decades in hydrogen extraction because oftheir high permeability and good surface properties and be-cause palladium, like all metals, is 100 % selective for hydrogentransport [9]. These membranes combine excellent hydrogentransport and discrimination properties with resistance to hightemperatures, corrosion, and solvents. Key requirements forthe successful development of palladium-based membranes arelow costs as well as permselectivity combined with good me-chanical, thermal and long-term stability [10]. These proper-ties make palladium-based membranes such as Pd-Ag mem-branes very attractive for use with petrochemical gases.

A thin palladium or palladium-based alloy layer is preparedon the surface or inside the pores of porous supports. Manyresearchers have developed supporting structures for palla-dium or palladium-based alloy membranes. The materials incommercial use for porous supports are: ceramics, stainlesssteel and glass. The membrane support should be porous,smooth-faced, highly permeable, thermally stable and metaladhesive [11].

There are a few investigations on methanol synthesis in Pd-Ag membrane-type methanol reactors [2, 8]. However, there isno information available in the literature regarding the use ofa Pd-membrane in an industrial methanol reactor. Therefore,it was decided to first study this system. The main goals of thiswork are the improvement of methanol production and the re-duction of catalyst deactivation in dual-type methanol reac-tors. In this new system, the walls of tubes in the second reac-tor are coated with a hydrogen permselective membrane. Thehydrogen partial pressure gradient is the driving force for hy-drogen permeation from feed synthesis gas to the reacting gas.The advantages of this concept will be discussed based on tem-perature and concentration profiles as well as catalyst activityprofiles along the reactors. The results are compared with theperformance of single and conventional dual-type type metha-nol reactors. This comparison shows that the production rateof membrane dual-type methanol reactors is greater than sin-gle and conventional dual-type methanol reactors. Also, theprofile of catalyst activity along the membrane dual-type reac-tor system shows that the catalyst activity along the second re-actor of the membrane system is maintained at a higher levelrelative to the second reactor of the conventional system andthis leads to a longer catalyst lifetime in membrane dual-typereactor.

2 Process Description

2.1 Single-Type Methanol Reactor

Fig. 1 shows the schematic diagram of a single-type methanolreactor. A single-type methanol reactor is basically a verticalshell and tube heat exchanger. The catalyst is packed in verticaltubes and surrounded by the boiling water. The methanol syn-thesis reactions are carried out over a commercial CuO/ZnO/Al2O3 catalyst. The heat of exothermic reactions is transferredto the boiling water and steam is produced.

The technical design data of the catalyst pellet and the inputdata of the single-type methanol reactor have been summa-rized in Tabs. 1 and 2.


Table 1. Catalyst and reactor specifications for the single-typemethanol reactor.

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 [Wm–1 K–1]

av 626.98 [m2 m–3]es

s0.123 [–]

Number of tubes 2962 [–]

Tube length 7.022 [m]

Chem. Eng. Technol. 2007, 30, No. 8, 1062–1076 Membrane reactors 1063

2.2 Conventional Dual-Type Methanol Reactor

Fig. 2 shows the schematic diagram of a conventionaldual-type methanol reactor. This system is mainlybased on the two-stage reactor system consisting of awater-cooled and a gas-cooled reactor. The synthesisgas is fed to the tube of the gas-cooled reactor (secondreactor). The cold feed synthesis gas for the first reac-tor is routed through tubes in the second reactor in acounter-current flow with the reacting gas and thenheated by the heat of reaction produced in the shell.Therefore, the reacting gas temperature is continuouslyreduced over the reaction path in the second reactor.The outlet synthesis gas from the second reactor is fedto tubes of the first reactor (water-cooled) and thechemical reaction is initiated by the catalyst. The heatof reaction is transferred to the cooling water insidethe shell of reactor. In this stage, the synthesis gas ispartly converted to methanol in a water-cooled single-type reactor.

The methanol-containing gas leaving the first reac-tor is directed into the shell of the second reactor. Fi-nally, the product is removed from the downstream ofthe second reactor. The large inlet gas preheater nor-mally required for synthesis by a single-type water-cooled reactor is replaced by a relatively small trimpreheater. As fresh synthesis gas is only fed to the firstreactor, no catalyst poisons reach the second reactor.The poison-free operation and the low operating tem-perature results in a virtually unlimited catalyst servicelife for the gas-cooled reactor. In addition, reactioncontrol also prolongs the service life of the catalyst inthe water-cooled reactor. If the methanol yields in thewater-cooled reactor decrease as a result of decliningcatalyst activity, the temperature in the inlet section ofthe gas-cooled reactor will rise with a resulting im-provement in the reaction kinetics and, hence, an in-creased yield in the second reactor.

The technical design data of the catalyst pellet and in-put data of the conventional dual-type methanol reactorhave been summarized in Tabs. 3 and 4.

2.3 Membrane Dual-Type Methanol Reactor

Fig. 3 shows the schematic diagram of a membrane dual-typereactor configuration for methanol synthesis. The methanolsynthesis process in the membrane dual-type methanol reactoris similar to that in the conventional dual-type methanol reac-tor, with the exception that in the membrane system the wallsof tubes in the second reactor (gas-cooled) consist of hydrogenpermselective membrane. The pressure difference between theshell (71.2 bars) and tube (76.98 bars) in conventional dual-type reactor permits diffusion of hydrogen through the Pd-Agmembrane layer. On the other hand, in the new system, themass and heat transfer process simultaneously occurs betweenshell and tube, while in the conventional reactor only a heattransfer process occurs between them.


Figure 1. A schematic diagram of a single-type methanol reactor of plant I.

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

Table 2. Input data for the single-type methanol reactor.

Feed conditions Value Unit

Composition [mol.-%]:

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 [mol s–1]

Inlet temperature 503 [K]

Pressure 76.98 [bar]

1064 M. R. Rahimpour et al. Chem. Eng. Technol. 2007, 30, No. 8, 1062–1076

The present simulation study was based on a Pd/Aglayer thickness of 0.8 lm. In this study all specifica-tions for the first and second reactors in the membranedual-type system are the same as those of the industrialmethanol reactor listed in Tabs. 3 and 4.

3 Mathematical Model

The mathematical model for the simulation of mem-brane dual-type methanol reactors was developedbased on the following assumptions: (1) one-dimen-sional plug flow in shell and tube sides; (2) axial dis-persion of heat is negligible compared to convection;(3) gases are ideal. An element of length Dz as depictedin Fig. 4 was considered. The differential equations de-scribing mass and heat transfer in the axial directionare described in the following subsections.

3.1 Water-Cooled Reactor (First Reactor)

The mass and energy balance for the solid phase (catalyst sur-face) are expressed by:

esct∂yis

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

qBcpsdTs

dt� avhf �T � Ts� � qBa

�N

i�1

g ri��DHf �i� (2)

where, yis and Ts are, respectively, the mole fraction and tem-perature of the solid-phase (catalyst surface), and i representsH2, CO2, CO, CH3OH, and H2O. Argon and methane are inertcomponents. The following two conservation equations arewritten for the fluid phase:

eBct∂yi

∂t� � Ft

Ac

∂yi

∂z� avctkgi�yis � yi� i = 1,2,...,N-1 (3)


Table 3. Catalyst and reactor specifications for the dual-typemethanol reactor.

Gas-cooled reactor(second reactor)

Water-cooled reactor(first reactor)

Value Value Parameter

4.5 5.5 D [m]

0.00574 0.00574 dp [m]

625.7 625.7 av [m2 m–3]

0.39 0.39 eS

0.39 0.39 eB

10 8 Tube length [m]

71.2 – Shell side pressure [bar]

76.98 75 Tube side pressure [bar]

Table 4. Input data for the dual-type methanol reactor.

Feed conditions Value

Composition [mol.-%]:

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

Pure

methanol

Water-Cooled

Methanol reactor (first reactor)

Gas-Cooled

Methanol reactor (second reactor)

Synthesis gas

Product

Boiling

water

Steam Drum

Synthesis gas

from reforming

Pd/Ag membrane

tube

Reaction side

To distillation unit

Fin , Tin

Ff ,Tf

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

Z

Z+∆Z

Pd/Ag membrane

Tube

Shell side 2H

j

Ft (Z

) F

t (Z+

∆Z

)

Fs (Z

) F

s (Z+

∆Z

)

Figure 4. A schematic diagram of an elemental volume of amembrane reactor.


eBctcpg∂T

∂t� � Ft

Accpg

∂T

∂z� avhf �Ts � T��

pDi

AcUshell�Tshell � T� (4)

where, yi and T are the fluid-phase mole fraction and tempera-ture, respectively. 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 additionaldetails are explained in the numerical solution:

z = 0; Ft = Fin, yi = yi,in, T = Tin (5)

while, the initial conditions are:

t � 0 � yi � yssi � yis � yss

is � T � Tss �Ts � Tsss � a � 1 (6)

3.2 Gas-Cooled Reactor (Second Reactor)

3.2.1 Shell Side (Reaction Side)

The overall mass balance is given by:

eB∂ct

∂t� � 1

Ashell

∂F

∂z

sh

� aH

Ashell�

��Pt

H

��

��Psh

H

�� (7)

where Fsh is the molar flow rate, aH is the hydrogen perme-ation rate constant, and Pt

H� PshH are the hydrogen partial pres-

sure in the tube and reaction sides, respectively. The mass andenergy balance for the solid phase in the gas-cooled reactor isthe same as that in the water-cooled reactor. The followingequations refer to the fluid phase:

eBct∂yi

∂t� � 1

Ashell

∂Fshi

∂t� avctkgi�yis � yi��

aH

Ashell�

��Pt

H

��

��Psh

H

��

i = 1,2, ..., N-1(8)

eBctcpg∂T

∂t� � 1

AshellCpg

∂�FshT�∂z

� avhf �Ts � T��

aH

Ashell�

��Pt

H

��

��Psh

H

��cph�Ttube � T� � pDi

AshellUtube�Ttube � T�

(9)

3.2.2 Tube Side (Feed Synthesis Gas Flow):

The overall mass balance is given by:

∂ct

∂t� � 1

Ac

∂Ft

∂z� aH

Ac�

��Pt

H

��

PsH

� � (10)

where, F t is the molar flow rate. The mass and energy balanceequations for the fluid phase are:

ct∂yi

∂t� � 1

Ac

∂Fti

∂z� aH

Ac�

��Pt

H

��

PsH

� � i = 1,2, ..., N–1 (11)

ctcpg∂Ttube

∂t� � 1

AcCpg

∂�FtTtube�∂z

�aH

Ac�

��Pt

H

��

PsH

� �Cph�T � Ttube� �pDi

AcUtube�T � Ttube� (12)

The boundary conditions are as follows:

z = L; yi = yif, T = Tf (13)

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)–(6) can beused to simulate the single-type methanol reactor.

3.3 Deactivation Model

The deactivation model of the CuO/ZnO/Al2O3 catalyst hasbeen investigated by several researchers, however the model of-fered by Hanken was found to be suitable for industrial appli-cations [12]:

∂a

∂t� �Kd exp

�Ed

R

1

T� 1

TR

� �� a5 (14)

where, TR, Ed and Kd are the reference temperature, activationenergy and deactivation constant of the catalyst, respectively.The numerical value of TR is 513 K, Ed is 91270 J/mol and Kd

is (0.00439 h–1) [12]. Unlike other deactivation models investi-gated by other authors, the above model has been fitted withindustrial operating conditions; that is, the model is the onlycandidate for the simulation and modeling of such industrialplants.

3.4 Hydrogen Permeation in the Pd/Ag Membrane

The flux of hydrogen permeating through the palladium mem-brane, j, will depends on the difference in the hydrogen partialpressure on the two sides of the membrane. Here, the hydro-gen permeation is determined assuming Sieverts’ law:

j � aH��Pt

H

��

PsH

� � (15)

Data for the permeation of hydrogen through the Pd/Agmembrane were determined experimentally. In Eqs. (7–12), aH

is the hydrogen permeation rate constant and is defined as[13]:

aH � 2pL P�

lnRo

Ri

� � (16)

where, Ro, Ri stand for outer and inner radius of the Pd/Aglayer. Here, the hydrogen permeability through the Pd/Ag layeris determined assuming the Arrhenius law, which is a functionof temperature as follows [14, 15]:

P� � P0exp

�Ep

RT

� �(17)



where the pre-exponential factor P0 above 200°C is reported as6.33 · 10–8 mol m–2 s–1 Pa–1/2 and the activation energy Ep is91.207 kJ kmol–1 [14, 15].

4 Numerical Solution

The basic structure of the model consists of the partial deriva-tive equations of mass and energy conservative rules of boththe catalyst and the fluid phase. These must be coupled withthe ordinary differential equation of the deactivation model,and also non-linear algebraic equations of the kinetic modeland auxiliary correlations. The system of equations is solvedusing a two-stage approach consisting of a steady-state simula-tion stage followed by a dynamic solution stage. In order tosolve the set of reactor model equations, a steady-state simula-tion was used prior to the dynamic simulation, and the steady-state simulation gives the initial values for the dynamic simula-tion.

4.1 Steady State Simulation

The steady-state simulation of the dual-type methanol reactoris performed by setting all the time-variation of the states tozero and also considering a fresh catalytic bulk with an activityof unity. In this way, the initial conditions for temperature andconcentration are determined for the dynamic simulation. Thesolving procedure is offered below.

After rewriting the model equations, a set of differentialalgebraic equations is obtained. This set of equations ischanged to non-linear equations using a backward finite dif-ference approximation. The set of non-linear equations are aboundary value problem and were solved using the shootingmethod. The temperature (Tin) and molar flow rate (Fin) ofthe inlet feed synthesis gas for the water-cooled reactor are un-known, while the temperature (Tf) and molar flow rate (Ff) offeed synthesis gas stream are known. The shooting methodconverts the boundary value problem to an initial value prob-lem. The solution can be obtained by guessing a value for Tin

and Fin of heated feed synthesis gas to the water cooled reactor.The water and gas-cooled reactors are divided into 14 and 16sections, respectively, and the Gauss-Newton method is usedto solve the non-linear algebraic equations in each section. Atthe end, the calculated values of temperature (Tf) and molarflow rate (Ff) of fresh feed synthesis gas stream are comparedwith the actual values. This procedure is repeated until the spe-cified terminal values are achieved within a small convergencecriterion.

4.2 Solution of Dynamic Model

The results of the steady-state simulation are used as initialconditions for the time-integration of the dynamic state equa-tions in each node through the reactor. The set of dynamicequations consists of simultaneous ordinary and partial differ-ential equations due to the deactivation model and conserva-tion rules, respectively, as well as the algebraic equations due

to auxiliary correlations, kinetics and thermodynamics of thereaction system. The set of equations have been discretizedwith respect to axial and time coordinate of the nodes. Glob-ally convergent multi-dimensional Newton’s method in For-tran Powerstation 4.0 numerical was used to solve these equa-tions. The process duration was considered to be 1400operating days. The shooting method procedure in the dy-namic simulation is the same as a steady state solution.

5 Results and Discussion

5.1 Steady State Model Validation

The validation of the steady state model was carried out bycomparing the model results with plant data at time zero forthe conventional dual-type reactor under the design specifica-tions and input data in Tabs. 3 and 4, respectively. The modelresults and the corresponding observed data of the plant arepresented in Tab. 5. It was observed that the steady state modelperformed satisfactorily well under industrial conditions andthere was a good agreement between plant data and simulationdata.

5.2 Dynamic Model Validation

In order to verify the goodness of the dynamic model, simula-tion results were compared with the historical process data ofa conventional single-type methanol reactor under the designspecifications and input data in Tabs. 1 and 2, respectively.The predicted results of production rate and the correspond-ing observed data of the plant are presented in Tab. 6. It wasobserved that the model performed satisfactorily well underindustrial conditions and there was a good agreement betweendaily-observed plant data and the simulation data.

A parametric analysis was carried out to address the vital is-sues, such as the temperature, catalyst activity, methanol mole


Table 5. Comparison between model results and observed dataof the dual-type methanol reactor with fresh 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

Temprature [K] 495 489.5 –1.2

Production rate [ton/day] 5200 5078.4 –2.3


fraction and methanol production rate profiles along the reac-tors.

Figs. 5(a) and (b) show the hydrogen partial pressure andthe flow rate profiles, respectively, along the membrane dual-type methanol reactor with fresh catalyst. As shown inFig. 5(a), there is a considerable difference between the hydro-gen partial pressure in the reaction (shell side) and permeation(feed synthesis gas) sides. Thus, the hydrogen can continuouslytransfer from feed synthesis gas zone to reacting gas zone.Therefore, the flow rate of the reacting gas should increasealong the second reactor due to the addition of hydrogen tothe reaction side, as shown in Fig. 5(b).

A comparison of temperature profiles and production rateprofiles along the conventional dual-type reactor and mem-

brane dual-type reactor systems for fresh catalyst is shown inFig. 6. In Fig. 6(a), the temperature profile in the first reactorof the membrane dual-type reactor is higher than in the con-ventional dual-type reactor because the feed synthesis gas tothe first reactor is at a higher temperature due to the higherheat gain from the reacting gas mixture in the second reactor.This means that the cooling of the reacting gas mixture in thesecond reactor is higher than in the conventional reactor. Sincethe reactions in the first reactor are kinetics limited, the highertemperature in the first reactor of the membrane dual-typereactor enhances the reaction and production rate comparedto the conventional reactor, as shown in Fig. 6(b).

Fig. 6(a) also shows a lower temperature for second rectorof the membrane system due to the addition of hydrogen tothe reacting material. Since the membrane reactor configura-tion permits the contact of reaction gases and feed synthesisgas, heat transfer increases between the feed synthesis gas andthe reacting gas mixture. Also, since the reactions in the secondreactor are equilibrium limited, the lower temperature en-hances the equilibrium conversion as shown in Fig. 6(b).Fig. 6 shows that the membrane reactor provides a better tem-perature profile along the reactor.

Simulations with position dependent catalyst activity pro-files in an attempt are carried out to show the reasons for thebetter performance of membrane dual-type reactors relative toconventional dual-type reactors. Temperature and activity pro-files along the reactors are plotted in Fig. 7 for both types ofsystems at the 2nd and 1000th day of operation. The localchange of activity along the reactor is due to local variation oftemperature, which consequently affects the catalyst activity ofthe bed. As seen in Fig. 7, the minimum activity level is ob-served near the first reactor inlet that is exposed to higher tem-peratures at all times. The catalyst in the gas cooled reactor ofboth reactor systems tends to have lower temperature, whichimproves the catalytic activity in this reactor.

As was observed in Figs. 7(a) and (c), the membrane reactorsystem provides a more favorable temperature profile alongthe reactor than the conventional reactor system at differenttimes. The lower temperature profile along the second reactor


Table 6. Comparison between the predicted methanol produc-tion rate and the plant data for the conventional single-typemethanol reactor.

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

(a) (b)

Figure 5. Profiles of (a) hydrogen partial pressure and (b) flow rate along the membrane dual-type methanol reactor for a fresh catalyst.



(a) (b)

Figure 6. Comparison of (a) temperature and (b) methanol production rate profiles in conventional and membrane dual-type reactors fora fresh catalyst.

(a) (b)

(c) (d)

Figure 7. Comparison between temperature profiles (a, c) and activity profiles (b, d) in conventional dual-type and membrane dual-typereactor systems on the 2nd and 1000th day of operation.


of the membrane dual-type reactor system leads to a lower rateof catalyst deactivation. Therefore, the membrane dual-typereactor provides favorable catalyst activity, as compared withthe conventional dual-type reactor, as shown in Fig. 7(b) and(d).

Simulation results are used to show the effect of catalyst ac-tivity on the production rate. The methanol production rateprofiles along the reactors are shown in Fig. 8 for both systemsat the 2nd and 1000th day of operation. In the first reactor ofboth systems, the catalyst at the last parts of the reactor tendsto maintain high temperatures, which cause a lower equilibri-um conversion so that the methanol mole fraction approachesan equilibrium value.

The catalyst in the gas-cooled reactor of both systems tendsto have a lower temperature, which improves the equilibriumconstant and catalyst activity. This results in a shift of the equi-librium conversion to a higher value as shown in Figs. 8(b)and (d). The thermodynamic equilibrium becomes favorableat lower temperatures for the exothermic systems. The lower

temperature in the membrane-type reactor is one reason forobtaining the higher production rate in comparison with theconventional system at any time of operation. Therefore, amembrane dual-type reactor provides a superior productionrate due to the desired close control of reactor temperature forefficient utilization of the catalyst, as compared with a conven-tional dual-type reactor.

The model is used to study the dependent variables profilesalong the membrane dual-type reactor during the first daysand at the end of catalyst life time (1400th day). Figs. 9(a) and(b) show the profiles of gas temperature and the activity alongthe reactor at the 2nd and 1400th day of operation. In the firstreactor, the temperature of the reacting gas mixture on the firstday is higher due to the fresh catalyst and higher conversion.As times goes on from the 1st to the 1400th day of operation,heat produced from the exothermic reactions decreases due toa reduction of conversion during operation. Since the reactionheat is continuously transferred to the cooling water, the tem-perature of the reacting gas mixture decreases with time.


(a) (b)

(c) (d)

Figure 8. Comparison between activity profiles (a, c) and methanol production rate profiles (b, d) in conventional dual-type and mem-brane dual-type reactor systems on the 2nd and 1000th day of operation.


In the second reactor, catalyst deactivation leads to an increaseof the methanol concentration gradient along the reactor, there-fore the heat of reaction increases with time. Also, since theexothermic reactions of methanol synthesis are limited by thethermodynamic equilibrium, hydrogen permeation through themembrane has a positive effect on the rate of heat transfer. Thehydrogen permeation rate through the membrane decreasesduring operation, as can be seen in Fig. 9. This means that therate of heat transfer between synthesis gas and the reacting gasmixture decreases along the second reactor during operation. Inaddition, the ability of the coolant gas to remove reaction heat isless than that of coolant water, thus the temperature increasesalong the second reactor with time. Activity on the 1400th day ofoperation is lower than on the first days because of poisoning aswell as thermal sintering, which is the loss of catalyst active sur-face area due to crystallite growth in either the support materialor the active phase, as seen in Fig. 9(b).

Fig. 10 shows the temperature profile of feed synthesis gasalong the second reactor of the membrane dual-type methanolreactor with a fresh catalyst, and also the effect of feed synthesisgas temperature on the hydrogen permeation rate. Thehydrogen permeability is a function of the feed synthesis gastemperature. Since hydrogen permeability is inversely propor-tional to temperature according to Eq. (17), reducing the tem-perature raises hydrogen permeability, as seen in Fig. 10(a).Also, since the temperature of the feed synthesis gas decreasesalong the second reactor (see Fig. 10(b)), a decreasing trend isobserved in the hydrogen permeation rate profile along this re-actor (see Fig. 11).

The profiles of the hydrogen partial pressure difference andhydrogen permeation rate along the second reactor on the 1stand 1400th day of operating are shown in Fig. 11(a) and (b),respectively. As it may be seen in Fig. 11(a), the hydrogen par-tial pressure difference on the 1400th day is lower than on the


(a) (b)

Figure 9. Profiles of (a) the reacting gas temperature, and (b) catalyst activity along the reactor on the 2nd and 1400th day.

(a) (b)

Figure 10. Profiles of (a) feed synthesis gas temperature along the membrane dual-type methanol reactor for fresh catalyst, and (b) thehydrogen permeation rate versus temperature.


first days due to the increase of hydrogen partial pressure inthe reacting gas mixture during operation. Since the methanolforming reaction rate decreases due to catalyst deactivation,the hydrogen concentration in the reacting gas increases withtime. This leads to a reduction in the driving force for hydro-gen permeation. Therefore, the hydrogen permeation rate de-creases during operation, as shown in Fig. 11(b).

Figs. 12(a) and (b) illustrate the methanol mole fractionand production rate profiles along the reactor at the two differ-ent times of operation, respectively. Between the 1st and1400th day of operation, catalyst deactivation leads to a con-version reduction. A decreasing hydrogen permeation rate dur-ing operation is another reason for reduced conversion.Fig. 12 shows that the methanol mole fraction and productionrate decreases during operation.

The average temperature and activity profiles during a peri-od of 1400 days of operation for three types of reactor systemsare shown in Fig. 13(a) and (b), respectively. That the averagetemperature in the membrane system is less than in the othertwo reactor systems due to the higher heat transfer in themembrane system is shown in Fig. 13(a). Also, a lower tem-perature profile is observed in the conventional dual-type reac-tor in comparison with the single-type reactor because the re-action heat in the second reactor is used to preheat the feedgas to the first reactor. Catalysts in the membrane reactor areexposed to less extreme temperatures than the two other reac-tor systems and catalyst deactivation via sintering is also cir-cumvented. Fig. 13(b) shows that the catalyst deactivation inthe membrane dual-type reactor is less than in the conven-tional single and dual-type methanol reactors.


(a) (b)

Figure 11. Profiles of (a) hydrogen partial pressure difference, (b) total hydrogen permeation along the second reactor at 1st day and1400th day.

(a) (b)

Figure 12. Profiles of (a) methanol mole fractions and production rate along the reactor after the 1st and 1400th day of operation.


Figs. 14(a) and (d) demonstrate the variations of averagemole fraction of methanol and production rates over a periodof 1400 operating days for the three types of reactor systems.Since the membrane dual-type system has a lower average tem-perature and also a lower average catalyst deactivation (seeFig. 13), it has the higer conversion during the operating peri-od. The higher methanol mole fraction and production rate isin the dual-type membrane reactor, and the lowest mole frac-tion and production rate is in the single-type reactor.

6 Conclusion

The methanol forming reactions are strongly exothermic andlimited by the thermodynamic equilibrium. Therefore, the de-velopment of a membrane-based process could open the wayto increasing the methanol production in the methanol syn-thesis process. In this work, the performance of a membrane

dual-type reactor system was compared with a conventionaldual-type and a single-type reactor for methanol synthesis.The potential possibilities of the membrane dual-type reactorsystem were analyzed using a one-dimensional heterogeneousmodel to obtain the necessary comparative estimates. A com-parison of the calculated temperature profile of the catalystalong the length of the reactors shows the extremely favorabletemperature profile of the catalyst beds of the membrane dual-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 time. Also, a favorable temperature profile of the catalystalong the three reactors plus a high level of catalyst activity inthe gas-cooled reactor of the membrane dual-type reactor sys-tem results in a higher production rate in this system. This fea-ture suggests that the concept of membrane dual-type reactorsystem is an interesting candidate for application in synthesisgas conversion to methanol.


(b)(a)

Figure. 13. Comparison of (a) average temperature and (b) the average activity in the reactor over a period of 1400 days of operation forsingle, conventional dual-type and membrane dual-type reactor systems. The feed specifications are given in Tab. 1.

(a) (b)

Figure 14. Comparison of (a) average mole fraction, and (b) production rate over a period of 1400 days of operation for single-type, con-ventional dual-type and membrane dual-type reactor systems. The feed specifications are given in Tab. 1.


Appendix A Reaction Kinetics

A.1 Reaction Kinetics

In methanol synthesis, three overall reactions are possible: hy-drogenation of carbon monoxide, hydrogenation of carbon di-oxide and the 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 ex-pressions have been selected from Graaf et al. [16]. The rateequations combined with the equilibrium rate constants [17]provide enough information about the kinetics of methanolsynthesis. The corresponding rate expressions due to the hy-drogenation of CO, CO2 and the reversed water-gas shift reac-tions are:

r1 � k1KCO �fCOf 3�2H2

� fCH3OH��f 1�2H2

KP1��1 � KCOfCO � KCO2

fCO2��f 1�2

H2� �KH2O�K1�2

H2�fH2O�

(A-4)

r2 � k1KCO �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 in theformulation of the kinetic expressions are listed in Tabs. 7through 9, respectively.

Appendix B Auxiliary Correlations

B.2 Mass Transfer Correlations

In the current work, mass transfer coefficients for the compo-nents have been taken from Cusler [18]. These are the masstransfer coefficients between the gas phase and the solid phase:

kgi � 1�17 Re�0�42Sc�0�67i ug�103 (B-1)

where the Reynolds and Schmidt numbers have been defined as:

Re � 2Rpug(B-2)

Sci � Dim�10�4

(B-3)

and the diffusivity of component i in the gas mixture is givenby [19]:

Dim � 1 � yii�j

yi

Dij

(B-4)

And also the binary diffusivities are calculated using theFuller-Schetter-Giddins equation that is reported by Reid andco-workers [20]. In the following Fuller-Schetter-Giddins cor-relation, vci and Mi are the critical volume and molecularweight of component i which are reported in Table A.1 [21].

Dij �10�7T3�2

��1

Mi

� 1

Mj

P�v3�2ci � v3�2

cj �2(B-5)

Knowing the fact that the diffusion path length along thepores is greater than the measurable thickness of the pellet, forthe effective diffusivity in the catalyst pore, a correction shouldbe implemented due to the structure of the catalyst. The cor-rection factor is ratio of catalyst void fraction to the tortuosityof the catalyst (s).

B.3 Heat transfer correlations

The overall heat transfer coefficient between the circulatingboiling 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)


Table A.1. Reaction rate constants [16].

k � A expB

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 [16].

K � A expB

RT

� �A B

KCO (2.16 ± 0.44) · 10–5 46800 ± 800

KCO2 (7.05 ± 1.39) · 10–7 61700 ± 800

�KH2O�K1�2H2

� (6.37 ± 2.88) · 10–9 84000 ± 1400

Table A.3. Reaction equilibrium constants [16].

KP � 10A

T�B

� �A B

KP1 5139 12.621

KP2 3066 10.592

KP3 –2073 –2.029


where, hi is the heat transfer coefficient between the gas phaseand the reactor wall and is obtained by the following correla-tion [22]:

hi

Cpql

Cpl

K

� �2�3

� 0�458

eB

qudp

l

� ��0�407

(B-7)

where, in the above equation, u is the superficial velocity of gasand the other parameters are those of the bulk gas phase anddp is the equivalent catalyst diameter, K is the thermal conduc-tivity of the gas, , l are the density and viscosity of the gas, re-spectively and eB is the void fraction of the catalyst bed.

In Eq. (B-6), ho is the heat transfer coefficient of boilingwater in the shell side and is estimated with the followingequation [23].

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 equationhas been introduced due to the effect of pressure on the boilingheat transfer coefficient. For the heat transfer coefficient be-tween bulk gas phase and solid phase (hf), Eq. (B-7) is applic-able.

Symbols used

Ac [m2] cross section area of each tubeAi [m2] inner area of each tubeAo [m2] outside area of each tubeAshell [m2] cross section area of the shella [–] activity of catalystav [m2 m–3] specific surface area of the

catalyst pelletCpg [J mol–1 K–1] specific heat of the gas at

constant pressureCph [J mol–1 K–1] specific heat of hydrogen at

constant pressureCps [J mol–1 K–1] specific heat of the catalyst at

constant pressure

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

component i in j

Dim

[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 the shell sideFt [mole s–1] total molar flow per tubefi [bar] partial fugacity of component ihf [Wm–2 K–1] gas-catalyst heat transfer

coefficienthi [Wm–2 K–1] heat transfer coefficient between

fluid phase and reactor wallho [Wm–2 K–1] heat transfer coefficient between

coolant stream and reactor wallK [Wm–1 K–1] conductivity of the fluid phaseKd [s–1] deactivation model parameter

constantKi [bar–1] adsorption equilibrium constant

for component iKPi [–] equilibrium constant based on

the partial pressure ofcomponent i

Kw [Wm–1 K–1] thermal conductivity of reactorwall

k1 [mol kg–1 s–1 bar–1/2] reaction rate constant for the 1strate equation

k2 [mol kg–1 s–1 bar–1/2] reaction rate constant for the2nd rate equation

k3 [mol kg–1 s–1 bar–1/2] reaction rate constant for the3rd rate equation

kgi [m s–1] mass transfer coefficient forcomponent i

L [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 pressurePt

H [bar] tube side pressure

PshH [bar] shell side pressure

�P [mol m–1 s–1 Pa–1/2] permeability of hydrogenthrough the Pd-Ag layer

P0 [mol m–1 s–1 Pa–1] pre-exponential factor ofhydrogen permeability

R [J mol–1 K–1] universal gas constantRe [–] Reynolds numberRi [m] inner radius of the Pd-Ag layerRo [m] outer radius of the 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


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


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 the solid phaseTsat [K] saturated temperature of boiling

water at the operating pressureTshell [K] temperature of coolant stream in

first reactorTtube [K] temperature of coolant stream in

second reactort [s] timeUshell [Wm–2 K–1] overall heat transfer coefficient

between coolant and processstreams

U [m s–1] superficial velocity of the fluidphase

ug [m s–1] linear velocity of the 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–1 s–1 Pa–1/2] 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 the catalytic bedes [–] void fraction of the catalystl [kg m–1 s–1] viscosity of the fluid phasem [–] stoichiometric coefficientmci [cm3 mol–1] critical volume of component iq [kg m–3] density of the fluid phaseqB [kg m–3] density of the catalytic bedqs [kg m–3] density of the catalyst,g [–] catalyst effectiveness factor

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

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