enhancement of simultaneous hydrogen production and methanol synthesis in thermally coupled...

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 2 8 4e2 9 8

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Enhancement of simultaneous hydrogen productionand methanol synthesis in thermally coupleddouble-membrane reactor

M.R. Rahimpour*, F. Rahmani, M. Bayat, E. Pourazadi

Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, Iran

a r t i c l e i n f o

Article history:

Received 17 May 2010

Received in revised form

20 September 2010

Accepted 23 September 2010

Available online 25 October 2010

Keywords:

Hydrogen production

Methanol synthesis

Thermally coupled

double-membrane reactor

Steady-state heterogeneous model

* Corresponding author. Tel.: þ98 711 230307E-mail address: [email protected] (

0360-3199/$ e see front matter ª 2010 Profedoi:10.1016/j.ijhydene.2010.09.074

a b s t r a c t

Coupling the methanol synthesis with the dehydrogenation of cyclohexane to benzene in

a co-current flow, catalytic fixed-bed double-membrane reactor configuration in order to

simultaneous pure hydrogen and methanol production was considered theoretically. The

thermally coupled double-membrane reactor (TCDMR) consists of two Pd/Ag membranes,

one for separation of pure hydrogen from endothermic side and another one for perme-

ation of hydrogen from feed synthesis gas side (inner tube) into exothermic side. A steady-

state heterogeneous model is developed to analyze the operation of the coupled methanol

synthesis. The proposed model has been used to compare the performance of a TCDMR

with conventional reactor (CR) and thermally coupled membrane reactor (TCMR) at iden-

tical process conditions. This comparison shows that TCDMR in addition to possessing

advantages of a TCMR has a more favorable profile of temperature and increased

productivity compared with other reactors. The influence of some operating variables is

investigated on hydrogen and methanol yields. The results suggest that utilizing of this

reactor could be feasible and beneficial. Experimental proof of concept is needed to

establish the validity and safe operation of the recuperative reactor.

ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.

1. Introduction transmitted and utilized to fulfill our energy needs [1e4].

Energy is an indispensable element in our everyday lives.

However, most of the energy we use nowadays comes from

fossil fuelsdanon-renewable energy source. Furthermore, our

dependence on fossil fuels as energy sources has caused

serious environmental problems, i.e. air pollutants and

greenhouse gas emissions, and natural resource depletion. In

order to remedy the depletion of fossil fuels and their envi-

ronmental misdeeds, hydrogen has been suggested as the

energy carrier of the future. It is not a primary energy source,

but rather serves as a medium through which primary energy

sources (such as nuclear and/or solar energy) can be stored,

1; fax: þ98 711 6287294.M.R. Rahimpour).ssor T. Nejat Veziroglu. P

Therefore, widespread usage of hydrogen could contribute to

alleviation of growing concerns about the world’s energy

supply, security, air pollution, and greenhouse gas emissions.

Moreover, the transformationofCO2 intouseful chemicals, e.g.

methanol, is an attractive way to protect the global environ-

ment since CO2 is an important greenhouse gas andmethanol

itself is a useful raw chemical, solvent, clean-burning and

transportation fuel that will play a major role in the energy

sector [5].

Hydrogen can be produced from a wide range of source

materials and different methods [6,7]. However, most

hydrogen currently produced is derived from fossil fuels, for

ublished by Elsevier Ltd. All rights reserved.

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http://dx.doi.org/10.1016/j.ijhydene.2010.09.074



i n t e r n a t i o n a l j o u rn a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 2 8 4e2 9 8 285

example from steam reforming process. Thus, the production

of hydrogen still results in the production of carbon dioxide. It

would be advantageous if carbon dioxide emissions to the

atmosphere could be eliminated, or at least reduced,while still

benefiting fromtheuseofhydrogenasanenergycarrier.On the

other hand, onboard hydrogen storage imposes a serious

challenge to the use of hydrogen energy. To overcome these

barriers, organic chemical hydrides such as cyclohexane are

among the proposed carriers of hydrogen because of main

advantage from the following points of view: (1) Higher

hydrogen content (e.g., 7.1 wt.% of cyclohexane) which is very

attractive compared with metal hydrides (at most 3 wt.%). (2)

More convenient for storage and transportation due to high

boiling point (bp ¼ 80.7 �C). (3) The dehydrogenated products,

benzene and toluene, can be reversibly hydrogenated and

reusedand thoseare all liquidsat ordinary temperatures [8]. (4)

Its essentially zeroCO2 impact, givingapositiveenvironmental

contribution and also solves the troubles and problems in

hydrogen storage conditions and medium preparation [9,10].

However, the separation of hydrogen from other gases

remains a major unsolved problem for hydrogen production

systems from organic chemical hydrides. The process of sepa-

rating hydrogen from other gases is generally expensive and

energy-intensive. Membrane reactors have been proposed to

solve theaboveproblems. Inaddition, endothermic equilibrium

reactions, such as dehydrogenation of organic chemical

hydrides, can be shifted favorably by extracting the generated

hydrogen using hydrogen-permselective membranes. Because

thedehydrogenationofcyclichydrocarbons isendothermicand

chemical equilibrium is favorable for dehydrogenation at high

temperature [11,12], the reactions are performed at high

temperature under steady-state operation in gas phase.

Methanol, on the other hand, is a clean-burning fuel with

versatile applications. As a combustion fuel, it provides

extremely low emissions. Methanol can also be used as

a solvent, cleaner or a fuel additive and especially as a building

block to produce chemical intermediates such as dimethyl

ether (DME) and methyl t-butyl ether [5].

Even thoughmany improvements from its first commercial

implementation in 1923 and a series of new technologies are

arising to get it [13,14], methanol is still largely produced by the

natural gas and specifically bymeans of syngas (CO, CO2 andH2

mixture) obtained via steam reforming operations [15]. Meth-

anol synthesis reactors aredesignedbasedon two technologies,

high-pressure synthesis operating at 300 bar and low-pressure

synthesis operating between 50 and 100 bar [14]. Themethanol

synthesis reactor studied here is operated in the low-pressure

regime [16]. As the conversion of the exothermal reaction in the

methanol synthesis reactor is equilibrium limited, it is of the

utmost importance that thereaction isoperated insuchawayto

drive the equilibrium composition towards the product. It is of

common practice to use a membrane reactor.

In many hydrogen-related reaction systems, Pd-alloy

membranes on stainless steel supports have been used as

hydrogen-permeable membranes [17]. The highest hydrogen

permeability was observed at an alloy composition of 23 wt.%

silver [18]. Palladium-based membranes have been used for

decades in hydrogen extraction because of their high perme-

ability and good surface properties and because palladium,

like all metals, is 100% selective for hydrogen transport [19].

These membranes combine excellent hydrogen transport and

discrimination properties with resistance to high tempera-

tures, corrosion, and solvents. Key requirements for the

successful development of palladium-based membranes are

low costs, as well as permselectivity combined with good

mechanical/thermal and long-term stability [20]. These

properties make palladium-based membranes such as PdeAg

membranes very attractive for use with petrochemical gases.

A new and very promising method for producing multiple

products, establishment of auto-thermal conditions and

enhancement of productivity (if the reaction is equilibrium)

simultaneously, is usage of thermally coupled membrane

reactors. In this type of reactor, an exothermic reaction is used

as theheat producing source to drive the endothermic reaction

(s). Moreover, to overcome the thermodynamic limitation on

the reactions or separation of a desired product, membranes

have been applied in these reactors.

Rahimpour et al. [10] investigated the performance of

a PdeAg membrane catalytic reactor in co-current mode of

operation to couple the dehydrogenation of cyclohexane to

benzenewith theconversionofsynthesisgas (CO,CO2andH2) to

methanol. In their simulated reactor, the exothermic reaction

(methanol synthesis) takes place in the inner tube and outer

tube (third tube) is permeation side. Besides, shell side and

endothermic side (second tube) separated by a PdeAg

membrane and selective permeation of hydrogen through the

Pd/Ag membrane is achieved by co-current flow of sweep gas

throughthepermeationside.Thisnewconfigurationrepresents

some important improvement in comparison to conventional

methanol reactor as follows: reduction reactors sizes; produc-

tion pure hydrogen in the permeation side; increasing rate of

methanol synthesis and shifting thermodynamics equilibrium;

lowering outlet temperature of product stream; production of

benzene as an additional valuable product; and auto-thermal

conditions are achieved within the reactors.

Moreover, methanol synthesis and cyclohexane dehydro-

genation in a hydrogen-permselective membrane and non-

membrane thermally coupled reactor using differential

evolution (DE) method is optimized by Rahimpour et al.

[21,22].

From previous studies, it is obvious that there is no infor-

mation available in the literature regarding the use of ther-

mally coupled double-membrane reactor for methanol and

pure hydrogen production simultaneously. Therefore, it was

decided to first study on this system.

In the present work, methanol synthesis and production of

pure hydrogen is investigated theoretically in a thermally

coupleddouble-membranemulti-tubularfixed-bedreactor.The

endothermic and exothermic reactions chosen are the catalytic

dehydrogenation of cyclohexane to benzene and methanol

synthesis, simultaneously. The simulated thermally coupled

reactor consists of twoPd/Agmembranes, one for productionof

purehydrogen inpermeationsideandanotherone forhydrogen

injection into exothermic side in order to control and maintain

the suitable hydrogen gradient in the whole length of the

exothermic and feed synthesis gas side. The motivation is to

combine the energy efficient concept of the coupling of endo-

thermiceexothermic reactions; and the membrane-assisted

selective separation of hydrogen and enhancement of valuable

chemicals production in a single reactor. The steady-state, 1-D



Table 1 e The operating conditions for methanolsynthesis process (exothermic side) in TCDMR.

Exothermic side

Parameter Value

Feed composition (mole fraction)


mathematical model of the thermally coupled double-

membrane reactor is presented to evaluate the performance of

the proposed reactor. Numerical simulation results of the

TCDMR were compared with that of conventional reactor and

TCMR at same process conditions such as pressure, tempera-

ture, catalyst mass and feed composition.

CH3OH 0.0050

CO2 0.0940

CO 0.0460

H2O 0.0004

H2 0.6590

N2 0.0930

CH4 0.1026

Total molar flow rate (mol s�1) 0.64

Inlet pressure (bar) 76.98

Inlet temperature (K) 503

Density (kg m�3) 1770

Particle diameter (m) 5.47 � 10�3

Heat capacity (kJ kg�1 K�1) 5.0

Specific surface area (m2 m�3) 626.98

Bed void fraction 0.39

Density of catalyst bed (kg m�3) 1140

Wall thermal conductivity (W m�1 K�1) 48

2. Process description

The conventional reactor is a fixed-bed type resembling

a vertical shell and tube heat exchanger. The tubes are packed

with catalyst pellet and boiling water is circulating in the shell

side to remove the heat of exothermic reactions whereas in

thermally coupled reactor, a catalytic dehydrogenation reac-

tion in the endothermic side is used instead of using cooling

water in the methanol synthesis reactor. The process of

methanol synthesis in the conventional reactor (CR) has been

studied by Rahimpour et al. [10].

2.1. Thermally coupled membrane reactor (TCMR)

Fig. 1 shows the schematic diagram of a thermally coupled

membrane reactor in co-current configuration. This system is

a three concentric tubes reactor where the inner tube is used

for methanol synthesis and the second one is used for dehy-

drogenation of cyclohexane instead of coolant water in the

shell of conventional methanol synthesis reactor. The wall

between second and third tubes is a hydrogen selective

membrane, so that the third tube receives hydrogen perme-

ating from the second one. The characteristics and input data

of thermally coupled membrane reactor are listed in Tables 1

and 2. The operating conditions for exothermic side were

extracted from Rahimpour’s studies [23,24].

2.2. Thermally coupled double-membrane reactor(TCDMR)

The integrated double-membrane reactor simulated for

simultaneous methanol and hydrogen production is shown

Fig. 1 e Schematic diagram of the co-current mode for a the

schematically in Fig. 2. Basically, the process in TCDMR is

similar to TCMR with exception of some changes. These

changes in the new proposed system are as follows:

Firstly, the synthesis gas is fed to the shell side of

exothermic section of reactor and the high-pressure product

is routed from recycle stream through tubes of this reactor in

a co-current mode with reacting gas. Secondly, the walls of

tubes between one and second tube consist of hydrogen

perm-selective membrane. The pressure difference between

these layers is the driving force for diffusion of hydrogen

through the PdeAg membrane layer. On the other word, it

consists of four concentric tubes that the inner tube is feed

synthesis gas side and separated by hydrogen-permselective

membrane from second tube (exothermic side). Catalytic

dehydrogenation of cyclohexane to benzene is assumed to

take place in the third tube, whereas methanol synthesis

occurs inside the exothermic side, with fixed beds of different

rmally coupled membrane reactor (TCMR) configuration.



Table 2 e The operating conditions for dehydrogenationof cyclohexane to benzene (endothermic side) andpermeation side in TCDMR.

Parameter Value

Endothermic side

Feed composition (mole fraction)a

C6H12 0.1

C6H6 0.0

H2 0.0

Ar 0.9


Inlet pressurea (Pa) 1.013 � 105


Particle diameterb (m) 3.55 � 10�3

Bed void fraction 0.39

Permeation side

Feed composition (mole fraction)

Ar (sweep gas) 1.0

H2 0.0



Inlet pressure (Pa) 0.1 � 105

Thermal conductivity of membrane (Wm�1 K�1) 153.95

a Obtained from Kusakabe et al. [30].

b Obtained from Markatos et al. [31].

Table 3 e The characteristics of TCDMR.

Thermally coupled double-membrane reactor

Parameter Value

Inner tube or feed synthesis gas side diameter (m) 0.038

Second tube or exothermic side diameter (m) 0.053

Third tube or endothermic side diameter (m) 0.068

Outer tube or permeation side diameter (m) 0.0827

Length of reactor (m) 7.022

Inner membrane thickness (m) 6 � 10�6

Outer membrane thickness (m) 6 � 10�6


catalysts on both sides. Synthesis gas feed passes through the

exothermic side and outlet of exothermic side goes to recy-

cling and then passes through the inner tube. Hydrogen

partial pressure in recycle stream (after being compressed) is

suitable to permeate to exothermic side. Finally, the high-

pressured methanol product is routed from recycle stream

through inner tube of the reactor in a co-current mode with

reacting synthesis gas. Therefore, the reacting synthesis gas is

Fig. 2 e Schematic diagram of the co-current mode for a therma

configuration.

cooled simultaneously with recycle gas in the inner tube and

reacting gas in endothermic side. Moreover, the wall of the

endothermic side is covered with a PdeAg membrane. Thus,

pure hydrogen can penetrate from the endothermic side into

the permeation side (outer tube). The specifications of

different sides of TCDMR have been summarized in Table 3.

The input data and operating conditions are the same as

TCMR (see Tables 1 and 2).

3. Reaction scheme and kinetics

3.1. Methanol synthesis

In the methanol synthesis, three overall reactions are

possible: hydrogenation of carbon monoxide, hydrogenation

of carbon dioxide reverse wateregas shift reaction. In the

current work, the rate expressions have been selected from

Graaf et al. [25]. The rate equations combined with the equi-

librium rate constants [26] provides enough information about

kinetics of methanol synthesis over commercial CuO/ZnO/

Al2O3 catalysts.

lly coupled double-membrane reactor (TCDMR)



Table 4 e The reaction rate constant, adsorptionequilibrium constant, reaction equilibrium constant fordehydrogenation of cyclohexane.

k ¼ AexpðB=TÞ A B

k 0.221 �4270

KB 2.03 � 10�10 6270

KP 4.89 � 1035 3190


3.2. Dehydrogenation of cyclohexane

The reaction scheme for the dehydrogenation of cyclohexane

to benzene is as follows:

C6H124C6H6 þ 3H2 DH298 ¼ þ206:2 kJ=mol (1)

The following reaction rate equation of cyclohexane, rc, is

used [27]:

rc ¼�k

�KPPC=P3

H2� PB

�

1þ�KBKPPC=P3

H2

� (2)

Where k, KB and KP are respectively the reaction rate constant,

the adsorption equilibrium constant for benzene and the

reaction equilibrium constant that are tabulated in Table 4. Piis the partial pressure of component i in Pa. The reaction

temperature is in the range of 423e523 K and the total

Table 5 e Mass and energy balances and boundary conditions

Solid phase avcjkgi;j

�ygi;j � ys

i;j

�

avhf

�Tj

g � Tjs�þ r

Fluid phase� Fj

Ac;j

dyi;jg

dzþ avcjkg

� Fj

Ac;jCgpj

dTjg

dzþ avh

þfpDi

Ac;jU1�2

�T1

g � T

Permeation side�F4

dygi;4

dzþ bJH3

¼

�F4Cgp4

dT4g

dzþ bJH3

Feed synthesis gas side�F1

dygi;1

dz� fJH1

¼

�F1Cgp1

dT1g

dz� fJH1

The initial value z ¼ 0ygi;j ¼ yg

i0;j;Tj ¼ T0g;

ygi;1 ¼ yg

if ;2;T1 ¼ Tfg

pressure in the reactor ismaintained at 101.3 Kpa. The catalyst

is Pt/Al2O3 [28].

4. Mathematical model

The following assumptions are considered during the

modeling of doubled and single-membrane heat exchangers

catalytic reactor:

� One-dimensional heterogeneous model (reactions take

place in the catalyst particles)

� Steady-state conditions

� Plug flow pattern is considered in each sides

� Axial diffusion of heat and mass are neglected compared

with the convection

� No radial heat and mass diffusion in catalyst pellet

� Bed porosity in axial and radial directions is constant

� Gas mixtures considered to be ideal

� Heat loss is neglected

According to the above assumptions and the differential

element along the axial direction inside the reactor, the mole

balance equation and the energy balance equation were

obtained. The balances typically account for convection,

transport to the solid-phase and reaction. The mass and

for solid and fluid phases in different sides of TCDMR.

Mass and energy balances equation

þ hri;jrb ¼ 0 (3)

b

XNi�1

hri;j��DHf ;i

� ¼ 0 (4)

i;j

�yi;js � yi;j

g�� b

JH3

Ac;jþ f

JH1

Ac;j¼ 0 (5)

f

�Tj

s � Tjg�� pDi

Ac;jU�T3

g � T2g�� b

jH3

Ac;j

ZT4

T3

CpdT� bpDi

Ac;jU3�4

�T3

g � T4g�

2g�þ f

jH1

Ac;j

ZT2

T1

CpdT ¼ 0 (6)

0 (7)

ZT4

T3

CpdTþ pDiU3�4

�T3

g � T4g� ¼ 0 (8)

0 (9)

ZT2

T1

CpdTþ pDiU1�2

�T2

g � T1g� ¼ 0 (10)

Pj ¼ P0g j ¼ 2;3;4 (11)

;2; P1 ¼ Pg

f ;2 j ¼ 1 (12)




energy balances and boundary conditions for solid and fluid

phases are summarized in Table 5. In equations (3) and (4), h

is effectiveness factor of kth reaction in jth side (the ratio of

the reaction rate observed to the real rate of reaction), which

is obtained from a dusty gas model calculations [23]. The

detail of such a dusty gas model is available in literature [10].

In equations (5) and (6), b and f is equal to 1 and 0 for the

endothermic and 0 and 1 for the exothermic side, respec-

tively. Besides, in equation (6), the positive sign is used for

the exothermic side and the negative sign for the endo-

thermic side. In equations (7) and (8), b is equal to 1 for

hydrogen component and 0 for the sweep gas. Moreover, in

equations (9) and (10), f is equal to 1 for hydrogen component

and 0 for CO2, CO, H2O, CH3OH and inert components. In the

boundary condition equationsygi0;j, Tg0and Pg0 are the fluid-

phase mole fraction of ith component, temperature and

pressure at the entrance of jth side of reactor, respectively

andygif ;2, Tgf ;2and Pgf ;2 are the fluid-phase mole fraction of ith

component, temperature and pressure at the end of

exothermic side, respectively.

4.1. Pressure drop

The Ergun momentum balance equation is used to give the

pressure drop along the reactor:

dPdz

¼ 150ð1� 3Þ2mug

33d2p

þ 1:75ð1� 3Þu2

gr

33dp(13)

where the pressure drop is in Pa.

4.2. Hydrogen permeation in Pd/Ag membrane

The composite membranes in this study are made of a 6 mm

thin layer of palladiumesilver alloy. The membrane is depos-

ited as a continuous layer on the outer surface of a thermo

stable support. The flux of hydrogen permeating through the

Table 6 e Physical properties, mass and heat transfer correlati

Parameter

Component heat capacity C

Mixture heat capacity B

Viscosity of reaction mixtures B

Mixture thermal conductivity

Mass transfer coefficient between gas and solid phases k

R

S

D

D

Overall heat transfer coefficient 1U

Heat transfer coefficient between gas phase and reactor wall

C

inner and outer Pd/Ag membrane is assumed to follow the

halfepower pressure law (Sievert’s law) and is expressed by:

JH1¼

2pLP0

ln

�Do

Di

�exp��Ep

RT

�� ffiffiffiffiffiffiffiffiffiffiPH2 ;1

p � ffiffiffiffiffiffiffiffiffiffiPH2 ;2

p �(14)

JH3¼

2pLP0

ln

�Do

Di

�exp��Ep

RT

�� ffiffiffiffiffiffiffiffiffiffiPH2 ;3

p � ffiffiffiffiffiffiffiffiffiffiPH2 ;4

p �(15)

PH2is hydrogen partial pressure in Pa.DO andDi stand for the

outer and inner diameters of the Pd/Ag layer. The pre-expo-

nential factor P0 above 200 �C is reported as

6.33 � 10�8 mol m�2 s�1 Pa�0.5 and the activation energy Ep is

15.7 Kj mol�1 [29].

4.3. Auxiliary correlations

Auxiliary correlations should be added to solve the set of

differential equations. The correlations used for heat and

mass transfer between two phases, physical properties of

chemical species and overall heat transfer coefficient between

two sides are summarized in Table 6. The heat transfer coef-

ficient between gas phase and reactor wall is applicable for

heat transfer between gas phase and solid catalyst phase.

5. Numerical solution

The formulated model composed of 17 ordinary differential

equations and the associated boundary conditions lends itself

to be an initial value problem. The algebraic equations in the

model incorporate the initial conditions, the reaction rates,

the ideal gas assumption, as well as aforementioned correla-

tions for the heat and mass transfer coefficients and the

physical properties of fluids. These equations along with the

ons.

Equation Reference

p ¼ aþ bTþ cT2 þ dT�2

ased on local compositions

ased on local compositions

Lindsay and Bromley [32]

gi ¼ 1:17Re�0:42Sc�0:67i ug � 103 Cussler [33]

e ¼ 2Rpug

m

ci ¼m

rDim � 10�4

im ¼ 1� yiPi¼j

yiDij

[34]

ij ¼1:43� 10�7T3=2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1=Mi þ 1=Mj

qffiffiffi2

pPðv1=3ci þ v1=3cj Þ2

Reid et al. [35]

¼ 1hi

þ AilnDo=Di

2pLKwþ Ai

Ao

1ho

h

prmðCpm

KÞ2=3 ¼ 0:458

3Bðrudp

mÞ�0:407 [36]



Fig. 3 e Schematic diagram of an elemental volume of reactor.

Table 7e Comparison between simulation and plant datafor conventional methanol synthesis reactor.

Reactor inlet Reactor outlet

Exp. Calc. Error%

Composition (mol %)

CO2 3.45 2.18 2.26 �3.67

CO 4.66 1.44 1.5 �4.167

H2 79.55 75.71 76.37 �0.87

CH4 11.72 12.98 12.88 0.77

N2 0.032 0.16 0.15 6.66

H2O 0.08 1.74 1.66 4.598

CH3OH 0.032 5.49 5.23 4.736

Feed flow rate (mols�1) 0.565 0.51 0.5 1.96

Temperature (K) 503 528 524.3 0.7


discretized ordinary differential equations using backward

finite difference form a set of non-linear algebraic equations.

The reactor length is then divided into 100 separate sections.

The discretized ordinary differential equations using back-

ward finite difference for node k are as follow (Fig. 3):

in

8>>>>>>><>>>>>>>:

zL¼ 0/k ¼ 0

zL¼ 1/k ¼ 101

DzL

¼ 1100

The mass and energy balance equations for the fluid phase

of reaction sides

��Fi;jg�k

��Fi;jg�k�1

Ac;jDzþavcj

�kgi;j

�k��ysi;j

�k

��ygi;j

�k��b

�JH3

�kAc;j

þf

�JH1

�kAc;j

¼0

(16)

� Cgpj

�FjTj

g�k

��FjTj

g�k�1

Ac;jDzþ avhf

��Tj

s�k

��Tgj

�k�

� pDi

Ac;jðUÞk

��T3

g�k��T2

g�k�� b

�jH3

�k

Ac;j

ZðT4Þk

ðT3ÞkCpdT

� bpDi

Ac;jðU3�4Þk

��T3

g�k��T4

g�k�þ fpDi

Ac;jðU1�2Þk

��T1

g�k��T2

g�k�

þ f

�jH1

�k

Ac;j

ZðT2Þk

ðT1Þk

CpdT ¼ 0 ð17Þ

The mass and energy balances for the permeation side:

��Fi;4g�k

��Fi;4g�k�1

Dzþ b

�JH3

�k¼ 0 (18)

� Cgp4

�F4T4

g�k��F4T4

g�k�1

Dzþ b

�JH3

�k ZðT4Þk

ðT3ÞkCpdTþ pDiðU3�4Þk

��

T3g�k��

T4g�k� ¼ 0 ð19Þ

The mass and energy balances for the feed synthesis gas

side:

��Fi;1

g�k

��Fi;1g�k�1

Dz� f

�JH1

�k¼ 0 (20)

� Cgp1

�F1T1

g�k��F1T1

g�k�1

Dz� f

�JH1

�k ZðT2Þk

ðT1ÞkCpdTþ pDiðU1�2Þk

��

T2g�k��

T1g�k� ¼ 0 ð21Þ

Finally, the GausseNewton method in MATLAB program-

ming environment is used to solve the obtained set of non-

linear algebraic equations in each section. This procedure

should be repeated for all the nodes in the reactor. The results

of node k are to be used as inlet conditions for the next node

(k þ 1). At the end of this procedure it is possible to plot the

concentration of components and temperature versus length.

6. Results and discussions

6.1. Model validation

The model of methanol synthesis side was validated against

conventional methanol synthesis reactor for a special case of




constant coolant temperature under the design specifications.

The comparison between simulation and plant data for

conventional methanol synthesis reactor is shown in Table 7.

It was observed that the model performed satisfactorily well

under special case of industrial conditions and the observed

plant data were in good agreement with simulation data.

Inthissection,varioussteady-statebehaviorsobserved in the

co-current coupled reactor is analyzed and the predicted mole

fraction, yield, conversion and temperature profiles are pre-

sented. The performance of the thermally coupled reactor is

analyzed,usingdifferentoperatingvariables, formethanolyield,

cyclohexaneconversionandhydrogen recovery yieldas follows:

Hydrogen recovery yield ¼ FH2 ;3

FC6H12 ;in(22)

Methanol yield ¼ FCH3OH;out

F þ F(23)

CO;in CO2 ;in

Methanol selectivity ¼ FCH3OH;out�FCO;in þ FCO2 ;in

�� FCO;out þ FCO2 ;out

�(24)

Cyclohexane conversion ¼ FC6H12 ;in � FC6H12 ;out

FC6H12 ;in(25)

0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03

0.04

0.05

0.06

Dimensionless length

HC

3n

oitc

arfel

om

HO

CRTCMRTCDMR

0 0.2 0.4 0.6 0.8 10.54

0.56

0.58

0.6

0.62

0.64

0.66

0.68

0.7

0.72


H2

noit

carf

elo

m

CRTCMRTCDMR

a

b

Fig. 4 e Comparison of (a) methanol and (b) H2 mole

fraction along the reactor axis between exothermic sides of

TCDMR, TCMR and CR.

Furthermore, an obvious measure for the performance of

the reactor concept is how much heat has to be supplied

through the exothermic reaction tomaintain the endothermic

reaction. The relative heat supply is defined by the fuel ratioJ:

J ¼ Available heat of exothermic reactionMaximum required heat of endothermic reaction

(26)

As efficiency of the reactor we define:

x ¼ Heat actually consumed for endothermic reactionHeat actually released for exothermic reaction

(27)

Optimal conditions imply J/1þ and x/1.

6.2. Molar behavior

Fig. 4(a) and (b) shows the comparison of components mole

fraction in exothermic side of thermally coupled double-

membrane reactor with TCMR and CR. The figures show signif-

icant difference between the outputs of TCDMR and two other

reactors due to hydrogen permeation from feed synthesis gas

side to exothermic side which results in a considerable

enhancement of the reaction yield. Indeed, these figures repre-

sent the effect of using membrane in exothermic side in

enhancing exothermic reaction conversion. The reactor length

0

0.02

0.04

0.06

0.08

0.1

CH

mo

le f

racti

on

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.02

0.04

0.06

0.08

0.1


CH

mo

le f

racti

on

TCMRTCDMR

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

7 x 10


Hm

ole

fra

cti

on

TCMRTCDMR

a

b

Fig. 5 e Comparison of (a) C6H12, C6H6 and (b) H2 mole

fraction along the reactor axis between endothermic sides

of TCMR and TCDMR.



Table 8 e Comparison of reactors performance.

Reactor Conversion (%) Selectivity (%) Yield

Synthesis gas C6H12 CH3OH CH3OH C6H6 H2 Recovery

CR 27.41 e 93.23 0.3635 e e

TCMR 27.21 82.31 93.22 0.3591 0.8231 2.455

TCDMR 31.57 92.29 93.58 0.4273 0.9229 2.8

0 0.2 0.4 0.6 0.8 1500

505

510

515

520

525

530


)k(

erut

are

pm

ete

dis

cimr

eht

ox

E

CRTCMRTCDMR

0 0.2 0.4 0.6 0.8 1498

500

502

504

506

508

510

512

514


)k(

erut

are

pm

ete

dis

cimr

eht

od

nE

TCMRTCDMR

a

b

c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1500

505

510

515


Te

mp

era

ture

(K

)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

515

520

Fe

ed

sy

nth

es

is g

as

sid

e t

em

pe

ratu

re(K

)TCDMRTCMR

Fig. 6 e Variation of temperature for CR and thermally

coupled membrane and double-membrane reactors in (a)

exothermic side, (b) endothermic side, (c) permeation and

feed synthesis gas sides along the reactor axis.


can be divided into two sections. The upper section where the

reaction kinetic controlling and in the other section the equi-

libriumiscontrolling.Thedifferencebetweensimulationresults

pattern of thermally coupled reactors and conventional reactor

is due to delay in thermodynamics equilibrium. The delay in

equilibriumforTCMRandTCDMRisdue to lower temperature in

the endothermic side, provided by the dehydrogenation of

cyclohexane, compared to the saturated water in the conven-

tional reactor. It supposes that methanol production in ther-

mally coupled reactors to be much higher than the CR by

increasing the reactor length where the lower temperature of

coupled reactor can break the equilibrium in the methanol

reaction.

Fig. 5(a) and (b) illustrates themole fraction of components

in the endothermic sides of TCMR and TCDMR. As can be seen,

the highest reaction yield is achieved in TCDMR reactor. Using

hydrogen perm-selective membrane in the endothermic side

enhances hydrogen and shifts the reaction to benzene

production so higher yield of reaction achieves in the ther-

mally coupled reactors. The small difference between TCDMR

and TCMR performances is attributed to the positive effect of

hydrogen permeation into the exothermic side due to utilizing

membrane between exothermic side and feed synthesis gas

side in TCDMR.

One of the greatest advantages of thermally coupled

reactors is production of useful chemicals, simultaneously.

The performance of CR, TCMR and TCDMR in the catalytic

conversion of synthesis gas to methanol and also in the

catalytic dehydrogenation of cyclohexane to benzene in order

to methanol and pure hydrogen production is summarized in

Table 8. The performance of the TCDMR was better than CR

and TCMR, as shown in Table 8.

Generally, using hydrogen permeation membrane in

exothermic side increases thehydrogen recovery, benzeneand

methanol yield, methanol selectivity; and feeding conversion

in both reaction sides. The simulation results represent 14.93

and 15.96% enhancement in themethanol yield and also 13.18

and 13.81% enhancement in the synthesis gas conversion in

comparisonwithCRandTCMR, respectively, as showninTable

8. However, the change in the reactor configuration does not

affect significantly themethanol selectivity. Besides, 12.32 and

10.81% enhancement in the hydrogen recovery yield and

cyclohexane conversion (or benzene yield) in comparisonwith

TCMR are seen, respectively. The purity of hydrogen recovery

in the both thermally coupled reactors is 100% due to using

hydrogen perm-selective PdeAg membrane between perme-

ation and endothermic side.

According to the above Table, this configuration of reactor

suggests that the concept of thermally coupled double-

membrane reactor is an interesting candidate forproductionof




pure hydrogen and methanol. However, from an industrial

point of view there are stillmany issues to be addressed before

putting a case for successful commercialization, such as:

difficulties to construct a leak-freemembrane reactorwith two

sides, the catalysts would not age identically, the cost of

membranes and It would require a situation where the quan-

tities of thematerials to be processed by the two reactions be in

the proper balance.

6.3. Thermal behavior

Fig. 6(a)e(c) shows axial temperature profiles for CR and

thermally coupled membrane and double-membrane reactor

in different sides of reactor configurations. The highest

temperature is observed at the exothermic side, since this is

where heat is generated. Part of this heat is used to drive the

endothermic reaction and the rest is used to heat themixtures

in both reaction sides (in case of both thermally coupled

reactors) and feed synthesis gas side (in case of TCDMR). The

0 0.2 0.4 0.6 0.8 1-1

0

1

2

3

4

5


ml

om(

etar

noit

ca

eR

3-s

1-)

TCMR TCDMR

Water-gas shift

Hydrogenation of CO

Hydrogenation of CO2

0 0.2 0.4 0.6 0.8 1 0.7

0.8

0.9

1

1.1

1.2

1.3

1.4


Cf

oet

arn

oitc

ae

R6H

21

ml

om(

noit

an

eg

ord

yh

ed

3-s

1-)

TCMR TCDMR

a

b

Fig. 7 e Variation of (a) rate of reaction for exothermic and

(b) endothermic sides for thermally coupled membrane

and double-membrane reactors along the reactor axis.

temperature of the endothermic side is always lower than that

of the exothermic side in order tomake a driving force for heat

transfer from the solid wall. Along the exothermic side of

thermally coupled reactors, temperature increases smoothly

and a hot spot develop as demonstrated in Fig. 6(a) and then

decreases. The exothermic temperature control of the TCDMR

is easier due to lower hot spot. There is not a suddenly rises of

temperature for this system at reactor entrance. Thus, the

most favourable exothermic temperature profile seems that

belongs to TCDMR system as a result of simultaneously heat

transfer with recycle gas in inner tube and reacting gas in

endothermic side. At the entrance of endothermic side of

TCRs, the temperature decreases rapidly and a cold spot form

and then the temperature increases (see Fig. 6(b)). Hydrogen

permeation into the exothermic side shifts the reaction to

methanol production and higher yield of reaction achieves

and thus more reaction heat is released. This is the reason

why endothermic temperature of TCDMR is higher than that

of TCMR. As it can be seen in Fig. 6(c), the temperature profile

0 0.2 0.4 0.6 0.8 10.5

1

1.5

2

2.5

3

3.5


)w(

xulf

ta

eH

Generated heat in exothermic side of TCMR

Generated heat in exothermic side of TCDMR

Consumed heat in endothermic side of TCMR

Consumed heat in endothermic side TCDMR

0 0.2 0.4 0.6 0.8 1 -1

-0.5

0

0.5

1

1.5

2

2.5

3


)w(

xulf

ta

eH

Transferred heat from solid wall in TCMR

Transferred heat from solid wall in TCDMR

Transferred heat from outer membrane in TCMR

Transferred heat from outer membrane in TCDMR

Transferred heat from inner membrane in TCDMR

a

b

Fig. 8 e Variation of (a) generated and consumed heat flux

and (b) transferred heat from solid wall andmembranes for

thermally coupled membrane and double-membrane

reactors along the reactor axis.




pattern in permeation and feed synthesis gas side is the same

as temperature profile pattern in endothermic side.

Fig. 7 (a)e(b) shows the variation of reaction rate in TCRs for

exothermic and endothermic sides, respectively. Near the

reactor entrance, the cyclohexane dehydrogenation is fast.

Comparing the values for the reaction rates present in the

exothermic side, it can be seen that the predominant reaction

is hydrogenation of CO; however neither wateregas shift nor

hydrogenation of CO2 can be neglected, their contribution

beingsignificant. Fig. 8 illustrates thevariationof thegenerated

and consumed heat flux from the exothermic and the endo-

thermic reaction in thermally coupled reactors, respectively,

and transferredheat from the solidwall andmembranes along

the reactors axis. In the first half of the reactor, methanol

reaction proceeds faster than dehydrogenation and as a result

more heat is produced by the exothermic reaction than heat

consumed by the endothermic one. The excess heat raises the

temperature of the system in the first half of the reactor as

illustrated by the temperature profile in Fig. 6(a). In this region,

the generated heat flux is higher than the consumed one. The

system heats up and a peak in the generated heat flux is

observed. Afterward, the generated heat flux decreases

rapidly, mainly due to fuel depletion. The opposite situation

occurs when the consumed heat flux is higher than the

generated one. If the consumed heat flux is higher than the

generated one, the system starts to cool down resulting to low

temperature, which in turn decreases both reaction rates.

Thus, after a certain position along the reactor the generated

heat flux becomes lower than the consumed one, which coin-

cides with a hot spot development (see Fig. 6).

A decrease in the reaction heat flux consumed is observed

near the thermally coupled reactors entrance, and is associ-

ated to the relatively low reaction rate in the endothermic

process in that region as shown in Fig. 7(a), which coincides

with a cold spot development at the certain position (see Fig. 6

(b)). This cold spot in TCDMR is upper than TCMRwhich is due

to less decreased reaction rate and transferredmore heat from

exothermic side and consequently the system becomes lower

cooled down. At the entrance of separation and feed synthesis

sides (Fig. 6(c)), the temperature decreases which is due to

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Fuel ratio Reactor efficiency

eul

aV

TCMR TCDMR

Optimal condition

Fig. 9 e The comparison of values of fuel ratio and reactor

efficiency for the thermally coupled membrane and

double-membrane reactors.

transferred heat from separation and feed synthesis sides to

endothermic and exothermic sides, respectively. After this

position, transferred heat direction is reversed and results in

temperature increases (see Fig. 6(c)). Along the reactor length,

the heat values consumed by the endothermic side and

transferred from the solid wall are close to each other. This

demonstrates the efficient thermal communication between

the exothermic and endothermic sides, and which is due to

high solid wall thermal conductivity and the relatively small

shell diameter of endothermic side. At the reactor entrance,

the transferred heat from the solid wall is lower than the

consumed heat by the endothermic side, which is due to low

temperature difference. A maximum in the reaction heat

fluxes consumed and transferred from the solidwall is located

at the same axial position, namely 0.5. After this position

along the reactor, the consumed heat by the endothermic side

becomes larger than the transferred heat from the solid wall

and the system starts to cool down (see Fig. 6(c)).

Fig. 9 shows the comparison of fuel ratio and reactor effi-

ciency for both of thermally couple reactors. As it can be seen

in this figure, fuel ratio and reactor efficiency values of TCDMR

are closer to the optimal conditions relative to those of TCMR.

Fig. 10 e Influence of inlet temperature of endothermic

stream on the temperature profiles in (a) endothermic and

(b) exothermic sides along the reactor length for thermally

coupled double-membrane reactors.



Fig. 11 e Influence of molar flow rate of endothermic stream on (a) axial temperature profile in exothermic side, (b) in

endothermic side, (c) methanol yield and (d) hydrogen recovery yield along the reactor length for thermally coupled double-

membrane reactor.


Therefore, the exothermic and the endothermic reaction can

be more efficiently coupled in this configuration and an effi-

cient auto-thermal coupling is achieved without the occur-

rence of extremely high temperatures.

Overall, the operating and design parameters chosen for

the reactor configuration lead to efficient coupling of the two

reactions. The efficient coupling of exothermic and endo-

thermic reaction in a single vessel reduces the thermal losses

associated with the supply of heat for the energy-intensive

endothermic process.

6.4. Influence of inlet temperature of endothermicstream

As it can be seen in Fig. 6(b), there is a cold spot in the

endothermic side. This may be attributed to the reasons

such as dissimilar reaction rates and heats of exothermic

and endothermic reactions. One way of eliminating this cold

spot is by using non-similar feed temperature for the

exothermic and endothermic streams. Fig. 10(a)e(b) shows

the influence of inlet temperature of endothermic stream on

the temperature profiles in endothermic and exothermic

sides along the reactor length for thermally coupled double-

membrane reactor, respectively. These are the cases where

the cold spot is not observed which are due to suitable

temperature driving force for transferred heat from the solid

wall. Here the inlet temperature of the endothermic stream

(T < 500 K) is lower than the exothermic stream. This

arrangement requires the pre-heating of the exothermic

stream and that can be carried out by utilizing the sensible

heat of the exothermic stream leaving the reactor. On the

other hand, low inlet temperatures of endothermic stream

help the exothermic side temperature to find lower peaks, as

can be seen in Fig. 10(b).

Decreasing the inlet temperature of endothermic stream

from 503 to 490 K, can decrease the methanol yield from

0.4279 to 0.4249, hydrogen recovery yield from 2.9719 to 2.8928

and cyclohexane conversion from 92.77% to 90.21%, which is

due to lower temperature at first parts of reactor and then

lower kinetics constants of reactions.




6.5. Influence of molar flow rate of endothermic stream

When reactor geometry, inlet operating conditions and cata-

lyst loading are fixed, variations of flow rates result in corre-

sponding variations of fluid velocities and residence times.

Fig. 11(a)e(b) shows the influence of molar flow rate of endo-

thermic stream on the temperature profiles of exothermic and

endothermic sides along the reactor length, respectively.With

increasing the flow rate of endothermic stream, axial

temperature variation of exothermic and endothermic sides

becomes lower which is due to higher transferred heat from

the solid wall. Fig. 11(c)e(d) illustrates how themethanol yield

and hydrogen recovery yield behave along the reactor axis

when the flow rate of endothermic stream increases from

0.093 to 0.2 mol s�1. Decreasing of methanol yield is due to

lower axial temperature profile (see Fig. 11(a)) and conse-

quently lower rate of reaction. As it can be seen in Fig. 11(d),

increasing of molar flow rate of endothermic stream results in

hydrogen recovery yield reduction from 2.99 to 1.25 which is

due to lower cyclohexane conversion. Cyclohexane conver-

sion significantly decreases from 99.22% to 45.48%. Decreasing

of cyclohexane conversion is an obvious consequence of the

fact that the amount of catalyst on endothermic side is not

enough for these higher flow rates. Besides, lower axial

temperature profile of endothermic side (see Fig. 11(b)) can be

result in cyclohexane conversion which is an endothermic

reversible reaction.

7. Conclusion

Coupling the methanol synthesis with the dehydrogenation of

cyclohexane to benzene in a simulated auto-thermal fixed-bed

double-membrane reactor in co-currentmodeof operationwas

studied by a one-dimensional model. This recuperative

configuration, in addition to possessing advantages of a TCMR

(production of methanol, benzene and pure hydrogen; estab-

lishment of auto-thermal conditions in both reaction sides,

reduction reactors sizes; shifting thermodynamics equilib-

rium), represents a more favorable profile of temperature and

increase productivity compare with other reactors. The simu-

lationresults showthat there is favorableprofileof temperature

in exothermic side and represent 17.61 and 18.81% enhance-

ment in the methanol productivity in comparison with CMSR

andTCMR, respectively.Also, 15.76and10.81%enhancement in

thehydrogen andbenzeneproduction rate relative toTCMRare

seen, respectively. The effect of inlet temperature and molar

flow rate of endothermic stream on the axial temperature

profile of exothermic side, methanol yield, cyclohexane

conversionandhydrogenrecoveryyield are shown.Higherflow

rate of endothermic stream results in lowermethanol yield due

to lower temperature profile in exothermic side and also lower

cyclohexane conversion and hydrogen recovery yield due to

this fact that the amount of catalyst on endothermic side is not

enough for these higher flow rates. The results indicate that

methanol synthesis reaction and cyclohexane dehydrogena-

tion ina thermally coupledmembranereactorare feasible if key

operating parameters are properly designed. The results

suggest that utilizing of thermally coupled double-membrane

reactor for pure hydrogen and methanol production could be

feasible and beneficial. However, the performance of reactor

needs to be proven experimentally and tested a range of

parameters under practical operating conditions.

Nomenclature

av specific surface area of catalyst pellet, m2 m�3

Ac cross section area of each tube, m2

Ai inside area of inner tube, m2

Ao outside area of inner tube, m2

C total concentration, mol m�3

Cp specific heat of the gas at constant pressure, J mol�1

dp particle diameter, m

Di tube inside diameter, m

Dij binarydiffusion coefficient of component i in j,m2 s�1

Dim diffusion coefficient of component i in the mixture,

m2 s�1

Do tube outside diameter, m

Dsh shell inside diameter, m

fi partial fugacity of component i, bar

F total molar flow rate, mol s�1

G mass velocity, kg m�2 s�1

hf gas-solid heat transfer coefficient, W m�2 K�1

hi heat transfer coefficient between fluid phase and

reactor wall in exothermic side, W m�2 K�1

ho heat transfer coefficient between fluid phase and

reactor wall in endothermic side, W m�2 K�1

DHf,i enthalpy of formation of component i, J mol�1

jH permeation rate of hydrogen through the PdeAg

membrane, mol/s

K rate constant of dehydrogenation reaction,

mol m�3 Pa�1 s�1

k1 rate constant for the 1st rate equation of methanol

synthesis reaction, mol kg�1 s�1 bar�1/2

k2 rate constant for the 2nd rate equation of methanol


k3 rate constant for the 3rd rate equation of methanol


kg mass transfer coefficient for component i, m s�1

K conductivity of fluid phase, W m�1 K�1

KB adsorption equilibrium constant for benzene, Pa�1

Ki adsorption equilibrium constant for component i in

methanol synthesis reaction, bar�1

Kp equilibrium constant for dehydrogenation reaction,

Pa3

Kpi equilibrium constant based on partial pressure for

component i in methanol synthesis reaction

Kw thermal conductivity of reactor wall, W m�1 K�1

L reactor length, m

Mi molecular weight of component i, g mol�1

N number of components (N¼ 6 formethanol synthesis

reaction, N ¼ 3 for dehydrogenation reaction)

P total pressure, for exothermic side, bar; for

endothermic side, Pa

Pi partial pressure of component i, Pa

r1 rate of reaction for hydrogenation of CO,

mol kg�1 s�1




r2 rate of reaction for hydrogenation of CO2,

mol kg�1 s�1

r3 rate of reversed wateregas shift reaction,

mol kg�1 s�1

r4 rate of reaction for dehydrogenation of cyclohexane,

mol m�3 s�1

ri reaction rate of component i, for exothermic

reaction, mol kg�1 s�1; for endothermic reaction,

mol m�3 s�1

R universal gas constant, J mol�1 K�1

Rp particle radius, m

Re Reynolds number

Sci Schmidt number of component i

T temperature, K

u superficial velocity of fluid phase, m s�1

ug linear velocity of fluid phase, m s�1

U overall heat transfer coefficient between exothermic

and endothermic sides, W m�2 K�1

vci critical volume of component i, cm3 mol�1

yi mole fraction of component i, mol mol�1

z axial reactor coordinate, m

Greek letters

m viscosity of fluid phase, kg m�1 s�1

r density of fluid phase, kg m�3

rb density of catalytic bed, kg m�3

s tortuosity of catalyst

Superscripts

g in bulk gas phase

s at surface catalyst

Subscripts

0 inlet conditions

B benzene

C cyclohexane

i chemical species

j reactor side

k reaction number index

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