production of ultrapure hydrogen via utilizing fluidization concept from coupling of methanol and...

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Production of ultrapure hydrogen via utilizing fluidizationconcept from coupling of methanol and benzene synthesis ina hydrogen-permselective membrane reactor

M.R. Rahimpour a,b,*, M. Bayat a

aDepartment of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, IranbGas Center of Excellence, Shiraz University, Shiraz 71345, Iran

a r t i c l e i n f o

Article history:

Received 6 December 2010

Received in revised form

13 February 2011

Accepted 17 February 2011

Available online 25 March 2011

Keywords:

Hydrogen production

Fluidized-bed reactor

Coupling reactor

Methanol synthesis

Pd/Ag membrane

* Corresponding author. Department of Chem71345, Iran. Tel.:þ98 711 2303071; fax: þ98 7

E-mail address: [email protected] (0360-3199/$ e see front matter Copyright ªdoi:10.1016/j.ijhydene.2011.02.095

a b s t r a c t

In this work, a novel fluidized-bed thermally coupled membrane reactor has been proposed

for simultaneous hydrogen, methanol and benzene production. Methanol synthesis is

carried out in exothermic side which is a fluidized-bed reactor and supplies the necessary

heat for the endothermic side. Dehydrogenation of cyclohexane is carried out in endo-

thermic side with hydrogen-permselective Pd/Ag membrane wall. Selective permeation of

hydrogen through the membrane in endothermic side is achieved by co-current flow of

sweep gas through the permeation side. A steady-state fixed-bed heterogeneous model for

dehydrogenation reactor and two-phase theory in bubbling regime of fluidization for

methanol synthesis reactor is used to model and simulate the integrated proposed system.

This reactor configuration solves some observed drawbacks of new thermally coupled

membrane reactor such as internal mass transfer limitations, pressure drop, radial

gradient of concentration and temperature in both sides. The proposed model has been

used to compare the performance of a fluidized-bed thermally coupled membrane reactor

(FTCMR) with thermally coupled membrane reactor (TCMR) and conventional methanol

reactor (CR) at identical process conditions. This comparison demonstrates that fluidizing

the catalytic bed in the exothermic side of reactor caused a favorable temperature profile

along the FTCMR. Furthermore, the simulation results represent 5.6% enhancement in the

yield of hydrogen recovery in comparison with TCMR.

Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

reserved.

1. Introduction

According to the problems induced by the shortage of fossil

energy and global warming, hydrogen is expected to be

a promising energy vector for the near future [1]. Hydrogenhas

been nominated as a renewable and alternative energy [2e4].

ical Engineering, School11 6287294.M.R. Rahimpour).2011, Hydrogen Energy P

1.1. Hydrogen

Hydrogen is the lightest chemical element and offers the best

energy-to-weight ratio of any fuel. Hydrogen is colorless,

odorless and its only by-product is water. Use of hydrogen in

combustion engine offers cost effective solution to reduce

of Chemical and Petroleum Engineering, Shiraz University, Shiraz

ublications, LLC. Published by Elsevier Ltd. All rights reserved.

mailto:[email protected]

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http://dx.doi.org/10.1016/j.ijhydene.2011.02.095



i n t e r n 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 ) 6 6 1 6e6 6 2 7 6617

greenhouse gas emissions, improve air quality, diversify

energy supply and reduce noise. In the short term, hydrogen

couldbeused inurbanvehicles,whichwould reduceemissions

in city centers. In the long term, it could be used in combined

heat/power generation, in industry, in residential applications

and in every form of transport like ships, trains and airplanes

[5]. However, most hydrogen currently produced is derived

from fossil fuels, for example from refining processes such as

catalytic reformingand steamreforming. Thus, theproduction

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 from the use of hydrogen as an energy source.

Dehydrogenation is an attractive choice and alternative for

hydrogen production due to it has essentially zero CO2 impact,

giving a positive environmental contribution and also solves

the troubles and problems in hydrogen storage conditions and

medium preparation, such as organic chemical and metal

hydrides [6].

1.2. Methanol synthesis

Methanol is an important multipurpose base chemical;

a simple molecule which can be recovered from many

resources, predominantly natural gas. It is produced from

synthesis gas on a large scale worldwide [6]. Rezaie et al.

compared the results of heterogeneous and homogeneous

models in a dynamic simulation for fixed-bed methanol

synthesis and reported similar predictions [7]. Many efforts

have been carried out to improve the yield and performance of

methanol reactors. In this way recently a dual-type reactor

system instead of a single-type reactor was developed by

Rahimpour et al. [8e10]. Rahimpour and Bayat [11] enhanced

themethanol yield by inserting themembrane concepts in the

conventional dual-type methanol reactors. The dual-type

methanol reactor is an advanced technology for converting

natural gas to methanol at low cost and in large quantities.

This system is mainly based on the two-stage reactor system

consisting of a water-cooled and a gas-cooled reactor. The

synthesis gas is fed to the tubes of the gas-cooled reactor

(second reactor). This cold feed synthesis gas is routed

through tubes of the second reactor in a counter-current flow

with reacting gas and heated by heat of reaction produced in

the shell. So, the reacting gas temperature is continuously

reduced over the reaction path in the second reactor. The

outlet synthesis gas from the second reactor is fed to tubes of

the first reactor (water-cooled) and the chemical reaction is

initiated by catalyst. The heat of reaction is transferred to the

cooling water inside the shell of reactor. In this stage, the

synthesis gas is partly converted to methanol in a water-

cooled single-type reactor. The methanol-containing gas

leaving the first reactor is directed into the shell of the second

reactor. Finally, the product is removed from the downstream

of the second reactor [11].

1.3. Fluidized-bed methanol reactor

Generally, the potential drawbacks of industrial packed-bed

methanol reactors are pressure drop across the reactor, poor

heat transfer rate, low production capacity, low catalyst

particle effectiveness factors because of severe diffusional

limitations with the catalyst particle sizes used [12]. Smaller

particle sizes are infeasible in fixed-bed systems because of

pressure drop considerations. In order to avoid pressure drop,

the effective diameter of catalyst particles in fixed-bed reactor

is usually over 3 mm, which brings a certain inner mass

transfer resistance. Considerable attention has been paid to

the fluidized-bed reactors because of their main advantages

such as enhancement of conversion, a small pressure drop,

elimination of diffusion limitations, good heat transfer capa-

bility and a more compact design [13]. Fluidized-bed reactor

concept instead of a packed-bed system for methanol

synthesis was proposed by Wagialla et al. to solve some

observed drawbacks of industrial fixed-bed reactors [14].

Although fluidized-bed reactor has above advantages, there

are some disadvantages such as: difficulties in reactor

construction, erosion of reactor internals and catalyst attri-

tion [15].

1.4. PdeAg membrane reactor

A membrane reactor combines the chemical reaction and

membrane in one system. The general advantages of

membrane reactors as compared to sequential reaction-

separation systems are (1) increased reaction rates, (2)

reduced by-product formation, (3) lower energy requirements,

and (4) the possibility of heat integration. These advantages

potentially lead to compact process equipment that can be

operated with a high degree of flexibility. Because of the

reduced by-product formation and the more efficient use of

energy, the development of membrane reactors clearly fits

into the scope of developing sustainable processes for the

future [16].

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.

1.5. Literature review

There are a few investigations on simultaneous pure hydrogen

production andmethanol synthesis in autothermalmembrane

reactors. Recently, Rahimpour et al. have investigated theo-

retically themethanol and hydrogen production in a thermally

coupled membrane single-type reactor in co-current mode of

operation [6]. In their simulated reactor, the first side is an

exothermic side, wheremethanol synthesis takes place on the

CuO/ZnO/Al2O3 catalyst. The second side is an endothermic




side, where dehydrogenation of cyclohexane to benzene takes

place on the Pt/Al2O3 catalyst. The sweep gas flows through the

third side (permeation side) which selectively removes the

hydrogen by permeation through the Pd/Agmembrane. Heat is

transferred continuously from the exothermic reaction side to

the endothermic reaction side. Fig. 1 shows a schematic

diagram for the co-current mode of a membrane heat-

exchanger reactor configuration with three sides.

Moreover, methanol synthesis and cyclohexane dehydro-

genation in a thermally coupled reactor using differential

evolution (DE)method has been optimized by Rahimpour et al.

[21].

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

mation available in the literature regarding the use of fluid-

ization concept in thermally coupled membrane reactor for

methanol synthesis and production of pure hydrogen, simul-

taneously. Therefore, it was decided to first study on this

system.

1.6. Objectives

In the present work, production of ultrapure hydrogen and

methanol synthesis is investigated theoretically in a fluidized-

bed thermally coupled membrane multitubular reactor. The

endothermic and exothermic reactions are chosen the catalytic

dehydrogenation of cyclohexane to benzene and methanol

synthesis, respectively.Themotivation is tocombine theenergy

efficient concept of the coupling of endothermiceexothermic

reactions, the membrane-assisted selective separation of

L= 7 m

CH3 OHCO2

COH2OH2

N2

CH4

C6 H12

Ar

C6H12

C6H6

H2

Ar

Sweep gas

Sweep gas+H2

Pd-Ag membrane layer

CH3OHCO2COH2OH2N2

CH4

Perm

eation s ide

Hydrogen permeation

Heat transfer

Exotherm

ic side

Endotherm

ic side

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

a thermally coupled membrane reactor (TCMR)

configuration.

hydrogen and using fluidized-bed concept in a single reactor.

Moreover, we aim to demonstrate the advantages of the fluid-

ized-bed and the viability of this new concept relative to

conventional reactor system using simulation. Numerical

simulation results of the FTCMR were compared with that of

TCMR and CR at same process conditions such as pressure,

temperature, catalyst mass and feed composition.

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. [7].

2.1. Thermally Coupled Membrane Reactor (TCMR)

The process of a thermally coupled membrane reactor in

co-current configuration was studied by Rahimpour et al. [6].

This system is a three concentric tubes reactor where the

inner tube is used for methanol synthesis and the second one

is used for dehydrogenation of cyclohexane instead of coolant

water in the shell of conventional methanol synthesis reactor.

The wall between second and third tubes is a hydrogen-

permselective membrane, so that the third tube receives

hydrogen permeating from the second one. The characteris-

tics 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

[7,22].

2.2. Fluidized-bed Thermally Coupled Membrane Reactor(FTCMR)

The integrated fluidized-bed membrane reactor simulated for

simultaneous methanol and hydrogen production is shown

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

Exothermic side

Parameter Value

Feed composition (mole fraction)

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



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

Endothermic side

Parameter Value

Feed compositiona (mole fraction)

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. [23].

b Obtained from Markatos et al. [24].


schematically in Fig. 2 [23,24]. Basically, the process in FTCMR

is similar to TCMR with exception of some changes. These

changes in the new proposed system are as follows:

Firstly, the fixed catalyst bed of the inner tube side has

been fluidized by applying small catalyst size. Secondly, in

order to fluidize the catalyst bed, the feed synthesis gas is

entered to the bottom of the exothermic side. Consequently,

the feed gas and argon as sweep gas are entered to the bottom

of endothermic and permeation side, respectively. On the

other word, it consists of three concentric tubes. The inner

tube is carried out methanol synthesis on the CuO/ZnO/Al2O3

catalyst which is a fluidized-bed reactor and supplies the

necessary heat for the endothermic side. Catalytic dehydro-

genation of cyclohexane to benzene is assumed to take place

in the second tube. Furthermore, the wall of the endothermic

side is covered with a PdeAg membrane layer. Thus, pure

hydrogen can penetrate from the endothermic side into the

permeation side (outer tube). 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 themethanol synthesis, three overall reactions are possible:

hydrogenation of carbon monoxide, hydrogenation of carbon

dioxide and reverse wateregas shift reaction, which are as

follows:

COþ 2H24CH3OH; DH298 ¼ �90:55 kJ=mol (1)

CO2 þ 3H24CH3OHþH2O; DH298 ¼ �49:43 kJ=mol (2)

CO2 þH24COþH2O; DH298 ¼ þ41:12 kJ=mol (3)

Reactions (1)e(3) are not independent so that one is a linear

combination of the other ones. In the current work, the rate

expressions have been selected from Graaf et al. [25]. The rate

equations combined with the equilibrium rate constants [26]

provides enough information about kinetics of methanol

synthesis over commercial CuO/ZnO/Al2O3 catalysts.

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 (4)

The following reaction rate equation of cyclohexane, rc, is

used [27]:

rc ¼�k

�KPPC=P3

H2� PB

�

1þ�KBKPPC=P3

H2

� (5)

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 3.

Pi is the partial pressure of component i in Pa. The reaction

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

sure in the reactor is maintained at 101.3 KPa. The catalyst is

Pt/Al2O3 [28].

4. Mathematical model

4.1. Thermally Coupled Membrane Reactor (TCMR)model

The following assumptions are considered during the

modeling 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 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

energy balances and boundary conditions for solid and fluid

phases for three sides of reactor are summarized in Table 4. In

Eqs. (6) and (7), h is effectiveness factor of kth reaction in jth

side (the ratio of the reaction rate observed to the real rate of



To Distillation Unit

Pure Methanol

Synthesis Gas

Cyclohexane

Seperator

Hydrogen

Benzene

Sweep gas

Sweep gas+H2

Fluidized -bed reactor (Exothermic side)

Fixed-bed reactor (Endothermic side )

Pd/Ag membranelayer

Fig. 2 e Schematic diagram of the co-current mode for a fluidized bed thermally coupled membrane reactor (FTCMR)

configuration.


reaction), which is obtained from a dusty gas model calcula-

tions [6]. The detail of such a dusty gas model is available in

literature [6]. In Eqs. (8) and (9), b is equal to 1 for the endo-

thermic and 0 for the exothermic side. Besides, in Eq. (9), the

positive sign is used for the exothermic side and the negative

sign for the endothermic side. In Eqs. (10) and (11), b is equal to

1 for hydrogen component and 0 for the sweep gas. In the

boundary condition equations ygi0;j, Tg0 and Pg0 are the fluid

phase mole fraction of ith component, temperature and

pressure at the entrance of jth side of reactor, respectively.

4.2. Fluidized-bed Thermally Coupled Membrane Reactor(FTCMR) model

The mathematical simulation for exothermic side of FTCMR

was developed based on the following assumptions:

Model assumptions:

(a) The dense catalyst bed is considered to be composed of

bubble phase and emulsion phase. (b) The operation is

assumed to be isothermal which means bubble and emulsion

phases have same temperature. (c) plug flow regime in bubble

Table 3 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

phase is assumed; (d) The bubble rise velocity is constant and

equal to average value. (e) Ideal gas behavior is assumed. (f)

Bubbles are assumed to be spherical with constant size and

equal to average value. (g) The gas in the bubble phase is in

plug flow and contains some catalyst particles, which involve

in reactions but the extent of reaction in bubble phase ismuch

less than emulsion phase.

Model structure:

An element of length dz as depicted in Fig. 3 was consid-

ered. On the basis of the aforementioned assumptions, the

bubble and emulsion phase mass conservation equations are

formulated as follows:

Bubble phase:

d

Ac

vFbi

vzþ dKbeictab

�yie � yib

�þ d� g� rs � aX3

j¼1

rbij

¼ 0; i ¼ 1;2;.;N ð13Þwhere Kbei is mass transfer coefficient between bubble phase

and emulsion phase, yie and yib are the emulsion phase and

bubble phase mole fraction, respectively and g is volume frac-

tion of catalyst bed occupied by solid particles in bubble phase.

Emulsion phase:

�ð1� dÞAc

vFei

vzþ dKbeictab

�yib � yie

�þ ð1� dÞre � h� a�X3

j¼1

rij ¼ 0

(14)

where, Fib and Fi

e are given as follows:

Fbi ¼ yibF

t; Fei ¼ yieF

t (15)



Table 4 e Mass and energy balances and boundary conditions for solid and fluid phases in different sides of TCMR.

Mass and energy balances equation Number

Solid phase (exothermic and

endothermic side) avcjkgi;j

�ygi;j � ys

i;j

�þ hri;jrb ¼ 0 (6)

avhf

�Tgj � Ts

j

�þ rb

XNi�1

hri;j��DHf;i

� ¼ 0 (7)

Fluid phase (exothermic and

endothermic side)� Fj

Ac;j

dygi;j

dzþ avcjkgi;j

�ysi;j � yg

i;j

�� b

JH2

Ac;j¼ 0 (8)

� Fj

Ac;jCgpj

dTgj

dzþ avhf

�Tsj � Tg

j

�� pDi

Ac;jU�Tg2 � Tg

1

� � bjH2

Ac;j

ZT3

T2

Cp dT

�bpDi

Ac;jU2�3

�Tg2 � Tg

3

� ¼ 0

(9)

Permeation side

�F3

dygi;3

dzþ bJH2

¼ 0 (10)

�F3Cgp3

dTg3

dzþ bJH2

ZT3

T2

Cp dTþ pDiU2�3

�Tg2 � Tg

3

� ¼ 0 (11)

Boundary conditions z ¼ 0; ygi;j ¼ yg

i0;j; Tj ¼ Tgj0; Pg

j ¼ Pgj0; j ¼ 1;2; 3 (12)


The heat transfer equation between bed (tubes) and shell

side (cooling water):

� Fj

Ac;jCgpj

dTdz

þ ð1� dÞre$h$a$X3

j¼1

rj��DHf ;j

�

þ d$g$rB$h$a$X3

j¼1

rbj��DHf ;j

� þ pDi

Ac;jU�Tg2 � Tg

1

� ¼ 0

(16)

The mass and energy equations for the endothermic side and

the permeation side are the same as thermally coupled

membrane reactor (TCMR).

Fig. 3 e Schematic diagram of an elemental volume of

reactor.

4.3. Hydrogen permeation in Pd/Ag membrane

Thecompositemembranes in this studyaremadeof a 6 mmthin

layer of palladiumesilver alloy. The membrane is deposited as

a continuous layer on the outer surface of a thermo stable

support.Thefluxofhydrogenpermeating throughthe innerand

outer Pd/Ag membrane is assumed to follow the halfepower

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

JH2¼ 2pLP0

lnðDo=DiÞ exp��Ep

RT

�� ffiffiffiffiffiffiffiffiffiffiPH2 ;2

p � ffiffiffiffiffiffiffiffiffiffiPH2 ;3

p �(17)

PH2is hydrogen partial pressure in Pa. Do and Di 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 molm�2 s�1 Pa�0:5 and the activation energy Ep is

15.7 kJmol�1 [9].

Auxiliary correlations for estimation of mass and heat

transfer coefficients and the empirical correlations for the

hydrodynamic parameters in the proposed model have been

summarized in Table 5.

5. Solution of model

The formulated model composed of 23 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,



Table 5 e Physical properties, mass and heat transfer correlations and the empirical correlations for the hydrodynamicparameters in the proposed model.

Parameter Equation Reference

Fixed-bed reactor

Component heat capacity Cp ¼ aþ bTþ cT2 þ dT�2

Mixture heat capacity Based on local compositions

Viscosity of reaction mixtures Based on local compositions

Mixture thermal conductivity Lindsay and Bromley [29]

Mass transfer coefficient between

gas and solid phases

kgi ¼ 1:17Re�0:42Sc�0:67i ug � 103 Cussler [30]

Re ¼ 2Rpug

m

Sci ¼m

rDim � 10�4

Dim ¼ 1� yiPi¼jðyi=DijÞ

[31]

Dij ¼1:43� 10�7T3=2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1=Mi þ 1=Mj

qffiffiffi2

pPðv1=3ci þ v1=3cj Þ2

Reid et al [32]

Overall heat transfer coefficient 1U¼ 1

hiþ AilnðDo=DiÞ

2pLKwþ Ai

Ao

1ho

Heat transfer coefficient between gas

phase and reactor wall

hCprm

ðCpm

KÞ2=3 ¼ 0:458

eBðrudp

mÞ�0:407 [33]

Fluidized-bed reactor

Superficial velocity at minimum fluidization 1:75

e3mf4s

½dprgumf

m�2 þ 150ð1� emf Þ

e3mf4s

½dprgumf

m� ¼ Ar

Kunii and Levenspiel [34]

Archimedes number Ar ¼ d3prgðrp � rgÞgm2

Kunii and Levenspiel [34]

Bubble diameter db;avg ¼ dbm � ðdbm � dboÞexpð�0:3z=DÞdbm ¼ 0:65

hp4D2ðuo � umfÞ

i0:4

dbo ¼ 0:376ðuo � umf Þ2

Mori and Wen [35]

Mass transfer coefficient (bubble-emulsion phase) Kbe ¼ umf

3þ ½ð4Djmemfub=pdbÞ�1=2 Sit and Grace [36]

Bubble rising velocity ub;avg ¼ u� umf þ 0:711ffiffiffiffiffiffiffiffigdb

pKunii and Levenspiel [34]

Volume fraction of bubble phase to overall bed d ¼ ðu� umfÞ=ub Kunii and Levenspiel [34]

Specific surface area for bubble ab ¼ 6d=db

Density for emulsion phase re ¼ rPð1� emfÞ


the ideal gas assumption, as well as aforementioned correla-

tions for the heat andmass transfer coefficients, fluidized-bed

hydrodynamic and the physical properties of fluids. In order

to solve the set of reactor model equations (the set of non-

linear differential-algebraic equations) at the steady-state

condition, backward finite difference approximation was

applied to the system of ordinary differential-algebraic equa-

tions. The reactor length is then divided into 100 separate

sections and the GausseNewton method in MATLAB

programming environment is used to solve the non-linear

algebraic equations in each section.

6. Results and discussions

6.1. Model validation

As stated before, Wagialla et al. [14] mathematically studied

a fluidized-bed configuration for methanol synthesis and

presented a steady-state model based on two-phase theory of

fluidization. The results ofWagialla’smodel [14] are compared

with the consequences of our suggested steady-statemodel to

check the fluidized-bed reactor (FBR) simulation in Table 6. It

was observed that, our numerical predictions are in good

qualitative agreement with the Wagialla’s model.

In this section, various steady-state behaviors observed in

the co-current coupled reactor is analyzed and the predicted

mole fractions, recovery yield of hydrogen and temperature

profiles are presented. One definition is introduced to examine

the hydrogen recovery yield through the reactor length:

Hydrogen recovery yield ¼ FH2 ;3

FC6H12 ;in(18)

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

methanol and hydrogen in exothermic side of fluidized-bed

thermally coupled membrane reactor with thermally coupled

membrane reactor and conventional reactor. Coupled reactor

consists of a shell compartment surrounding a tube



Table 6 e Comparison between simulation andWagialla’s model.

Parameter Wagialla’s model FBR model Error (%)

Composition (%)

CO 1.881 1.79 �4.84

H2 73.512 75.38 2.54

CH3OH 4.744 4.92 3.71

CO2 2.838 3.12 9.93

H2O 1.809 1.68 �7.131

N2 2.356 2.31 �1.95

CH4 12.86 11.21 �12.8


compartment. Catalytic dehydrogenation of cyclohexane to

benzene is assumed to take place in the shell, whereas

methanol synthesis occurs inside the tube. Fig. 4(a) illustrates

the mole fraction profile of methanol along the reactor, at

steady-state for exothermic side of FTCMR, TCMR and CR. As

shown, it is observed that there is not a difference between the

behavior of variables in output of the fluidized-bed thermally

coupled membrane reactor, TCMR and CR. The reactor length

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

Dimensionless length

Met

hano

l mol

e fra

ctio

n

CR TCMR FTCMR

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.54

0.56

0.58

0.6

0.62

0.64

0.66


H 2 m

ole

fract

ion

CR TCMR FTCMR

a

b

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

fraction along the reactor axis between exothermic sides of

FTCMR, TCMR and CR.

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

reaction kinetic controlling and in the other section the

equilibrium is controlling. The difference between simulation

results pattern of thermally coupled reactors and conven-

tional reactor is due to delay in thermodynamics equilibrium.

The delay in equilibrium for TCMR and FTCMR is due to lower

temperature in the endothermic side, provided by the dehy-

drogenation of cyclohexane, compared to the saturated water

in the conventional reactor. It supposes that methanol

production in thermally coupled reactors to be higher than the

CR by increasing the reactor length where the lower temper-

ature of coupled reactor can break the equilibrium in the

methanol reaction.

Fig. 5(a) and (b) shows axial temperature profiles for CR,

thermally coupled membrane reactor and fluidized-bed ther-

mally coupled 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 the mixtures in both reaction sides. The

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 (see Fig. 5(a) and (b)). Along the

exothermic side of fluidized-bed thermally coupled reactor,

temperature increases smoothly and a hot spot develop as

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 500

505

510

515

520

525

530


Tem

pera

ture

of e

xoth

erm

ic s

ide

CR TCMR FTCMR

0 1 498

500

502

504

506

508

510

512

Tem

pera

ture

of e

ndot

herm

ic s

ide

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 502.99

503

503.01

503.02


Tem

pera

ture

of p

erm

eatio

n si

de

FTCMR TCMR

a

b

Fig. 5 e Variation of temperature for CR and TCMR and

FTCMR in (a) exothermic side, (b) endothermic side and

permeation side along the reactor axis.



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4


Rat

e of

reac

tion

in e

xoth

erm

ic s

ide(

mol

e m

-3 s

-1 )

TCMR FTCMR Hydrogenation of CO

Water-gas shift

Hydrogenation of CO 2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15


Rat

e of

reac

tion

in e

ndot

herm

ic s

ide(

mol

e m

-3 s

-1 ) TCMR FTCMR

a

b

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

and (b) the endothermic sides for TCMR and FTCMR along

the reactor axis.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.05

0.1

C 6 H

12 m

ole

fract

ion

0 1 0

0.05

0.1

0.15

0.2

0.25

0.3


H 2 m

ole

fract

ion

TCMR FTCMR

Fig. 6 e Comparison of C6H12 and H2 mole fraction along

the reactor axis in the endothermic sides of TCMR and

FTCMR.


demonstrated in Fig. 5(a) and then decreases. The exothermic

temperature control of the FTCMR is easier due to lower hot

spot. There is not a suddenly rises of temperature for this

system. Thus, the fluidized-bed thermally coupledmembrane

reactor provides a more favorable temperature profile along

the reactor than the CR and even TCMR, due to excellent heat

transfer characteristics of fluidization.

At the entrance of endothermic side of TCRs, the

temperature decreases rapidly and a cold spot form and then

the temperature increases (see Fig. 5(b)). As it can be seen in

this figure, the temperature profile pattern in permeation

side is the same as temperature profile pattern in endo-

thermic side.

Fig. 6 shows the mole fraction of cyclohexane and

hydrogen in the endothermic side of fluidized-bed thermally

coupledmembrane and thermally coupledmembrane reactor

along the reactor axis. Because of the fluidization concept is

used in exothermic side and excellent heat transfer of fluid-

ized-beds overcome the limitations often prevailing in meth-

anol packed-bed reactors, the endothermic side is performed

in higher temperature at the reactor entrance relative to the

thermally coupled membrane reactor (see Fig. 5(b)). Near the

reactor entrance, the cyclohexane dehydrogenation is fast.

Consequently, the heat transferred from the solid wall cannot

provide necessary heat to drive the endothermic reaction.

Hence, the temperature in the endothermic side decreases in

reactor entrance. Nevertheless, fluidized-beds eliminate the

radial and axial temperature gradients due to excellent heat

transfer characteristics. The fixed-beds have relatively poor

heat transfer coefficients as compared to fluidized-bed reac-

tors. Therefore, the fluidized bed thermally coupled

membrane reactor is implementing a higher temperature at

the first zone of reactor that will cause to obtain more

component conversion in the endothermic side (shown in

Fig. 6). Increasing hydrogen partial pressure in endothermic

side enhances hydrogen permeability along the reactor;

hydrogen permeation depends on the hydrogen partial pres-

sure square root difference between the reaction zone and the

permeation zone. Consequently, the mole fraction of

hydrogen in permeation side of fluidized bed thermally

coupled membrane reactor is higher than TCMR.

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

for exothermic and endothermic sides, respectively.

Comparing the values for the reaction rates present in the

exothermic side, it can be seen that the predominant reac-

tion is hydrogenation of CO; however neither wateregas

shift nor hydrogenation of CO2 can be neglected, their

contribution being significant. Fig. 8 illustrates the variation

of the generated and consumed heat flux from the

exothermic and the endothermic reaction in thermally

coupled reactors, respectively. 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. 5. In this region, the generated heat flux is higher



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6


Hea

t flu

x(W

)

TCMR FTCMR

Consumed heat in endothermic side

Generated heat in exothermic side

Fig. 8 e Variation of generated and consumed heat flux for

TCMR and FTCMR along the reactor axis.

TCMR FTCMR 2

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

Hyd

roge

n re

cove

ry y

ield

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

20

40

60

80

100

120

140

160

180


Ben

zene

pro

duct

ion

rate

(ton

/day

)

TCMR FTCMR

a

b

Fig. 9 e The comparison of (a) hydrogen recovery yield and

(b) benzene production rate in TCMR and FTCMR.


than the consumed one. The system heats up and a peak in

the generated heat flux is observed. Afterward, the gener-

ated heat flux decreases rapidly, mainly due to fuel deple-

tion. 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. A decrease in the reaction

heat flux consumed is observed near the thermally coupled

membrane reactor entrance, and is associated to the rela-

tively low reaction rate in the endothermic process in that

region as shown in Fig. 8. The cold spot in FTCMR is upper

than TCMR which is due to less decreased reaction rate and

transferred more heat from exothermic side and conse-

quently the system becomes lower cooled down. At the

entrance of separation side (Fig. 5(b)), the temperature

decreases which is due to transferred heat from separation

to endothermic side. After this position, transferred heat

direction is reversed and results in temperature increases

(see Fig. 5(b)).

Fig. 9(a) and (b) present the comparison of hydrogen

recovery yield and benzene production in TCMR and FTCMR.

As demonstrated, the hydrogen recovery yield of FTCMR

increases about 5.6% relative to that TCMR. Additionally, an

increase about 8.52% in benzene production is achieved for

FTCMR in comparison with TCMR. This considerable

improvement in the hydrogen recovery yields and benzene

production rate of FTCMR is due to utilizing the fluidization

concept and overcoming high pressure drop, mass and heat

transfer limitations.

7. Conclusion

In this study, the performance of a fluidized-bed thermally

coupled membrane reactor was compared with thermally

coupledmembrane reactor and conventionalmethanol reactor.

This recuperative configuration as same as TCMR represents

some important improvement in comparison to conventional

methanol reactor as follows: reduction reactors sizes; produc-

tion pure hydrogen in the permeation side; production of

benzene as an additional valuable product; and autothermal

conditions are achieved within the reactors. The potential

possibilities of the FTCMR were analyzed using a steady-state

fixed-bed heterogeneous model for dehydrogenation reactor

and two-phase theory in bubbling regime of fluidization for

methanol synthesis reactor tomodelandsimulate theproposed

reactor. In FTCMR, the advantages of fluidization concept

including low pressure drop, high heat transfer and etc are

added to the coupled configuration and identifies more proper

candidate for methanol synthesis process.

In addition to above mentioned, the advantages of using

fluidized-bed thermally coupled membrane reactor are

summarized as follows:

� The profile temperature is lower in comparison with CR and

even TCMR which decreases the catalyst deactivation rate.

� Enhancement of hydrogen recovery yield and benzene

production in comparison with TCMR.




The results suggest that utilizing of fluidized-bed ther-

mally coupled membrane reactor for enhancement pure

hydrogen 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, m2m�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, molm�3

Cp Specific heat of the gas at constant pressure, Jmol�1

dp Particle diameter, m

Di Tube inside diameter, m

Dij Binary diffusion 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

Fb molar flow in bubble side, mol s�1

Fe molar flow in emulsion side, mol s�1

G Mass velocity, kgm�2 s�1

hf Gasesolid heat transfer coefficient, Wm�2 K�1

hi Heat transfer coefficient between fluid phase and

reactor wall in exothermic side, Wm�2 K�1

ho Heat transfer coefficient between fluid phase and

reactor wall in endothermic side, Wm�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,

molm�3 Pa�1 s�1

k1 Rate constant for the first rate equation of methanol

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

k2 Rate constant for the second rate equation of

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

k3 Rate constant for the third rate equation ofmethanol

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

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

K Conductivity of fluid phase, Wm�1 K�1

KB Adsorption equilibrium constant for benzene, Pa�1

Kbei Mass transfer coefficient for component i in

fluidized-bed, m s�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, Wm�1 K�1

L Reactor length, m

Mi Molecular weight of component i, gmol�1

N Number of components (N¼ 6 for methanol

synthesis reaction, N¼ 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,

molm�3 s�1

ri Reaction rate of component i, for exothermic

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

molm�3 s�1

R Universal gas constant, Jmol�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, Wm�2 K�1

vci Critical volume of component i, cm3mol�1

yi Mole fraction of component i, molmol�1

yib Mole fraction of component i in the bubble phase,

molmol�1

yie Mole fraction of component i in the emulsion phase,

molmol�1

Z Axial reactor coordinate, m

Greek letters

m Viscosity of fluid phase, kgm�1 s�1

r Density of fluid phase, kgm�3

rb Density of catalytic bed, kgm�3

s Tortuosity of catalyst

d Bubble phase volume as a fraction of total bed

volume

3mf Void fraction of catalytic bed at minimum

fluidization

3B Void fraction of catalytic bed

g Volume fraction of catalyst occupied by solid particle

in bubble

Superscripts

G In bulk gas phase

S At surface catalyst

E Emulsion phase

B Bubble phase

Subscripts

0 Inlet conditions

B Benzene

C Cyclohexane

I Chemical species

J Reactor side

K Reaction number index




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