enhancement of carbon dioxide removal

8/14/2019 Enhancement of Carbon Dioxide Removal

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Enhancement of carbon dioxide removal

in a hydrogen-permselective methanol

synthesis reactor

M.R. Rahimpour*, K. Alizadehhesari

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

a r t i c l e i n f o

Article history:

Received 4 September 2008

Received in revised form

23 October 2008

Accepted 24 October 2008

Published online -

Keywords:

CO2 removal

Hydrogen-permselective

Membrane reactor

Dynamic modelGlobal warming

Greenhouse gases

a b s t r a c t

One of the major problems facing mankind in 21st century is the global warming which is

induced by the increasing concentration of carbon dioxide and other greenhouse gases in

the atmosphere. One of the most promising processes for controlling the atmospheric CO2level is conversion of CO2 to methanol by catalytic hydrogenation. In this paper, the

conversion of CO2 in a membrane dual-type methanol synthesis reactor is investigated. A

dynamic model for this methanol synthesis reactor was developed in the presence of long-

term catalyst deactivation. This model is used to compare the removal of CO2 in

a membrane dual-type methanol synthesis reactor with a conventional dual-type meth-

anol synthesis reactor. A conventional dual-type methanol synthesis reactor is a vertical

shell and tube heat exchanger in which the first reactor is cooled with cooling water and

the second one is cooled with synthesis gas. In a membrane dual-type methanol synthesis

reactor, the wall of the tubes in the conventional gas-cooled reactor is covered witha palladiumsilver membrane, which is only permeable to hydrogen. Hydrogen can

penetrate from the feed synthesis gas side into the reaction side due to the hydrogen

partial pressure driving force. Hydrogen permeation through the membrane shifts the

reaction towards the product side according to the thermodynamic equilibrium. The

proposed dynamic model was validated against measured daily process data of a methanol

plant recorded for a period of 4 years and a good agreement was achieved.

2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights

reserved.

1. Introduction

The increase in concentration of carbon dioxide and other

greenhouse gases in the atmosphere since the industrial

revolution (about 250 years ago) has led to the serious irre-

versible changes to the global climate. Due to the global

population growth and increase in living standards espe-

cially in developing countries the greenhouse gas emissions

will undoubtedly increase during the next years [1]. One

possible approach to mitigate the emissions of carbon

dioxide to the atmosphere would be to recycle the carbon in

a chemical process to form useful products such as meth-

anol. Methanol is produced by catalytic conversion of

synthesis gas (CO2, CO and H2) [2]. It has the advantage that

it is liquid under normal conditions. It can be stored and

transported as easily as gasoline, and can be used in

conventional combustion engines without requiring any

major adjustments. Methanol has twice the energy density

* Corresponding author.E-mail address: [email protected] (M.R. Rahimpour).

A v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / h e

ARTICLE IN PRESS

0360-3199/$ see front matter 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijhydene.2008.10.089

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 e n e r g y x x x ( 2 0 0 8 ) 1 1 4

Please cite this article in press as: Rahimpour MR, Alizadehhesari K, Enhancement of carbon dioxide removal in a hydrogen-permselective methanol synthesis reactor, International Journal of Hydrogen Energy (2008), doi:10.1016/j.ijhydene.2008.10.089
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of liquid hydrogen and can be more conveniently stored and

transported [3,4].

The conversion of CO2 to methanol is an exothermic

reversible reaction, therefore low temperature causes higher

conversion but this must be balanced against a slower rate of

reaction, which leads to the requirement of a large amount of

catalyst. In order to reach the highest removal rate, increasing

temperature improves the rate of reaction, which leads tomore CO2 conversion. Nevertheless, as the temperature

increases beyond this point, the failing effect of equilibrium

conversion decreases CO2 removal [5]. Therefore, imple-

menting a higher temperature at the entrance of the reactor

for a higher reaction rate, and then reducing temperature

gradually towards the exit from reactor for increasing ther-

modynamic equilibrium conversion is one of the significant

issues in methanol synthesis reactor configuration. Recently,

a dual-type methanol synthesis reactor system instead of

a single-type methanol synthesis reactor was developed for

CO2 conversion to methanol. The configuration of dual-type

reactor system permits high temperature in the first reactor

and a low temperature in the second reactor. In this system,the first reactor, isothermal water-cooled reactor is combined

in series with a gas-cooled reactor which accomplishes partial

conversion of CO2 to methanol. In the reaction system, the

addition of hydrogen to the reacting gas selectively leads to

a shift of the chemical equilibrium towards the product side,

resulting in a higher conversion of CO2 to methanol [6].

One of the critical issues of the dual-type methanol

synthesis reactor configurations is the addition of H2 to the

reacting gas by using membrane [6]. The main advantages of

a membrane dual-type methanol synthesis reactor are:

simultaneous CO2 conversion and methanol synthesis, the

possibility of overcoming the limitation imposed by thermo-

dynamic equilibrium [6], enhancement of kinetics-limitedreactions in the first methanol synthesis reactor due to the

higher feed temperature, enhancement of equilibrium-

limited reactions in the second methanol synthesis reactor

due to a lower temperature, and stochiometric control of

reacting gases in the methanol synthesis reactor. A

membrane methanol synthesis reactor is a system or device

which combines the chemical conversion and membrane in

one system [7].

The application of membrane conversion technology in

chemical reaction processes is now mainly focused on reac-

tion systems containing hydrogen and oxygen, and is based

on inorganic membranes such as Pd and ceramic membranes

[7]. In many hydrogen-related reaction systems, Pdalloymembranes on a stainless steel support were used as the

hydrogen-permeable membrane [8]. It is also well known that

the use of pure palladium membranes is hindered by the fact

that palladium shows a transition from the a-phase

(hydrogen-poor) to the b-phase (hydrogen-rich) at tempera-

tures below 300 C and pressures below 2 MPa, depending on

the hydrogen concentration in the metal. Since the lattice

constant of the b-phase is 3% larger than that of the a-phase,

this transition leads to lattice strain and, consequently, after

a few cycles,to a distortion of the metal lattice [9]. Alloying the

palladium, especially with silver, reduces the critical

temperature for this embitterment and leads to an increase in

the hydrogen permeability. The highest hydrogen

permeability was observed at an alloy composition of 23 wt%

silver [10]. Palladium-based membranes have been used for

decades in hydrogen extraction because of their high perme-

ability and good surface properties and because palladium is

100% selective for hydrogen transport [11]. These membranes

combine excellent hydrogen transport and discrimination

properties with resistance to high temperatures, corrosion,

and solvents. Key requirements for the successful develop-ment of palladium-based membranes are low costs as well as

permselectivity combined with good mechanical, thermal and

long-term stability [12]. These properties make palladium-

based membranes such as PdAg membranes very attractive

for use with petrochemical gases. A thin palladium or palla-

dium-based alloy layer is prepared on the surface or inside the

pores of porous supports. Many researchers have developed

supporting structures for palladium or palladium-based alloy

membranes. The materials in commercial use for porous

supports are: ceramics, stainless steel and glass. The

membrane support should be porous, smooth-faced, highly

permeable, thermally stable and metal adhesive [13].

Basically, the membrane reactor can be used in methanolproduction in different ways. The first way is to supply the

reactants on the catalytic zone in a controlled manner. In this

case, it is useful to introduce hydrogen through a dense

membrane, in order to have the best reactants molar ratio on

the catalytic surface [14]. Tosti et al. have described different

configurations of palladium membrane reactors used for

separating ultra pure hydrogen [15]. Considerable attention

has been paid to the fluidized bed membrane reactors as

multi-functional reactors because of their main advantages

such as shifting the thermodynamic equilibrium, enhance-

ment of conversion, simultaneous reaction and separation of

hydrogen, elimination of diffusion limitations, good heat

transfer capability and a more compact design [16]. Roy et al.studied economics and simulation of fluidized bed membrane

reforming reactors [17].

There are a few investigations on conversion of CO2 to

methanol in PdAg membrane-type methanol synthesis

reactors [6, 10]. However, there is no information available in

the literature regarding the use of a Pd-membrane for

enhancement of CO2 removal. Therefore, it was decided to

first study on this system.

The main goal of this work is enhancement of carbon

dioxide conversion in dual-type methanol synthesis reactors.

In this new system, the walls of tubes in the second methanol

synthesis reactor are coated with a hydrogen-permselective

membrane. The hydrogen partial pressure gradient is thedriving force forhydrogen permeation from feed synthesis gas

to the reacting gas. The advantages of this concept will be

discussed based on temperature, catalyst activity and

concentration profiles. The results are compared with the

performance of conventional dual-type methanol synthesis

reactor. This comparison shows that the CO2 removal rate in

membrane dual-type methanol synthesis reactor is greater

than conventional dual-type methanol synthesis reactor.

Also, the profile of catalyst activity along the membrane dual-

type system shows that the catalyst activity along the second

methanol synthesis reactor of the membrane system is

maintained at a higher level relative to the second methanol

synthesis reactor of the conventional system and this leads to


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a longer catalyst lifetime in the membrane dual-type meth-

anol synthesis reactor.

2. The methanol synthesis reactorconfigurations

2.1. Single-type reactor

Fig. 1 shows the schematic diagram of a single-type methanol

synthesis reactor. A single-type methanol synthesis reactor is

basically a vertical shell and tube heat exchanger. The catalyst

is packed in vertical tubes and surrounded by the boiling

water. The CO2 conversion reactions are carried out over

commercial CuO/ZnO/Al2O3 catalyst. The heat of exothermic

reactions is transferred to the boiling water and steam is

produced. The technical design data of the catalyst pellet and

the input data of the single-type methanol synthesis reactor

are summarized in Tables 1 and 2.

2.2. Conventional dual-type reactor

Fig. 2 shows the schematic diagram of a conventional dual-

type methanol synthesis reactor. This system is mainly based

on the two-stage methanol synthesis reactor system consist-

ing of a water-cooled and a gas-cooled methanol synthesis

reactor. The cold feed synthesis gas is fed to the tubes of the

gas-cooled methanol synthesis reactor (second reactor) and

flowing in counter-current mode with reacting gas mixture in

theshell of this reactor. Thenthe synthesisgas is heatedby the

heat of reaction produced in the shell. Therefore, the reacting

gas temperature is continuously reduced through the reaction

path in the second methanol synthesis reactor. The outletsynthesis gas from the second methanol synthesis reactor is

fedto tubes of the first reactor (water-cooled) and the chemical

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

transferred to the cooling water inside the shell of methanol

synthesis reactor. In this stage, CO2 is partly converted to

methanol.

The 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 (gas-cooled). The low

operating temperature results in more catalyst service life forthe gas-cooled methanol synthesis reactor.

The technical design data of the catalyst pellet and input

data of the conventional dual-type methanol synthesis

reactor have been summarized in Tables 3 and 4.

2.3. Membrane dual-type methanol synthesis reactor

Fig. 3 shows the schematic diagram of a membrane dual-type

methanol synthesis reactor configuration for CO2 conversion.

This process is similar to conventional dual-type methanol

synthesis reactor, with the exception that in the membrane

system the walls of tubes in the second reactor (gas-cooled)

consist of hydrogen-permselective membrane. The pressuredifference between the shell (71.2 bar) and tubes (76.98 bar) in

conventional dual-type reactor permits the diffusion of

hydrogen through the PdAg membrane layer. On the other

hand, in the new system, the mass and heat transfer process

simultaneously occurs between the shell and tube, while in

the conventional-type only a heat transfer process occurs

between them.

This simulation study is based on a PdAg layer thickness

of 0.8 mm. In this study all specifications for the first

Steam DrumSynthesis Gas

(CO2, CO and H2)

Product

Saturated Steam

Shell side

Tube side

Boiling water

Fig. 1 A schematic diagram of a single-type methanol

synthesis reactor.

Table 1 Specifications of catalyst and reactor for single-type methanol synthesis reactor.

Parameter Value Unit

rs 1770 [kg m3]

dp 0.00547 [m]

cps 5.0 [kJ kg 1 K1]

lc 0.004 [W m

1

K

1

]av 626.98 [m2 m3]

3s/s 0.123 []

Number of tubes 2962 []

Tube length 7.022 [m]

Table 2 Input data of single-type methanol synthesisreactor.

Feed conditions Value

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 [mol s1] 0.64

Inlet temperature [K] 503

Pressure [bar] 76.98

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and second methanol synthesis reactors in the membrane

dual-type system are the same as those of the industrial

methanol synthesis reactor listed in Tables 3 and 4.

3. Mathematical model

The mathematical model for the simulation of membrane

dual-typemethanol synthesis reactorwas developedbased on

the following assumptions: (1) one-dimensional plug flow in

shell and tube sides; (2) axial dispersion of heat is negligible

compared to convection; (3) gases are ideal; (4) the axial

diffusion of hydrogen through the membrane is neglected

compared to the radial diffusion. We consider an element oflength Dz as depicted in Fig. 4.

3.1. Water-cooled reactor (first reactor)

In the water-cooled reactor the reactions are carried out in

tube side while cooling in shell side is used to remove the

heat of reaction from reacting material in tube. The mass

and energy balance for solid phase in tube side are expressed

by:

3scvytisvt

kgiyti y

tis

hrirBa i 1; 2;.; N 1 (2)

rBcpsvTtsvt

avhf

Tt Tts rBa

XNi1

hriDHf;i

(3)

where ytis and Tts are the mole fraction and temperature of solid

phase in tube side, respectively, and i represents H2, CO2, CO,

CH3OH, H2O. Argon and methane are inert components. The

following two conservation equations are written for the fluid

phase:

3Bcvytivt

Ft

Ac

vytivz

avctkgi

ytis y

ti

i 1; 2;.; N 1 (4)

3BccpgvTt

vt

Ft

Accpg

vTt

vz avhfT

ts T

t

pDiAc

UsTs Tt (5)

where yti and Tt are the fluid-phase mole fraction and

temperature in tube side, respectively. Ft is total molar flow

rate in each tube and Ac is cross-sectional of each tube. As can

be seen in Fig. 2, the outlet synthesis gas from the second

reactor is the inlet synthesis gas to the first reactor. The

boundary conditions are unknown and the more details are

explained in numerical solution.

z 0; Ft Fin; yti yi;in; T

t Tin (6)

Second Convertor

(Gas-cooled convertor)

First Convertor

(Water-cooled convertor)

Steam Drum

Synthesis Gas

(CO2, CO and H2)

Product

Shell side

Tube side

Fig. 2 Schematic flow diagram of conventional dual-type

methanol synthesis reactor.

Table 3 Specifications of catalyst and reactors ofindustrial dual-type methanol synthesis.

Water-cooled methanolsynthesis reactor

Gas-cooled methanolsynthesis reactor

Parameter Value Value Unit

D 4500 5500 [mm]

Di 40.3 21.2 [mm]

Do 4.5 25.4 [mm]

dp 0.00574 0.00574 [mm]

av 625.7 625.7 [m2 m3]

3s 0.39 0.39 []

3B 0.39 0.39 []

Tube length 8000 10,000 [mm]

Number of tubes 5955 3026 []

Shell side pressure 71.2 [bar]

Tube side pressure 75 76.98 [bar]

Table 4 Input data of the industrial dual-type methanolsynthesis.

Feed conditions Value

Feed composition (mol%):

CO2 8.49

CO 8.68

H2 64.61CH4 9.47

N2 8.2

H2O 0.1

CH3OH 0.37

Argon 0.24

Inlet temperature [K] 401

Pressure [bar] 76

Second Convertor

(Gas-cooled convertor)First Convertor

(Water-cooled convertor)

Steam

Drum

Synthesis Gas

(CO2, CO and H2)

Product

Shell side

Tube side

Coated with

membrane

Fig. 3 Schematic flow diagram of membrane dual-type

methanol synthesis reactor.


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while, the initial conditions are:

t 0 ; yti y

ssi ; y

tis y

ssis ; T

t

Tss

; Tts T

sss ; a 1 (7)

3.2. Gas-cooled reactor (second reactor)

3.2.1. Shell side (reaction side)

Overall mass balance:

3Bvcs

vt

1As

vF

vz

s

aH

As

ffiffiffiffiffiffiPtH

qffiffiffiffiffiffi

PsHp

(8)

where cs, Fs are total concentration and flow rate of reacting

gas mixture in shell side. As is cross-sectional area of shell and

aH is hydrogen permeation rate constant. PtH and PsH are

hydrogen partial pressure of hydrogen in tube and conversionsides, respectively. The mass and energy balance for solid

phase in the gas-cooled reactor are the same as that in the

water-cooled reactor. The following equations are written for

fluid phase:

3Bcvysivt

1

AsvFsivt

avckgi

ysis y

si

aH

As


qffiffiffiffiffiffi

PsHp

i 1; 2;.; N 1 (9)

3BccpgvTs

vt

1

A

sCpg

vFsTs

vz

avhfTssTsaH

As


qffiffiffiffiffiffiffi

PshH

q cpH

TtTspDiAs

Ut

TtTs

(10)

The mass andenergy balance forsolid phase are expressed by:

3sctvysisvt

kgi

ysi y

sis

hrirBa i1;2;.;N1 (11)

rBcpsvTssvt

avhfTsTsrBa

XNi1

hriDHfi

(12)

where ysis and Tss are the mole fraction and temperature of solid

phase in shell side, respectively, and i represents H2, CO2, CO,

CH3OH, H2O. Argon and methane are inert components.

3.2.2. Tube side (feed synthesis gas flow)

Overall mass balance:

vct

vt

1Ac

vFt

vzaH

Ac


qffiffiffiffiffiffi

PsHp

(13)

where ct and Ft are total concentration and flow rate in tube

side and Ac is cross-sectional area of tube side. The mass and

energy balance equations for fluid phase are given:

ctvytivt

1

Ac

vFsivz

aH

Ac


qffiffiffiffiffiffi

PsHp

i 1; 2;.; N 1 (14)

ctcpgvTt

vt

1Ac

Cpgv

FtTt

vzaH

Ac


qffiffiffiffiffiffi

PsHp

Cph

Ts Tt

pDiAc

Ut

Ts Tt

(15)

The boundary conditions are as follow:

z L; yti yif; Tt Tf (16)

when aH is 0, the membrane is not permeable to hydrogen

and the model is used for conventional dual-type system.

3.3. Equilibrium model

Equilibrium conversions can be estimated by solving two

reaction equilibrium expressions simultaneously. Equilibrium

constants for reactions (A-1) and (A-2) which are presented in

Appendix A are as follows:

Kp1 FCH3 OHF

2

FCO

FH22P2

(17)

Kp2 FCOFH2OFCO2 FH2

(18)

Reaction (A-3) is not necessary for thermodynamic analysis

because it is a linear combination of the first two reactions

(A-1) and (A-3) [18]. The equilibrium constants of reactions

(A-1) and (A-3), Kp1 and Kp3 were determined to be the func-

tions of temperature and pressure by Klier et al. [19]:

Kp1 3:27 1013 exp11; 678=T

1

1:95 104 exp1703=T

P(19)

Kp33:8231013 exp11;678=T

1

1:95104 exp1703=TP

14:24104 exp1107=TP

(20)

where T is in kelvin and P is in atm; Kp2 is obtained from Kp1and Kp3 by the equilibrium relationship:

Kp2Kp3Kp1

(21)

These equations can be used to calculate equilibrium

conversion by first defining X as the moles of CH3OH formed

and Yas the moles of H2O formed, and then writing material

balances around the methanol reactor:

FCH3OHFCH3 OHin X (22)

Tube side coated with

membrane

Shell side

Synthesis

gasProduct

dzH2

Fig. 4 Schematic diagram of an elemental volume of

membrane methanol synthesis reactor.


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FH2OFH2Oin Y (23)

FCO2 FCO2in Y (24)

FCOFCOin XY (25)

FH2 FH2in 2XYFpH2in

FpH2out

(26)

FN2 FN2in (27)

Summation of Eqs. (20)(25) results in total flow rate of reac-

tion side gas:

FFin2XFpH2in

FpH2out

(28)

Substitution of Eqs. (17)(26) into Eqs. (15) and (16) yields two

equations in two unknown extents of reactions, X and Y.

These equations can be solved numerically, but it has been

found advantageous to work with the logarithms of both sides

of Eqs. (15) and (16). The resulting equations used in the

calculations are:

F1X;Y ln

Kp1ln

FCH3OH

F2

FCO

FH22P2

!(29)

F2X;Y ln

Kp2ln

FCOFH2OFCO2 FH2

(30)

Globally convergent multi-dimensional Newtons method in

Fortran PowerStation 4.0 numerical recipes was used to solve

equilibrium model equations (29) and (30).

3.4. Deactivation model

The deactivation model of the CuO/ZnO/Al2O3 catalyst hasbeen investigated by several researchers, however, the model

offered by Hanken was found to be suitable for industrial

applications [20]:

exp

Ed

R

1T

1TR

a5

dadt

Kd (31)

where TR, Ed and Kd are the reference temperature, activation

energy and deactivation constant of the catalyst, respectively.

The numerical value ofTR is 513 K, Ed is 91,270 J/mol and Kd is

(0.00439 h1) [20]. The above model has been fitted with

industrial operating conditions and this model is the only

candidate for the simulation and modelling of such industrial

plants.

3.5. Hydrogen permeation in the Pd/Ag membrane

The flux of hydrogen permeating through the palladium

membrane, j, will depend on the difference in the hydrogen

partial pressure on the two sides of the membrane. Here, the

hydrogen permeation is determined assuming Sieverts law:

jH aH


qffiffiffiffiffiffi

PsHp

(32)

Data for the permeation of hydrogen through Pd/Ag

membrane were determined experimentally. In Eqs. (8)(13),

aH is hydrogen permeation rate constant and is defined as [21]:

aH 2pLP

lnRo

Ri

(33)

where Ro, Ri stand for outer and inner radius of PdAg layer.

Here, the hydrogen permeability through PdAg layer isdetermined assuming the Arrhenius law, which is a function

of temperature as follows [22,23]:

P P0 exp

EpRT

(34)

where the pre-exponential factor P0 above 200 C is reported

as 6.33 108 (mol/m2 s Pa1/2) and activation energy Ep is

15.7 kJ/mol [22, 23].

4. Numerical solution

The basic structure of the model is consisted of the partial

derivative equations of mass and energy conservative rules of

both the solid and fluid phase, which have to be coupled with

the ordinary differential equation of the deactivation model,

and also non-linear algebraic equations of the kinetic model

and auxiliary correlations. The system of equations is solved

using a two-stage approach consisting of a steady-state

simulation stage followed by a dynamic solution stage. In

Table 6 Comparison between predicted CO2 removalrate and plant data for the single-type methanolsynthesis reactor.

Time(day)

CO2 removalrate

(ton/day)Model

CO2 removal rate(ton/day) plant

data

Relative error(%)

0 171.54 145.71 0.15

100 169.48 147.51 0.13

200 173.83 146.32 0.16

300 165.89 146.16 0.12

400 163.76 154.83 0.05

500 162.02 144.54 0.11

600 160.54 135.98 0.15

700 165.36 141.89 0.14

750 164.46 137.13 0.17

Table 5 Comparison between model results with plantdata for fresh catalyst.

Product condition Plant Predicted Error%

Composition (%mole):

CH3OH 0.104 0.1023 3.4

CO2 0.0709 0.0764 4.38

CO 0.0251 0.0228 9.16H2O 0.0234 0.0211 9.82

H2 0.5519 0.5323 3.55

N2 /Ar 0.0968 0.09056.5

CH4 0.114 0.103 9.64

Temperature [K] 495 489.5 1.2

CO2 removal rate [ton/day] 2500 2542.5 1.7


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order to solve the set of reactor model equations, a steady-

state simulation has been used prior to a dynamic simulation,

and the steady-state simulator gives the initial values of the

dynamic one.

4.1. Solution of steady state

Steady-state model solution is performed by setting all the

time-variation of the states to 0 and also considering a fresh

catalytic bulk with the activity of unity. In this way the initial

conditions for temperature and concentration are determined

for dynamic simulation. To solve the set of non-linear differ-

ential-algebraic equations at the steady-state condition,

backward finite difference approximation was applied to the

system of ordinary differential-algebraic equations. The set of

non-linear algebraic equations has been solved using the

shooting method. In fact, the temperature (Tin) and molar flow

rate (Fin) of inlet feed synthesis gas for water-cooled methanolsynthesis reactor are unknown, while the temperature (Tf)

and molar flow rate (Ff) of feed synthesis gas stream are

known. The shooting method converts the boundary value

problem to an initial value one. The solution is possible by

guessing a value for Tin and Fin of heated feed synthesis gas to

the water-cooled methanol synthesis reactor. The water-

cooled and gas-cooled reactors are divided into 14 and 16

sections, respectively, and then GaussNewton method is

used to solve the non-linear algebraic equations in each

section. At the end, the calculated values of temperature (Tf)

and molar flow rate (Ff) of fresh feed synthesis gas stream are

compared with the actual values. This procedure is repeated

until the specified terminal values are achieved within small

convergence criterion.

4.2. Solution of dynamic model

The results of the steady-state simulation are used as initial

conditions for time-integration of dynamic state equations in

each node through the methanol synthesis reactor. The set of

dynamic equations consists of simultaneous ordinary and

partial differential equations due to the deactivation model

and conservation rules, respectively, as well as the algebraic

equations due to auxiliary correlations, kinetics and thermo-

dynamics of the reaction system. The set of equations have

been discretized respect to axial coordinate, and modified

Rosenbrock formula of order 2 has been applied to the dis-

cretized equations in each node along the reactor to integratethe set of equations with respectto time. The processduration

has been considered to be 1400 operating days.

5. Results and discussion

5.1. Steady-state model validation

The validation of steady-state model was carried out by

comparison of model results with plant data at time 0 for

0 2 4 6 8 10 12 14 16 180

0.05

0.1

0.15

0.2

0.25

0.3

0.35

CO

2Conversion

Length (m)

0 2 4 6 8 10 12 14 16 18

Length (m)

Rate base

Equlibruim base

a

0

0.2

0.4

0.6

0.8

1

CO

Conversion

b

Equlibruim base

Rate base

Fig. 5 Comparison of equilibrium conversion in conventional dual-type methanol synthesis reactor for (a) CO2 and (b) CO.

0 5 10 15480

490

500

510

520

530

540

lenght (m)

TemperatureofGasPhase

Fresh catalyst

ConventionalMembrane

0 5 10 150.065

0.07

0.075

0.08

0.085

0.09

lenght (m)

CO2molFraction

Fresh catalyst


a b

Fig. 6 Comparison between (a) temperature profiles and (b) CO2 mole fraction profiles along the reactors in conventional

dual-type methanol synthesis reactor for fresh catalyst.


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conventional dual-type methanol synthesis reactor aH 0

under the design specifications and input data tabulated in

Tables 3 and 4, respectively. The model results and the

corresponding observed data of the plant are presented in

Table 5. It was observed that, the steady-state model per-

formed satisfactorily well under industrial conditions and

a good agreement between plant data and simulation data

existed.

5.2. Dynamic model validation

In order to verify the goodness of dynamic model, simulation

results have been compared with the historical process data

for single-type methanol synthesis reactor under the design

specifications and input data tabulated in Tables 1 and 2,

respectively. The predicted results of removal rate and the

corresponding observed data of the plant are presented in

Table 6. It was observed that, the model performed satisfac-

torily well under industrial conditions and a good agreement

between daily-observed plant data and simulation data

existed.

Fig. 5 shows the equilibrium conversion of (a) CO2 and (b)

CO in conventional dual-type methanol synthesis reactorsystems. Conversion of CO and CO2 is exothermic therefore

reaction equilibrium constants increase by decrease in

temperature and vice versa. As can be seen in both figures,

equilibrium conversion values along the first methanol

synthesis reactor are more than kinetic (rate based model)

conversion values due to higher temperature in this reactor.

But, kinetic conversion at the end of first methanol synthesis

0 5 10 15480

490

500

510

520

530

540

lenght (m)

TemperatureofGasP

hase

1st day

0 5 10 15480

490

500

510

520

530

540

lenght (m)

TemperatureofGasP

hase

1400th day

0 5 10 150.75

0.8

0.85

0.9

0.95

1

length (m)

Activity

1st day


0 5 10 15

0.4

0.5

0.6

0.7

0.8

0.9

1

length (m)

Activity

1400th day

0 5 10 150

500

1000

1500

2000

2500

3000

lenght (m)

CO2RemovalRate

1st day

0 5 10 150

500

1000

1500

2000

2500

lenght (m)

CO2RemovalRate

1400th day




Conventional

Membrane


a b

c d

e f

Fig. 7 Comparison between temperature profiles (a, b) activity profiles (c, d) and CO 2 removal rate profiles (e, f) in

conventional and membrane dual-type methanol synthesis reactor systems on the first and 1400th day of operation.


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reactor and along the second methanol synthesis reactor

reaches close to equilibrium conversion.

Fig. 6 demonstrates a comparison of temperature profiles

and CO2 mole fraction profiles along the conventional dual-

type reactor and membrane dual-type reactor systems for

fresh catalyst. In Fig. 6(a), the temperature profile in the first

reactor of membrane system up to the length of 8 m is higher

than conventional one because the feed synthesis gas to thefirst reactor is at a higher temperature due to the higher heat

gained from the reacting gas mixture in the second reactor.

Since the reactions in the first reactor are kinetics limited, the

higher temperature in the first reactor of membrane system

enhances the conversion of CO2 compared to conventional

system, as shown in Fig. 6(b).

Fig. 6(a) also shows a lower temperature for second reactor

of membrane system due to the addition of hydrogen to the

reacting materials. Since the membrane configuration

permits the contact of reaction gases and feed synthesis gas,

heat transfer increases between the feed synthesis gas and

reacting gas mixture. Also, the reactions in second methanol

synthesis reactor are equilibrium limited thus the lowertemperature enhances the equilibrium conversion as shown

in Fig. 6(b).

Simulation results fortemperature and catalyst activity are

used to show their effects on CO2 removal rate and also to

show the reasons for the better performance of membrane

dual-type methanol synthesis reactor. Temperature, activity

and CO2 removal rate profiles along the reactors are plotted in

Fig. 7 for both types of systems at 1st and 1400th day of

operation. The catalyst activity is a function of temperature

according to Eq. (29), therefore local change of activity along

the methanol synthesis reactor is due to local variation of

temperature. As seen in Fig. 7 the minimum activity level is

observed near the first reactor inlet that is exposed to highertemperature at all times. The catalyst in the gas-cooled

methanol synthesis reactor of both systems tends to have

lower temperature, which improves both the catalyst activity

in this reactor. As is shown in Fig. 7(a) and (b), the membrane

methanol synthesis reactor system provides a more favour-

able temperature profile along the reactor than the conven-

tional one at different times. The lower temperature profile

along the second reactor of membrane dual-type reactor leads

to lower rate of catalyst deactivation. Hence, the membrane

dual-type methanol synthesis reactor provides favourable

0 5 10 150.065

0.07

0.075

0.08

0.085

0.09

lenght (m)

CO2molFraction

1st day

700th day

1400th day

Fig. 8 CO2 mole fraction profiles along the membrane

dual-type methanol synthesis reactor at 1st, 700th and

1400th day of operation.

0 5 10 150

500

1000

1500

2000

2500

3000

lenght (m)

C

O2RemovalRate

1st day

1400th day

Fig. 9 Profiles of CO2 removal rate along the membrane

dual-type methanol synthesis reactor after first and 1400th

day of operation.

0500

10001500

0

10

20400

450

500

550

time(da

y)

length(m)time

(day)

length(m)

Temperatureofcoolant

0500

10001500

0

10

200

2

4

6

8

x10-4ba

H2permeationrate(mol/s)

Fig. 10 Profiles of (a) temperature of coolant and (b) permeation rate of hydrogen versus time and length for a membrane

dual-type reactor.


ARTICLE IN PRESS



10/14

catalyst activity, as compared to conventional dual-type

methanol synthesis reactor, shown in Fig. 7(c) and (d).

The catalyst in gas-cooled methanol synthesis reactor of

both systems tends to have a lower temperature, whichimproves both the equilibrium constant and catalyst activity.

This desired lower temperature results in a shift of the equi-

librium conversion to a higher value as shown in Fig. 7(e) and

(f). The thermodynamic equilibrium becomes favourable at

lower temperatures for the exothermic systems and lower

temperature in the membrane-type methanol synthesis

reactor is one reason for obtaining the higher CO2 removal

rate in comparison with the conventional system at any time

of operation. Therefore, a membrane dual-type methanol

synthesis reactor provides a superior removal rate of carbon

dioxide as compared with a conventional dual-type methanol

synthesis reactor.

Fig. 8 illustrates CO2 mole fraction profiles along themembrane dual-type methanol synthesis reactor at three

different times of operation. Between the 1st and 1400th day

of operation, catalyst deactivation leads to a conversion

reduction. It is shown in this figure that mole fraction ofCO2 in

product stream increases as times passes.

Fig. 9 shows the CO2 removal rate profiles along the

methanol synthesis reactor at two different times of opera-

tion, respectively. Between the 1st and 1400th day of opera-

tion, catalyst deactivation leads to a conversion reduction. A

decreasing hydrogen permeation rate during operation is

another reason for reduction of conversion. Fig. 9 shows that

the CO2 removal rate decreases during operation.

Fig. 10 demonstrates temperature profiles of the coolantwhich is feed synthesis gas for the second methanol synthesis

reactor and cooling water for the first methanol synthesis

reactor and permeation rate of hydrogen profiles versus

operation time and length of the reactor. In Fig. 10(a) the

horizontal surface shows the temperature of cooling satu-

rated water in the first methanol synthesis reactor and the

other profile demonstrates the temperature of gas coolant

entering the tube side of second methanol synthesis reactor.

In first methanol synthesis reactor, because of vaporization of

saturated liquid water to saturated water vapour the

temperature doesnt change, but the temperature of gas

coolant increases along the length and also during the oper-

ation time. It should be remembered that hydrogen perme-ation follows the Arrhenius law. On the other hand, hydrogen

permeation is exponentially proportional to temperature, so it

increases with time, as shown in Fig. 10(b). The first methanol

synthesis reactor doesnt have membrane; consequently, H2permeation rate is 0 for this methanol synthesis reactor.

Fig. 11 shows a three-dimensional plot of CO2 mole fraction

and CO2 removal rate along the reactor length and time. In

Fig. 11(a) the profile is similar to two-dimensional plots where

CO2 mole fraction decreases along the methanol synthesis

0500

10001500

0

10

200.065

0.07

0.075

0.08

0.085

0.09

time(day

)

CO2 mole fractiona b

length(m)

CO

2molfraction

0500

10001500

0

10

200

1000

2000

3000

time(day

)

CO2 Removal Rate

length(m)

CO2removalrate

(ton/day)

Fig. 11 Profile of (a) CO2 mole fraction and (b) CO2 removal rate along the length of membrane dual-type methanol synthesis

reactor as time goes on.

Fig. 13 Optimal temperature of inlet coolant fresh

synthesis gas.Fig. 12 Optimal temperature of water coolant.


ARTICLE IN PRESS



11/14

reactor. Fig. 11(b) demonstrates that CO2 removal rate

increases along the length of the methanol synthesis reactor.

Catalyst deactivation is the main reason for increase in CO2mole fraction and reduction in CO2 removal rate as time goes

on.

A steady-state simulation was carried out and CO2 removal

rate is plotted versus inlet fresh feed and coolant tempera-

tures. The results are shown in Figs. 12 and 13. As shown in

these figures there are optimum temperature values for both

reacting and cooling materials. There are optimum values of

reacting gas and coolant temperatures in other locations of

the reactor [24].

Fig. 14(a) and (b) demonstrates the variations of average

mole fraction and removal rates of CO2 over a period of 1400

operating days for both types of methanol synthesis reactor

systems. Since the membrane system has a lower tempera-ture and therefore, has a lower catalyst deactivation (see

Fig. 7), it has higher conversion during the operating period.

The lower CO2 mole fraction and higher CO2 removal rate are

in dual-type membrane methanol synthesis reactor.

6. Conclusion

In this work, the performance of a membrane dual-type

methanol synthesis reactor system was compared with

a conventional dual-type methanol synthesis reactor for

removal of CO2. The potential possibilities of the membrane

dual-type methanol synthesis reactor system for CO2 removalwere analysed using one-dimensional heterogeneous model

to obtain the necessary comparative estimates. A comparison

of the calculated temperature profile of the catalyst along the

length of the methanol synthesis reactors shows the

extremely favourable temperature profile of the catalyst beds

of the membrane dual-type methanol synthesis reactor

system. A favourable temperature profile of the catalyst along

the membrane dual-type reactor system leads to higher

activity along the reactor and results in a longer catalyst life-

time. Also a favourable temperature profile of the catalyst

along the two reactors plus a high level of catalyst activity in

the gas-cooled reactor of the membrane dual-type system

results in a higher CO2 conversion which means higher CO2

removal rate in this system. This feature suggests that the

concept of membrane dual-type methanol synthesis reactor

system is an interesting candidate for application in conver-sion of CO2 to methanol.

Appendix A. Reaction kinetics

A.1. Reaction kinetics

In the conversion of synthesis gas to methanol, three overall

reactions are possible: hydrogenation of carbon monoxide,

hydrogenation of carbon dioxide and reverse water-gas shift

reaction, which follow as:

CO 2H24CH3OH DH298 90:55 kJ=mol (A-1)

CO2 H24CO H2O DH298 41:12 kJ=mol (A-2)

CO2 3H24CH3OH H2O DH298 49:43 kJ=mol (A-3)

Reactions (A-1)(A-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] provide enough information about kinetics of

methanol synthesis. The correspondent rate expressions due

to the hydrogenation of CO, CO2 and the reversed watergas

shift reactions are:

r1 k1KCO

hfCOf

3=2H2

fCH3OH=f1=2H2 KP1

i

1 KCOfCO KCO2fCO2

hf1=2H2

KH2O=K

1=2H2

fH2 O

i (A-4)

r2 k3KCO2

hfCO2fH2 fH2OfCO=Kp3

i

1 KCOfCO KCO2fCO2

hf1=2H2

KH2O=K

1=2H2

fH2 O

i (A-5)

r3 k2KCO2

hfCO2f

3=2H2

fCH3OHfH2O=f3=2H2 Kp2

i

1 KCOfCO KCO2fCO2

hf1=2H2

KH2O=K

1=2H2

fH2 O

i (A-6)The reaction rate constants, adsorption equilibrium constants

and reaction equilibrium constants which occur in the

0 200 400 600 800 1000 1200 1400

0.0698

0.070.0702

0.0704

0.0706

0.0708

0.071

0.0712

0.0714

time (day)

CO2

molefraction


0 200 400 600 800 1000 1200 14002380

2400

24202440

2460

2480

2500

2520

2540

2560

time (day)

CO2

RemovalRate


a b

Fig. 14 Comparison of (a) average mole fraction, (b) production rate over a period of 1400 days of operation for conventional

and membrane dual-type reactor systems.


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formulation of kinetic expressions are tabulated in Tables A-1

through A-3, respectively.

Appendix B. Auxiliary correlations

B.1. Mass transfer correlations

In the current work, mass transfer coefficients for the

components have been taken from Cusler [27]. These are mass

transfer coefficients between gas phase and solid phase.

kgi 1:17 Re0:42Sc0:67i ug 10

3 (B-1)

where the Reynolds and Schmidt numbers have been defined

as:

Re 2Rpugm

(B-2)

Sci m

rDim 104 (B-3)

and the diffusivity of component i in the gas mixture is given

by [28]:

Dim 1 yiPij

yiDij

(B-4)

And also the binary diffusivities are calculated using the

FullerSchetterGiddins equation that is reported by Reid and

his co-workers [29]. In the following FullerSchetterGiddins

correlation, vci, Mi are the critical volume and molecular

weight of component i which are reported in Table B1 [30].

Dij

107T3=2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1Mi

1

Mj

s

P

v3=2ci v3=2cj

2 (B-5)

Knowing the fact that diffusion path length along the pores isgreater than the measurable thickness of the pellet, for the

effective diffusivity in the catalyst pore, correction should be

implemented due to the structure of the catalyst. The correc-

tion factor is ratio of catalyst void fraction to the tortuosity of

the catalyst (s).

B.2. Heat transfer correlations

The overall heat transfer coefficient between circulating

boiling water of the shell side and bulk of the gas phase in the

tube side is given by the following correlation:

1Ushell

1hi

Ai ln

DoDi

2pLKw

AiAo

1ho

(B-6)

where hi is the heat transfer coefficient between the gas

phase and reactor wall and is obtained by the following

correlation [31]:

hiCprm

Cpm

K

2=3

0:4583B

rudpm

0:407(B-7)

where in the above equation, u is superficial velocity of gas

and the other parameters are those of bulk gas phase and dp is

the equivalent catalyst diameter, K is thermal conductivity of

gas, r, m are density and viscosity of gas, respectively, and 3B is

void fraction of catalyst bed.

In Eq. (B-6), ho is the heat transfer coefficient of boiling

water in the shell side which is estimated by the following

equation [32]:

ho 7:96T Tsat3

P

Pa

0:4(B-8)

T and P are temperature and pressure of boiling water in the

shell side, Tsat is the saturated temperature of boiling water at

the operating pressure of shell side and Pa is the atmospheric

pressure. The last term of the above equation has been

considered due to effect of pressure on the boiling heat

transfer coefficient. For the heat transfer coefficient between

bulk gas phase and solid phase (hf), Eq. (B-7) is applicable.

Table B1 Molecular weight and critical volume of thecomponents.

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

Table A-1 Reaction rate constants [25].

k A exp

B

RTA B

K1 (4.89 0.29) 107 113,000 300

K2 (9.64 7.30) 107 152,900 11,800

K3 (1.09 0.07) 107 87,500 300

Table A-2 Adsorption equilibrium constants [25].

k A exp B

RT

A BKCO (2.16 0.44) 10

5 46,800 800

KCO2 (7.05 1.39) 107 61,700 800

KH2O=K1=2H2 (6.37 2.88) 109 84,000 1400

Table A-3 Reaction equilibrium constants [25].

k A exp B

RT

A BKp1 5139 12.621

Kp2 2073 2.029

Kp3 3066 10.592


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Appendix C. Nomenclature

Ac cross-section area of each tube, m2

Ai inner area of each tube, m2

Ao outside are of each tube, m2

As

cross-section area of shell, m2

a activity of catalyst []

av specific surface area of catalyst pellet, m2 m3

cpg specific heat of the gas at constant pressure,

J mol1 k1

cp;h specific heat of the hydrogen at constant pressure,

J mol1 k-1

cPs specific heat of the catalyst at constant pressure,

J mol1 k1

c total concentration, mol m3

Di tube inside diameter, m

Dij binarydiffusion coefficient of component i inj, m2 s1

Dim diffusion coefficient of component i in the mixture,

m2

s1

Do tube outside diameter, m

dp particle diameter, m

Ed activation energy used in the deactivation model,

J mol1

Ft flow rate of gas in tube side, mol/s

Fs total molar flow in shell side, mol s1

fi partial fugacity of component i, bar

hf gas-catalyst heat transfer coefficient, W m2 K1

hi heat transfer coefficient between fluid phase and

reactor wall, W m2 K1

ho heat transfer coefficient betweencoolant stream and

reactor wall, W m2 K1

K conductivity of fluid phase, W m1

K1

Kd deactivation model parameter constant, s1

Ki adsorption equilibrium constant for component i,

bar1

KPi equilibrium constant based on partial pressure for

component i []

Kw thermal conductivity of reactor wall, W m1 K1

k1 reaction rate constant for the 1st rate

equation, mol kg1 s1 bar1/2

k2 reaction rate constant for the 2nd rate


k3 reaction rate constant for the 3rd rate


kgi mass transfer coefficient for component i, m s1

L length of reactor, m

Mi molecular weight of component i, g mol1

N number of components []

Ni molar flux, mol s1 m2

P total pressure, bar

Pa atmospheric pressure, bar

PtH hydrogen partial pressure in tube side, bar

PsH hydrogen partial pressure in tube side shell side, bar

P permeability of hydrogen through PdAg layer,

molm1 s1 Pa1/2

P0 pre-exponential factor of hydrogen permeability,

molm1 s1 Pa1

R universal gas constant, J mol1

K1

Re Reynolds number []

Ri inner radius of PdAg layer, m

Ro outer radius of PdAg layer, m

ri reaction rate of component i, mol kg1 s1

r1 rate of reaction forhydrogenation of CO, mol kg1 s1

r2 rateofreactionforhydrogenationofCO 2,molkg1 s1

r3 reversed water-gas shift reaction, mol kg1 s1

Sci Schmidt number of component i []T bulk gas phase temperature, K

TR reference temperature used in the deactivation

model, K

Ts temperature of solid phase, K

Tsat saturated temperature of boiling water at operating

pressure, K

Ts shell side temperature, K

Tt tube side temperature, K

t time, s

Us overall heat transfer coefficient between coolant and

process streams, W m2 K1

U superficial velocity of fluid phase, m s1

ug linear velocity of fluid phase, m s1

ysi mole fraction of component i in the fluid

phase in shell, mol mol1

ysis mole fraction of component i in the solid

phase in shell, mol mol1

yti mole fraction of component i in the fluid

phase in tube side, molmol1

ytis mole fraction of component i in the solid

phase in tube side, molmol1

z axial reactor coordinate, m

Greek letters

aH hydrogen permeation rate constant,

molm1

s1

Pa0.5

DHf,i enthalpy of formation of component i, J mol1

DH298 enthalpy of reaction at 298 K, J mol1

3B void fraction of catalytic bed []

3s void fraction of catalyst []

m viscosity of fluid phase, kg m1 s1

n stoichiometric coefficient []

nci critical volume of component i, cm3 mol1

r density of fluid phase, kg m3

rB density of catalytic bed, kg m3

rs density of catalyst, kg m3

h catalyst effectiveness factor []

s tortuosity of catalyst []

U auxiliary variable []d thickness of membrane, m

Superscripts

p permeation side

s shell side

ss initial conditions (i.e., steady-state condition)

t tube side

Subscripts

f feed conditions

in inlet conditions

out outlet conditions

k reaction number index (1, 2 or 3)

s catalyst surface


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