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8/14/2019 Enhancement of Carbon Dioxide Removal
1/14
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: rahimpor@shirazu.ac.ir (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
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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
ffiffiffiffiffiffiPtH
qffiffiffiffiffiffi
PsHp
i 1; 2;.; N 1 (9)
3BccpgvTs
vt
1
A
sCpg
vFsTs
vz
avhfTssTsaH
As
ffiffiffiffiffiffiPtH
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
ffiffiffiffiffiffiPtH
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
ffiffiffiffiffiffiPtH
qffiffiffiffiffiffi
PsHp
i 1; 2;.; N 1 (14)
ctcpgvTt
vt
1Ac
Cpgv
FtTt
vzaH
Ac
ffiffiffiffiffiffiPtH
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
ffiffiffiffiffiffiPtH
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
ConventionalMembrane
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
ConventionalMembrane
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
ConventionalMembrane
ConventionalMembrane
ConventionalMembrane
Conventional
Membrane
ConventionalMembrane
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.
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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.
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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
ConventionalMembrane
0 200 400 600 800 1000 1200 14002380
2400
24202440
2460
2480
2500
2520
2540
2560
time (day)
CO2
RemovalRate
ConventionalMembrane
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
equation, mol kg1 s1 bar1/2
k3 reaction rate constant for the 3rd rate
equation, mol kg1 s1 bar1/2
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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