Enhancement of carbon dioxide removal in a hydrogen-permselective methanol synthesis reactor

international journal of hydrogen energy 34 (2009) 1349–1362

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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

article info

abstract

Article history:

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

Received 4 September 2008

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

Received in revised form

the atmosphere. One of the most promising processes for controlling the atmospheric CO2

23 October 2008

level is conversion of CO2 to methanol by catalytic hydrogenation. In this paper, the

Accepted 24 October 2008

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

Available online 21 December 2008

dynamic model for this methanol synthesis reactor was developed in the presence of longterm catalyst deactivation. This model is used to compare the removal of CO2 in

Keywords:

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

CO2 removal

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

Hydrogen-permselective

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

Membrane reactor

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

Dynamic model

reactor, the wall of the tubes in the conventional gas-cooled reactor is covered with

Global warming

a palladium–silver membrane, which is only permeable to hydrogen. Hydrogen can

Greenhouse gases

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. ª 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 irreversible changes to the global climate. Due to the global population growth and increase in living standards especially 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 methanol. 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). 0360-3199/$ – see front matter ª 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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international journal of hydrogen energy 34 (2009) 1349–1362

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 to more CO2 conversion. Nevertheless, as the temperature increases beyond this point, the failing effect of equilibrium conversion decreases CO2 removal [5]. Therefore, implementing 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 thermodynamic 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 thermodynamic equilibrium [6], enhancement of kinetics-limited reactions in the first methanol synthesis reactor due to the higher feed temperature, enhancement of equilibriumlimited 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 reaction systems containing hydrogen and oxygen, and is based on inorganic membranes such as Pd and ceramic membranes [7]. In many hydrogen-related reaction systems, Pd–alloy membranes 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 temperatures 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 permeability 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 development of palladium-based membranes are low costs as well as permselectivity combined with good mechanical, thermal and long-term stability [12]. These properties make palladiumbased membranes such as Pd–Ag membranes very attractive for use with petrochemical gases. A thin palladium or palladium-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 methanol production 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, enhancement 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 Pd–Ag 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 the driving force for hydrogen 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 dualtype 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

international journal of hydrogen energy 34 (2009) 1349–1362

a longer catalyst lifetime in the membrane dual-type methanol synthesis reactor.

2. The methanol synthesis reactor configurations 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 dualtype methanol synthesis reactor. This system is mainly based on the two-stage methanol synthesis reactor system consisting 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 the shell of this reactor. Then the synthesis gas is heated by 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 outlet synthesis gas from the second methanol synthesis reactor is fed to tubes of the first reactor (water-cooled) and the chemical reaction is initiated by the catalyst. The heat of reaction is

Synthesis Gas (CO2, CO and H2)

Steam Drum

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Table 1 – Specifications of catalyst and reactor for singletype methanol synthesis reactor. Parameter

Value

Unit

rs dp cps lc av 3s/s Number of tubes Tube length

1770 0.00547 5.0 0.004 626.98 0.123 2962 7.022

[kg m3] [m] [kJ kg1 K1] [W m1 K1] [m2 m3] [–] [–] [m]

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 for the 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 pressure difference between the shell (71.2 bar) and tubes (76.98 bar) in conventional dual-type reactor permits the diffusion of hydrogen through the Pd–Ag 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 Pd–Ag layer thickness of 0.8 mm. In this study all specifications for the first

Boiling water Shell side

Table 2 – Input data of single-type methanol synthesis reactor. Tube side

Feed conditions

Saturated Steam

Product

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

Composition [%mol]: CH3OH CO2 CO H2O H2 N2 CH4 Total molar flow rate per tube [mol s1] Inlet temperature [K] Pressure [bar]

Value 0.50 9.40 4.60 0.04 65.90 9.30 10.26 0.64 503 76.98

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international journal of hydrogen energy 34 (2009) 1349–1362

Second Convertor (Gas-cooled convertor)

First Convertor (Water-cooled convertor)

Table 4 – Input data of the industrial dual-type methanol synthesis. Steam Drum

Shell side

Tube side

Product

Synthesis Gas (CO2, CO and H2)

Fig. 2 – Schematic flow diagram of conventional dual-type methanol synthesis reactor.

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-type methanol synthesis reactor was developed based 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 of length 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

Feed conditions

Value

Feed composition (mol%): CO2 CO H2 CH4 N2 H2O CH3OH Argon Inlet temperature [K] Pressure [bar]

8.49 8.68 64.61 9.47 8.2 0.1 0.37 0.24 401 76

and energy balance for solid phase in tube side are expressed by:   vyt 3s c is ¼ kgi yti  ytis þ hri rB a i ¼ 1; 2; .; N  1 vt rB cps

N X     vTts ¼ av hf Tt  Tts þ rB a hri DHf;i vt i¼1

Water-cooled methanol synthesis reactor

Gas-cooled methanol synthesis reactor

Parameter

Value

Value

Unit

D Di Do dp av 3s 3B Tube length Number of tubes Shell side pressure Tube side pressure

4500 40.3 4.5 0.00574 625.7 0.39 0.39 8000 5955 – 75

5500 21.2 25.4 0.00574 625.7 0.39 0.39 10,000 3026 71.2 76.98

[mm] [mm] [mm] [mm] [m2 m3] [–] [–] [mm] [–] [bar] [bar]

(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:   vyt Ft vyti þ av ct kgi ytis  yti 3B c i ¼  vt Ac vz 3B ccpg

i ¼ 1; 2; .; N  1

(4)

  pDi s  s  vTt Ft vTt ¼  cpg þ av hf Tts  Tt þ U T  Tt vt Ac vz Ac

(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 ¼ 0;

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

(2)

Ft ¼ Fin ; yti ¼ yi;in ; Tt ¼ Tin

Second Convertor (Gas-cooled convertor) Shell side Tube side Coated with membrane

Product

(6)

First Convertor (Water-cooled convertor) Steam Drum

Synthesis Gas (CO2, CO and H2)

Fig. 3 – Schematic flow diagram of membrane dual-type methanol synthesis reactor.

international journal of hydrogen energy 34 (2009) 1349–1362

3.2.2.

Tube side (feed synthesis gas flow)

Overall mass balance:  qffiffiffiffiffiffi pffiffiffiffiffiffi vct 1 vFt aH PtH  PsH ¼  vt Ac vz Ac

Tube side coated with membrane

H2

dz

Shell side

Synthesis gas

(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:  qffiffiffiffiffiffi pffiffiffiffiffiffi vyt 1 vFsi aH i ¼ 1; 2; .; N  1 (14) PtH  PsH  ct i ¼  vt Ac vz Ac

Product

ct cpg

Fig. 4 – Schematic diagram of an elemental volume of membrane methanol synthesis reactor.

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   qffiffiffiffiffiffi pffiffiffiffiffiffi   v Ft Tt vTt 1 aH þ PtH  PsH Cph Ts  Tt ¼  Cpg vz vt Ac Ac  pDi t  s þ U T  Tt Ac

(15)

The boundary conditions are as follow: while, the initial conditions are: ytis

t

ss

Gas-cooled reactor (second reactor)

3.3.

3.2.1.

Shell side (reaction side)

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:

T ¼T ;

Tts

¼

Tss s ;

(16)

3.2.

¼

yss is ;

yti ¼ yif ; Tt ¼ Tf

t¼0;

¼

yss i ;

z ¼ L;

yti

a¼1

Overall mass balance:  qffiffiffiffiffiffi pffiffiffiffiffiffi vcs 1 vFs aH PtH  PsH ¼ s þ s 3B vt A A vz

(7)

(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 conversion sides, 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:   vys 1 vFs 3B c i ¼  s i þ av ckgi ysis  ysi vt A vt aH þ s A

3B ccpg

 qffiffiffiffiffiffi pffiffiffiffiffiffi i ¼ 1; 2; .; N  1 PtH  PsH

(9)

  vTs 1 vðFs Ts Þ ¼  s Cpg þ av hf Tss  Ts vt A vz aH þ s A

qffiffiffiffiffiffi qffiffiffiffiffiffiffi   pDi   cpH Tt  Ts þ s Ut Tt  Ts PtH  Psh H A

when aH is 0, the membrane is not permeable to hydrogen and the model is used for conventional dual-type system.

Equilibrium model

Kp1 ¼

FCH3 OH ðFÞ2  2 FCO FH2 ðPÞ2

(17)

Kp2 ¼

FCO FH2 O FCO2 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 functions of temperature and pressure by Klier et al. [19]: Kp1 ¼

Kp3 ¼

3:27  1013 expð11; 678=TÞ   1  1:95  104 expð1703=TÞ P



4

1 1:9510

(19)

3:8231013 expð11;678=TÞ   expð1703=TÞP 14:24104 expð1107=TÞP

(10)

(20)

The mass and energy balance for solid phase are expressed by:

where T is in kelvin and P is in atm; Kp2 is obtained from Kp1 and Kp3 by the equilibrium relationship:

3s ct

  vysis ¼ kgi ysi  ysis þ hri rB a vt

rB cps

i ¼ 1;2;.;N  1

N X   vTss ¼ av hf ðTs  Ts Þ þ rB a hri DHfi vt i¼1

(11)

(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.

Kp2 ¼

Kp3 Kp1

(21)

These equations can be used to calculate equilibrium conversion by first defining X as the moles of CH3OH formed and Y as the moles of H2O formed, and then writing material balances around the methanol reactor: FCH3 OH ¼ FCH3 OHin þX

(22)

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international journal of hydrogen energy 34 (2009) 1349–1362

FH2 O ¼ FH2 Oin þY

(23)

FCO2 ¼ FCO2in Y

(24)

FCO ¼ FCOin XþY

(25) p

p

FH2 ¼ FH2in 2XY þFH2 FH2

(26)

FN2 ¼ FN2in

(27)

out

in

Summation of Eqs. (20)–(25) results in total flow rate of reaction side gas: p

p

(28)

F ¼ Fin 2XþFH2 FH2 in

out

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:   F1 ðX;YÞ ¼ ln Kp1 ln

!  FCH3 OH ðFÞ2  2 ðFCO Þ FH2 ðPÞ2 

    FCO FH2 O F2 ðX;YÞ ¼ ln Kp2 ln FCO2 FH2

(29)

(30)

Globally convergent multi-dimensional Newton’s 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 has been investigated by several researchers, however, the model offered by Hanken was found to be suitable for industrial applications [20]:    Ed 1 1 da a5 (31)  ¼ Kd exp R T TR dt where TR, Ed and Kd are the reference temperature, activation energy and deactivation constant of the catalyst, respectively. The numerical value of TR 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:  qffiffiffiffiffiffi pffiffiffiffiffiffi (32) PtH  PsH jH ¼ aH 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]:

Table 5 – Comparison between model results with plant data for fresh catalyst. Product condition

Plant

Predicted

Error%

Composition (%mole): CH3OH CO2 CO H 2O H2 N2/Ar CH4 Temperature [K] CO2 removal rate [ton/day]

0.104 0.0709 0.0251 0.0234 0.5519 0.0968 0.114 495 2500

0.1023 0.0764 0.0228 0.0211 0.5323 0.0905 0.103 489.5 2542.5

3.4 4.38 9.16 9.82 3.55 6.5 9.64 1.2 1.7

aH ¼

2pLP R  o ln Ri

(33)

where Ro , Ri stand for outer and inner radius of Pd–Ag layer. Here, the hydrogen permeability through Pd–Ag layer is determined assuming the Arrhenius law, which is a function of temperature as follows [22,23]:   Ep (34) P ¼ P0 exp RT 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 removal rate and plant data for the single-type methanol synthesis reactor. Time (day)

0 100 200 300 400 500 600 700 750

CO2 removal CO2 removal rate Relative error rate (ton/day) plant (%) (ton/day) data Model 171.54 169.48 173.83 165.89 163.76 162.02 160.54 165.36 164.46

145.71 147.51 146.32 146.16 154.83 144.54 135.98 141.89 137.13

0.15 0.13 0.16 0.12 0.05 0.11 0.15 0.14 0.17

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international journal of hydrogen energy 34 (2009) 1349–1362

a

0.35

b CO Conversion

CO2 Conversion

0.3 0.25 0.2 0.15 0.1 Rate base Equlibruim base

0.05 0

0

2

4

6

8

1 0.8 0.6 0.4 0.2

Equlibruim base Rate base

0

10 12 14 16 18

2

0

4

6

Length (m)

8

10

12

14

16

18

Length (m)

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

order to solve the set of reactor model equations, a steadystate simulation has been used prior to a dynamic simulation, and the steady-state simulator gives the initial values of the dynamic one.

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.

4.1.

4.2.

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 differential-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 methanol synthesis 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 watercooled and gas-cooled reactors are divided into 14 and 16 sections, respectively, and then Gauss–Newton method is used to solve the non-linear algebraic equations in each section. At the end, the calculated values of temperature (Tf)

530 520 510 500 Conventional Membrane

490 480

0

5

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

b

Fresh catalyst

540

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 thermodynamics 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 discretized equations in each node along the reactor to integrate the set of equations with respect to time. The process duration has been considered to be 1400 operating days.

CO2 mol Fraction

Temperature of Gas Phase

a

10

lenght (m)

15

Solution of dynamic model

Fresh catalyst

0.09

Conventional Membrane

0.085 0.08 0.075 0.07 0.065

0

5

10

15

lenght (m)

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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international journal of hydrogen energy 34 (2009) 1349–1362

conventional dual-type methanol synthesis reactor ðaH ¼ 0Þ 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 performed 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,

b

1st day

540

Temperature of Gas Phase

Temperature of Gas Phase

a

530 520 510 500 490 480

Conventional Membrane 0

5

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 satisfactorily 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 reactor systems. 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

10

530 520 510 500 490 480

15

1400th day

540

Conventional Membrane 0

5

c

d

1st day

1

10

15

lenght (m)

lenght (m)

1400th day 1 Conventional Membrane

0.9

0.95

Activity

Activity

0.8 0.9 0.85

0.7 0.6 0.5

0.8 0.75

Conventional Membrane 0

5

10

0.4 0

15

5

length (m)

f

1st day

3000 2500 2000 1500 1000 500 0

Conventional Membrane 0

5

10

lenght (m)

15

CO2 Removal Rate

CO2 Removal Rate

e

10

15

length (m) 1400th day

2500 2000 1500 1000 500 0

Conventional Membrane 0

5

10

15

lenght (m)

Fig. 7 – Comparison between temperature profiles (a, b) activity profiles (c, d) and CO2 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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international journal of hydrogen energy 34 (2009) 1349–1362

1st day 700th day 1400th day

CO2 mol Fraction

0.085

0.08

0.075

0.07

0.065

0

5

10

15

lenght (m) Fig. 8 – CO2 mole fraction profiles along the membrane dual-type methanol synthesis reactor at 1st, 700th and 1400th day of operation.

3000 1st day 1400th day

CO2 Removal Rate

2500

2000

1500

1000

500

0

0

5

10

15

lenght (m)

Temperature of coolant

Fig. 9 – Profiles of CO2 removal rate along the membrane dual-type methanol synthesis reactor after first and 1400th day of operation.

a 550 500 450 400 20 1500

len

gth 10 (m )

1000 0 0

500

time

)

(day

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 dualtype 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 the first 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 lower temperature enhances the equilibrium conversion as shown in Fig. 6(b). Simulation results for temperature 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 higher temperature 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 favourable temperature profile along the reactor than the conventional 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

H2 permeation rate (mol/s)

0.09

b

x10-4

8 6 4 2 0 20

len 10 gth (m )

1500 1000 0 0

500

time

) (day

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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international journal of hydrogen energy 34 (2009) 1349–1362

CO2 mole fraction 0.09

0.085 0.08 0.075 0.07 0.065 20

1500

len 10 gth (m

1000

)

0

500 0

CO2 Removal Rate

b CO2 removal rate (ton/day)

CO2 mol fraction

a

time

)

(day

3000 2000 1000 0 20

1500

len 10 gth (m)

1000 0

500 0

time

) (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.

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, which improves both the equilibrium constant and catalyst activity. This desired lower temperature results in a shift of the equilibrium 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 the membrane 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 of CO2 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 operation, respectively. Between the 1st and 1400th day of operation, catalyst deactivation leads to a conversion reduction. A

Fig. 12 – Optimal temperature of water coolant.

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 coolant which 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 saturated 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 doesn’t change, but the temperature of gas coolant increases along the length and also during the operation time. It should be remembered that hydrogen permeation 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 doesn’t have membrane; consequently, H2 permeation 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

Fig. 13 – Optimal temperature of inlet coolant fresh synthesis gas.

international journal of hydrogen energy 34 (2009) 1349–1362

Conventional Membrane

0.0712

CO2 mole fraction

b

0.0714

2560 Conventional Membrane

2540

CO2 Removal Rate

a

0.071 0.0708 0.0706 0.0704 0.0702 0.07

1359

2520 2500 2480 2460 2440 2420 2400

0.0698 0

200

400

600

800 1000 1200 1400

2380

time (day)

0

200

400

600

800 1000 1200 1400

time (day)

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.

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 CO2 mole 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 temperatures. 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 temperature 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 removal were 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 lifetime. 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 conversion 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 þ 2H2 4CH3 OH DH298 ¼ 90:55 kJ=mol

(A-1)

CO2 þ H2 4CO þ H2 O DH298 ¼ þ41:12 kJ=mol

(A-2)

CO2 þ 3H2 4CH3 OH þ H2 O DH298 ¼ 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 water–gas shift reactions are:  h i k1 KCO fCO fH3=2  fCH3 OH = fH1=2 KP1 2 2  h  i (A-4) r1 ¼  1=2 þ KH2 O =KH fH2 O 1 þ KCO fCO þ KCO2 fCO2 fH1=2 2 2 h i k3 KCO2 fCO2 fH2  fH2 O fCO =Kp3  h  i r2 ¼  1=2 1=2 1 þ KCO fCO þ KCO2 fCO2 fH2 þ KH2 O =KH2 fH2 O

(A-5)

h i  k2 KCO2 fCO2 fH3=2  fCH3 OH fH2 O = fH3=2 Kp2 2 2 h  i  r3 ¼  1=2 fH2 O 1 þ KCO fCO þ KCO2 fCO2 fH1=2 þ KH2 O =KH 2 2

(A-6)

The reaction rate constants, adsorption equilibrium constants and reaction equilibrium constants which occur in the

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international journal of hydrogen energy 34 (2009) 1349–1362

formulation of kinetic expressions are tabulated in Tables A-1 through A-3, respectively.

K1 K2 K3

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 þ Mi Mj 2  3=2 3=2 þ vcj P vci

107 T3=2

Table A-1 – Reaction rate constants [25]. B k ¼ A exp RT

correlation, vci, Mi are the critical volume and molecular weight of component i which are reported in Table B1 [30].

Dij ¼

A

B

(4.89  0.29)  107 (9.64  7.30)  107 (1.09  0.07)  107

113,000  300 152,900  11,800 87,500  300

(B-5)

Knowing the fact that diffusion path length along the pores is greater 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 correction factor is ratio of catalyst void fraction to the tortuosity of the catalyst (s).

Table A-2 – Adsorption equilibrium constants [25]. B k ¼ A exp RT KCO KCO2 1=2 KH2 O =KH2

Table B1 – Molecular weight and critical volume of the components.

A

B

(2.16  0.44)  105 (7.05  1.39)  107 (6.37  2.88)  109

46,800  800 61,700  800 84,000  1400

Component CH3OH CO2 CO H2O H2 CH4 N2

Mi (g/mol)

vci (m3/mol)  106

32.04 44.01 28.01 18.02 2.02 16.04 28.01

118.0 94.0 18.0 56.0 6.1 99.0 18.5

Table A-3 – Reaction equilibrium constants [25]. B k ¼ A exp RT Kp1 Kp2 Kp3

A

B

B.2. 5139 2073 3066

12.621 2.029 10.592

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. ug  103 kgi ¼ 1:17 Re0:42 Sc0:67 i

(B-1)

where the Reynolds and Schmidt numbers have been defined as: Re ¼

2Rp ug m

(B-2)

Sci ¼

m rDim  104

(B-3)

and the diffusivity of component i in the gas mixture is given by [28]: Dim

1  yi ¼Py i i¼j Dij

(B-4)

And also the binary diffusivities are calculated using the Fuller–Schetter–Giddins equation that is reported by Reid and his co-workers [29]. In the following Fuller–Schetter–Giddins

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:   Do Ai ln 1 1 Ai 1 Di ¼ þ þ (B-6) 2pLKw Ao ho Ushell hi where hi is the heat transfer coefficient between the gas phase and reactor wall and is obtained by the following correlation [31]:  2=3  0:407 hi Cp m 0:458 rudp ¼ (B-7) Cp rm K m 3B 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]:  0:4 P (B-8) ho ¼ 7:96ðT  Tsat Þ3 Pa 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.

international journal of hydrogen energy 34 (2009) 1349–1362

Appendix C. Nomenclature

Ac Ai Ao As a av cpg cp;h cPs c Di Dij Dim Do dp Ed Ft Fs fi hf hi ho K Kd Ki KPi Kw k1 k2 k3 kgi L Mi N Ni P Pa PtH PsH P P0 R

cross-section area of each tube, m2 inner area of each tube, m2 outside are of each tube, m2 cross-section area of shell, m2 activity of catalyst [–] specific surface area of catalyst pellet, m2 m3 specific heat of the gas at constant pressure, J mol1 k1 specific heat of the hydrogen at constant pressure, J mol1 k-1 specific heat of the catalyst at constant pressure, J mol1 k1 total concentration, mol m3 tube inside diameter, m binary diffusion coefficient of component i in j, m2 s1 diffusion coefficient of component i in the mixture, m2 s1 tube outside diameter, m particle diameter, m activation energy used in the deactivation model, J mol1 flow rate of gas in tube side, mol/s total molar flow in shell side, mol s1 partial fugacity of component i, bar gas-catalyst heat transfer coefficient, W m2 K1 heat transfer coefficient between fluid phase and reactor wall, W m2 K1 heat transfer coefficient between coolant stream and reactor wall, W m2 K1 conductivity of fluid phase, W m1 K1 deactivation model parameter constant, s1 adsorption equilibrium constant for component i, bar1 equilibrium constant based on partial pressure for component i [–] thermal conductivity of reactor wall, W m1 K1 reaction rate constant for the 1st rate equation, mol kg1 s1 bar1/2 reaction rate constant for the 2nd rate equation, mol kg1 s1 bar1/2 reaction rate constant for the 3rd rate equation, mol kg1 s1 bar1/2 mass transfer coefficient for component i, m s1 length of reactor, m molecular weight of component i, g mol1 number of components [–] molar flux, mol s1 m2 total pressure, bar atmospheric pressure, bar hydrogen partial pressure in tube side, bar hydrogen partial pressure in tube side shell side, bar permeability of hydrogen through Pd–Ag layer, mol m1 s1 Pa1/2 pre-exponential factor of hydrogen permeability, mol m1 s1 Pa1 universal gas constant, J mol1 K1

Re Ri Ro ri r1 r2 r3 Sci T TR Ts Tsat Ts Tt t Us U ug ysi ysis yti ytis z

1361

Reynolds number [] inner radius of Pd–Ag layer, m outer radius of Pd–Ag layer, m reaction rate of component i, mol kg1 s1 rate of reaction for hydrogenation of CO, mol kg1 s1 rate of reaction for hydrogenation of CO2, mol kg1 s1 reversed water-gas shift reaction, mol kg1 s1 Schmidt number of component i [–] bulk gas phase temperature, K reference temperature used in the deactivation model, K temperature of solid phase, K saturated temperature of boiling water at operating pressure, K shell side temperature, K tube side temperature, K time, s overall heat transfer coefficient between coolant and process streams, W m2 K1 superficial velocity of fluid phase, m s1 linear velocity of fluid phase, m s1 mole fraction of component i in the fluid phase in shell, mol mol1 mole fraction of component i in the solid phase in shell, mol mol1 mole fraction of component i in the fluid phase in tube side, mol mol1 mole fraction of component i in the solid phase in tube side, mol mol1 axial reactor coordinate, m

Greek letters hydrogen permeation rate constant, aH mol m1 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 [–] void fraction of catalyst [–] 3s m viscosity of fluid phase, kg m1 s1 n stoichiometric coefficient [–] critical volume of component i, cm3 mol1 nci 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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