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Dynamic simulation of a cascade fluidized-bed membrane reactor in the presence of long-term catalyst deactivation for methanol synthesis
ARTICLE IN PRESS Chemical Engineering Science 65 (2010) 4239–4249
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Dynamic simulation of a cascade fluidized-bed membrane reactor in the presence of long-term catalyst deactivation for methanol synthesis M.R. Rahimpour , M. Bayat, F. Rahmani Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, Iran
a r t i c l e in fo
abstract
Article history: Received 15 January 2010 Received in revised form 11 March 2010 Accepted 16 April 2010 Available online 21 April 2010
In this work, a dynamic model for a cascade fluidized-bed hydrogen permselective membrane methanol reactor (CFBMMR) has been developed in the presence of long-term catalyst deactivation. In the first catalyst bed, the synthesis gas is partly converted to methanol in a water-cooled reactor, which is a fluidized-bed. In the second bed, which is a membrane assisted fluidized-bed reactor, the reaction heat is used to preheat the feed gas to the first bed. This reactor configuration solves some observed drawbacks of new conventional dual type methanol reactor (CDMR) and even fluidized-bed membrane dual type methanol reactor (FBMDMR) such as pressure drop, internal mass transfer limitations, radial gradient of concentration and temperature in both reactors. A dynamic two-phase theory in bubbling regime of fluidization is used to model and simulate the proposed reactor. The proposed model has been used to compare the performance of a cascade fluidized-bed membrane methanol reactor with fluidized-bed membrane dual-type methanol reactor and conventional dual-type methanol reactor. The simulation results show a considerable enhancement in the methanol production due to the favorable profile of temperature and activity along the CFBMMR relative to FBMDMR and CDMR systems. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Dynamic simulation Cascade fluidized-bed Membrane reactor Methanol synthesis Hydrogen permselective membrane Catalyst deactivation
1. Introduction Improvement in production efficiency of important chemicals by only a few percent can sometimes result in significant profit increases, energy conservation and environmental protection, especially for a chemical such as methanol, which is produced in a worldwide range (Schack et al., 1989).
1.1. Methanol synthesis process Methanol is a bulk chemical, a kind of transportation fuel and energy material for fuel cell. It is a clean-burning fuel with versatile applications. As a combustion fuel, it provides extremely low emissions. Methanol can also be used as a solvent or a fuel additive and especially as a building block to produce chemical intermediates such as dimethyl ether (DME) and methyl t-butyl ether. Methanol is basically synthesized in three steps: synthesis gas generation, methanol synthesis and methanol distillation. The main step of methanol process is methanol synthesis. Even though many improvements from its first commercial implementation in 1923 and a series of new technologies are arising to get it (Lange, 2001; Olah et al., 2009), methanol is still largely produced Corresponding author. Tel.: + 98 711 2303071; fax: + 98 711 6287294.
E-mail address: [email protected] (M.R. Rahimpour). 0009-2509/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2010.04.018
by natural gas and specifically by means of syngas (CO and H2 mixture) obtained via steam reforming operations. Methanol synthesis reactors are designed based on two technologies, high-pressure synthesis operating at 300 bar and low-pressure synthesis operating between 50 and 100 bar (Lange, 2001). The methanol synthesis reactor studied here is operated in the low-pressure regime (Lurgi, 1995). 1.2. Literature review The importance of methanol has motivated numerous studies whose aim was to improve the efficiency of industrial methanol synthesis reactor. Dynamic simulation of conventional methanol synthesis reactor was investigated by Lovik et al. (1988) for longterm optimization. Rahimpour et al. (1998) studied the deactivation of methanol synthesis catalyst and proposed mechanisms for deactivation of this type of catalyst. Velardi and Barresi (2002) proposed a multi-stage methanol reactor network with autothermal behavior to promote reactor performance. To improve the performance of the methanol reactor, a number of configurations have been proposed including conventional dual-type reactor (Rahimpour, 2008; Rahimpour and Lotfinejad, 2008a), fixed bed with hydrogen permselective membrane reactors (Rahimpour et al., 2008; Rahimpour and Ghader, 2004), membrane dual-type reactor (Rahimpour and Lotfinejad, 2007, 2008b; Rahimpour and Alizadehhesari, 2009), fluidized-bed reactor (Wagialla and Elnashaie, 1991), fluidized-bed membrane dual-type reactors
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(Rahimpour and Alizadehhesari, 2008; Rahimpour and Elekaei, 2009; Rahimpour and Bayat, 2010) and cascade fluidized-bed membrane reactor (Rahimpour et al., 2010). 1.3. Dual type methanol reactor Implementing a higher temperature at the entrance of the reactor for a higher reaction rate, and then reducing the temperature gradually towards the exit from the 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 singletype methanol synthesis reactor was developed for methanol synthesis (Rahimpour and Lotfinejad, 2007). 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 synthesis gas to methanol. 1.4. Pd–Ag membrane reactor A membrane reactor combines the chemical reaction and membrane in one system. Membrane reactors have been applied to many common classes of catalytic reactions including dehydrogenation, hydrogenation, and partial and total oxidation reactions. For hydrogenation reactions involving liquid hydrocarbons, the membrane’s role is to separate the liquid from the gaseous reactant (e.g., hydrogen) and to provide a means for delivering this reactant at a controlled rate. Doing the latter reportedly helps to avoid hot spots in the reactor or undesirable side reactions (Marcano and Tsotsis, 2002). The general advantages of membrane reactors as compared to sequential reactionseparation systems are (1) increased reaction rates, (2) reduced byproduct formation, (3) lower energy requirements, and (4) the possibility of heat integration. These advantages potentially lead to compact process equipment that can be operated with a high degree of flexibility (Nunes and Peinemann, 2001). In many hydrogen-related reaction systems, Pd-alloy membranes on stainless steel supports have been used as hydrogenpermeable membranes (Lin and Rei, 2001). The highest hydrogen permeability was observed at an alloy composition of 23 wt% silver (Rahimpour and Ghader, 2003). Palladium-based membranes have been used for decades in hydrogen extraction because of their high permeability and good surface properties and because palladium, like all metals, is 100% selective for hydrogen transport (Buxbaum and Kinney, 1996). 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 (Dittmeyer et al., 2001). These properties make palladium-based membranes such as Pd–Ag membranes very attractive for use with petrochemical gases. 1.5. Fluidized-bed reactor One of the new possibilities for improving the efficiency of the conventional fixed-bed reactor synthesis is the fluidized-bed technology. Conventional packed bed reactors (PBRs) are seriously limited by poor heat transfer and low catalyst particle effectiveness factors because of severe diffusion limitations with the catalyst particle sizes used (Adris et al., 1991). Smaller particle sizes are infeasible in packed-bed systems because of pressure
drop considerations (Santos et al., 1994). Considerable attention has been paid to the fluidized-bed reactors because of their main advantages such as enhancement of conversion, a small pressure drop, elimination of diffusion limitations, good heat transfer capability and a more compact design (Abashar, 2004). The excellent tube-to-bed heat transfer allows a safe and efficient reactor operation even for highly exothermic reactions. Also for highly endothermic reactions, where the hot catalyst is circulated between the reactor and the regenerator, the excellent gas–solid heat transfer characteristics of the fluidized-beds can be effectively exploited (Deshmukh et al., 2007). Other advantages of fluidized bed membrane reactors (FBMR) include the possibility of using inexpensive metal alloys (i.e. due to its lower operating temperatures) as well as continuous/periodic catalyst replacement (Grace et al., 2005). However, FBMRs present challenges such as the possibility of catalyst attrition/erosion, a more complex design/scale-up/construction process as well as the need for reliable membranes. Given these advantages of membrane assisted fluidized bed reactor, a number of theoretical and experimental studies have been performed in recent years (Adris, 1994; Deshmukh, 2004; Patil, 2005). 1.6. Process deficiencies and modifications The recent operating data of the conventional dual-type reactor shows high pressure drop, plug in and low performance of fixed bed reactors (Rahimpour and Lotfinejad, 2007). Therefore, using fluidized-bed concept provides a uniform temperature along the reactor, which prolongs the service life of the catalyst. In addition, 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 methanol production. Using a fluidized-bed concept in gas-cooled reactor has been considered by Rahimpour and Alizadehhesari (2008). Moreover, proficiency of this reactor in the presence of long-term catalyst deactivation has been investigated by Rahimpour and Elekaei (2009). One potentially interesting idea for enhancement of efficiency in methanol synthesis process is using a cascade fluidized-bed membrane methanol reactor concept in the presence of catalyst deactivation, which is the subject of this work. 1.7. Dynamic simulation The extreme complexity of the processes involved in methanol synthesis justifies the computer simulation of such processes in order to get further understanding of the system without the need for conducting costly and time-consuming experiments. The dynamic simulation of methanol synthesis processes, in particular, has a wide range of applications including the start-up and shutdown investigations, system identification, safety, control, optimization, and transient behavior and operability studies. The dynamic simulation is preferred to steady-state simulations in operability studies since the former provides a realistic description of the transient states of the reactor owing to the fact that the numerical solution strategies employed in dynamic models are more robust than the solution of a typical steady-state model. Thus it allows for safe and trustworthy studies of the control and optimization of the reactor (Vasco de Toledo et al., 2001; Setinc and Levecb, 2001). 1.8. Objectives In this paper, a dynamic two-phase theory in bubbling regime of fluidization is developed to analyze the performance of a cascade
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fluidized-bed membrane dual-type reactor in the presence of catalyst deactivation. Moreover, we aim to demonstrate the advantages of the cascade fluidized-bed and the viability of this new concept relative to a conventional dual-type reactor system using dynamic simulation. Results show that the methanol production rate in CFBMMR is greater than CDMR and even FBMDMR.
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reacting gas leaving the first reactor is routed to the bottom of the second reactor. Finally, the product is removed from the upstream of the second reactor (gas-cooled reactor). The technical design data of the catalyst pellet for CFBMMR have been summarized in Table 1.
3. Mathematical model
2. Process description 2.1. Cascade fluidized-bed membrane methanol reactor (CFBMMR) The process of methanol synthesis in the conventional dual type methanol reactor (CDMR) and fluidized-bed membrane dualtype methanol reactor (FBMDMR) has been studied in the literature (Rahimpour and Lotfinejad, 2007; Rahimpour and Alizadehhesari, 2008). A schematic diagram of a CFBMMR configuration is presented in Fig. 1. This system is mainly based on the two-stage reactor system consisting of a water-cooled and a gas-cooled reactor, where both the reactors are fluidized-bed. The cold feed synthesis gas is fed to the tubes of the gas-cooled reactor (second reactor) from top of the reactor and flowing in counter-current mode with reacting gas mixture in the shell of the reactor. Moreover, the walls of tubes in this reactor (gas-cooled reactor) consist of a hydrogen permselective membrane. The pressure difference between the shell (71.2 bar) and tube (76.98 bar) sides is the driving force for 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 the tube. This simulation study is based on a Pd–Ag layer thickness of 1.1 mm. Then the outlet synthesised gas from the second reactor is fed to the bottom of tubes in 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 the reactor. In the first stage, methanol is partly produced. Then the
3.1. CDMR model Model assumptions: (a) one-dimensional plug flow; (b) axial diffusions of mass and heat are negligible compared to convection term; (c) gases are ideal; (d) radial variations in mass and heat are negligible.
Table 1 Catalyst and specifications of both reactors of CFBMMR. Parameter
Water-cooled reactor (fluidized-bed)
D (m) Di (mm) Do (mm) rs (kg m 3) cps (kJ kg 1 K1) lc (W m 1 K 1)
es Tube length (m) Shell side pressure (bar) Tube side pressure (bar)
Value
Gas-cooled reactor (membrane fluidized-bed) Value
4.5 40.3 4.5 1770 5.0 0.004 0.39 8 – 75
5.5 21.2 25.4 1770 5.0 0.004 0.39 10 71.2 76.98
Steam Drum
Feed syngas
Saturated water Reacting gas
Synthesis gas from reforming Pd-Ag membrane tube
Reaction side (Fluidized-bed)
Fluidized-bed membrane reactor (Gas-cooled reactor)
Fluidized-bed reactor (Water-cooled reactor)
To distillation unit
Pure methanol Fig. 1. A schematic diagram of cascade fluidized-bed membrane methanol reactor (CFBMMR).
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3.1.1. Water-cooled reactor (first reactor) The mass and energy equations for the bulk gas phase can be written as follows:
eB ct
@yi 1 @Fit ¼ þ av ct kgi ðyis yi Þ @t Ac @z
eB ct cpg
i ¼ 1,2, . . . ,N
ð1Þ
@T Ft @T pDi U ðT TÞ ¼ cpg þav hf ðTs TÞ þ Ac Ac shell shell @t @z
ð2Þ
where yi and T are the gas-phase mole fraction and temperature, respectively, and i represents H2, CO2, CO, CH3OH, and H2O. Argon, Nitrogen and methane are inert components. The mass and energy balance equations for the catalyst pellets can be formulated as follows: dy es ct is ¼ kgi av :ct :ðyi yis Þ þ Zri rB a dt
rB cps es
i ¼ 1,2, . . . ,N
ð3Þ
N X dTs ¼ av hf ðTTs Þ þ rB a Zri ðDHf ,i Þ dt i¼1
ð4Þ
where Z is effectiveness factor of catalyst and is calculated according to the procedure explained by Rezaie et al. (2005). Moreover, the kinetic model and the equilibrium rate constants are selected from Graaf’s studies (Graaf et al., 1990, 1986). yis and Ts are the mole fractions on the catalyst surface and solid-phase temperature, respectively. The boundary conditions are as follows: z ¼ 0;
t
F ¼ Fin ,
yi ¼ yi, in ,
T ¼ Tin
ð5Þ
while the initial conditions are t¼0 :
yti ¼ yi ss ,
ytis ¼ yss is ,
T t ¼ T ss ,
Tst ¼ Tsss ,
a¼1
The gas in the bubble phase is in plug flow and contains some catalyst particles, which are involved in reactions but the extent of reaction in bubble phase is much less than emulsion phase. Model structure An element of length dz as depicted in Fig. 2 was considered. On the basis of the aforementioned assumptions, the bubble and emulsion phase mass conservation equations are formulated as follows: Bubble phase:
d:ct :
3 X @yib d @Fib rbij ¼ þ dKbei ct ab ðyie yib Þ þ d:g:rs :a: @t Ac @z j¼1
ð10Þ where Kbei is mass transfer coefficient between bubble phase and emulsion phase, yie and yib are the emulsion phase and bubble phase mole fraction, respectively, and g is volume fraction of catalyst bed occupied by solid particles in bubble phase. Emulsion phase: ð1dÞ:ct :
where Fib and Fie are given as follows: Fi b ¼ yib F t ,
ct cpg
@Ttube 1 @ðF t TÞ pDi ¼ cpg U ðTTtube Þ þ @t Ac tube Ac @z
Fi e ¼ yie F t
ð12Þ
The heat transfer equation between bed (tubes) and shell side (cooling water):
ct :cpg
3.1.2.2. Tube side (feed synthesis gas flow). The energy balance equation for the fluid phase is given
3 X @yie ð1dÞ @Fie ¼ þ dKbei ct ab ðyib yie Þ þ ð1dÞre :Z:a: rij @t Ac @z j¼1
ð11Þ
ð6Þ
3.1.2. Gas-cooled reactor (second reactor) 3.1.2.1. Shell side (reaction side). The mass and energy balance for solid and gas phase in the gas-cooled reactor is the same as that in the water-cooled reactor.
i ¼ 1,2, . . . ,N
3 X dT pDi U ðT TÞ þ ð1dÞre :Z:a: rj ðDHf ,j Þ ¼ Ac Tube shell dt j¼1
þ d:g:rB :Z:a:
3 X
rbj ðDHf ,j Þ
ð13Þ
j¼1
where Tshell is temperature in shell side, which is constant (Chen et al., 2003).
F t |z+dz ð7Þ
The boundary conditions are as follows: z ¼ L;
yti ¼ yif ,
T t ¼ Tf
F t ¼ Ff
ð8Þ
3.2. CFBMMR model
Emulsion 3.2.1. Water-cooled reactor (first reactor) The mathematical simulation for first and second reactor of CFBMMR was developed based on the following assumptions: Model assumptions The conservation of mass and heat in fluidized-bed reactor (tube side) was developed based on the following assumptions: (a) The dense catalyst bed is considered to be composed of bubble phase and emulsion phase; (b) the operation is assumed to be isothermal, which means bubble and emulsion phases have same temperature; (c) plug flow regime in bubble phase is assumed; (d) the bubble rise velocity is constant and equal to average value; (e) Ideal gas behavior is assumed; (f) The solids concentration in the freeboard is assumed to decay exponentially as proposed by Kunii and Levenspiel (1991): f ¼ f þ ðfd f Þexpðafreeborad zfreeboard Þ ð9Þ (g) Bubbles are assumed to be spherical with constant size and equal to average value.
Bubble plug flow
Well mixed Heat transfer
dz Tb = Te
t
F |z Shellside (Saturated water)
Tube side (Reaction side)
Fig. 2. Schematic diagram of an elemental volume of first reactor.
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3.2.2. Gas-cooled reactor (second reactor) 3.2.2.1. Shell side (reaction side). Model assumptions: The assumptions considered for the first reactor are also valid in the gas-cooled reactor. Moreover, the assumption in the second reactor are (a) hydrogen is the only species that permeates through the membrane tube walls; (b) the gas fed to the fluidized-bed via membranes is assumed to be first perfectly mixed in or extracted from the emulsion phase (because of the relatively small bubble fraction); and (c) the axial diffusion of hydrogen through the membrane is neglected compared to the radial diffusion. Model structure: We consider an element of length dz as depicted in Fig. 3. The resulting mass balances for bubble and emulsion phases are given in Eqs. (14) and (15). Bubble phase:
d:ct :
3 X @yib d @Fi b ¼ þ dKbei ct ab ðyie yib Þ þ dgrs :a: rbij @t Ashell @z j¼1
Table 2 Hydrodynamic parameters. Parameter
Equation
Superficial velocity at minimum fluidization Archimedes number
e3mf js
1:75
Ar ¼
hd r u i2 p g mf m d3p
þ
h
150ð1emf Þ dp rg umf
m
e3mf js
i
¼ Ar
rg ðrp rg Þg m2
Bubble diameter
hp i0:4 dbm ¼ 0:65 D2 ðuo umf Þ 4 dbo ¼ 0:376ðuo umf Þ2
Mass transfer coefficient (bubbleemulsion phase) Bubble rising velocity
Kbe ¼
db ¼ dbm ðdbm dbo Þ expð0:3z=DÞ
Specific surface area for bubble Volume fraction of bubble phase to overall bed Density for emulsion phase
umf 3
þ ½ð4Djm emf ub =pdb Þ1=2
ub ¼ uumf þ 0:711 d ¼ (u umf)/ub ab ¼6d/db
pffiffiffiffiffiffiffiffi gdb
re ¼ rp(1 emf)
i ¼ 1,2, . . . ,N
ð14Þ where Kbei is mass transfer coefficient between bubble phase and emulsion phase, yie and yib are the emulsion phase and bubble phase mole fraction, respectively, and g is volume fraction of catalyst bed occupied by solid particles in bubble phase. Emulsion phase: ð1dÞ:ct :
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The heat transfer equation between bed and tubes: ffi dT aH qffiffiffiffiffit ffi qffiffiffiffiffiffi pDi pH psh ¼ ð1dÞ ct :cpg : U ðT TÞ H cph ðT-Ttube Þþ dt As Ashell shell tube þ ð1dÞ:Z:a:re
3 X j¼1
rj ðDHf ,j Þ þ d:g:rB :a:Z
3 X
rbj ðDHf ,j Þ
j¼1
ð17Þ
3 X
@yie ð1dÞ @Fie ¼ þ dKbei ct ab ðyib yie Þ þ ð1dÞre :Z:a: rij @t Ashell @z j¼1 þ ð1dÞ
ffi aH qffiffiffiffiffit ffi qffiffiffiffiffiffi sh As
PH
PH
ð15Þ
where aH is hydrogen permeation rate constant, PHt ,PHsh are hydrogen partial pressure in tube and reaction side (shell side), respectively. Fib and Fie are given as follows: Fi b ¼ yib F sh ,
Fi e ¼ yie F sh
F
sh
where Ttube is temperature in tube side (Chen et al., 2003). 3.2.2.2. Tube side (fresh feed synthesis gas flow). The mass and energy balance equations for fluid phase are given as follows: qffiffiffiffiffiffi qffiffiffiffiffiffiffi @y F t @yi aH i ¼ 1,2, . . . ,N ð18Þ PHt PHsh ct : i ¼ @t Ac @z As ct :cpg :
ð16Þ
| z+dz
z ¼ L;
Emulsion Well mixed Hydrogen through membrane
Tb = Te
t F |z F
sh
ð19Þ
where Ft is molar flow rate and Ttube is temperature of synthesis gas in tube side. The boundary conditions are as follows:
t F | z+dz
Bubble plug flow
ffi @Ttube Ft @T aH qffiffiffiffiffit ffi qffiffiffiffiffiffi ¼ cpg tube þ PH PHsh cph ðTTtube Þ @t Ac @z As pDi U ðTTtube Þ þ Ac tube
dz
yi ¼ yif ,
T ¼ Tf
ð20Þ
Auxiliary correlations for estimation of mass and heat transfer coefficients are given by Rahimpour and Alizadehhesari (2008d). The empirical correlations for the hydrodynamic parameters in the proposed model have been extracted from the published literature, which is summarized in Table 2 (Kunii and Levenspiel, 1991; Mori and Wen, 1975; Davidson and Harisson, 1963). Also catalyst deactivation model for the commercial methanol synthesis catalyst CuO/ZnO/Al2O3 was adopted from Hanken’s studies (Hanken, 1995). The permeation rate of hydrogen through the Pd–Ag membrane jH (mol/s) is assumed to obey the half-power pressure law (Sievert’s law). qffiffiffiffiffiffi qffiffiffiffiffiffiffi ð21Þ jH ¼ aH PHt - PHsh Hydrogen permeation rate constant (aH) is calculated according to the procedure explained by Hara et al. (1999).
|z
Shell side (Reaction side)
Tube side (Permeation side)
Fig. 3. Schematic diagram of an elemental volume of second reactor.
4. Numerical solution The governing equations of the model form a system of coupled equations comprising partial derivative equations of
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mass and energy conservative rules that set forth the catalyst, fluid, bubble and emulsion phases, ordinary differential equation of the deactivation model and also non-linear algebraic equations of the kinetic model, auxiliary and hydrodynamic correlations. The system of equations is solved using a two-stage approach consisting of a steady-state identification stage followed by a dynamic solution stage. Solution of the steady-state model is carried out by equaling all the time-variations of the states to zero and also considering the activity to be unity. A boundary value problem (BVP) is
obtained by means of backward finite difference approximation. Using the shooting method, BVP converts to an initial value problem (IVP). So, the solution is possible by trial and error procedure. In this way the initial conditions for temperature and components concentrations are determined for dynamic simulation. The set of dynamic equations has been discretized with respect to axial and time coordinates on the nodes. Globally convergent multi-dimensional Newton’s method in Matlab programming environment was used to solve these equations. Fig. 4 shows the trend of solving the model.
5. Results and discussion
Input data 5.1. Model validation The validation of steady-state and dynamic model of conventional dual type methanol reactor with plant data was previously performed by Rahimpour and Lotfinejad (2008a). 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 (Rahimpour and Lotfinejad, 2008a, 2007). As stated before, Wagialla and Elnashaie (1991) mathematically studied a fluidized-bed configuration for methanol synthesis and presented a steady state model based on two phase theory of fluidization. In Table 3, the results of Wagialla’s model and plant data are compared with the consequences of our suggested model of fluidized-bed and packed-bed reactor, respectively. Evidently, our numerical predictions are in good qualitative agreement with validated data. A parametric analysis was performed to address the vital issues, such as temperature, catalyst activity, methanol mole fraction and methanol production rate profiles along the reactors. The reacting gas temperature profiles for fresh catalyst along the conventional dual-type methanol reactor (CDMR), fluidized-bed membrane dual-type methanol reactor (FBMDMR) and cascade fluidized-bed membrane methanol reactor (CFBMMR) systems have been illustrated by Rahimpour et al. (2010). For exothermic systems such as methanol synthesis thermodynamic equilibrium becomes favorable at lower temperatures. The temperature control of the CFBMMR is easier in the first reactor. There is no sudden rise of temperature for this system during the first 2 m of reactor. For simulation purposes, the maximum temperature for the CuO/ZnO/Al2O3 catalyst to remain active is assumed to be 543 K. In CDMR and FBMDMR systems, the temperature of catalyst bed cannot be controlled (i.e., a hot spot is likely), whereas in CFBMMR it is achievable. Consequently the most favorable temperature profile seems that belonging to CFBMMR system as a result of excellent heat-transfer characteristics of fluidization (Rahimpour et al., 2010).
Guessun known Tin,yin
Replace new value of Tin,yh,in in Eqs.
Solve model of reactor
Calculate new value of Tf,yh (Tfcalc , yhcalc)
calc
Tf -Tf < 0.1 yh-yhcalc < 0.001
Output data
Fig. 4. Flowchart of solving the model.
Table 3 Comparison between the results of model with validated data. Parameter composition (%)
CO H2 CH3OH CO2 H2O N2 CH4
Cascade fluidized-bed reactor
Conventional dual-type reactor
Wagialla’s model
FBR model
Error (%)
Plant data
PBR(CDMR)
Error (%)
1.881 73.512 4.744 2.838 1.809 2.356 12.86
1.38 75.38 4.92 3.12 1.68 2.31 11.21
26.6 2.54 3.71 9.93 7.131 1.95 12.8
0.0251 0.5519 0.104 0.0709 0.0234 0.0968 0.114
0.0228 0.5323 0.1023 0.0764 0.0211 0.0905 0.103
9.16 3.55 3.4 4.38 9.82 1.2 9.64
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The comparison of simulation results of methanol production rate for the three types of reactor systems (CDMR, FBMDMR and CFBMMR) at first day is presented in Fig. 5. As can be seen, the highest methanol production rate is achieved in CFBMMR reactor. Since the FBMDMR and CFBMMR systems both have lower pressure drop, overcome mass transfer limitations due to small particle size, they have higher conversion during the operation. The small difference between CFBMMR and FBMDMR performances is attributed to the positive effect of fluidization of catalyst in the tubes of water-cooled reactor in CFBMMR. We carried out simulations with position dependent catalyst activity profiles to investigate the effect of catalyst activity on the production rate by using simulation results and showing the reasons for better performance of CFBMMR with respect to others. Fig. 6 exhibits activity, methanol production rate profiles along the three types of systems at 20th day and 1000th day of operation. The local change of activity along the reactor is due to local variation of temperature, which consequently affects the catalyst activity of the bed (Rahimpour et al., 2008). As can be seen from Fig. 6(a) and (c), the activity level sharply decreases in the first reactor because the catalyst is exposed to higher temperatures at that time. Since temperature profile declines along the gas-cooled reactor of three reactor
Fresh catalyst 6000
Methanol production rate (ton/day)
CDMR FBMDMR CFBMMR
5000
4000
First reactor
3000
2000 Second reactor
1000
0
0
5
10
15
length (m) Fig. 5. Comparison of methanol production rate profile in CFBMMR, FBMDMR and CDMR systems for fresh catalyst.
20th day
20th day
1
6000 CDMR FBMDMR CFBMMR
0.98 Methanol production rate(ton/day)
First reactor
0.96
Activity
0.94 0.92 0.9 Second reactor
0.88 0.86 CDMR FBMDMR CFBMMR
0.84 0.82
0
2
4
6
8
10
12
14
16
5000
4000
3000
2000 Second reactor
1000
0
18
First reactor
0
2
4
6
length(m)
8
10
12
14
16
18
16
18
length(m)
1000th day
1000th day
1
6000 CDMR
CDMR
FBMDMR
CFBMMR
0.8 First reactor
0.7 0.6 0.5 Second reactor
0.4
Methanol production rate(ton/day)
FBMDMR
0.9
Activity
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5000
4000
5
10 length (m)
15
First reactor
3000
2000
Second reactor 1000
0
0
CFBMMR
0
2
4
6
8
10
12
14
length (m)
Fig. 6. Comparison between (a, c) activity profiles and (b, d) methanol production rate profiles in three types of systems on the 20th day and 1000th day of operation.
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systems (Rahimpour et al., 2010), the catalyst activity improves in this stage. The lower temperature profile along both the reactors of CFBMMR system leads to the lower rate of catalyst deactivation along these reactors. Therefore, cascade fluidized-bed membrane reactor configuration provides favorable catalyst activity, as compared with CDMR and even FBMDMR, as shown in Fig. 6(a) and (c). Subsequently the methanol production rate in CFBMMR is higher than the others as can be seen in Fig. 6(b) and (d). Fig. 7 presents the profiles of reactor temperature, the catalyst activity versus time and length, for a CFBMMR. In the first reactor (from the reactor entrance to 8 m), the temperature of the reacting gas mixture on the first days is higher due to fresh catalyst and higher conversion. The rate of reaction heat decreases during further operation as the catalyst is deactivated. Since reaction heat is continuously removed by the water coolant, the temperature of the reacting gas mixture is reduced with time in the first reactor. In the second reactor (from 8 to 18 m), catalyst deactivation leads to an increase in methanol concentration gradient along the reactor and therefore reaction heat rises with time. Since the ability of the coolant gas to remove reaction heat is less than that of coolant water, temperature along the second reactor decreases with time, as shown in Fig. 7(a). The minimum activity level is observed near the first reactor inlet that is exposed to higher temperatures at different time. The catalyst in the gascooled reactor tends to have a lower temperature, which improves catalyst activity in this reactor, as shown in Fig. 7(b). Also, this figure shows that during operation time the catalyst is
deactivated due to poisoning and mainly due to thermal sintering, which is the loss of a catalyst active surface area owing to crystallite growth of either the support material or the active phase.
1
0.8
0.7
0.6
0.5
0.4
0
200
400
600
800
1000
1200
1400
time (day) Fig. 9. Comparison of the average activity in the reactor at a period of 1400 days of operating for three types of reactors.
540
1
520
0.8
500
Activity
Gas phase temperature (K)
CDMR FBMDMR CFBMMR
0.9
Average activity
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480
0.6 0.4
460 20 15
0.2 20
1500
len
10
g th
(m
1500
1000 5
)
500 0
0
len
day) time (
1000
10
g th
(m )
0
0
500 ay) time (d
0.12
0.1
0.1
CO2 mole fraction
Methanol mole fraction
Fig. 7. The profiles of (a) reactor temperature and (b) catalyst activity for a CFBMMR system.
0.08 0.06 0.04 0.02 0 20 15
len
1500 10 g th (m)
1000 5
500 0
0
time (d
ay)
0.08 0.06 0.04 0.02 20 15
len
1500 10
g th
(m
1000 5
)
500 0
0
(day) time
Fig. 8. Profiles of (a) mole fraction of methanol and (b) mole fraction of CO2 versus time and length for a CFBMMR.
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5700
0.076
CDMR
CDMR
5600
FBMDMR CFBMMR
0.072
Methanol production rate(ton/day)
Average methanol mole fraction
0.074
0.07 0.068 0.066 0.064 0.062 0.06
FBMDMR CFBMMR
5500 5400 5300 5200 5100 5000 4900 4800
0.058 0.056
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200
400
600
800
1000
1200
1400
0
200
400
600
800
1000
1200
1400
time (day)
time (day)
Fig. 10. Comparison of (a) average mole fraction and (b) production rate over a period of 1400 days of operation for CFBMMR, FBMDMR and CDMR systems.
Figs. 8(a) and (b) illustrate the methanol mole fraction and CO2 mole fraction profiles versus time and length for a CFBMMR, respectively. The mole fraction of methanol increases along the reactor, while it decreases as time goes on due to catalyst deactivation, as shown in Fig. 8(a). Catalysts in the CFBMMR are exposed to less extreme temperature than FBMDMR and CDMR, and catalyst deactivation via sintering is circumvented. The result of Fig. 9 shows that the least rate of average catalyst deactivation belongs to cascade fluidized-bed membrane methanol reactor and the maximum rate of average catalyst deactivation belongs to CDMR. Figs. 10(a) and (b) demonstrate the variations of average mole fraction of methanol and production rates over a period of 1400 operating days for the three types of reactor systems. Since the cascade fluidized-bed membrane system has the lowest average catalyst deactivation (see Fig. 9), it has the highest conversion during the operating period. The highest methanol mole fraction and production rate is in the CFBMMR, and the lowest mole fraction and production rate is in the CDMR.
6. Conclusion The methanol forming reactions are strongly exothermic and limited by the thermodynamic equilibrium. Moreover, the dualtype methanol reactor is limited by the poor heat transfer and low catalyst particle effectiveness factors because of severe diffusional limitations with the catalyst particle sizes used in the packed-bed reactor. From this concept, one potentially interesting idea for industrial methanol synthesis is using a cascade fluidized-bed membrane reactor concept, which has inherently lower pressure drop through the catalytic bed. A dynamic two phase theory of bubbling regime was developed for simulation of cascade fluidized-bed membrane methanol reactor in the presence of catalyst deactivation. Due to favorable temperature profile of catalyst along this system, the catalyst activity in both reactors is maintained at a higher level than conventional dual type system and results in a longer catalyst life-time. Moreover, the simulation results represent good enhancement in the yield of methanol production during 1400 days of the operation in the cascade fluidized-bed membrane methanol reactor (CFBMMR) in comparison with conventional dual type methanol reactor (CDMR) and fluidized-bed membrane dual type methanol reactor (FBMDMR),
respectively. This feature suggests that the concept of cascade fluidized-bed membrane reactor system is an interesting candidate for application in synthesis gas conversion to methanol.
Notation Ac Ar As Ashell a afreeboard ab an cPg cph cPs ct D Di dp db F sh Ft Fe Fb hf Kbei Kgi L PHt PHsh ri rbi T Ts Tshell
cross section area of each tube, m2 Archimedes number, dimensionless lateral area of each tube, m2 cross section area of shell, m2 activity, dimensionless freeboard decay constant, m 1 specific surface area of bubble, m2 m 3 specific surface area of catalyst pellet, m2 m 3 specific heat of the gas at constant pressure, J mol 1 K 1 specific heat of the hydrogen at constant pressure, J mol 1 K 1 specific heat of the catalyst at constant pressure, J mol 1 K 1 total concentration, mol m 3 reactor diameter, m inner diameter, m particle diameter, m bubble diameter, m total molar flow in shell side, mole s 1 total molar flow per tube, mole s 1 molar flow in emulsion side, mole s 1 molar flow in bubble side, mole s 1 gas–solid heat transfer coefficient, W m 2 K 1 mass transfer coefficient for component i in fluidized-bed, m s 1 mass transfer coefficient for component i, m s 1 reactor length, m tube side pressure, bar shell side pressure, bar reaction rate of component i, mol kg 1 s 1 reaction rate of component i in bubble phase, mol kg 1 s 1 bulk gas phase temperature, K temperature of solid phase, K temperature of coolant stream, in first reactor, K
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Ttube Ushell
Utube
U ub ue yi yis yib yie t z zfreeboard
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temperature of coolant stream, in second reactor, K overall heat transfer coefficient between coolant and process streams (gas-cooled reactor), W m2 K1 overall heat transfer coefficient between coolant and process streams (water-cooled reactor), W m2 K1 superficial velocity of fluid phase, m s 1 velocity of rise of bubbles, m s 1 linear velocity of emulsion phase, m s 1 mole fraction of component i in the fluid phase, mol mol 1 mole fraction of component i in the solid phase, mol mol 1 mole fraction of component i in the bubble phase, mol mol 1 mole fraction of component i in the emulsion phase, mol mol 1 time, s axial reactor coordinate, m axial coordinate in freeboard zone, m
Greek letters
aH DHf,i
eB es emf r rB rs Z d f* f fd
g m js
hydrogen permeation rate constant, mol m 1 s 1 Pa 0.5 enthalpy of formation of component i, J mol 1 void fraction of catalytic bed, dimensionless void fraction of catalyst, dimensionless void fraction of catalytic bed at minimum fluidization, dimensionless density of fluid phase, kg m 3 density of catalytic bed, kg m 3 density of catalyst, kg m 3 catalyst effectiveness factor, dimensionless bubble phase volume as a fraction of total bed volume, dimensionless saturation carrying capacity, dimensionless solids volume fraction, dimensionless solids volume fraction in dense phase, dimensionless volume fraction of catalyst occupied by solid particle in bubble, dimensionless viscosity of fluid phase, kg m 1 s 1 sphericity of catalyst, dimensionless
Superscripts and subscripts i j f in p s sh ss t b e mf g
component i reaction j feed conditions inlet conditions particle at catalyst surface shell side steady state condition tube side bubble phase emulsion phase minimum fluidization gas phase
Abbreviations CFBMMR
cascade fluidized-bed membrane methanol reactor
FBMDMR CDMR FBMR FBR PBR
fluidized-bed membrane dual type methanol reactor conventional dual type methanol reactor fluidized-bed membrane reactor fluidized-bed reactor packed-bed reactor
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Rahimpour, M.R., Lotfinejad, M., 2008. A comparison of co-current and countercurrent modes of operation for a dual type industrial methanol reactor. Chem. Eng. Process. 47, 1819–1830. Rahimpour, M.R., Lotfinejad, M., 2008. Co-current and counter-current configurations for a membrane dual type methanol reactor. Chem. Eng. Technol. 31 (1), 38–57. Rahimpour, M.R., Alizadehhesari, K., 2009. Enhancement of carbon dioxide removal in a hydrogen-permselective methanol synthesis reactor. Int. J. Hydrogen Energy 34 (3), 1349–1362. Rahimpour, M.R., Elekaei, H., 2009. Enhancement of methanol production in a novel fluidized bed hydrogen-permselective membrane reactor in the presence of catalyst deactivation. Int. J. Hydrogen Energy 34 (5), 2208–2223. Rahimpour, M.R., Bayat, M., 2010. Comparative study of two different hydrogen redistribution strategies along a fluidized-bed hydrogen permselective membrane reactor for methanol synthesis. Ind. Eng. Chem. Res. 49, 472–480. Rahimpour, M.R., Bayat, M., Rahmani, F., 2010. Enhancement of methanol production in a novel cascading fluidized-bed hydrogen permselective membrane methanol reactor. Chem. Eng. J. 157, 520–529.
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Contents lists available at ScienceDirect
Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Dynamic simulation of a cascade fluidized-bed membrane reactor in the presence of long-term catalyst deactivation for methanol synthesis M.R. Rahimpour , M. Bayat, F. Rahmani Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, Iran
a r t i c l e in fo
abstract
Article history: Received 15 January 2010 Received in revised form 11 March 2010 Accepted 16 April 2010 Available online 21 April 2010
In this work, a dynamic model for a cascade fluidized-bed hydrogen permselective membrane methanol reactor (CFBMMR) has been developed in the presence of long-term catalyst deactivation. In the first catalyst bed, the synthesis gas is partly converted to methanol in a water-cooled reactor, which is a fluidized-bed. In the second bed, which is a membrane assisted fluidized-bed reactor, the reaction heat is used to preheat the feed gas to the first bed. This reactor configuration solves some observed drawbacks of new conventional dual type methanol reactor (CDMR) and even fluidized-bed membrane dual type methanol reactor (FBMDMR) such as pressure drop, internal mass transfer limitations, radial gradient of concentration and temperature in both reactors. A dynamic two-phase theory in bubbling regime of fluidization is used to model and simulate the proposed reactor. The proposed model has been used to compare the performance of a cascade fluidized-bed membrane methanol reactor with fluidized-bed membrane dual-type methanol reactor and conventional dual-type methanol reactor. The simulation results show a considerable enhancement in the methanol production due to the favorable profile of temperature and activity along the CFBMMR relative to FBMDMR and CDMR systems. & 2010 Elsevier Ltd. All rights reserved.
Keywords: Dynamic simulation Cascade fluidized-bed Membrane reactor Methanol synthesis Hydrogen permselective membrane Catalyst deactivation
1. Introduction Improvement in production efficiency of important chemicals by only a few percent can sometimes result in significant profit increases, energy conservation and environmental protection, especially for a chemical such as methanol, which is produced in a worldwide range (Schack et al., 1989).
1.1. Methanol synthesis process Methanol is a bulk chemical, a kind of transportation fuel and energy material for fuel cell. It is a clean-burning fuel with versatile applications. As a combustion fuel, it provides extremely low emissions. Methanol can also be used as a solvent or a fuel additive and especially as a building block to produce chemical intermediates such as dimethyl ether (DME) and methyl t-butyl ether. Methanol is basically synthesized in three steps: synthesis gas generation, methanol synthesis and methanol distillation. The main step of methanol process is methanol synthesis. Even though many improvements from its first commercial implementation in 1923 and a series of new technologies are arising to get it (Lange, 2001; Olah et al., 2009), methanol is still largely produced Corresponding author. Tel.: + 98 711 2303071; fax: + 98 711 6287294.
E-mail address: [email protected] (M.R. Rahimpour). 0009-2509/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2010.04.018
by natural gas and specifically by means of syngas (CO and H2 mixture) obtained via steam reforming operations. Methanol synthesis reactors are designed based on two technologies, high-pressure synthesis operating at 300 bar and low-pressure synthesis operating between 50 and 100 bar (Lange, 2001). The methanol synthesis reactor studied here is operated in the low-pressure regime (Lurgi, 1995). 1.2. Literature review The importance of methanol has motivated numerous studies whose aim was to improve the efficiency of industrial methanol synthesis reactor. Dynamic simulation of conventional methanol synthesis reactor was investigated by Lovik et al. (1988) for longterm optimization. Rahimpour et al. (1998) studied the deactivation of methanol synthesis catalyst and proposed mechanisms for deactivation of this type of catalyst. Velardi and Barresi (2002) proposed a multi-stage methanol reactor network with autothermal behavior to promote reactor performance. To improve the performance of the methanol reactor, a number of configurations have been proposed including conventional dual-type reactor (Rahimpour, 2008; Rahimpour and Lotfinejad, 2008a), fixed bed with hydrogen permselective membrane reactors (Rahimpour et al., 2008; Rahimpour and Ghader, 2004), membrane dual-type reactor (Rahimpour and Lotfinejad, 2007, 2008b; Rahimpour and Alizadehhesari, 2009), fluidized-bed reactor (Wagialla and Elnashaie, 1991), fluidized-bed membrane dual-type reactors
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(Rahimpour and Alizadehhesari, 2008; Rahimpour and Elekaei, 2009; Rahimpour and Bayat, 2010) and cascade fluidized-bed membrane reactor (Rahimpour et al., 2010). 1.3. Dual type methanol reactor Implementing a higher temperature at the entrance of the reactor for a higher reaction rate, and then reducing the temperature gradually towards the exit from the 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 singletype methanol synthesis reactor was developed for methanol synthesis (Rahimpour and Lotfinejad, 2007). 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 synthesis gas to methanol. 1.4. Pd–Ag membrane reactor A membrane reactor combines the chemical reaction and membrane in one system. Membrane reactors have been applied to many common classes of catalytic reactions including dehydrogenation, hydrogenation, and partial and total oxidation reactions. For hydrogenation reactions involving liquid hydrocarbons, the membrane’s role is to separate the liquid from the gaseous reactant (e.g., hydrogen) and to provide a means for delivering this reactant at a controlled rate. Doing the latter reportedly helps to avoid hot spots in the reactor or undesirable side reactions (Marcano and Tsotsis, 2002). The general advantages of membrane reactors as compared to sequential reactionseparation systems are (1) increased reaction rates, (2) reduced byproduct formation, (3) lower energy requirements, and (4) the possibility of heat integration. These advantages potentially lead to compact process equipment that can be operated with a high degree of flexibility (Nunes and Peinemann, 2001). In many hydrogen-related reaction systems, Pd-alloy membranes on stainless steel supports have been used as hydrogenpermeable membranes (Lin and Rei, 2001). The highest hydrogen permeability was observed at an alloy composition of 23 wt% silver (Rahimpour and Ghader, 2003). Palladium-based membranes have been used for decades in hydrogen extraction because of their high permeability and good surface properties and because palladium, like all metals, is 100% selective for hydrogen transport (Buxbaum and Kinney, 1996). 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 (Dittmeyer et al., 2001). These properties make palladium-based membranes such as Pd–Ag membranes very attractive for use with petrochemical gases. 1.5. Fluidized-bed reactor One of the new possibilities for improving the efficiency of the conventional fixed-bed reactor synthesis is the fluidized-bed technology. Conventional packed bed reactors (PBRs) are seriously limited by poor heat transfer and low catalyst particle effectiveness factors because of severe diffusion limitations with the catalyst particle sizes used (Adris et al., 1991). Smaller particle sizes are infeasible in packed-bed systems because of pressure
drop considerations (Santos et al., 1994). Considerable attention has been paid to the fluidized-bed reactors because of their main advantages such as enhancement of conversion, a small pressure drop, elimination of diffusion limitations, good heat transfer capability and a more compact design (Abashar, 2004). The excellent tube-to-bed heat transfer allows a safe and efficient reactor operation even for highly exothermic reactions. Also for highly endothermic reactions, where the hot catalyst is circulated between the reactor and the regenerator, the excellent gas–solid heat transfer characteristics of the fluidized-beds can be effectively exploited (Deshmukh et al., 2007). Other advantages of fluidized bed membrane reactors (FBMR) include the possibility of using inexpensive metal alloys (i.e. due to its lower operating temperatures) as well as continuous/periodic catalyst replacement (Grace et al., 2005). However, FBMRs present challenges such as the possibility of catalyst attrition/erosion, a more complex design/scale-up/construction process as well as the need for reliable membranes. Given these advantages of membrane assisted fluidized bed reactor, a number of theoretical and experimental studies have been performed in recent years (Adris, 1994; Deshmukh, 2004; Patil, 2005). 1.6. Process deficiencies and modifications The recent operating data of the conventional dual-type reactor shows high pressure drop, plug in and low performance of fixed bed reactors (Rahimpour and Lotfinejad, 2007). Therefore, using fluidized-bed concept provides a uniform temperature along the reactor, which prolongs the service life of the catalyst. In addition, 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 methanol production. Using a fluidized-bed concept in gas-cooled reactor has been considered by Rahimpour and Alizadehhesari (2008). Moreover, proficiency of this reactor in the presence of long-term catalyst deactivation has been investigated by Rahimpour and Elekaei (2009). One potentially interesting idea for enhancement of efficiency in methanol synthesis process is using a cascade fluidized-bed membrane methanol reactor concept in the presence of catalyst deactivation, which is the subject of this work. 1.7. Dynamic simulation The extreme complexity of the processes involved in methanol synthesis justifies the computer simulation of such processes in order to get further understanding of the system without the need for conducting costly and time-consuming experiments. The dynamic simulation of methanol synthesis processes, in particular, has a wide range of applications including the start-up and shutdown investigations, system identification, safety, control, optimization, and transient behavior and operability studies. The dynamic simulation is preferred to steady-state simulations in operability studies since the former provides a realistic description of the transient states of the reactor owing to the fact that the numerical solution strategies employed in dynamic models are more robust than the solution of a typical steady-state model. Thus it allows for safe and trustworthy studies of the control and optimization of the reactor (Vasco de Toledo et al., 2001; Setinc and Levecb, 2001). 1.8. Objectives In this paper, a dynamic two-phase theory in bubbling regime of fluidization is developed to analyze the performance of a cascade
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fluidized-bed membrane dual-type reactor in the presence of catalyst deactivation. Moreover, we aim to demonstrate the advantages of the cascade fluidized-bed and the viability of this new concept relative to a conventional dual-type reactor system using dynamic simulation. Results show that the methanol production rate in CFBMMR is greater than CDMR and even FBMDMR.
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reacting gas leaving the first reactor is routed to the bottom of the second reactor. Finally, the product is removed from the upstream of the second reactor (gas-cooled reactor). The technical design data of the catalyst pellet for CFBMMR have been summarized in Table 1.
3. Mathematical model
2. Process description 2.1. Cascade fluidized-bed membrane methanol reactor (CFBMMR) The process of methanol synthesis in the conventional dual type methanol reactor (CDMR) and fluidized-bed membrane dualtype methanol reactor (FBMDMR) has been studied in the literature (Rahimpour and Lotfinejad, 2007; Rahimpour and Alizadehhesari, 2008). A schematic diagram of a CFBMMR configuration is presented in Fig. 1. This system is mainly based on the two-stage reactor system consisting of a water-cooled and a gas-cooled reactor, where both the reactors are fluidized-bed. The cold feed synthesis gas is fed to the tubes of the gas-cooled reactor (second reactor) from top of the reactor and flowing in counter-current mode with reacting gas mixture in the shell of the reactor. Moreover, the walls of tubes in this reactor (gas-cooled reactor) consist of a hydrogen permselective membrane. The pressure difference between the shell (71.2 bar) and tube (76.98 bar) sides is the driving force for 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 the tube. This simulation study is based on a Pd–Ag layer thickness of 1.1 mm. Then the outlet synthesised gas from the second reactor is fed to the bottom of tubes in 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 the reactor. In the first stage, methanol is partly produced. Then the
3.1. CDMR model Model assumptions: (a) one-dimensional plug flow; (b) axial diffusions of mass and heat are negligible compared to convection term; (c) gases are ideal; (d) radial variations in mass and heat are negligible.
Table 1 Catalyst and specifications of both reactors of CFBMMR. Parameter
Water-cooled reactor (fluidized-bed)
D (m) Di (mm) Do (mm) rs (kg m 3) cps (kJ kg 1 K1) lc (W m 1 K 1)
es Tube length (m) Shell side pressure (bar) Tube side pressure (bar)
Value
Gas-cooled reactor (membrane fluidized-bed) Value
4.5 40.3 4.5 1770 5.0 0.004 0.39 8 – 75
5.5 21.2 25.4 1770 5.0 0.004 0.39 10 71.2 76.98
Steam Drum
Feed syngas
Saturated water Reacting gas
Synthesis gas from reforming Pd-Ag membrane tube
Reaction side (Fluidized-bed)
Fluidized-bed membrane reactor (Gas-cooled reactor)
Fluidized-bed reactor (Water-cooled reactor)
To distillation unit
Pure methanol Fig. 1. A schematic diagram of cascade fluidized-bed membrane methanol reactor (CFBMMR).
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3.1.1. Water-cooled reactor (first reactor) The mass and energy equations for the bulk gas phase can be written as follows:
eB ct
@yi 1 @Fit ¼ þ av ct kgi ðyis yi Þ @t Ac @z
eB ct cpg
i ¼ 1,2, . . . ,N
ð1Þ
@T Ft @T pDi U ðT TÞ ¼ cpg þav hf ðTs TÞ þ Ac Ac shell shell @t @z
ð2Þ
where yi and T are the gas-phase mole fraction and temperature, respectively, and i represents H2, CO2, CO, CH3OH, and H2O. Argon, Nitrogen and methane are inert components. The mass and energy balance equations for the catalyst pellets can be formulated as follows: dy es ct is ¼ kgi av :ct :ðyi yis Þ þ Zri rB a dt
rB cps es
i ¼ 1,2, . . . ,N
ð3Þ
N X dTs ¼ av hf ðTTs Þ þ rB a Zri ðDHf ,i Þ dt i¼1
ð4Þ
where Z is effectiveness factor of catalyst and is calculated according to the procedure explained by Rezaie et al. (2005). Moreover, the kinetic model and the equilibrium rate constants are selected from Graaf’s studies (Graaf et al., 1990, 1986). yis and Ts are the mole fractions on the catalyst surface and solid-phase temperature, respectively. The boundary conditions are as follows: z ¼ 0;
t
F ¼ Fin ,
yi ¼ yi, in ,
T ¼ Tin
ð5Þ
while the initial conditions are t¼0 :
yti ¼ yi ss ,
ytis ¼ yss is ,
T t ¼ T ss ,
Tst ¼ Tsss ,
a¼1
The gas in the bubble phase is in plug flow and contains some catalyst particles, which are involved in reactions but the extent of reaction in bubble phase is much less than emulsion phase. Model structure An element of length dz as depicted in Fig. 2 was considered. On the basis of the aforementioned assumptions, the bubble and emulsion phase mass conservation equations are formulated as follows: Bubble phase:
d:ct :
3 X @yib d @Fib rbij ¼ þ dKbei ct ab ðyie yib Þ þ d:g:rs :a: @t Ac @z j¼1
ð10Þ where Kbei is mass transfer coefficient between bubble phase and emulsion phase, yie and yib are the emulsion phase and bubble phase mole fraction, respectively, and g is volume fraction of catalyst bed occupied by solid particles in bubble phase. Emulsion phase: ð1dÞ:ct :
where Fib and Fie are given as follows: Fi b ¼ yib F t ,
ct cpg
@Ttube 1 @ðF t TÞ pDi ¼ cpg U ðTTtube Þ þ @t Ac tube Ac @z
Fi e ¼ yie F t
ð12Þ
The heat transfer equation between bed (tubes) and shell side (cooling water):
ct :cpg
3.1.2.2. Tube side (feed synthesis gas flow). The energy balance equation for the fluid phase is given
3 X @yie ð1dÞ @Fie ¼ þ dKbei ct ab ðyib yie Þ þ ð1dÞre :Z:a: rij @t Ac @z j¼1
ð11Þ
ð6Þ
3.1.2. Gas-cooled reactor (second reactor) 3.1.2.1. Shell side (reaction side). The mass and energy balance for solid and gas phase in the gas-cooled reactor is the same as that in the water-cooled reactor.
i ¼ 1,2, . . . ,N
3 X dT pDi U ðT TÞ þ ð1dÞre :Z:a: rj ðDHf ,j Þ ¼ Ac Tube shell dt j¼1
þ d:g:rB :Z:a:
3 X
rbj ðDHf ,j Þ
ð13Þ
j¼1
where Tshell is temperature in shell side, which is constant (Chen et al., 2003).
F t |z+dz ð7Þ
The boundary conditions are as follows: z ¼ L;
yti ¼ yif ,
T t ¼ Tf
F t ¼ Ff
ð8Þ
3.2. CFBMMR model
Emulsion 3.2.1. Water-cooled reactor (first reactor) The mathematical simulation for first and second reactor of CFBMMR was developed based on the following assumptions: Model assumptions The conservation of mass and heat in fluidized-bed reactor (tube side) was developed based on the following assumptions: (a) The dense catalyst bed is considered to be composed of bubble phase and emulsion phase; (b) the operation is assumed to be isothermal, which means bubble and emulsion phases have same temperature; (c) plug flow regime in bubble phase is assumed; (d) the bubble rise velocity is constant and equal to average value; (e) Ideal gas behavior is assumed; (f) The solids concentration in the freeboard is assumed to decay exponentially as proposed by Kunii and Levenspiel (1991): f ¼ f þ ðfd f Þexpðafreeborad zfreeboard Þ ð9Þ (g) Bubbles are assumed to be spherical with constant size and equal to average value.
Bubble plug flow
Well mixed Heat transfer
dz Tb = Te
t
F |z Shellside (Saturated water)
Tube side (Reaction side)
Fig. 2. Schematic diagram of an elemental volume of first reactor.
ARTICLE IN PRESS M.R. Rahimpour et al. / Chemical Engineering Science 65 (2010) 4239–4249
3.2.2. Gas-cooled reactor (second reactor) 3.2.2.1. Shell side (reaction side). Model assumptions: The assumptions considered for the first reactor are also valid in the gas-cooled reactor. Moreover, the assumption in the second reactor are (a) hydrogen is the only species that permeates through the membrane tube walls; (b) the gas fed to the fluidized-bed via membranes is assumed to be first perfectly mixed in or extracted from the emulsion phase (because of the relatively small bubble fraction); and (c) the axial diffusion of hydrogen through the membrane is neglected compared to the radial diffusion. Model structure: We consider an element of length dz as depicted in Fig. 3. The resulting mass balances for bubble and emulsion phases are given in Eqs. (14) and (15). Bubble phase:
d:ct :
3 X @yib d @Fi b ¼ þ dKbei ct ab ðyie yib Þ þ dgrs :a: rbij @t Ashell @z j¼1
Table 2 Hydrodynamic parameters. Parameter
Equation
Superficial velocity at minimum fluidization Archimedes number
e3mf js
1:75
Ar ¼
hd r u i2 p g mf m d3p
þ
h
150ð1emf Þ dp rg umf
m
e3mf js
i
¼ Ar
rg ðrp rg Þg m2
Bubble diameter
hp i0:4 dbm ¼ 0:65 D2 ðuo umf Þ 4 dbo ¼ 0:376ðuo umf Þ2
Mass transfer coefficient (bubbleemulsion phase) Bubble rising velocity
Kbe ¼
db ¼ dbm ðdbm dbo Þ expð0:3z=DÞ
Specific surface area for bubble Volume fraction of bubble phase to overall bed Density for emulsion phase
umf 3
þ ½ð4Djm emf ub =pdb Þ1=2
ub ¼ uumf þ 0:711 d ¼ (u umf)/ub ab ¼6d/db
pffiffiffiffiffiffiffiffi gdb
re ¼ rp(1 emf)
i ¼ 1,2, . . . ,N
ð14Þ where Kbei is mass transfer coefficient between bubble phase and emulsion phase, yie and yib are the emulsion phase and bubble phase mole fraction, respectively, and g is volume fraction of catalyst bed occupied by solid particles in bubble phase. Emulsion phase: ð1dÞ:ct :
4243
The heat transfer equation between bed and tubes: ffi dT aH qffiffiffiffiffit ffi qffiffiffiffiffiffi pDi pH psh ¼ ð1dÞ ct :cpg : U ðT TÞ H cph ðT-Ttube Þþ dt As Ashell shell tube þ ð1dÞ:Z:a:re
3 X j¼1
rj ðDHf ,j Þ þ d:g:rB :a:Z
3 X
rbj ðDHf ,j Þ
j¼1
ð17Þ
3 X
@yie ð1dÞ @Fie ¼ þ dKbei ct ab ðyib yie Þ þ ð1dÞre :Z:a: rij @t Ashell @z j¼1 þ ð1dÞ
ffi aH qffiffiffiffiffit ffi qffiffiffiffiffiffi sh As
PH
PH
ð15Þ
where aH is hydrogen permeation rate constant, PHt ,PHsh are hydrogen partial pressure in tube and reaction side (shell side), respectively. Fib and Fie are given as follows: Fi b ¼ yib F sh ,
Fi e ¼ yie F sh
F
sh
where Ttube is temperature in tube side (Chen et al., 2003). 3.2.2.2. Tube side (fresh feed synthesis gas flow). The mass and energy balance equations for fluid phase are given as follows: qffiffiffiffiffiffi qffiffiffiffiffiffiffi @y F t @yi aH i ¼ 1,2, . . . ,N ð18Þ PHt PHsh ct : i ¼ @t Ac @z As ct :cpg :
ð16Þ
| z+dz
z ¼ L;
Emulsion Well mixed Hydrogen through membrane
Tb = Te
t F |z F
sh
ð19Þ
where Ft is molar flow rate and Ttube is temperature of synthesis gas in tube side. The boundary conditions are as follows:
t F | z+dz
Bubble plug flow
ffi @Ttube Ft @T aH qffiffiffiffiffit ffi qffiffiffiffiffiffi ¼ cpg tube þ PH PHsh cph ðTTtube Þ @t Ac @z As pDi U ðTTtube Þ þ Ac tube
dz
yi ¼ yif ,
T ¼ Tf
ð20Þ
Auxiliary correlations for estimation of mass and heat transfer coefficients are given by Rahimpour and Alizadehhesari (2008d). The empirical correlations for the hydrodynamic parameters in the proposed model have been extracted from the published literature, which is summarized in Table 2 (Kunii and Levenspiel, 1991; Mori and Wen, 1975; Davidson and Harisson, 1963). Also catalyst deactivation model for the commercial methanol synthesis catalyst CuO/ZnO/Al2O3 was adopted from Hanken’s studies (Hanken, 1995). The permeation rate of hydrogen through the Pd–Ag membrane jH (mol/s) is assumed to obey the half-power pressure law (Sievert’s law). qffiffiffiffiffiffi qffiffiffiffiffiffiffi ð21Þ jH ¼ aH PHt - PHsh Hydrogen permeation rate constant (aH) is calculated according to the procedure explained by Hara et al. (1999).
|z
Shell side (Reaction side)
Tube side (Permeation side)
Fig. 3. Schematic diagram of an elemental volume of second reactor.
4. Numerical solution The governing equations of the model form a system of coupled equations comprising partial derivative equations of
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mass and energy conservative rules that set forth the catalyst, fluid, bubble and emulsion phases, ordinary differential equation of the deactivation model and also non-linear algebraic equations of the kinetic model, auxiliary and hydrodynamic correlations. The system of equations is solved using a two-stage approach consisting of a steady-state identification stage followed by a dynamic solution stage. Solution of the steady-state model is carried out by equaling all the time-variations of the states to zero and also considering the activity to be unity. A boundary value problem (BVP) is
obtained by means of backward finite difference approximation. Using the shooting method, BVP converts to an initial value problem (IVP). So, the solution is possible by trial and error procedure. In this way the initial conditions for temperature and components concentrations are determined for dynamic simulation. The set of dynamic equations has been discretized with respect to axial and time coordinates on the nodes. Globally convergent multi-dimensional Newton’s method in Matlab programming environment was used to solve these equations. Fig. 4 shows the trend of solving the model.
5. Results and discussion
Input data 5.1. Model validation The validation of steady-state and dynamic model of conventional dual type methanol reactor with plant data was previously performed by Rahimpour and Lotfinejad (2008a). 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 (Rahimpour and Lotfinejad, 2008a, 2007). As stated before, Wagialla and Elnashaie (1991) mathematically studied a fluidized-bed configuration for methanol synthesis and presented a steady state model based on two phase theory of fluidization. In Table 3, the results of Wagialla’s model and plant data are compared with the consequences of our suggested model of fluidized-bed and packed-bed reactor, respectively. Evidently, our numerical predictions are in good qualitative agreement with validated data. A parametric analysis was performed to address the vital issues, such as temperature, catalyst activity, methanol mole fraction and methanol production rate profiles along the reactors. The reacting gas temperature profiles for fresh catalyst along the conventional dual-type methanol reactor (CDMR), fluidized-bed membrane dual-type methanol reactor (FBMDMR) and cascade fluidized-bed membrane methanol reactor (CFBMMR) systems have been illustrated by Rahimpour et al. (2010). For exothermic systems such as methanol synthesis thermodynamic equilibrium becomes favorable at lower temperatures. The temperature control of the CFBMMR is easier in the first reactor. There is no sudden rise of temperature for this system during the first 2 m of reactor. For simulation purposes, the maximum temperature for the CuO/ZnO/Al2O3 catalyst to remain active is assumed to be 543 K. In CDMR and FBMDMR systems, the temperature of catalyst bed cannot be controlled (i.e., a hot spot is likely), whereas in CFBMMR it is achievable. Consequently the most favorable temperature profile seems that belonging to CFBMMR system as a result of excellent heat-transfer characteristics of fluidization (Rahimpour et al., 2010).
Guessun known Tin,yin
Replace new value of Tin,yh,in in Eqs.
Solve model of reactor
Calculate new value of Tf,yh (Tfcalc , yhcalc)
calc
Tf -Tf < 0.1 yh-yhcalc < 0.001
Output data
Fig. 4. Flowchart of solving the model.
Table 3 Comparison between the results of model with validated data. Parameter composition (%)
CO H2 CH3OH CO2 H2O N2 CH4
Cascade fluidized-bed reactor
Conventional dual-type reactor
Wagialla’s model
FBR model
Error (%)
Plant data
PBR(CDMR)
Error (%)
1.881 73.512 4.744 2.838 1.809 2.356 12.86
1.38 75.38 4.92 3.12 1.68 2.31 11.21
26.6 2.54 3.71 9.93 7.131 1.95 12.8
0.0251 0.5519 0.104 0.0709 0.0234 0.0968 0.114
0.0228 0.5323 0.1023 0.0764 0.0211 0.0905 0.103
9.16 3.55 3.4 4.38 9.82 1.2 9.64
ARTICLE IN PRESS M.R. Rahimpour et al. / Chemical Engineering Science 65 (2010) 4239–4249
The comparison of simulation results of methanol production rate for the three types of reactor systems (CDMR, FBMDMR and CFBMMR) at first day is presented in Fig. 5. As can be seen, the highest methanol production rate is achieved in CFBMMR reactor. Since the FBMDMR and CFBMMR systems both have lower pressure drop, overcome mass transfer limitations due to small particle size, they have higher conversion during the operation. The small difference between CFBMMR and FBMDMR performances is attributed to the positive effect of fluidization of catalyst in the tubes of water-cooled reactor in CFBMMR. We carried out simulations with position dependent catalyst activity profiles to investigate the effect of catalyst activity on the production rate by using simulation results and showing the reasons for better performance of CFBMMR with respect to others. Fig. 6 exhibits activity, methanol production rate profiles along the three types of systems at 20th day and 1000th day of operation. The local change of activity along the reactor is due to local variation of temperature, which consequently affects the catalyst activity of the bed (Rahimpour et al., 2008). As can be seen from Fig. 6(a) and (c), the activity level sharply decreases in the first reactor because the catalyst is exposed to higher temperatures at that time. Since temperature profile declines along the gas-cooled reactor of three reactor
Fresh catalyst 6000
Methanol production rate (ton/day)
CDMR FBMDMR CFBMMR
5000
4000
First reactor
3000
2000 Second reactor
1000
0
0
5
10
15
length (m) Fig. 5. Comparison of methanol production rate profile in CFBMMR, FBMDMR and CDMR systems for fresh catalyst.
20th day
20th day
1
6000 CDMR FBMDMR CFBMMR
0.98 Methanol production rate(ton/day)
First reactor
0.96
Activity
0.94 0.92 0.9 Second reactor
0.88 0.86 CDMR FBMDMR CFBMMR
0.84 0.82
0
2
4
6
8
10
12
14
16
5000
4000
3000
2000 Second reactor
1000
0
18
First reactor
0
2
4
6
length(m)
8
10
12
14
16
18
16
18
length(m)
1000th day
1000th day
1
6000 CDMR
CDMR
FBMDMR
CFBMMR
0.8 First reactor
0.7 0.6 0.5 Second reactor
0.4
Methanol production rate(ton/day)
FBMDMR
0.9
Activity
4245
5000
4000
5
10 length (m)
15
First reactor
3000
2000
Second reactor 1000
0
0
CFBMMR
0
2
4
6
8
10
12
14
length (m)
Fig. 6. Comparison between (a, c) activity profiles and (b, d) methanol production rate profiles in three types of systems on the 20th day and 1000th day of operation.
ARTICLE IN PRESS M.R. Rahimpour et al. / Chemical Engineering Science 65 (2010) 4239–4249
systems (Rahimpour et al., 2010), the catalyst activity improves in this stage. The lower temperature profile along both the reactors of CFBMMR system leads to the lower rate of catalyst deactivation along these reactors. Therefore, cascade fluidized-bed membrane reactor configuration provides favorable catalyst activity, as compared with CDMR and even FBMDMR, as shown in Fig. 6(a) and (c). Subsequently the methanol production rate in CFBMMR is higher than the others as can be seen in Fig. 6(b) and (d). Fig. 7 presents the profiles of reactor temperature, the catalyst activity versus time and length, for a CFBMMR. In the first reactor (from the reactor entrance to 8 m), the temperature of the reacting gas mixture on the first days is higher due to fresh catalyst and higher conversion. The rate of reaction heat decreases during further operation as the catalyst is deactivated. Since reaction heat is continuously removed by the water coolant, the temperature of the reacting gas mixture is reduced with time in the first reactor. In the second reactor (from 8 to 18 m), catalyst deactivation leads to an increase in methanol concentration gradient along the reactor and therefore reaction heat rises with time. Since the ability of the coolant gas to remove reaction heat is less than that of coolant water, temperature along the second reactor decreases with time, as shown in Fig. 7(a). The minimum activity level is observed near the first reactor inlet that is exposed to higher temperatures at different time. The catalyst in the gascooled reactor tends to have a lower temperature, which improves catalyst activity in this reactor, as shown in Fig. 7(b). Also, this figure shows that during operation time the catalyst is
deactivated due to poisoning and mainly due to thermal sintering, which is the loss of a catalyst active surface area owing to crystallite growth of either the support material or the active phase.
1
0.8
0.7
0.6
0.5
0.4
0
200
400
600
800
1000
1200
1400
time (day) Fig. 9. Comparison of the average activity in the reactor at a period of 1400 days of operating for three types of reactors.
540
1
520
0.8
500
Activity
Gas phase temperature (K)
CDMR FBMDMR CFBMMR
0.9
Average activity
4246
480
0.6 0.4
460 20 15
0.2 20
1500
len
10
g th
(m
1500
1000 5
)
500 0
0
len
day) time (
1000
10
g th
(m )
0
0
500 ay) time (d
0.12
0.1
0.1
CO2 mole fraction
Methanol mole fraction
Fig. 7. The profiles of (a) reactor temperature and (b) catalyst activity for a CFBMMR system.
0.08 0.06 0.04 0.02 0 20 15
len
1500 10 g th (m)
1000 5
500 0
0
time (d
ay)
0.08 0.06 0.04 0.02 20 15
len
1500 10
g th
(m
1000 5
)
500 0
0
(day) time
Fig. 8. Profiles of (a) mole fraction of methanol and (b) mole fraction of CO2 versus time and length for a CFBMMR.
ARTICLE IN PRESS M.R. Rahimpour et al. / Chemical Engineering Science 65 (2010) 4239–4249
5700
0.076
CDMR
CDMR
5600
FBMDMR CFBMMR
0.072
Methanol production rate(ton/day)
Average methanol mole fraction
0.074
0.07 0.068 0.066 0.064 0.062 0.06
FBMDMR CFBMMR
5500 5400 5300 5200 5100 5000 4900 4800
0.058 0.056
4247
4700 0
200
400
600
800
1000
1200
1400
0
200
400
600
800
1000
1200
1400
time (day)
time (day)
Fig. 10. Comparison of (a) average mole fraction and (b) production rate over a period of 1400 days of operation for CFBMMR, FBMDMR and CDMR systems.
Figs. 8(a) and (b) illustrate the methanol mole fraction and CO2 mole fraction profiles versus time and length for a CFBMMR, respectively. The mole fraction of methanol increases along the reactor, while it decreases as time goes on due to catalyst deactivation, as shown in Fig. 8(a). Catalysts in the CFBMMR are exposed to less extreme temperature than FBMDMR and CDMR, and catalyst deactivation via sintering is circumvented. The result of Fig. 9 shows that the least rate of average catalyst deactivation belongs to cascade fluidized-bed membrane methanol reactor and the maximum rate of average catalyst deactivation belongs to CDMR. Figs. 10(a) and (b) demonstrate the variations of average mole fraction of methanol and production rates over a period of 1400 operating days for the three types of reactor systems. Since the cascade fluidized-bed membrane system has the lowest average catalyst deactivation (see Fig. 9), it has the highest conversion during the operating period. The highest methanol mole fraction and production rate is in the CFBMMR, and the lowest mole fraction and production rate is in the CDMR.
6. Conclusion The methanol forming reactions are strongly exothermic and limited by the thermodynamic equilibrium. Moreover, the dualtype methanol reactor is limited by the poor heat transfer and low catalyst particle effectiveness factors because of severe diffusional limitations with the catalyst particle sizes used in the packed-bed reactor. From this concept, one potentially interesting idea for industrial methanol synthesis is using a cascade fluidized-bed membrane reactor concept, which has inherently lower pressure drop through the catalytic bed. A dynamic two phase theory of bubbling regime was developed for simulation of cascade fluidized-bed membrane methanol reactor in the presence of catalyst deactivation. Due to favorable temperature profile of catalyst along this system, the catalyst activity in both reactors is maintained at a higher level than conventional dual type system and results in a longer catalyst life-time. Moreover, the simulation results represent good enhancement in the yield of methanol production during 1400 days of the operation in the cascade fluidized-bed membrane methanol reactor (CFBMMR) in comparison with conventional dual type methanol reactor (CDMR) and fluidized-bed membrane dual type methanol reactor (FBMDMR),
respectively. This feature suggests that the concept of cascade fluidized-bed membrane reactor system is an interesting candidate for application in synthesis gas conversion to methanol.
Notation Ac Ar As Ashell a afreeboard ab an cPg cph cPs ct D Di dp db F sh Ft Fe Fb hf Kbei Kgi L PHt PHsh ri rbi T Ts Tshell
cross section area of each tube, m2 Archimedes number, dimensionless lateral area of each tube, m2 cross section area of shell, m2 activity, dimensionless freeboard decay constant, m 1 specific surface area of bubble, m2 m 3 specific surface area of catalyst pellet, m2 m 3 specific heat of the gas at constant pressure, J mol 1 K 1 specific heat of the hydrogen at constant pressure, J mol 1 K 1 specific heat of the catalyst at constant pressure, J mol 1 K 1 total concentration, mol m 3 reactor diameter, m inner diameter, m particle diameter, m bubble diameter, m total molar flow in shell side, mole s 1 total molar flow per tube, mole s 1 molar flow in emulsion side, mole s 1 molar flow in bubble side, mole s 1 gas–solid heat transfer coefficient, W m 2 K 1 mass transfer coefficient for component i in fluidized-bed, m s 1 mass transfer coefficient for component i, m s 1 reactor length, m tube side pressure, bar shell side pressure, bar reaction rate of component i, mol kg 1 s 1 reaction rate of component i in bubble phase, mol kg 1 s 1 bulk gas phase temperature, K temperature of solid phase, K temperature of coolant stream, in first reactor, K
ARTICLE IN PRESS 4248
Ttube Ushell
Utube
U ub ue yi yis yib yie t z zfreeboard
M.R. Rahimpour et al. / Chemical Engineering Science 65 (2010) 4239–4249
temperature of coolant stream, in second reactor, K overall heat transfer coefficient between coolant and process streams (gas-cooled reactor), W m2 K1 overall heat transfer coefficient between coolant and process streams (water-cooled reactor), W m2 K1 superficial velocity of fluid phase, m s 1 velocity of rise of bubbles, m s 1 linear velocity of emulsion phase, m s 1 mole fraction of component i in the fluid phase, mol mol 1 mole fraction of component i in the solid phase, mol mol 1 mole fraction of component i in the bubble phase, mol mol 1 mole fraction of component i in the emulsion phase, mol mol 1 time, s axial reactor coordinate, m axial coordinate in freeboard zone, m
Greek letters
aH DHf,i
eB es emf r rB rs Z d f* f fd
g m js
hydrogen permeation rate constant, mol m 1 s 1 Pa 0.5 enthalpy of formation of component i, J mol 1 void fraction of catalytic bed, dimensionless void fraction of catalyst, dimensionless void fraction of catalytic bed at minimum fluidization, dimensionless density of fluid phase, kg m 3 density of catalytic bed, kg m 3 density of catalyst, kg m 3 catalyst effectiveness factor, dimensionless bubble phase volume as a fraction of total bed volume, dimensionless saturation carrying capacity, dimensionless solids volume fraction, dimensionless solids volume fraction in dense phase, dimensionless volume fraction of catalyst occupied by solid particle in bubble, dimensionless viscosity of fluid phase, kg m 1 s 1 sphericity of catalyst, dimensionless
Superscripts and subscripts i j f in p s sh ss t b e mf g
component i reaction j feed conditions inlet conditions particle at catalyst surface shell side steady state condition tube side bubble phase emulsion phase minimum fluidization gas phase
Abbreviations CFBMMR
cascade fluidized-bed membrane methanol reactor
FBMDMR CDMR FBMR FBR PBR
fluidized-bed membrane dual type methanol reactor conventional dual type methanol reactor fluidized-bed membrane reactor fluidized-bed reactor packed-bed reactor
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