A Comparative Study Between a Fluidized-bed and a Fixed-bed Water Perm-selective Membrane Reactor With in Situ H2O Removal for Fischer-Tropsch Synthesis of GTL Technology

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Journal of Natural Gas Science and Engineering 3 (2011) 484e495

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Journal of Natural Gas Science and Engineering

journal homepage: www.elsevier .com/locate/ jngse

A comparative study between a fluidized-bed and a fixed-bedwater perm-selective membrane reactor with in situ H2O removalfor FischereTropsch synthesis of GTL technology

M.R. Rahimpour a,*, A. Mirvakili a, K. Paymooni a, B. Moghtaderi b

aChemical Engineering Department, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, IranbDiscipline of Chemical Engineering, Faculty of Engineering and Built Environment, The University of Newcastle, University Drive, Callaghan NSW 2308, Australia

a r t i c l e i n f o

Article history:Received 17 January 2011Received in revised form25 May 2011Accepted 26 May 2011Available online 28 June 2011

Keywords:FischereTropsch synthesisWater perm-selective membrane layerFluidized-bed membrane reactorFT reactor combinationIn situ water removalGTL technology

* Corresponding author. Tel.: þ98 711 2303071; faxE-mail address: [email protected] (M.R. Rahi

1875-5100/$ e see front matter � 2011 Elsevier B.V.doi:10.1016/j.jngse.2011.05.003

a b s t r a c t

In order to eliminate the pressure drop problem and mal distribution of the temperature profile along thereactors, fluidized-bed membrane reactors are proposed as an alternative for FischereTropsch synthesis(FTS) in gas-to-liquid (GTL) technology. Regarding this, a novel cascading fluidized-bedmembrane reactor(CFMR) is proposed in this study and compared with a fixed-bed membrane cascading with fluidized-bedmembrane reactor (FMFMR). The CFMR configuration consists of a fluidized-bed water perm-selectivemembrane reactor followed by a fluidized-bed hydrogen perm-selective membrane reactor. The perfor-mance of CFMR is compared with FMFMR in order to investigate the effect of fluidization concept on thereactor performance. Unlike CFMRwhere a fluidized-bed concept is applied in the first reactor, a fixed-bedconcept is used in the first reactor of FMFMR. Themodeling results show 5.3% increase in the gasoline yieldand 12% decrease in CO2 yield in CFMR in comparison with FMFMR owing to applying a fluidized-bedconcept instead of a fixed-bed concept in which more effective temperature management is achieved.According to the modeling results, CFMR is superior to FMFMR for FTS in GTL technology owing toachieving excellent temperature control and a small pressure drop and consequently higher gasoline yieldand lower CO2 yield.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

The conversion of natural gas to hydrocarbons (Gas-To-Liquidsroute) is currently one of the most promising topics in the energyindustry due to economic utilization of remote natural gas toenvironmentally clean fuels. For FT to be competitivewith crude oil,while the latter is still available, the cost of coal or methane needsto be low (Dry Mark, 1999). FT products are of high quality, beingfree of sulfur, nitrogen, aromatics, and other contaminants typicallyfound in petroleum products, which is especially true forFT-gasoline with a very high octane number. However, drawbacksalso exist for the FT process: the capital costs of FT conversionplants are relatively higher and the energy efficiency of producingFT liquids is relatively lower than the one for other alternative fuelssuch as hydrogen, methanol, dimethyl ether (DME) and conven-tional biofuels (Takayuki and Kenji, 2008).

: þ98 711 6287294.mpour).

All rights reserved.

1.1. Process and model

In order to realize more comprehensive description of FTSprocess and model, the kinetics model and a few mathematicalmodeling studies on FTS are provided as follows:

The kinetics of the gasesolid FTS over a commercialFeeCueKeSiO2 catalyst was studied in a continuous spinningbasket reactor (van der Laan, 1999). Schulz et al. (1999) extendedtheir existing kinetic model by taking into account olefin hydro-genation, isomerization (double bond shift) and incorporation andin particular chain length dependent product solubilities. The val-idity of their model was checked with experimental data obtainedfrom FTS runs in a slurry reactor with cobalt and iron catalysts.Eliason et al. obtained rate data for FTS on unsupported Fe and Fe/Kcatalysts at total pressure, temperature, and H2 and CO partialpressures of 10 atm, 200e240 �C, 0.9e1.4 and 0.4e0.9, respectively(Eliason and Bartholomew, 1999). Nowicki et al. (2001) developeda new hydrocarbon product distribution model for FTS reaction.Themodel was based on the assumption that there are two types ofactive sites on the catalyst surface: type-1, where growth ofhydrocarbon intermediates occurs, and type-2, where reversible re

SteamReforming Steam Drum

Product

Fig. 1. Schematic diagram of a conventional fixed-bed reactor (CR).

M.R. Rahimpour et al. / Journal of Natural Gas Science and Engineering 3 (2011) 484e495 485

adsorption of 1-ole00ns occur. Nakhaei Pour et al. (2011) investigatedthe kinetic modeling of the water-gas-shift (WGS) reaction overa Fe/Cu/La/Si catalyst under FTS reaction condition. A new GTLprocess based on a single stage fixed-bed FTS was developed in theResearch Institute of Petroleum Industry (RIPI) to produce highoctane and low sulfur gasoline (RIPI-NIOC, 2004). Ahmadi Marvastet al. considered a water-cooled fixed-bed reactor with a length of12 m (Marvast et al., 2005). Rahimpour et al. optimized a fluidized-bed hydrogen perm-selective membrane reactor for FTS(Rahimpour and Alizadehhesari, 2008). Rahimpour and Elekaeicompared the performance of fluidized-bed membrane dual-typereactor (FMDR) with CR for FTS (Rahimpour, 2008). Moreover,several investigations are performed by Rahimpour et al. to applymembranes in dual-type reactors (Rahimpour and Elekaei,2009a,b; Forghani et al., 2009; Rahimpour et al., 2010).

1.2. Hydroxy sodalite (H-SOD) membrane

H-SODmembrane has been used as highly water perm-selectivemembrane for water permeation. H-SOD is a zeolite-like materialwhich consists of sodalite cages exclusively (Fernandes and Soares,2006; Gielens et al., 2007). H-SOD membrane shows excellentlyideal selectivity (near to absolute) of water to hydrogen. It can beconsidered as a capable candidate for water separation in FTSwhich requires a high H2O/H2 perm-selectivity (Rohde et al., 2008).The exceptional property of H-SOD membrane in comparison withthe other widely studied membranes (Rohde et al., 2008; Peterset al., 2008; Dittmeyer et al., 2001) is its 100% selectivity of wateron the basis of molecular sieving in hybrid processes (Rohde et al.,2008; Breck, 1974). No traces of the other components are detectedin permeate (water selectivity w 1,000,000). Thus, H-SOD isa promising candidate for in situ H2O removal during FTS (Breck,1974).

1.3. Effect of in situ H2O removal

Water is a primary product of FT reactions and CO2 can only beproduced by WGS reaction which is a reversible paral-leleconsecutive reaction in respect to CO (Rohde et al., 2008;Khajavi et al., 2010). In case of Fe catalysts, oxidation and hydro-thermal sintering lead to formation of an inactive magnetite coreand losing the active surface area, respectively (David et al., 1991).The WGS reaction can be displaced selectively in favor of CO by insitu H2O removal (Rohde et al., 2008). Since in situ H2O removalaccelerates the reverse WGS of CO2 with H2 toward CO, CO2 can beutilized as a constituent in the synthesis gas which reacts ina subsequent step toward long-chain hydrocarbons (Rohde et al.,2008). The effect of the in situ water removal is extensively dis-cussed in the previous publication (Rahimpour et al., 2011).

1.4. Fluidized-bed reactor

One of the new possibilities for improving the efficiency ofa conventional fixed-bed reactor is the application of a fluidized-bed technology. Fluidized-bed reactors are particularly attractivefor highly exothermic reactions because of their superior heatmanagement ability, proper mixing and excellent temperaturecontrol, a small pressure drop and elimination of diffusion limita-tions (van der Laan and Beenackers, 2000). Other advantages offluidized-bed membrane reactors include the possibility of usinginexpensive metal alloys as well as continuous/periodic catalystreplacement (Dry, 1990). Despite such obvious advantages,fluidized-bed membrane reactors have not been widely exploitedby industry (Dry, 1990; Unruh et al., 2004). Rahimpour et al.improved methanol synthesis reactor and FTS reactor by using

a fluidized-bed reactor instead of a fixed-bed reactor (Rahimpourand Elekaei, 2009a,b; Forghani et al., 2009; Rahimpour et al.,2010, 2011).

1.5. Objectives

The underlying goal of this study is to investigate the effect ofapplying a fluidization concept in the first reactor of CFMR insteadof a fixed-bed concept in FMFMR on the reactors performance.Altering the first reactor from a fixed-bed in FMFMR to a fluidized-bed in CFMR is comprehensively investigated in this study.Modeling results of CFMR are compared with the results of FMFMRand the CR plant data. Some criteria such as the gasoline yield, theCO2 yield and temperature profile are considered for recognizingthe best configuration. Moreover, the simultaneous effects of the insitu water removal and fluidization are investigated on CFMR andFMFMR performances. Owing to simultaneously applying a fluid-ized-bed concept and H-SOD membrane layer in CFMR, the prod-ucts yield increase considerably in CFMR compared with FMFMR asdemonstrated further.

2. Process description

CFMR, FMFMR and CR are packed by a bi-functional Fe-HZSM5catalyst (metal part: 100 Fe/5.4 Cu/7K2O/21SiO2, acidic part: SiO2/Al2O3 ¼ 28).

2.1. Conventional fixed-bed FTS reactor (CR)

A schematic process diagramof CR is depicted in Fig.1 (RIPI-NIOC,2004; Marvast et al., 2005). CR is extensively discussed in theprevious publication (Rahimpour and Elekaei, 2009a).

2.2. Membrane dual-type reactors (FMFMR and CFMR)

A schematic diagram of CFMR configuration is depicted inFig. 2(a). A schematic diagram of FMFMR is depicted in Fig. 2(b).Unlike FMFMR where the first reactor is a fixed-bed water perm-selective membrane reactor, a fluidized-bed water perm-selectivemembrane reactor is fabricated in the first reactor of CFMR. The

SteamReformer

GTLProduct

Steam Drum

Synthesis Gas

Reaction Gas

Pd-Agmembrane

H-SODmembrane

N2

N2 + H2OSecond ReactorGas-cooled reactor

First ReactorWater-cooled reactor

Catalyst

N2

N2 & H2O

Steam drumSteamreformer

Product

Synthesis gas

H-SODmembrane

Pd-Agmembrane

Reaction gas

Fluidized-bed membrane reactor(the second reactor)

Fixed-bed membrane reactor( the first reactor)

a

b

Fig. 2. Schematic diagram of (a) cascading fluidized-bed membrane dual-type FTS reactor (CFMR), (b) FMFMR.

M.R. Rahimpour et al. / Journal of Natural Gas Science and Engineering 3 (2011) 484e495486

Table 1Specifications of FMFMR.

Parameter Water-cooledreactor(first reactor)

Gas-cooledreactor(second reactor)

Catalyst density [kg$m�3] 1290 1290Catalyst equivalent diameter [m] Ø 3.83 � 10�3 Ø 0.2 � 10�3

Molar ratio of H2/CO in feed 0.96 e

Flow rate per tube [gmol$s�1] 0.0335 0.377Feed temperature [K] 565 e

Reactor pressure [kPa] 1700 2200Cooling temperature [K] 566 e

Bulk density [kg$m�3] 730 e

Tube length [m] 7.2 4.8Tube size [mm] Ø 21.2 � 4.2 Ø 21.2 � 4.2Number of tubes 180 16Bed voidage 0.488 0.56 (min fluidization)Catalyst thermal conductivity

[kJ$m�1 s�1 K�1]0.00625 0.00625

Table 3Kinetic parameters data (RIPI-NIOC, 2004).

Reaction No. M n k E

1 �1.0889 1.5662 142583.8 83423.92 0.7622 0.0728 51.556 650183 �0.5645 1.3155 24.717 497824 0.4051 0.6635 0.4632 34885.55 0.4728 1.1389 0.00474 27728.96 0.8204 0.5026 0.00832 25730.17 0.5850 0.5982 0.02316 23564.38 0.5742 0.710 410.667 58826.3

H-SOD membrane

N2 + H2O

coolant

M.R. Rahimpour et al. / Journal of Natural Gas Science and Engineering 3 (2011) 484e495 487

CFMR configuration consists of a fluidized-bed water perm-selective membrane reactor (the first reactor) followed by a fluid-ized-bed hydrogen perm-selective membrane reactor (the secondreactor). The structure of the first reactor (water-cooled reactor) issuch that the primary and secondary shell sides are fabricatedwhere a coolant stream flows in the former one and the latter one ispacked by catalyst particles. The walls of the tubes in bothfluidized-bed membrane reactors of CFMR are coated by H-SOD ona-Al2O3 support and PdeAg membrane layers. In the first reactor ofCFMR, water permeates through the H-SOD membrane layer to thetube side owing to awater partial pressure difference between bothsides of themembrane layer. The inert gas (i.e., N2) is directed to thetube side and carries the permeated water. In the second reactor,a cold feed synthesis gas is preheated in the tube side and subse-quently fed into the secondary shell side of the first reactor wherethe chemical reaction is initiated by catalysts. The partially reactedgas leaves the first reactor and it is subsequently fed to the bottomof the second reactor. It is directed to the shell side of the secondreactor in a counter-current mode with synthesis gas flowingthrough the tube side and it fluidizes the catalyst particles in theshell side. Hydrogen permeates through the PdeAg membranelayer to the reaction side due to a hydrogen partial pressure drivingforce in the second reactor. The reaction is completed in the secondreactor. Specifications of the FMFMR configuration are presented inTable 1. Specifications of the first reactor (fluidized-bed reactor) inCFMR configuration are presented in Table 2.

3. Mathematical model

A heterogeneous one-dimensional model including a set ofcoupled energy andmass balances as well as kinetics’ equations aretaken into consideration.

Table 2Specifications of the first reactor in the CFMR.

Parameter Water-cooled reactor(first reactor)

Flow rate per tube [gmol$s�1] 0.05Flow rate per shell [gmol$s�1] 0.06Catalyst equivalent diameter [m] Ø 3.83 � 10�4

Tube pressure [Kpa] 1700Shell pressure [kPa] 1700Cooling temperature [K] 566Bulk density [kg$m�3] 730Tube length [m] 7.2Tube size [mm] Ø 21.2 � 4.2Shell side size [mm] Ø 50.8 � 4.2Number of tubes 180

3.1. Reaction network

The FT components consist of H2, CO, CO2, H2O, CH4, C2H6, C3H8,i-C4H10, n-C4H10, and Cþ

5 . The principal FTS reactions are as follows(RIPI-NIOC, 2004):

COþ 3H2/R1

CH4 þ H2O (1)

2COþ 4H2/R2

C2H2 þ 2H2O (2)

2COþ 5H2/R3

C2H6 þ 2H2O (3)

3COþ 7H2/R4

C3H8 þ 3H2O (4)

4COþ 9H2/R5

n-C4H10 þ 4H2O (5)

4COþ 9H2/R6

i-C4H10 þ 4H2O (6)

6:05 COþ 12:23 H2/R7

C6:05H12:36

�Cþ5

�þ 6:05 H2O (7)

COþH2O4R8

CO2 þH2 ðWGS reactionÞ (8)

H2O

Catalyst

N2

H2OZ

Fig. 3. Schematic diagram of an elemental volume in the first reactor of CFMR.

Table 5Hydrodynamic parameter (Kunii and Levenspiel, 1991; Deshmukh et al., 2005).

Parameter Equation

Superficial velocity at minimumfluidization

Umf ¼0:01�

m

rgdp

�½ð27:22þ0:0408ArÞ0:5�27:2�

Archimedes number Ar ¼ d3prgðrp � rgÞgm2

Bubble diameter db ¼ dbm � ðdbm � dboÞexpð�0:3z=DÞd ¼ 411:38½AðU � U Þ�0:4

M.R. Rahimpour et al. / Journal of Natural Gas Science and Engineering 3 (2011) 484e495488

Kinetic parameters are presented in Table 3 and the reaction rateequation is as follows:

Ri ¼ 0:278 ki exp��EiRT

�PmCO$P

nH2

hmol$kg�1

cat$si

(9)

The kinetic model is valid in the temperature, the pressure andthe H2/CO molar ratio range of 290e310 �C, 15e23 bar and0.76e1.82, respectively (RIPI-NIOC, 2004).

bm 0 mf

dbo ¼ 0:376ðU0 � Umf Þ2

Volume fraction of bubble phaseto overall bed

d ¼ ðU0 � Umf Þ=Ub

Bubble rising velocity Ub ¼ U0 � Umf þ ðgdbÞ0:5

Bed voidage at minimum velocity 3mf ¼ 0:586ð1=ArÞ0:029�rgrp

�0:021

3.2. Mathematical model of FMFMR

The mathematical model of FMFMR was extensively developedin the previous publication (Rahimpour et al., 2011).

Overall mass transfer coefficient Kbe ¼ Umf3

þ ½ð4Djm$3mf $Ub=pdbÞ�0:5

3.3. Mathematical model of CFMR

3.3.1. Fluidized-bed water perm-selective membrane reactor(the first reactor)

The walls of the tubes in the first reactor and the second reactorof CFMR configuration are coated by the H-SOD and PdeAgmembrane layer, respectively. The following assumptions are madein the mathematical modeling of the first reactor in CFMR:

1) Due to rapid mixing, the operation is assumed to be isothermalwhichmeans that the bubble and the emulsion phases have thesame temperature.

2) Both phases have the plug flow regimes.3) Hydrogen is only added to the emulsion phase and water is

only removed from the emulsion phase.4) Axial diffusion of water and hydrogen through the membrane

is negligible in comparison with radial diffusion.5) Catalyst particles can be found in the bubble phase and

therefore components can react well in rising bubbles. The

Table 4Mass and heat transfer coefficients.

Parameter Equation

Component heat capacity Cp ¼ aþ bT þ cT2 þ dT3

Viscosity of reaction mixtures m ¼ C1TC2

1þ C3T

þ C4T2

Mixture thermal conductivity Based on the Chung et al. method

Mass transfer coefficientbetween gas and solid phases

kgi ¼ 1:17Re�0:42Sc�0:67i ug � 103

Re ¼ 2Rpugm

Sci ¼ m

rDim � 10�4

Dim ¼ 1� yiPi¼ j

yiDij

Dij ¼10�7T3=2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1=Mi þ 1=Mj

q

P�v3=2ci þ v

2=3cj

�2

Overall heat transfer coefficient1U

¼ 1hi

þ AilnðDo=DiÞ2pLKw

þ Ai

Ao

1ho

Heat transfer coefficient betweengas phase and reactor wall

hCprm

�CpmK

�2=3

¼ 0:4583B

�rudpm

��0:407

Effectiveness factor for reactionk (pore diffusion resistance)

hk ¼R RP0 rkdrRPrsk

Water permeation rate JH2O ¼ AsVr

$QH2OðPtH2O � PshH2OÞ

Hydrogen permeation rate(Sieverts law)

JH ¼2pLp0:exp

��EpRT

�

lnRoRi

� ffiffiffiffiffiffiPtH

q�

ffiffiffiffiffiffiffiPshH

q �

extension of chemical reactions in the bubble phase, however,is less than the emulsion phase.

6) Gas flow through the emulsion phase remains constant at theminimum fluidization velocity.

7) Gases are assumed to be ideal.8) Steady state condition exists.9) Ideal condition is assumed for H-SOD membrane (Ideal selec-

tivity of water to hydrogen) (Rohde et al., 2008).10) The variation of water concentration in the tube side is

negligible.11) The temperature of the inert gas is constant.

As seen in Fig. 3, the element with the length of Dz is taken intoconsideration. The differential equations describing mass andenergy balances in the axial direction of CFMR are discussed in thefollowing subsections.

Mass balance equation for the bubble phase:

�dft

Ashell$dyibdz

þ d$kbei$ct$ab$ðyie�yibÞþ d$g$rp$þX8j¼1

rbij ¼ 0 ;

i ¼ 1;2;.;N�1 (10)

Table 6A comparison between the modeling results of FMFMR and CFMR configurationsand plant data.

Parameter Pilotplant

Modelpredicted(CFMR)

Relativeerror (%)

Modelpredicted(FMFMR)

Relativeerror (%)

Xco (%) 77.94 92 18 86 14XH2

(%) 93.83 99.8 6.36 99.4 5.93C5þ Selectivity

(g/Nm3 (CO þ H2))42.55 54.46 27.99 51.99 22.18

CO2 Selectivity(g/Nm3 (CO þ H2))

339.77 248.87 �26.75 305.15 �10.01

CH4 Selectivity(g/Nm3 (CO þ H2))

44.15 38.26 �13.34 41.5 �6.00

H2O Selectivity(g/Nm3 (CO þ H2))

120.67 146.18 21.14 112.8 �6.5

C2H4 Selectivity(g/Nm3 (CO þ H2))

3.95 4.5 13.92 5.5 39

C2H6 Selectivity(g/Nm3 (CO þ H2))

11.78 11.9 1.02 12.4 5.26

C3H8 Selectivity(g/Nm3 (CO þ H2))

9.33 6.8 �27.11 7 �24.97

n-C4 Selectivity(g/Nm3 (CO þ H2))

11.07 10.24 �7.49 9.5 �14.18

i-C4 Selectivity(g/Nm3 (CO þ H2))

14.45 12.82 �11.28 12.22 �15.43

0 2 4 6 8 10 12

0

2

4

6

8

10

Length (m)

Ga

so

lin

e y

ield

(g

r/g

r f

ee

d *

10

0)

CFMR

CR

FMFMR

0

3

6

9

12

535

540

545

550

555

0

5

10

15

Length (m)Temperature (K)

Ga

so

lin

e y

ield

(g

r/g

r f

ee

d *

10

0)

0

3

6

9

12557

558

559

560

0

2

4

6

8

10

12

Length (m)Feed Temperatur (K)

Ga

so

lin

e y

ield

( g

r/g

r f

ee

d *

10

0)

0

3

6

9

12

18

19

20

21

22

0

5

10

15

Length (m)Pressure (bar)

Ga

so

lin

e y

ield

(g

r/g

r f

ee

d *

10

0)

a

b d

c

Fig. 4. Comparison of (a) Gasoline yield in three types of reactors: CR, CFMR and FMFMR configurations (b) Yield of gasoline as a function of pressure and FMFMR length (c) Yield ofgasoline as a function of pressure and CFMR length (d) Gasoline yield as a function of inlet temperature and CFMR length.

M.R. Rahimpour et al. / Journal of Natural Gas Science and Engineering 3 (2011) 484e495 489

Mass balance equation for the emulsion phase:

�ð1�dÞ$ ftAshell

$dyiedz

þð1�dÞ$re$h$X8j¼1

rijþd$kbei$ab$ct$ðyib�yieÞ

�ð1�dÞ$s$JH2Oþð1�dÞ$U$ JH2

As¼ 0 ð11Þ

The energy balance of the reaction side in the first reactor is asfollows:

ð1�dÞ$h$re$X8j¼1

rj$��DHfj

�þg$rB$d$h$

X8j¼1

rbj$��DHfj

�þ p$Di

Ashell

�$Ushell$ðTshell�TÞ þs$ð1�dÞ$JH2O�U$ð1�dÞ$ JH2

As¼ 0 ð12Þ

s andU equal 0 and 1 for the first reactor and 1 and 0 for the secondreactor, respectively. Water, JH2O, and hydrogen permeation rates,

JH2, are reported in Table 4. As is the equivalent area around each

tube, Ashell is the equivalent cross sectional area of the shell aroundeach tube.

Boundary conditions for the bulk phase are expressed as:

at z ¼ 0; yi ¼ yi; in T ¼ Tin (13)

3.3.2. Fluidized-bed hydrogen perm-selective membrane reactor(the second reactor)

The mathematical modeling of the second reactor in CFMR issimilar to the one of FMFMR (Rahimpour et al., 2011).

3.4. Auxiliary correlations

In order to simulate the reactor, heat and mass transfersbetween solid and fluid phases have been taken into consideration.Physical properties of the components are also important for the

M.R. Rahimpour et al. / Journal of Natural Gas Science and Engineering 3 (2011) 484e495490

calculations. Therefore, some other correlations are used to coverthese issues. The correlations of physical properties, mass and heattransfer coefficients are listed in Table 4 and also hydrodynamicproperties are presented in Table 5.

4. Numerical solution

The CFMR model consists of a set of differential-algebraicequations (DAE) including mass and energy balances for bubbleand emulsion phases in the first and the second reactors. Moreover,these equations are coupled with non-linear algebraic equations ofthe kinetic model, fluidized-bed hydrodynamic and transportproperty correlations and other auxiliary correlations. In order tosolve the set of equations, a backward finite difference approxi-mation is applied.

5. Model validation

Model validation is carried out by comparison of model resultsof fixed-bed FT reactor with the RIPI pilot plant data (Marvast et al.,2005) under the design specifications and input data. The CFMRmodeling results and the corresponding observed data of the pilotplant is presented in Table 6. A good agreement is observedbetween the estimated results and the pilot plant data.

6. Result and discussion

The performance of CFMR configuration is investigated andcompared with the FMFMR and CR performances in the followingfigures:

0 2 4 6 8 10 12

0

1

2

3

4

5

6

Length (m)

Me

th

an

e y

ield

(g

r/g

r f

ee

d *

10

0)

CFMR

CR

FMFMR

0 2 4 6 8 10 120

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Length (m)

Eth

an

e y

ield

(g

r/g

r f

ee

d *

10

0)

CFMR

CR

FMFMR

0 2 4 6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Leng

Eth

yle

ne

yie

ld (

gr/g

r f

ee

d *

10

0)

0 2 4 60

1

2

3

4

5

6

7

Leng

Pro

pa

ne

yie

ld (

gr/g

r f

ee

d *

10

0)

a

b d

c

Fig. 5. Comparison of components yield along different reactors for

Fig. 4(a) illustrates the gasoline yield in three different config-urations. As seen, the performances of both dual-type reactors (i.e.,CFMR, FMFMR) are superior to CR owing to achieving remarkablyhigher gasoline yield in dual-type reactors. The in situ waterremoval shifts the FTS reactions to the products side according tothe thermodynamic equilibrium which enhances the yields ofheavy hydrocarbons such as gasoline. The highest gasoline yield isachieved in CFMR as a consequence of the in situ water removalfrom the secondary shell side (reaction side) of the first reactor andapplying the fluidization concept. Since a fluidized-bed reactor hassome superiorities such as better heat management ability, excel-lent temperature control and a small pressure drop to the fixed-bedreactor, the gasoline yield in CFMR is higher than FMFMR. More-over, the reaction side temperature profile in CFMR is lower thanFMFMR owing to good controlling of heat transfer in the fluidized-bed reactor. Therefore, gasoline and other heavier components areproduced in CFMR more than the ones in FMFMR owing to theirlower temperature. Also, the effect of the in situ water removal onthe enhancement of the gasoline yield in CFMR is more consider-able than the one in FMFMR owing to a slight pressure drop ina fluidized-bed reactor. Thus, lower temperature and pressuredrops in fluidized-bed reactor enhance the gasoline yield in CFMRcompared with FMFMR.

Fig. 4(bec) illustrates the 3D plot of gasoline yield as a functionof feed temperature and reactor length in CFMR and FMFMRconfigurations. As seen, the gasoline yield increases along CFMRand FMFMR and rises slightly by temperature ascending howeverthe gasoline yield in CFMR is higher than the one in FMFMR. Highergasoline yield is achieved at higher feed temperatures. Fig. 4(d)illustrates the 3D plot of gasoline yield as a function of pressure andCFMR length. The water permeation rate increases with increasing

0 2 4 6 8 10 12

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Length (m)

)0

01

*d

ee

fr

g/r

g(

dlei

ye

na

tu

b-l

am

ro

N

CFMR

CR

FMFMR

0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Length (m)

)0

01

*d

ee

fr

g/r

g(

dlei

ye

na

tu

b-

osI

CFMR

CR

FMFMR

8 10 12

th (m)

CFMR

CR

FMFMR

8 10 12

th (m)

CFMR

CR

FMFMR

e

f

(a) CH4, (b) C2H6, (c) C2H4, (d) C3H8, (e) n-C4H10 and (f) i-C4H10.

0 2 4 6 8 10 12

0

5

10

15

20

25

30

35

40

45

Length (m)

CO

2 y

ield

(g

r/g

r f

ee

d *

10

0)

CFMR

CR

FMFMR

0

3

6

9

12

18

19

20

21

22

0

10

20

30

40

Length(m)Pressure (bar)

CO

2)

00

1*

de

ef

rg/

rg

(dl

eiy

a

b

Fig. 6. (a) Comparison of CO2 yield along CR, CFMR and FMFMR (b) CO2 yield asa function of pressure and CFMR length.

0 2 4 6 8 10 12

0

2

4

6

8

10

12

14

16

18

Length (m)

H2O

yie

ld (

gr/g

r f

ee

d *

10

0)

CFMR

CR

FMFMR

0 2 4 6 8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

x 10

-6

Length (m)

H2O

Pe

rm

ea

tio

n r

ate

CFMR

FMFMR

a

b

Fig. 7. Comparison of (a) yield of water in CR, CFMR and FMFMR configurations (b) thewater permeation rate in the first reactor of CFMR and FMFMR.

M.R. Rahimpour et al. / Journal of Natural Gas Science and Engineering 3 (2011) 484e495 491

the pressure of the secondary shell side according to Fig. 7(b).Moreover, the in situ water removal increases the reaction rates ofheavy hydrocarbons. Therefore, the production rate of gasolineincreases along CFMR.

Fig. 5 illustrates the production yields of hydrocarbons such asmethane, ethane, ethylene, propane, normal butane and iso-butane. Fig. 5(a) shows the production yield of methane. Theleast methane yield is achieved in CFMR configuration. Methane isan undesired product. The methane production rate is highlytemperature dependent. Therefore, the methane production rateincreases at higher temperatures. Since the temperature of CFMR islower than FMFMR and CR (mainly due to applying a fluidizationconcept in the first reactor), the methane production rate in CFMRis considerably lower than the one in FMFMR and CR. According tothe fact that the production rates of light hydrocarbons are higherat elevated temperatures, the ethane, ethylene, and propane yieldin CFMR are lower than the ones in FMFMR and CR. As shown in

Fig. 5(bed), the ethane, ethylene and propane yield in CFMR are5.6%, 4.8% and 4.6% lower than the ones in FMFMR. The in situ waterremoval has a little effect on the production rates of lighthydrocarbons.

The normal butane yield is compared with the iso-butane yieldin Fig. 5(eef). The normal butane and iso-butane yields in CFMRincrease 3.2% and 2.8% more than the ones in FMFMR, respectively.Since the production rate of butane increases with temperaturedecreasing, the butane production rate increases in CFMRcompared with the other hydrocarbon products. Moreover, theeffect of the in situ water removal on the increasing of heaviercomponents is more considerable than lighter one. Therefore, thein situ water removal via the H-SOD membrane layer increases theproduction rates of normal and iso-butane components.

Fig. 6(a) illustrates the CO2 yield along CR, FMFMR and CFMR.The decrease in CO2 yield in CFMR and FMFMR ismore considerablethan the one in CR. The in situ water removal in the first reactor of

0 2 4 6 8 10 12

0

20

40

60

80

100

Length (m)

CO

co

nv

ers

ion

(%

)

FMFMR

CFMR

CR

0 2 4 6 8 10 12

0

20

40

60

80

100

Length (m)

H2 c

on

ve

rs

ion

(%

)

CFMR

FMFMR

CR

a

b

Fig. 8. Comparison of (a) CO conversion and (b) H2 conversion profiles along the threedifferent FT configurations.

0 2 4 6 8 10 12

520

530

540

550

560

570

580

590

Length (m)

Te

mp

era

tu

re

of G

as

Ph

as

e (

K)

FMFMR

CR

CFMR

Fig. 9. Comparison of reacting gas temperature profiles along three different FTconfigurations.

M.R. Rahimpour et al. / Journal of Natural Gas Science and Engineering 3 (2011) 484e495492

CFMR and FMFMR shifts theWGS reaction to the reactants side andcauses more CO2 consumption in both configurations. Moreover,the CO2 yield decreases in CFMR owing to better heat transfer inthe fluidized-bed reactor and the in situ water removal. The CO2yield, as an undesired product, decreases considerably in CFMRtherefore it performs better than CR and FMFMR. CO2 is one of themain air pollutants consequently the decrease in CO2 yield isbeneficial for the environment. A considerable increase in thegasoline yield and a remarkable decrease in the CO2 yield can becounted as the superiority of CFMR to FMFMR. Fig. 6(b) illustratesthe 3D plot of CO2 yield as a function of pressure and reactorlength in CFMR. In CFMR, the in situ water removal shifts the WGSreaction to the reactant side and CO2 is consumed. Furthermore,lower temperature in the exothermic side of CFMR decreases thereactions rates of WGS. These two factors decrease the CO2 yieldin CFMR more considerably than FMFMR and CR. Also, the CO2yield decreases with pressure rising in CFMR. Therefore, CFMR

performs well at higher operating pressures owing to more CO2

consumption.The water yield along three configurations is depicted in

Fig. 7(a). The highest water yield is achieved in CFMR. In CFMR andFMFMR, the water yield increases along the first reactor owing tothe in situ water removal via the H-SOD membrane layer whichincreases the reaction rates of heavy hydrocarbons. The increase inthe reaction rates of heavy hydrocarbons leads to an increase in thewater production as a byproduct. The water permeation ratethrough the H-SOD membrane layer is much lower than the waterproduction rate as a byproduct. It is worth mentioning that thewater yield increases along CFMR not only due to the in situ waterremoval via the H-SOD membrane layer but also due to applyingthe fluidization concept. The water production rate in CFMR ismuch higher than its permeation rate through the H-SODmembrane layer (See Fig. 7(b)) and the in situ water removalcannot satisfactorily decrease the water amount in the reactionside. Fig. 7(b) illustrates the water permeation rate through theH-SOD membrane layer along the first reactors of CFMR andFMFMR. The water permeation rate increases along the first reac-tors of CFMR and FMFMR owing to an increase in the water partialpressure in the reaction side. The water permeation rate alongCFMR is higher than FMFMR owing to applying the fluidized-bedreactor which enhances the FTS reactions and the water produc-tion rate (due to higher water partial pressure). The water perme-ation rate increases with increasing the partial pressure differencebetween shell and tube sides. A partial pressure difference betweenshell and tube sides of CFMR is higher than FMFMR.

Fig. 8(aeb) illustrates hydrogen and carbon monoxide conver-sions in CFMR in comparison with the ones in CR and FMFMR. TheCO and H2 conversions in CFMR and FMFMR are higher than theones in CR. Hydrogen and carbon monoxide conversions increaseowing to awater removal. The increase in H2 and CO conversions inCFMR has the same trend as the ones in FMFMR. The first reactors(water-cooled reactor) of CFMR and FMFMR play the major role inincreasing the CO and H2 conversions. The highest conversion ofreactants is achieved in CFMR owing to the in situ water removalfrom the first reactor as well as the application of the fluidized-bedconcept in the first reactor. These observations can be justified bythe mentioned advantages of fluidized-bed concept (Sotudeh-Gharebagh et al., 2007).

0 2 4 6 8 10 12

0

2

4

6

8

10

Length (m)

)0

01

*d

ee

fr

g/r

g(

dlei

yn

oit

cu

do

rP

C5+

C3H

8

C2H

6

CH4

i-C4

n-C4

C2H

4

0 2 4 6 8 10 12

0

2

4

6

8

10

Length (m)

)0

01

*d

ee

fr

g/r

g(

dlei

yn

oit

cu

do

rP

n-C4

i-C4

CH4

C2H

6

C3H

8

C5+

C2H

4

0

0.5

1

1.5

2

2.5

3

3.5

Se

lec

tiv

ity

CFMR

FMFMR

CR

C5+ CH

4CO

2H

2O i-C

4n-C

4C

2H

4C

3H

8C

2H

6

Components

a

b

c

Fig. 10. (a) Components yield profiles along the FMFMR configuration (b) componentsyield profiles along the CFMR configuration (c) comparison of components selectivityin three reactor configurations.

M.R. Rahimpour et al. / Journal of Natural Gas Science and Engineering 3 (2011) 484e495 493

Fig. 9 demonstrates the gas phase temperature profile alongCFMR, FMFMR and CR. Two temperature peaks are observed in thezones close to the entrance of reactors. One peak is occurred in eachreactor owing to high exothermic reactions. One temperature jumpis clearly seen in the first 0.5 m of thewater-cooled reactor (the firstreactor) and the second one arises in the first 0.5 m of the gas-cooled reactor (the second reactor). The average temperatures inCFMR and FMFMR are lower than the one in CR which can promotethe durability of catalyst activity. It is observed that the tempera-ture control in the dual-type reactor is easier than the one in thesingle type. The superior heat management capability and excellenttemperature control are the advantages of fluidized-bed reactors.Therefore, the average temperature in CFMR is lower than the onein FMFMR owing to applying a fluidized-bed reactor instead ofa fixed-bed reactor.

There is a jump of temperature for all systems in the first 0.5 mof each reactor that is caused by high heat of reaction in FTS. Forsimulation purposes, the maximum temperature for the Fe-HZSM5catalyst to remain active is assumed to be 620 K (Marvast et al.,2005). As shown in this figure, in the single fixed-bed reactorsystem, the risk of temperature runaway makes alert in closing tohotspot. However, as evident in this figure, dual-type configura-tions have better temperature performance. Due to highexothermic reactions, temperature jump occurs in the first sectionof reactor because the temperature runaway inmost cases occurs ata zone close to the inlet of the reactor.

Fig. 10(aeb) presents the profile of the component yield alongCFMR and FMFMR for FTS, respectively. According to Fig. 10(aeb),the Cþ5 yield is the highest among hydrocarbon products. Acomparison of carbon molar selectivity of products between CR,CFMR and FMFMR configurations is presented by Fig. 10(c). Thecarbon molar selectivity of each component is defined as (Changet al., 2007):

S ¼ mole of C� atom in productmole of CO consumed

� 100

According to this figure, the CFMR configuration shows satis-fying results relative to the others. CO2 declines considerably in thisconfiguration in conjunction with the Cþ5 increasing. Moreover,methane is an undesired product which decreases considerably inthis novel configuration. The best results have been achieved byCFMR, whether for desired products or undesired products.

7. Conclusions

In this study, a cascading fluidized-bed membrane dual-typereactor (CFMR) is proposed as an alternative configuration forconventional tubular reactors for FTS in GTL technology. Theperformance of CFMR is investigated and compared with the one ofFMFMR. CFMR configuration is fabricated as two subsequentfluidized-bed reactors where the PdeAg and H-SOD membranelayers are assisted in both reactors to enhance the main productsyield. A desirable temperature profile is achieved in CFMR owing toan excellent heat management in fluidized-bed reactors. Themodeling results of CFMR configuration is compared with themodeling results of FMFMR and CR pilot plant data. The modelingresults demonstrate that the gasoline yield increases remarkablywhile the CO2 yield decreases considerably in CFMR compared withFMFMR and CRmainly due to applying the fluidization concept. Themodeling results show 5.3% increase in gasoline yield and 12%decrease in CO2 yield in CFMR compared with the ones in FMFMR.Therefore, the in situ water removal as well as applying the fluid-ization concept can effectively improve the performance of CFMRcompared with FMFMR and propose it as more promising config-uration for GTL technology.

M.R. Rahimpour et al. / Journal of Natural Gas Science and Engineering 3 (2011) 484e495494

Appendix

Nomenclature

Symbol Unit Definition

Ac m2 cross sectional area of each tubeAi m2 inner area of each tubeAs m2 lateral area of each tubeAshell m2 cross sectional area of shellab m2 interface area between bubbles and emulsion phaseav m2$m�3 specific surface area of catalyst pelletcPg J$mol�1$k�1 specific heat of the gas at constant pressurecPgt J$mol�1$k�1 specific heat of the gas inside the tube at constant pressurecpH J$mol�1$k�1 specific heat of hydrogen at constant pressurecPs J$mol�1$k�1 specific heat of the catalyst at constant pressurect mol$m�3 total concentrationDi m tube inside diameterDij m2$s�1 binary diffusion coefficient of component i in component jDim m2$s�1 diffusion coefficient of component i in the mixture

Do m tube outside diameterdp m particle diameterhf W$m�2$K�1 gas-catalyst heat transfer coefficienthi W$m�2$K�1 heat transfer coefficient between fluid phase and reactor wallho W$m�2$K�1 heat transfer coefficient between coolant stream and reactor wallFt mol$s�1 total molar flow rate in shell sideft0 mol$s�1 total molar flow rate in tube sideK W$m�1$K�1 conductivity of fluid phaseKw W$m�1$K�1 thermal conductivity of reactor wallkgi m$s�1 mass transfer coefficient between gas and solid phase for component ikbei m$s�1 mass transfer coefficient between bubble and emulsion phase for component iL m length of reactorMi g$mol�1 molecular weight of component iN [e] number of componentsNH2O mol s�1 molar flow rate penetrate from membrane

PtH bar tube side pressure

PshH bar shell side pressure

P mol m�1$s�1$Pa�1/2 permeability of hydrogen through PdeAg layerP0 mol m�1$s�1$Pa�1 pre-exponential factor of hydrogen permeabilityQH2O mol$s�1$m�2$Pa�1 permeance of waterR J$mol�1$K�1 universal gas constantRe [e] Reynolds numberRi [m] inner radius of PdeAg layerRo [m] outer radius of PdeAg layerri mol$kg�1$s�1 reaction rate of component irbi mol$kg�1$s�1 reaction rate of component i in bubble phaseSci [e] Schmidt number of component iT K bulk gas phase temperatureTs K temperature of solid phaseTshell K temperature of coolant stream in first reactorTt K temperature of coolant stream in second reactorUshell W$m�2$K�1 overall heat transfer coefficient between coolant and process streamsUtube W$m�2$K�1 overall heat transfer coefficient between coolant and process streamsug m$s�1 linear velocity of gas phaseub m$s�1 rising bubble velocityVr m3 volume of reactoryi mol$mol�1 mole fraction of component i in the fluid phaseyis mol$mol�1 mole fraction of component i in the solid phaseyie mol$mol�1 mole fraction of component i in the emulsion phaseyib mol$mol�1 mole fraction of component i in the bubble phasez m axial reactor coordinateGreek lettersaH mol m�1$s�1$Pa�0.5 hydrogen permeation rate constantDHf,i J$mol�1 enthalpy of formation of component iDH298 J$mol�1 enthalpy of reaction at 298 Kd [e] bubble phase fraction3B [e] void fraction of catalytic bed3s [e] void fraction of catalyst3mf [e] void fraction of bed at minimum fluidizationg [e] volume fraction of catalyst occupied by solid particles in bubblem kg$m�1$s�1 viscosity of fluid phasenci cm3$mol�1 critical volume of component ir kg$m�3 density of fluid phaserB kg$m�3 density of catalytic bedre kg$m�3 density of emulsion phaserp kg$m�3 density of catalysth [e] catalyst effectiveness factor

Superscripts and subscriptsf feed conditionsin inlet conditionsout outlet conditionss catalyst surfacesh shell sidee emulsion phaseb bubble phaset tube sidemf minimum fluidization

M.R. Rahimpour et al. / Journal of Natural Gas Science and Engineering 3 (2011) 484e495 495

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