a comparison of co-current and counter-current modes of operation for a novel hydrogen-permselective...

Fuel Processing Technology 91 (2010) 33–44

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A comparison of co-current and counter-current modes of operation for a novelhydrogen-permselective membrane dual-type FTS reactor in GTL technology

M.R. Rahimpour ⁎, A.A. Forghani, A. Khosravanipour Mostafazadeh, A. ShariatiChemical Engineering Department, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, Iran

⁎ Corresponding author. Tel.: +98 7112303071; fax:E-mail address: [email protected] (M.R. Rahim

0378-3820/$ – see front matter © 2009 Elsevier B.V. Aldoi:10.1016/j.fuproc.2009.08.013

a b s t r a c t
a r t i c l e i n f o
Article history:Received 12 February 2009Received in revised form 14 August 2009Accepted 17 August 2009

Keywords:Fischer–Tropsch synthesisGTL technologyHydrogen-permselective membraneCounter-current modeCo-current mode

In this work, a comparison of co-current and counter-current modes of operation for a novel hydrogen-permselective membrane reactor for Fischer–Tropsch Synthesis (FTS) has been carried out. In both modes ofoperations, a system with two-catalyst bed instead of one single catalyst bed is developed for FTS reactions.In the first catalytic reactor, the synthesis gas is partly converted to products in a conventional water-cooledfixed-bed reactor, while in the second reactor which is a membrane fixed-bed reactor, the FTS reactions arecompleted and heat of reaction is used to preheat the feed synthesis gas to the first reactor. In the co-currentmode, feed gas is entered into the tubes of the second reactor in the same direction with the reacting gasstream in shell side while in the counter-current mode the gas streams are in the opposite direction.Simulation results for both co-current and counter-current modes have been compared in terms oftemperature, gasoline and CO2 yields, H2 and CO conversion, selectivity of components as well as permeationrate of hydrogen through the membrane. The results showed that the reactor in the co-current configurationoperates with lower conversion and lower permeation rate of hydrogen, but it has more favorable profile oftemperature. The counter-current mode of operation decreases undesired products such as CO2 and CH4 andalso produces more gasoline.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

The Fischer–Tropsch synthesis (FTS) refers to the conversion ofsynthesis gas (CO+H2) into hydrocarbons such as C5+ and diesel. FTShas become a subject of renewed interest in recent years due to anescalation in the price of oil and the discovery of several gas reserves.Parts of the world gas reserves are located in remote areas and severalof them are in offshore regions so that transport of natural gas in thesecases can become expensive and uneconomical. Over the last decadesnoteworthy ameliorates were made both on the reactor [1] andcatalyst technologies [2,3].

This catalytic synthesis directs to awide variety of products such asgasoline and diesel, whose abundance depends on the catalystsemployed, as well as on operating conditions [4]. The main incentivesfor this conversion are the increased availability of natural gas inremote locations for which no nearby markets exist, environmentalpressure to minimize the flaring of associated gas, the growingdemand for middle distillate transportation fuels (gasoil andkerosene) especially in the Asia-Pacific regions, and improvementsin the cost effectiveness of GTL technology, resulting from the

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development of more active catalyst and improved reactor design.FTS reactor being the heart of gas-to-liquid technology, that it hasgreat significance on the economics of the overall plant [5].

Because of the high demand on gasoline in theworld and its higherprice relative to that of diesel, production of gasoline from the FTS,becomes more favorable. Fuels produced from the FTS have highquality such as a very low aromaticity and absence of sulfur that helpin diminishing world pollution. However due to the limitation ofSchulz–Flory distribution [6], the yield of the hydrocarbons within therange of those presented in gasoline is low. Also, the octane number ofFTS gasoline is lower than that of the gasoline obtained from crude oilprocessing since the FTS gasoline mainly consists of n-paraffin. Topromote the yield and quality of the gasoline from FTS, bifunctionalcatalysts have received extensive attention in the recent years [7,8].

The various types of reactors in this synthesis, including multi-tubular fixed-bed reactor; slurry three-phase catalytic reactor; three-phase fluidized-bed reactor; bubbling fluidized-bed reactor; andcirculating fluidized-bed reactor have been considered in the historyof FTS development. FTS is either low temperature (LTFT) or hightemperature process (HTFT) depending on the product required. Hightemperature process is mainly used for the production of gasoline andlinear olefins while low temperature process is applied for theproduction of waxy material [5]. The LTFT synthesis takes place in athree-phase system. The gas phase contains the reactants and watervapor and gaseous hydrocarbon products. The higher hydrocarbons

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34 M.R. Rahimpour et al. / Fuel Processing Technology 91 (2010) 33–44

compose the liquid phase, and the catalyst is the solid phase. DuringHTFT all products are often vaporized under reaction conditions andso there are only two phases present.

Ahmadi Marvast et al. considered a water-cooled fixed-bed reactorwith length of 12 m [9]. The simulation results showed a dispensablechange in temperature and concentrationprofiles over 7mreactor length.In this research, the mentioned reactor is divided in two reactors nameddual-type reactor system. First reactor has 7.2m length, and amembranedual-type concept is used for second reactor to inspect the reactantsconversion and components production in a high temperature HTFT pro-cess. The presence of a permselective membrane in a reacting systemshowed that hydrogen feeding through palladiummembranes can ame-liorate the selectivity of hydrogenation [10], and achieve optimal axialconcentration profiles with corresponding higher product yields [11].

The application of membrane technology in chemical reactionprocesses are now mainly focused on reaction systems containinghydrogen and oxygen, and are based on inorganic membranes such asPd and ceramic membranes [12]. Palladium is 100% selective forhydrogen transport and Pd-alloy membranes on a stainless steelsupport were used as the hydrogen-permeable membrane. Alloyingthe palladium, especially with silver (23 wt.% silver), reduces thecritical temperature for this embitterment and leads to an increase inthe hydrogen permeability [13–16]. Palladium-based membranes arelow costs as well as permselectivity combined with good mechanical,thermal and long-term stability. Also the membrane support shouldbe porous, smooth-faced, highly permeable, thermally stable andmetal adhesive [17,18]. In this way, diffusion of hydrogen through thePd–Ag film from the shell side to reaction space makes it possible topromote the conversion of carbon monoxide.

Several works have been done on using Pd–Ag membrane anddual-type reactor. Rahimpour and Lotfinejad presented dynamicmodel for studying Pd–Ag membrane in a dual-type reactor formethanol production [19]. They showed methanol production can beincreased in membrane dual-type reactor. Rahimpour and Lotfinejadcompared auto-thermal and conventional dual-typemethanol reactor[20]. Also they investigated co-current and counter-current modes ofoperation for methanol synthesis [21]. Rahimpour proposed a two-stage catalyst beds concept for conversion of carbon dioxide intomethanol [22]. Rahimpour and Alizadehhesari investigated enrich-ment of carbon dioxide removal in a hydrogen-permselective dual-type methanol reactor [23]. Rahimpour and Ghader investigated Pd–Ag membrane reactors performance for methanol synthesis [24].Khosravanipour Mostafazadeh and Rahimpour proposed membranecatalytic bed for naphtha reforming [25]. Rahimpour et al. suggested anew approach to improve the methanol production in an industrialsingle stage methanol synthesis reactor by applying selectivepermeation of hydrogen from synthesis gas and adding it to thereaction side [26]. Rahimpour and Alizadehhesari developed fluid-ized-bed membrane reactor for methanol synthesis [27]. Rahimpourand Elekaei presented a novel fluidized-bed hydrogen-permselectivemembrane reactor [28]. Recently, Rahimpour published the article onhydrogen production in a fluidized-bed membrane reactor fornaphtha reforming [29]. Tosti et al. studied design of palladiummembrane reactors [30]. Gallucci et al. investigated co-current andcounter-current configurations for ethanol steam reforming in adense Pd–Ag membrane reactor [31].

The main idea of this work is increasing of gasoline and decreasingof CO2 and CH4 as undesired products in a membrane dual-type FTSreactor. The permeation of H2 in the second reactor of dual-type FTSsystem causes enhancement of gasoline yield and reduction ofundesired products in comparison with single-type reactor system.Effect of water removal with membrane was investigated by Rohleet al. [32] while in this work the effect of H2 permeation was used as anovel concept. In this research, it is shown that the membrane dual-type concept is an interesting candidate for application in HTFTprocess. However, from industrial and economical standpoints there

are still many issues to be investigated before putting a case forsuccessful commercialization, such as difficulties in reactor construc-tion, and the cost of membranes. The suggested reactor is supposedlyinvestigated to reveal the advantages and capability of this concept.The operating conditions of a real fixed-bed FTS reactor are used as abasis for simulating the proposed membrane dual-type FTS reactor.The consequences of simulation are contrasted with the performanceof conventional fixed-bed FTS reactor model. The comparison showedthat the gasoline production rate of membrane dual-type FTS reactorsis greater than single fixed-bed FTS reactor.

2. Process description

The FTS is investigated in a fixed-bed single and fixed-bedmembrane dual-type reactor which are packed with bifunctional Fe-HZSM5 catalyst (metal part: 100 Fe/5.4 Cu/7K2O/21SiO2, acidic part:SiO2/Al2O3=28) [33].

2.1. Conventional FTS reactor (CR)

In industrial fixed-bed FTS reactor, multi-tubular reactor cooled bypressurized boiling water is often used. An FTS pilot plant was designedand constructed by the Research Institute of Petroleum Industry (RIPI)and National Iranian Oil Company (RIPI-NIOC) in 2004 [9]. A single-type(conventional-type) FTS reactor is basically a vertical shell and tube heatexchanger. The catalyst is packed in vertical tubes and surrounded by theboiling water. The FTS reactions are carried out over commercial catalyst.The heat of exothermic reactions is transferred to the boiling water andsteam is produced. Fig. 1 shows a schematic diagram of the fixed-bedmulti-tubular FTS reactor. Table 1 presents the characteristics of thefixed-bed single type reactor developed by Research Institute of PetroleumIndustry (RIPI) [9,33].

2.2. Membrane dual- type FTS reactor (MDR)

Fig. 2 shows the schematic diagram of a membrane dual-typereactor configuration for FTS in counter-current mode. The Fischer–Tropsch synthesis in themembrane dual-type reactor is similar to thatone in the fixed-bed dual-type reactor with exception of a changewhich is applied to gas-cooled reactor (second reactor). This changein the proposed system is as follows: the walls of the tubes in the gas-cooled reactor consist of hydrogen permselective membranes. In thisway, the mass and heat transfer processes simultaneously occurbetween both sides and hydrogen permeation due to the hydrogenpartial pressure gradient can improve the product yields. The allspecifications of first reactor in membrane dual-type FTS reactor arethe same as fixed-bed dual-type FTS reactor. In co-current mode, thefeed synthesis gas is entered from the top of the gas-cooled reactor.

For more precise information, a membrane dual-type reactor is ashell and tube heat exchanger reactor in which the first one, water-cooled reactor, is combined in series with the second one, synthesisgas-cooled reactor. The cold feed synthesis gas is preheated inside thetubes of the second reactor, and then is fed into the tubes of the water-cooled reactor and the chemical reaction is initiated by the catalyst. Inthis stage synthesis gas is partly converted to hydrocarbons. Thereacting gas leaving water-cooled reactor is directed into the shellside of the gas-cooled reactor in co and counter-current modes withsynthesis gas flowing through the tubes and the reaction is completedin this reaction side of second reactor. The wall of the tubes in the gas-cooled reactor is coated with the permselective palladiummembranewhich transmits hydrogen to the reaction side due to the hydrogenpartial pressure driving force.

The purpose of adding membrane in second reactor is achievinghigher conversion of synthesis gas to relatively light hydrocarbonssuch as gasoline. Catalyst characteristics and specifications ofmembrane dual-type reactor (MDR) have been listed in Table 2.

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

35M.R. Rahimpour et al. / Fuel Processing Technology 91 (2010) 33–44

3. Reactor model

A one-dimensional heterogeneous model comprising a set of heatand mass transfer equations and kinetics of the main reactions isselected for modeling the membrane dual-type FTS reactor.

3.1. Reactions

The Fischer–Tropsch synthesis components include H2, CO, CO2,H2O, CH4, C2H6, C3H8, n-C4H10, i-C4H10 and C5+. The following reactionsare considered as governing Fischer–Tropsch reactions [34]:

1) CO + 3H2→R1

CH4 + H2O

2) 2CO + 4H2→R2

C2H4 + 2H2O

3) 2CO + 5H2→R3

C2H6 + 2H2O

4) 3CO + 7H2→R4

C3H8 + 3H2O

5) 4CO + 9H2→R5

n� C4H10 + 4H2O

6) 4CO + 9H2→R6

i� C4H10 + 4H2O

Table 1FTs pilot plant characteristics [33].

Parameter Value

Tube dimension [mm] Ø38.1×3×12,000Molar ratio of H2/CO in feed 0.96Feed temperature [K] 569Reactor pressure [kPa] 1700Cooling temperature [K] 566.2Catalyst sizes [mm] Ø2.51×5.2Catalyst density [kg m−3] 1290Bulk density [kg m−3] 730Number of tubes 1Tube length [m] 12GHSV [hr−1] 235Bed voidage 0.488Feed molar flow rate [gmol/s] 0.0335

7) 6:05CO + 12:23H2→R7

C6:05H12:36ðCþ5 Þ + 6:05H2O

8) CO + H2O↔R8

CO2 + H2

The reaction rate equation is as follows and the kinetic parametersare given in Table 3.

Ri = 0:278 ki⋅ exp−EiRT

� �⋅Pm

CO⋅PnH2

½mol:kg−1cat :sec

−1� ð1Þ

3.2. Mathematical model for fixed-bed FTS

A FTS pilot plant was designed and constructed by the ResearchInstitute of Petroleum Industry (RIPI) and National Iranian OilCompany (RIPI-NIOC) in 2004. This reactor (CR) has been modeledregarding the following assumptions: (a) One-dimensional plug flow;(b) axial dispersion of heat is negligible compared to convection;(c) Gases are ideal.

The mass and energy balance equations for the bulk gas phase canbe written as follows:

−ft0Ac

⋅ dyidz

+ av⋅ct⋅kgiðyis−yiÞ = 0: i = 1;2;…;N−1 ð2Þ

−ft0Ac

⋅cpgdTdz

+ av⋅hf ⋅ðTs−TÞ + πDi

AcUshellðTshell−TÞ = 0 ð3Þ

where, yi, fto, and T are the gas-phase mole fraction, inlet molar flowfor tube side and temperature, respectively.

The boundary conditions for the bulk phase are expressed by:

z = O; yi = yi;in; T = Tin ð4Þ

The mass and energy balance equations for the catalyst pellets canbe formulated as follows:

kgi⋅av⋅ct⋅ðyi−yisÞ + ρB⋅η⋅ri = 0 i = 1;2;…;N−1 ð5Þ

Fig. 2. Schematic diagram of a membrane dual-type FTS reactor (MDR) in counter-current mode of operation.


av⋅hf ⋅ðT−TsÞ + η⋅ρB⋅∑8

j=1rjð−ΔHf ⋅jÞ = 0 ð6Þ

where yis and Ts are the mole fractions on the catalyst surface andsolid-phase temperature, respectively.

3.3. Membrane dual-type FTS reactor model

The mathematical model for the simulation of membrane dual-type FTS reactors was developed based on the following assumptions:

(1) One-dimensional plug flow in shell and tube sides.

Table 2Specifications of catalyst and reactor of fixed-bed andmembrane dual-type FTS reactor.

Parameter Water-cooled reactor(first reactor)

Gas - cooled reactor(second reactor)

MDR MDR

Catalyst density [kg m−3] 1290 1290Catalyst equivalent diameter [m] 3.83×10−3 3.83×10−3

Molar ratio of H2/CO in feed 0.96 –

flow rate per tube [gmol sec−1] 0.0335 0.754Feed temperature [K] 565 –

Reactor pressure [kPa] 1700 2200tube side pressure [bar] – 30Cooling temperature [K] 566.2 –

Inner radius of Pd–Ag layer [mm] 19.05 19.05Membrane thichness (μm) – 15Bulk density[kg.m−3] 730 –

Tube length[m] 7.2 4.8Tube size [mm] Ø38.1×3 Ø21.2×4.2Number of tubes 360 16Bed voidage 0.488 0.488Catalyst thermal conductivity[kj.m−1s−1K−1]

0.00625 0.00625

(2) Axial dispersion of heat is negligible compared to convection.(3) Gases are ideal.(4) Steady state condition.

An element of length Δz as depicted in Fig. 3 was considered. Thedifferential equations describing mass and heat transfer in the axialdirection are described in the following subsections.

3.3.1. Water-cooled reactor (first reactor)The mass and energy balance equations for the bulk gas phase can

be written as follows:

− ft0Ac

dyidz

+ av⋅ct⋅kgiðyis−yiÞ = 0: i = 1;2;…N−1 ð7Þ

− ft0Ac

⋅cp⋅dTdz


AcUshellðTshell−TÞ = 0 ð8Þ

where yi and T are the gas-phase mole fraction and temperature,respectively.

Table 3Kinetic parameters data [34].

Reaction no. m n k E

1 −1.0889 1.5662 142,583.8 83,423.92 0.7622 0.0728 51.556 65,0183 −0.5645 1.3155 24.717 49,7824 0.4051 0.6635 0.4632 34,885.55 0.4728 1.1389 0.00474 27,728.96 0.8204 0.5026 0.00832 25,730.17 0.5850 0.5982 0.02316 23,564.38 0.5742 0.710 410.667 58,826.3

Fig. 3. A schematic diagram of an elemental volume of a membrane reactor for counter-current mode of operation.


The boundary conditions for the bulk phase are expressed by:

z = 0; yi = yi⋅in; T = Tin ð9Þ

The mass and energy balance equations for the catalyst pellets canbe formulated as follows:

kgi⋅av⋅ct⋅ðyi−yisÞ + ρBη⋅ri = 0 i = 1;2;…N−1 ð10Þ

avhf ðT−TsÞ + η⋅ρB∑8

j=1rjð−ΔHf ;jÞ = 0 ð11Þ

In these equations yis and Ts are the mole fractions and temperatureon the catalyst surface, respectively. Conventional fixed-bed FTS reactor(CR) is modeled similar to water-cooled reactor system.

3.3.2. Gas-cooled reactor (second reactor)

3.3.2.1. Shell side (reaction side). The mass and energy balances forsolid phase in gas-cooled reactor are the same as that in the water-cooled reactor. The following equations are written for fluid phase:

− FtAshell

⋅ dyidz

+ av⋅ct⋅kgiðyis−yiÞ +αH

Asð ffiffiffiffiffi

PHt

q−

ffiffiffiffiffiffiffiPHsh

q Þ= 0

i = 1;2;…;N−1

ð12Þ

− FtAshell

⋅cpg⋅dTdz


AshellUtðTt−TÞ

+αH

Asð ffiffiffiffiffi

PHt

q−


q Þ⋅cph⋅ðTt−TÞ = 0

ð13Þ

where yi and T are the mole fraction of component i and gas-phasetemperature, respectively. αH is the hydrogen permeation rateconstant, P t

H and PshH are the hydrogen partial pressure in the tube

and shell sides, respectively.

3.3.2.2. Tube side (feed synthesis gas flow). The mass and energybalance equations for fluid phase are given as:

F1Ac

∂Fti∂z −αH

Acð ffiffiffiffiffi

PHt

q−


q Þ = 0 ð14Þ

Fft0Ac

cpgtdTtdz

+πDi

AcUtðT−TtÞ = 0 ð15Þ

The boundary conditions are as follows:

z = L; yi = yif ; T = Tf ð16Þ

The auxiliary and hydrogen permeation correlations are given inAppendices A and B, respectively. In the above equations, the positivesign is used for the counter-current mode while the negative sign isemployed for the co-current mode of operation.

4. Numerical solution

The governing equations of this model form a set of differential andalgebraic equations which is consisted of the equations of massand energy conservative rules of both solid and fluid phases in firstand second reactor. These equations have to be coupledwith non-linearalgebraic equations of the kinetic model.

4.1. Solving procedure for counter-current mode

In the counter-current mode of operation, the temperature, molarflow rate and composition of the gas flow entering to the catalyst bedof the first reactor are unknown, while the temperature, molar flowrate and composition of the gas flow entering to the second reactorare known. The shooting method converts the boundary valueproblem to an initial value problem. The solution is possible byguessing mentioned values for the gas flow to the first reactor. Theequations of the first reactor are solved from up to down of the firstreactor; when it comes to the second reactor; the same pattern isfollowed for solution procedure. At the end of the solution, thecalculated values of temperature, molar flow rate and composition offresh feed gas flow to the second reactor are compared with the actualvalues. This procedure is repeated until the specified terminal valuesare achieved within small convergence criterion.

4.2. Solving procedure for co-current mode

In the co-current mode of operation, calculation is started with aninitial guess for unknown values (initial condition). New calculatedvariables using Gauss–Newton method is replaced in its previousvalues in subsequence calculations. Substitution is continued until theconvergence criterion is met. The temperature of feed gas to the firstreactor is only unknown variable.

5. Results and discussion

Fig. 4 shows the H2 and CO conversions along the single-type anddual-type FTS reactors. As can be seen from Fig. 4 (a.1), the H2

conversion increases along the reactor for three types of reactors but theconversion of dual-type reactors is higher than conventional fixed-bedreactor. Also thisfigure demonstrates the conversion in counter-currentmode of operation is slightly higher than co-current configuration. Tofocus on this point, Fig. 4 (a.2) was drawn and it is observed that outletconversion of hydrogen in counter-current mode is higher than co-current one. Fig. 4 (b.1) presents theCOconversion along the reactor. COconversion enlarges with constant slop in conventional reactor, but itsharply enhances at the initial section of the reactor and then slightlygrows for dual-type reactors. At the end of the reactor the three curvesare close to each other but the conversion in counter-current mode ishighest. Fig. 4 (b.2) reveals this result.

To focus on the subject of this work, a comparison of gasolineproduction yield as a main product in co-current and counter-currentmodes of MDR and CR configurations is presented by Fig. 5. The highestgasoline production is related to counter-current mode of MDRconfiguration as consequence of hydrogen permeation through mem-brane. Gasoline yield increases with constant slop in conventionalreactor, but it suddenly boosts at the initial section of theMDRs and thensmoothly increases. At the end of reactor the three curves approach toeachotherbut conversion in counter-currentmode is greatest. Also, it canbe understood from this figure that if the length of the reactor is shorterthan 12 m, the gasoline production was enough for dual-type reactors.

Fig. 4. A comparison of conversions for 3 types of reactors: conventional fixed-bed, co-current and counter-current modes of dual-type FTS. (a.1) Hydrogen conversion(a.2) Hydrogen conversion enlarged at the end of reactor, (b. 1) Carbon monoxide conversion (b.2) Carbon monoxide conversion enlarged at the end of reactor.


Fig. 6demonstrates thegasphase temperatureprofile of CR andMDRsalong three types of reactors. This profile has two temperature picks atthe zones close to the entrances of reactors. There is one pick in anyreactor that occurs owing to high exothermic reactions. One temperaturerunaway is clearly seen in the first 0.5 m length of the water-cooledreactor (first reactor) and the secondone arises in thefirst 0.5 m length ofthe gas-cooled reactor (second reactor). There is a favorable profile of gastemperature inMDRs. The average temperature inMDRs is lower thanCRand it can help durability of catalyst activity. Also it is understood that inco-current mode of operation, the temperature is slightly lower thancounter-current mode. It is observed that the temperature control of thedual-type reactor is easier than single type. There is a jump oftemperature for all systems at first 0.5 m length of each reactor thatcaused by high heat of reaction in FTS. For simulation purposes, themaximum temperature for the Fe-HZSM5 catalyst to remain active isassumed to be 620 K [9]. As shown in this figure, in single fixed-bedreactor system, the risk of temperature runawaymakes alert in closing to

hotspot. But, as it seems in this figure, MDRs have better temperatureperformance. According to high exothermic reactions, temperature jumpoccurs in the first section of reactor because the temperature runaway inmost cases occurs at a zone close to the inlet of reactor (the distance fromentrance depends on the feed and cooling temperatures) [9]. Therefore,good temperature control along this reactor is crucial. This rising oftemperature in CR is higher than MDR and it is dangerous. The risk oftemperature runaway makes alert in closing to hotspot but MDR showmore favorable performance of temperature because the lower temper-ature postpones deactivation of catalyst. Controlling of temperature isone of the advantages of MDR. Since in the second reactor of MDR, inletfeed has lower H2 (due to H2 permeation) in comparison with CR,therefore heat of reaction is lower and results in lower temperature peak.Also, temperature profile in dual-type configuration causes betterproducts distribution in MDR.

Fig. 7 shows the production yields of hydrocarbons such as methane,ethylene, ethane, propane, normal butane, and iso-butane respectively.

Fig. 5. A comparison of gasoline yield for 3 types of reactors: conventional fixed-bed, co-current and counter-current modes of dual-type FTS. (a.1) Gasoline yield (a.2) Gasoline yieldenlarged at the end of the reactor.


Fig. 7(a) shows the methane yield in conventional reactor is higher thanMDRs.As canbe seen fromFig. 7(b), theethyleneyield inMDRs is stronglyhigher than CR and both modes of operations in dual-type reactors reachto each other at the end of reactor. Ethane yield is shown by Fig. 7(c). LikeC2H4 result, the yield of ethane is alsohigher inMDRsbut, thedifference atthe endof reactor is declined. Propaneyieldhas the same trend (Fig. 7(d)).There is interesting result in Fig. 7(e); in fact, normal butane yield in CR ishigher than MDRs. At the MDRs, the normal butane increases at the 4 mlength of reactor entrance and then gets smooth. In this point, the profileof CR intersects the MDRs curves. Fig. 7(f) demonstrates iso-butanetrajectory. Counter-current configuration shows the higher yield relatedto co-current and CR configurations. The lightest and undesired product(methane) is important and the favorable trajectory forMDRs is observedin this figure. Fig. 8(a) describes the yield of CO2 profiles of CR andMDRs.The CO2 yield in CR is higher than MDRs. In MDRs, the co-current modehas more CO2 yield in comparison with counter-current mode; this pointcan be seen clearly in Fig. 8(b).

Fig. 9 (a) depicts theyield ofH2Oprofiles of CRandMDRs. In fact, H2Oyield in CR is lower than MDRs. In MDRs system, the co-current modehas more H2O yield in comparison with counter-current mode (Fig. 9(b)). Diffusion of hydrogen to reaction side affects water gas shiftreaction in favor of CO2 consumption, on the other hand, enhancementin water production as a by product is not suitable for this system.

Fig. 10 shows the hydrogen mole fraction in tube side along thereactor for co and counter-current modes of operation. As it is

Fig. 6. A comparison of temperature profiles along the reactors of CR and MDR.

expected, themole fraction of hydrogen in co-currentmode decreaseswhile the hydrogen mole fraction increases in counter-current mode.Also, due to the more permeation of hydrogen in counter-currentmode of operation, the slope of its profile is greater than that one.

Fig. 11 illustrates the permeation rate of hydrogen versus length ofreactor. The permeation rate of hydrogen in counter-current mode israther fewer than co-current mode.

Fig. 12 confirms the temperature of reaction side versus hydrogenpermeation rate for two dual-bed configurations. In co-current mode,the hydrogen permeation reduces when the temperature rises. But, incounter-current mode, the hydrogen permeation amplifies when thetemperature ascends.

Fig. 13 demonstrates 3D plots of gasoline mole percent as afunction of inlet temperature and reactor length. It is understood fromFig. 13 (a) that the C5+ mole fraction increases along the reactor andslightly enhances by rising temperature in MDR. The similar behavioris observed from CR (Fig. 13 b) but the final mole percent of C5+ islower than MDR.

A comparison of hydrocarbon products, water and carbon dioxideselectivity between conventional reactor and membrane dual-typereactors is presented in Fig. 14. According to this contrast, MDRssystems show favorable results relative to CR system. Membraneconcept enhances the C5+ selectivity which is an objective of theproposed design and likely declines methane and carbon dioxide(undesired products) selectivity. Therefore, this membrane reactorcan be an appropriate reactor type for FTS process. Indeed, forFischer–Tropsch synthesis, CO and H2 conversions in first segments ofreactor are high in CR, so that at the end of CR, lack of reactants isobvious; therefore the MDR was suggested because of hydrogensaving at second reactor. At this stage the new catalyst bed exists, andCO2, FTS products and reactants come from previous reactor, so that atthe second bed (after H2 permeation from Pd–Ag membrane)reactants and CO2 convert to FTS products (WGS reaction).

6. Conclusion

This study focused on comparison of dual-type Pd–Ag membranereactor in co and counter-current modes of operation and conven-tional fixed-bed reactor for Fischer–Tropsch synthesis (FTS). In thisconfiguration, the synthesis gas is converted to hydrocarbons in twocatalytic reactors in which the generated heat in the first reactor isremoved with water circulating on the shell side and in the secondreactor; the heat of reaction is utilized to preheat the synthesis gas fedto the first reactor. In the gas-cooled reactor, the phenomenon of

Fig. 7. A comparison of components yields along the different reactors for (a) CH4, (b) C2H4, (c) C3H6, (d) C3H8, (e) n-C4H10, and (f) i-C4H10.


selective permeation of hydrogen through palladium–silver mem-brane has been used to obtain a major increasing in reactorperformance by process intensification. The permselective palladiumlayer on inner tube allows hydrogen to penetrate from the tube side to

the reaction side. The reacting gas in the shell side is cooledsimultaneously with passing gas in the tube side and saturatedwater in outer shell side. The results shows the counter-currentconfiguration has favorable profile for C5+ and carbon dioxide and

Fig. 8. Yield of carbon monoxide for CR, co-current MDR and counter-current MDR, (a) along the reactor and (b) enlarged at the end of the reactor.


methane selectivity, but the temperature profile in co-currentmode isbetter than counter-current mode. Also, in dual-type reactors water isproduced slightly more than single-type reactor. In general, it wasfound that both configurations of dual-type reactors have priority tosingle-type reactor for FTS.

Acknowledgment

The authors acknowledge the National Iranian Gas and CentralRegion Oil Company and also South Zagross Gas and Oil Company fortheir financial supports.

Appendix A. Auxiliary correlations

A.1. Fixed-bed reactor correlations

The mass transfer coefficients between the gas phase and the solidphase infixed-bed reactor (first reactor)havebeen taken fromCusler [35].

kgi = 1:17Re−0:42Sc−0:67i ug × 103 ðA� 1Þ

Fig. 9. Yield of water for CR, co-current MDR and counter-current MDR

Re =2Rpug

μðA� 2Þ

Sci =μ

ρ⋅Dim⋅10−4 ðA� 3Þ

The diffusivity of each component in the gas mixture is given by[36]:

Dim =1−yiΣi≠j

yiDij

ðA� 4Þ

Dij =10−7⋅T3=2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1Mi

+ 1Mj

q

Pðϑ3=2ci + ϑ3=2

cj Þ2ðA� 5Þ

where, Dij is the binary diffusivity calculated using the Fuller–Schetter–Giddins equation. Mi and υci are the molecular weight andcritical volume of component i which are reported in Table A.1.

, (a) along the reactor and (b) enlarged at the end of the reactor.

Fig. 10. Hydrogen mole fraction in permeation side as a function of reactor length inMDR for co and counter-current modes of operation.

Fig. 11. Hydrogen permeation rate as a function of reactor length in MDRs for co andcounter-current modes of operation.


The overall heat transfer coefficient between the circulatingboiling water of the shell side and the bulk of the gas phase in thetube side is given by the following correlation:

1Ushell

=1hi

+Ai⋅ ln Do

Di

2πLKw+

Ai

Ao⋅ 1ho

ðA� 6Þ

where, hi is the convection heat transfer coefficient between the gasphase and the reactor wall and is obtained by the followingcorrelation [37]:

hicpρμ

⋅cp⋅μk

� �23 =

0:458εB

⋅ρ⋅u⋅dp

μ

� �−0:407

ðA� 7Þ

Table A.1Molecular weight and critical volume of the components.

Component
Mi (g/mol) vci (m3/mol)×106
C5+
85.084 370
i-C4H10
58.123 262.7 n-C4H10 58.123 255 C3H8 44.096 200 C2H6 30.07 145.5 C2H4 28.054 129.1 CO2 44.01 94.0 CO 28.01 18.0 H2O 18.02 56.0 H2 2.02 6.1 CH4 16.04 99.0 N2 28.01 18.5
Fig. 12. Tube side temperature as a function of hydrogen permeation rate in MDR for coand counter-current operations.

whereas ɛB is the void fraction of the catalytic bed and dp is theequivalent catalyst diameter and the other parameters are related tobulk gas phase.

To calculate the heat transfer coefficient of boiling water in theshell side at high pressure, Leva correlation is applied: [37]

ho = 282:2P 4=3⋅ΔT2 0:7 < P < 14Mpa ðA� 8Þ

Appendix B. Hydrogen permeation correlations

The flux of hydrogen permeating through the palladium mem-brane, jH, will depends on the difference in the hydrogen partial

pressure on the two sides of the membrane. Here, the hydrogenpermeation is determined assuming the Sieverts law [38].

jH = αHð ffiffiffiffiffiPHt

q−


q Þ ðB� 1Þ

αH is hydrogen permeation rate constant and is defined as [38]:

αH =2πL—p

ln RoRi

ðB� 2Þ

where,Ro andRi stand for outer and inner radius of Pd–Ag layer. Here, thehydrogen permeability through Pd–Ag layer is determined assuming theArrhenius law as a function of temperature as follows [39,40]:

—p = p0⋅ exp−EpRT

� �ðB� 3Þ

where, the pre-exponential factor P0 above 200 °C is reported as 6.33×10−8mol m−2s−1pa−1/2 and activation energy EP is 91270 kJ/kmol[39,40].


Appendix C. Nomenclature

Symbol
Unit Definition
Ac
m2 Cross section area of tube Ai m2 Inner area of tube As m2 Lateral area of tube Ashell m2 Cross section area of shell av m2.m−3 Specific surface area of catalyst pellet cPg J.mol−1.k−1 Specific heat of the gas at constant pressure CPgt J.mol−1.k−1 Specific heat of the tube gas at constant pressure CpH J.mol−1.k−1 Specific heat of the hydrogen at constant pressure CPs J.mol−1.k−1 Specific heat of the catalyst at constant pressure Ct mol.m−3 Total concentration CO-MDR – Co-current mode of membrane dual-type reactor COUN-MDR – Counter-currentmode ofmembrane dual-type reactor CR – Conventional reactor Di m Tube inside diameter Dij m2.s−1 Binary diffusion coefficient of component i in j Dmi m2.s−1 Diffusion coefficient of component i in the mixture
Dro
m Reaction outside diameter dp m Particle diameter GTL – Gas to Liquid hf W.m−2.K−1 Gas-catalyst heat transfer coefficient hi W.m−2.K−1 Heat transfer coefficient between fluid phase and
reactor wall
ho W m−2 K−1 Heat transfer coefficient between coolant stream and
reactor wall
F r mol.s−1 Total molar rate for shell side F t mol.s−1 Total molar rate for tube side K W.m−1.K−1 Conductivity of fluid phase Kw W.m−1.K−1 Thermal conductivity of reactor wall kgi m.s−1 Mass transfer coefficient between gas and solid
phase for component i
L m Length of reactor Mi g.mol−1 Molecular weight of component i MDR – Membrane dual-type reactor N [–] Number of components P bar Total pressure Pa bar Atmospheric pressure PHt bar Tube side pressure
PHsh
bar Shell side pressure
P̄
mol m−1s−1Pa−1/2
Permeability of hydrogen through Pd–Ag layer

P0
mol m−1s−1Pa−1
Pre-exponential factor of hydrogen permeability

R
J.mol-1.K−1 Universal gas constant Re [–] Reynolds number Ri [m] Inner radius of Pd–Ag layer Ro [m] Outer radius of Pd–Ag layer ri mol.kg−1.s−1 Reaction rate of component i rbi mol.kg−1.s−1 Reaction rate of component i in bubble phase Sci [–] Schmidt number of component i T K Bulk gas phase temperature Ts K Temperature of solid phase Tsat K Saturated temperature of boiling water at operating
pressure
Tshell K Temperature of water stream Ushell,Ut W.m−2.K−1 Overall heat transfer coefficient between coolant and
process streams
ug m.s−1 Linear velocity of gas phase yi mol.mol−1 Mole fraction of component i in the fluid phase yis mol.mol−1 Mole fraction of component i in the solid phase z m Axial reactor coordinate
Greek letters

Symbol
Unit Definition
αH
mol m−1s−1Pa−0 5 Hydrogen permeation rate constant ΔHf,i J.mol−1 Enthalpy of formation of component i ΔH298 J.mol−1 Enthalpy of reaction at 298K μ kg m−1.s−1 Viscosity of fluid phase νci cm3.mol−1 Critical volume of component i ρ kg.m−3 Density of fluid phase ρB kg.m−3 Density of catalytic bed ρp kg.m−3 Density of catalyst η [–] Catalyst effectiveness factor
Superscripts and subscripts

f
Feed conditions s At catalyst surface sh Shell side t Tube side
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