International Communications in Heat and Mass Transfer 38 (2011) 1119–1124

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International Communications in Heat and Mass Transfer

j ourna l homepage: www.e lsev ie r.com/ locate / ichmt

An investigation on the performance of a FTS fixed-bed reactor using CFD methods☆

Mohammad Irani a, Asghar Alizadehdakhel b,⁎, Ali Nakhaei Pour a, Pierre Proulx c, Ahmad Tavassoli a

a Gas Division, Research Institute of Petroleum Industry (RIPI), Tehran, Iranb Process Engineering Development Division, Research Institute of Petroleum Industry (RIPI), Tehran, Iranc Department of Chemical Engineering, Université de Sherbrooke, Sherbrooke, Que., Canada J1K 2R1

☆ Communicated by W.J. Minkowycz⁎ Corresponding author at: Process Engineering De

Institute of Petroleum Industry (RIPI), West Blvd., NearIran.

E-mail addresses: Alizadehdakhela@ripi.ir, A_Alizade(A. Alizadehdakhel).

0735-1933/$ – see front matter © 2011 Elsevier Ltd. Aldoi:10.1016/j.icheatmasstransfer.2011.05.005

a b s t r a c t

a r t i c l e i n f o

Available online 19 May 2011

Keywords:Fischer–Tropsch synthesisIron-based catalystCFD simulationSaturated water

In the present work, a numerical model was developed and validated in order to simulate and improve theconversion of synthesis gas (CO+H2) to higher hydrocarbons in a Fischer–Tropsch Synthesis (FTS) fixed-bedreactor. The reactor was a 3.1 cm diameter and 2.75 m length steel tube in which saturated water wasemployed to control the peak temperature within the catalyst bed. A 2-D CFD model with an optimized meshof 22,016 square cells was developed tomodel hydrodynamics, chemical reaction, non-ideality of themixture,heat andmass transfer in the reactor. Good agreement was achieved between pilot experimental data and themodel. The result showed that adjusting the boiling water flow rate in the range of 25–250 g.min–1 allowsmaintaining the FTS temperature at suitable values. An optimum value of 573 K was obtained for feedtemperature.

velopment Division, ResearchAzadi Sports Complex, Tehran,

hdakhel@yahoo.com

l rights reserved.

© 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Fischer–Tropsch Synthesis (FTS) is a set of catalytic chemicalreactions that convert a mixture of carbon monoxide and hydrogen(so-called synthesis gas) into liquid hydrocarbons. Fixed-bed is one ofthe most competing reactor technologies for FT [1]. Bi-functionalcatalysts are used to promote the yield and quality of the gasolinefrom FTS [2]. Although the reaction scheme has been studied and usedfor a long time, its study today is still of interest because of the highpressure on hydrocarbon prices all over the planet. Butt et al. [3]prepared and characterized Fe and FeCo catalysts on ZSM-5 supportfor FTS. Schulz et al. [4] studied the selective conversion of syngas togasoline on iron/HZSM5 catalysts. Calleja et al. [5] carried out someexperiments to investigate the effects of process variables includingtemperature, space velocity; CO/H2 feed ratio and pressure on theactivity of a Co/HZSM5 zeolite bifunctional catalyst. They reportedthat their catalyst exhibits higher selectivity and yield in comparisonwith conventional catalysts. Liu et al. [6] used a two-dimensionalheterogeneous model to simulate steady and unsteady behavior of afixed bed FTS reactor. They also reported the impact of feedtemperature, flow rate and the wall temperature on the steady state

behavior of the reactor [7]. Wang et al. [8] developed a one-dimensional heterogeneous model to predict the performance offixed-bed Fischer–Tropsch reactors. Marvast et al. [9] simulated thebehavior of the FT fixed-bed reactor using a two-dimensionalheterogeneous model at steady state condition.

In the recent years the remarkable increases in computation speedmade CFD a powerful and effective tool to model and understandcomplex processes [10–12]. Selma et al. [13,14] and Bannari et al. [15]developed advanced methods for describing gas–liquid hydrodynam-ics in bubble column reactors. Troshko and Zdravistch [16] employedan Eulerian multifluid formulation CFD method to model Fischer–Tropsch synthesis in bubble column reactors. They applied theirexperimentally validated model to an industrial scale bubble columnreactor. Their model was qualitatively successful in predicting thehydrodynamic effects, but heat transfer effects were not considered.Arzamendi et al. [17] developed a three dimensional CFD model tomodel heat transfer in a low-temperature Fischer–Tropsch synthesismicrochannel reactor. In their experiments, boiling water was used ascoolant. Arzamendi et al. [18] formulated a kinetic model fordescribing the preferential oxidation of CO (CO-PrOx) in H2 richstreams with CO2 and H2O in the feed. They studied the influence ofthe operating variables on the CO-PrOx in microchannels andmicroslits by implementing the rate equations in CFD codes.

In the present work, a CFD model was developed to model FTS in afixed bed reactor. Adequate equation of state was employed to modelthe non-ideality of the gas mixture. A heat sink was defined to modelthe performance of boiling water which was used to establishisothermal condition in the reactor. The model predictions werevalidated with pilot experimental data.

Nomenclature

Ci concentration, kmol.m3

D total Diffusivity Coefficient, m2.s−1

Ei Activation Energy, kJ.kmol−1

f fugacity, barg gravity acceleration, m.s−2

h enthalpy of species, kJ.kg−1

H Total enthalpy, kJ.kg−1

j Mass flux, kg.m−2.s−1

ki kinetic constant, mol.h−1.g−1.bar−1

km thermal conductivity, kJ.m−1.K−1

Mi molecular weight, kg.kmol−1

P pressure, barq heat flux, kJ.m−2.s−1

R global gas factor, kJ.kmol−1.K−1

S momentum source term, kg.m−2.s−2

T temperature, Kv velocity, m.s−1

V volume, m3

xi mass fractionZ compressibility Factor

Greek lettersρ density, kg.m−3

μ viscosity, kg.m−1.s−1

φi fugacity coefficient

Subscripti species numberj second species numberm mixture

1120 M. Irani et al. / International Communications in Heat and Mass Transfer 38 (2011) 1119–1124

2. Material and methods

2.1. Process description

A photograph and a schematic view of the pilot plant are shown inFig. 1. It was designed and constructed by the Research Institute ofPetroleum Industry, National IranianOil Company (RIPI-NIOC) in 2008[19]. The reactor was packed with a bi-functional Fe-HZSM5 catalyst(metal part: 100 Fe/5.4 Cu/7K2O/21SiO2, acidic part: SiO2/Al2O3=14).There was a jacket around the reactor through which boiling waterflows to remove the heat of reaction. The temperature of boiling waterwas controlled by adjusting the pressure of the system. Thecharacteristics of the pilot plant are shown in Table 1. The experimentswere carried out at different operating conditions and the temperatureprofile along the reactor and the product composition were analyzed.

2.2. CFD modeling

2.2.1. Solution strategy and convergence criterionIn this work, a two-dimensional CFDmodel was developed and the

finite volume method was used to discretize the partial differentialequations of the model. The SIMPLE algorithm was employed forpressure–velocity coupling. The solution procedure is described inFig. 2. The convergence criterionwas based on the residual value of thecalculated variables, namely mass, velocity components, energy andspecies mass fractions. In the present calculations, the numerical

computation was considered to be converged when the scaledresiduals of the different variables were lower than 10−4 forcontinuity andmomentumequations and 10−7 for the other variables.

2.2.2. Computational domain and boundary conditionsThe 2.75 m×15.5 mm axisymetric reactor was divided into one

entrance preheating fluid zone followed by a packed reaction zone.The packed bed was considered as a porous media due to the largevalue of N (tube-to-catalyst diameter ratio) [20]. Three differentnumbers of structured meshes were used to verify that the resultswere sufficiently independent of the grid size. It was found that22,016 meshes were adequate with respect to computational effortand precision. Mass-flow-inlet and pressure-outlet boundary condi-tions were used for reactor inlet and outlet, respectively. A constanttemperature of 573 C and a no-slip condition was employed for thereactor walls.

2.2.3. Conservation equationsThe mass conservation, momentum, energy and species, can be

expressed as:

Mass : ∇: →vρ� �

= 0 ð1Þ

Momentum : ∇: ρ→v →v� �

= −∇P + ∇: μ ∇→v + ∇→v T� �h i

+ ρg + S

ð2Þ

Energy : ∇: →v ρ H + Pð Þ� �

+ ∇: ∑n

i=1hi ji

� �= −∇: qð Þ + SR ð3Þ

Species : ∇: →v Ci–Di∇Ci

� �= Ri ð4Þ

where, ρ represents mixture density,→v is velocity vector, H and hi aretotal enthalpy and enthalpy of species, respectively. P is the staticpressure and Ci stands for concentration of chemical species. Thecatalyst zone was considered as a porous media and modeled by theaddition of a momentum source term:

S = − ∑2

j=1Dijμvj + ∑

2

j=1Cij

12ρvvj

!: ð5Þ

The momentum source term is composed of two parts: a viscous lossterm (Darcy, the first term on the right-hand side of Eq. (5)) and aninertial loss term (the second term on the right-hand side of Eq. (5)). |v|is themagnitude of the velocity andD and C are the prescribedmatrices.In this work, the flow in the reactor is laminar; therefore, the inertialterm was ignored [21]. SR in Eq. (3) is the source of energy caused bychemical reaction:

SR = − ∑j

h0jMj

Rj

!−SW ; Sw = − H T′ð Þ−H Tð Þð Þ for wall� adjacent cells

0:0 for other cells

�

ð6Þ

SW is a source term that was defined to establish isothermalcondition at wall boundaries. As mentioned in process descriptionsection, saturated water was used for heat removal and creatingisothermal condition at reactor walls. H(T′) in Eq. (6) is enthalpy attemperature T′ (the increased temperature due to releasing heat ofreaction) and H(T) is enthalpy at temperature T (the desiredtemperature for reaction).

2.2.4. Physical propertiesDue to complexity of the FTS reaction system, variety of products

(C1–C20) and operating condition of the process, the non-idealthermodynamic behavior of the system should be considered

I =

a) b)

The reactor

Cold trap for

gathering liquid

products

System for

producing saturated

water

Fig. 1. FTS fixed-bed reactor; (a) real photograph (b) schematic view.

Determine the source terms for all the

conservation equations

Update properties (Diffusivity & Density)

Calculate rates of reactions

Calculate the thermodynamic

properties such as fugacity coefficients and

compressibility factor

1121M. Irani et al. / International Communications in Heat and Mass Transfer 38 (2011) 1119–1124

[22,23]. In this study, the Peng–Robinson equation was chosen as asuitable EOS (equation of state) to calculate the mixture density andspecies fugacity (fi) as follows:

ln⌢φi = Z−1ð Þ bibm

− ln Z−betað Þ−I qi; q =a

bRT; qi = q 2: ×

∂a∂xia

�bi½i�b

0BB@

1CCA

1ε1−ε2

lnZ + ε1 × betaZ + ε2 × beta

� �; beta =

bPRT

; fi =⌢φi × P × yi ð7Þ

where, R is the universal gas constant, MG is the molecular weight ofgas mixture and P is the operating pressure (taken to be 17 bar). Z isthe compressibility factor for calculation of the mixture density:

ρ =PMZRT

: ð8Þ

Table 1FTS pilot plant characteristics.

Tube dimension(mm) 31×3×2.75

Number of tubes 1Molar ratio of H2/Co 1Feed temperature(K) 563,573 and 583Catalyst sizes (mm) 1.5×4Catalyst density(kg/m3) 1290Bulk density(kg/m3) 730Reactor pressure(bar) 17Cooling temperature (K) Saturated water (563,573 and 583)GHSV(nl/h) 3Bed Voidage 0.38

Converged?

Yes No

Solve continuity, momentum equations

(to obtain velocity and pressure fields)

and species equations consequently.

Report \Results

Fig. 2. The solution procedure.

Table 2Parameters of Peng–Rabinson EOS.

σ ε Ω Ψ

1 +ffiffiffi2

p1−

ffiffiffi2

p0.07779 0.45724

α Tr;ωð Þ = 1 + 0:37464 + 1:54226ω−0:26992ω2� �

1−Tr1=2

!" #2

Z = β + Z + εβð Þ Z + σβð Þ 1 + β−Zqβ

� �; β = Ω

PrTr

; q =α Trð ÞψΩTr

Table 4Rates parameters for reactions 1 to 7 in Table3.

Reaction No. K1(mol s−1 kgcat−1/kPa) E1(J mol−1)

1 2.044e-2 15,6932 6.255 e-5 20.3843 3.423 e-4 1.56074 5.972 e-6 164.065 6.482 e-6 86.9346 6. 482e-6 81.7537 3.168e-5 738.78

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

0 0.5 1 1.5 2 2.5 3

Reactor length(m)

Z F

acto

r

1122 M. Irani et al. / International Communications in Heat and Mass Transfer 38 (2011) 1119–1124

The parameters of Eq. (7) are listed in Table 2. The specific heat ofeach species was defined as piecewise-polynomial function oftemperature. Other thermal properties of the mixture such asmolecular viscosity, thermal conductivity and diffusivity coefficientwere calculated from Poling et al. [24].

2.2.5. Reaction rate expressionsTwelve chemical species including CO, H2, CO, CO2, H2O, CH4, C2H4,

C2H6, C3H8, n-C4H10, i-C4H10 and C5+were considered as reactants andproducts of the FTS reactions. The leading Fischer–Tropsch chemicalreactions are listed in Table 3. The general form of rate equations forreactions 1–7 are expressed as:

Rimol=hr:grcat

!= ki exp

−EiRT

� � f 2h2fco

ð9Þ

The kinetic parameters of these equations are given in Table 4 [25].Reaction (8) is known as water–gas shift reaction and its rate can beexpressed as [26]:

Rwgs =15:7 exp −45080= RTð ÞðPCOPH2O

= P0:5H2

−PCO2P0:5H2

= KWGS

1 + 1:13 × 10−3 PCOPH2O= P0:5

H2

� � ð10Þ

where, KWGS is the equilibrium constant and can be calculated asfollows:

KWGS =5078:0

T−5:8972 + 13:959 × 10−4T−27:593 × 10−8T2

: ð11Þ

3. Result and discussion

The predicted fluid compressibility factor along the reactor isdrawn in Fig. 3. The figure interprets that due to formation of C5+ andH2O, the system deviates from ideal gas so that Z descends below 0.94,thus employing a real-gas equation of state is necessary. The predictedvalues of C5+ selectivity and COmole percent in the reactor outlet andtemperature at three points along the reactor (point 1: beginning ofcatalytic bed; point 2: middle of catalytic bed; point 3: end of catalyticbed) were compared with experimental measurements and theresults are given in Table 5. The values in this table show that the errorvalues are less than 4% for all of the compared variables. That is to say,

Table 3List of FTS reactions.

Num. Reaction stoichiometry

1 CO + 3H2 →CH4 + H2O2 2CO + 4H2 →C2H4 + 2H2O3 2CO + 5H2 →C2H6 + 2H2O4 3CO + 7H2 →C3H8 + 3H2O5 4CO + 9H2 →n� C4H10 + 4H2O6 4CO + 9H2 → i� C4H10 + 4H2O7 8:96CO + 18:05H2 →C8:96H12:36 C5 +

� + 8:96H2O

8 CO + H2O↔ CO2 + H2

the model in this work can successfully describe the fixed-bed FTprocess. The distribution of temperature inside the reactor ispresented in Fig. 4. The figure shows that the inside temperature ofthe reactor was well fixed at the desired inlet temperature using theconstant temperature with heat sink applied at wall boundaries.However, there is a temperature raise of about 17 K in the beginningof the reaction zone due to the high concentration of the reactants andthe consequent high rate of exothermic reactions in this region. Fig. 5shows the mass fraction profiles of product species along the reactorlength for the case with the inlet gas temperature of 573 K. The figureinterprets that the main changes in the concentrations of reactantsand products occur in the first 25 cm of the reaction zone. Therefore,the effective length of the reactor length is about 25 cm. It should bementioned that usually longer reactors are employed in order toextend the overhaul time of the reactor. In other words, whencatalysts in the first part of reactor are deactivated, the catalyst in theremaining length will convert the reactants to products. Due to theconsumption of reactants, the reduction of the concentrationsdecreases the rate of reactions and consequently the slopes ofconcentration curves along the reactor decrease. Fig. 6 shows thatthe mixture density increases along the reactor length due to theproduction of heavier hydrocarbons. Fig. 7 presents the contours ofvelocity in the reactor. As can be seen, the radial velocity distributionand zero velocity near the walls due to the non-slip wall boundarycondition are well predicted, as is naturally expected. Pressure drop inthe porous region causes the gas velocity to become almost uniform inthe radial direction. In addition, because of the production of heavyproducts, the velocity magnitude significantly reduces by entering thereaction region. In order to investigate the effect of temperature on

Fig. 3. Fluid compressibility factor along the reactor.

Table 5Comparison between measured and predicted values for the pilot-scale FTS processes.

Experimental Simulation Error (%)

CO conversion (%) 60.7 58.59 3.476112C5+ selectivity (g/g feed) 18 17.29 3.944444Temperature at point 1(K) 588 590 0.34014Temperature at point 2(K) 575 573 0.347826Temperature at point 3(K) 573 573 0

Fig. 6. Contour of density (operating condition: T=573, P=17 bar).Fig. 4. Contour of temperature (operating condition: T=573, P=17 bar).

1123M. Irani et al. / International Communications in Heat and Mass Transfer 38 (2011) 1119–1124

the reactor performance, the reactor operation was modeled at threedifferent temperatures. In all cases, reactor pressure andH2/CO ratio arekept constant at 17 bar and 1, respectively. The C5+ selectivity (g C5+/gfeed) along the reactor for three different temperatures are drawn inFig. 8. As depicted in this figure, increasing the temperature from 563 to

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

reactor length, m

com

pone

nt d

ry m

ass

frac

tion

COH2

a) Reactants

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 0.5 1 1.5 2 2.5

0 0.5 1 1.5 2 2.5 3

reactor length, m

com

pone

nt d

ry m

ass

frac

tion

BUTANEC5+EthaneEthyleneMethanePropane

b) Products

Fig. 5. Mass fraction of species along the reactor length at T=573.

573 K increases the C5+ selectivity. However, further increasing thetemperature to 583 K decreases C5+ selectivity. It should be noted thatincreasing the reactor temperature has, as a consequence, two oppositeeffects: firstly it increases the rate of reactions and secondly, it shiftsWGS reaction into reactants. In increasing the temperature from 573 to583 K, the second effect is dominant and the production of C5+ reducesdue to the reduction in the concentration of H2.

Fig. 7. Contour of velocity (operating condition: T=573, P=17 bar).

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5Reactor length (m)

C5+

Sel

ectiv

ity T=563T=573T=583

Fig. 8. Selectivity of C5+ at different temperatures along the reactor length.

1124 M. Irani et al. / International Communications in Heat and Mass Transfer 38 (2011) 1119–1124

4. Conclusions

A two-dimensional CFD model was developed to model fluid flow,chemical reaction, heat and mass transfer in a fixed bed reactor. Thenon-ideal thermodynamic behavior of mixture was correlated usingPeng–Robinson EOS. The temperature runaway of the process hasbeen quenched using saturated boiling water. The model wasvalidated against the measured data from a pilot-scale FTS reactorand satisfactory agreements were found between predictions of themodel and the experimental results. The results showed that thereactor temperature significantly affects the C5+ yield and anoptimum temperature can be found to reach the maximum yield.For the conditions of operating pressure, feed composition and flowrate, it was found that an optimum temperature exists between 563and 583 K. The model has proven to be in good agreement with theexperimental data and it could be used in further studies to find amore accurate value for the optimum temperature.

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