Modelling of Fischer Tropsch Reactor

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Latin American Applied Research 36:141-148 (2006)

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MODELING OF FISCHER-TROPSCH SYNTHESIS IN A TUBULAR

REACTOR

L.C.A. MAZZONE and F.A.N. FERNANDES

Universidade Federal do Cear, Departamento de Engenharia Qumica,

Campus do Pici, Bloco 709, 60455-760 Fortaleza CE, Brazil

[email protected]

Abstract

Fischer-Tropsch synthesis is an im-

portant chemical process for the production of liq-

uid fuels and olefins. In recent years, the abundant

availability of natural gas and the increasing de-

mand of olefins and liquid fuels have led to a high

interest to further develop this process. A mathe-

matical model of a tubular reactor used for syngas

polymerization was developed and the carbonmonoxide polymerization was studied from a mod-

eling point of view. Simulation results show that

different parameters affect syngas conversion andcarbon product distribution, such as operating

pressure, gas velocity and syngas composition. Op-

timization of several hydrocarbon products were

done in order to search for the best operating con-

ditions for their production.

Keywords Multitubular Reactor, Fischer-

Tropsch Synthesis, Liquid Fuels, Olefins

I. INTRODUCTIONIn recent years, the Fischer-Tropsch Synthesis (FTS)became a subject of renewed interest particularly inthe context of the conversion of remote natural gas

into liquid transportation fuels and due to an escala-tion in the price of oil. Natural gas, biomass and coal

can be converted to carbon monoxide and hydrogen(synthesis gas) via the existing processes, such assteam reforming, carbon dioxide reforming, partialoxidation and catalytic partial oxidation. The syngascan be converted into hydrocarbons (paraffins andolefins) by the FT synthesis reaction:

( ) OHHCn1

Hn2/m1CO 2mn2 +++. (1)

The FT synthesis can be carried out in iron, cobaltand ruthenium based catalysts. Fe-based catalysts aremuch less expensive than the Co-based catalysts,which can be an important economical factor for theprocess specially because the catalyst has to be re-placed due to deactivation. When iron catalysts areused, the carbon monoxide polymerization occurs in

combination with the water gas shift reaction (WGS):

222 HCOOHCO ++ . (2)Many researchers have been working on catalyst

development (Raje and Davis, 1997; van Steen and

Schulz, 1999) and reactor design (Maretto andKrishna, 1999; Krishna and Sie, 2000; Krishna et al.,

2001; Wanget al.,2003), but few investigations havebeen done in order to optimize the production of spe-cific products.

The Fischer-Tropsch reaction yields predominately

straight chain hydrocarbons (-olefins and alkanes)where the main reaction products are -olefins. Thereis general agreement that the reaction may be viewed

as a methylene polymerization reaction where themonomer unit (=CH2), is not initially present. Theproducts are formed by hydrogenation of CO to gen-erate the methylene monomer, in situ. Polymerization

occurs through initiation of chains, competing chainpropagation and chain termination steps. Theories onthe CO polymerization mechanism are based in thesuperposition of two ASF (Anderson-Schulz-Flory)distributions and rely in the dual site theory (Madonand Taylor, 1981), secondary chain growth of read-sorbed alkenes theory (Schulz and Claeys, 1990; Igle-

sia et al., 1991), or the dual mechanism of chaingrowth theory (Patzlaff et al., 1999, 2002). Iron cata-

lysts are more likely to obey a dual mechanism ofchain growth theory.

In this work a mathematical model of a tubular re-actor used for CO polymerization was developed andthe carbon monoxide polymerization was studied froma modeling point of view based on the kinetics of aniron catalyst obeying a dual mechanism theory.

II. TUBULAR REACTOR

The tubular reactor for Fischer-Tropsch synthesis con-sists of a multitube reactor where the synthesis gas isfed at the top of the reactor and passes through the bedof catalyst inside the tubes. The synthesis gas passes

through the reactor in plug-flow regime. Water passesthrough the shell side of the multitube reactor to re-move the heat released by the FTS reaction and to

control the reactor temperature, ensuring an isothermalcondition inside the reactor, in spite of the high heat of

reaction (H = - 170 kJ/mol CO).

III. MATHEMATICAL MODEL

A. Tubular Reactor Model

The basic assumptions made for the reactor were:steady-state operation, isothermal conditions, gaspassing through the reactor in plug-flow regime due to

its velocity, hydrocarbon products in the gas and in theliquid phases are assumed to be in equilibrium at the


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reactor outlet; mass and heat transfer resistances be-tween the catalyst and the gas phase is negligible; neg-

ligible radial concentration and temperature gradientwithin the tube; negligible concentration and tempera-ture gradient within the catalyst; intrinsic kinetics forFischer-Tropsch synthesis and water-gas shift reac-

tions.The kinetic model for the FTS reaction on an iron

catalyst and for the WGS reaction are given by (Raje

and Davis, 1997):

( )O2HCO2HCOFTS

FTSPaP

PPkR

+

= . (3)

( )2O2H2CO

1

2H2COO2HCOWGS

WGSPKP

K

PPPPk

R+

= . (4)

The material balance for component iin the reactoras a function of its axial position is given by:

( )WGSFTSCO RRA

dzdF = , (5)

( )WGSFTS2H RR2A

dz

dF+= , (6)

( )WGSFTSO2H RRA

dz

dF+= , (7)

( )WGS2CO RA

dz

dF= . (8)

The partial pressure of the species is given by:

T

i

ii P

F

FP =

. (9)

Due to the assumption of isothermal condition inthe reactor, which can be considered based on the aca-

demic and patent reports (Freide et al., 2003, 2004;Wang et al., 2003), only the mass balances and popu-

lation balances for the hydrocarbon species were con-sidered in this work. As such, all heat produced by thereaction is assumed to be removed by the coolingjacket of the reactor.

The momentum equation was modeled consideringthe flow through a packed bed, following the Ergun

equation:

( )

+

=u75.1

d11501

du

dzdP g

P3

P

T . (10)

To solve the mathematical model, the model equa-tions were numerically integrated using a 5th orderRunge-Kutta method. The kinetic parameters for thereaction are presented in Table 1, the operating condi-tions used in the simulations are presented in Table 2.The overall kinetic rates for the Fischer-Tropsch reac-

tion and the WGS reaction were taken from Raje andDavis (1997). The physical properties of the gaseswere calculated according to Peng-Robinson equationof state.

Table 1.Kinetic parameters for Fischer-Tropsch synthesisin iron catalyst and for water gas shift (Raje and Davis,

1997).

kFTSa

kWGS

K1K2

0.1106 [mol/kg.s.MPa]3.016

0.0292 [mol/kg.s]

85.813.07

* Obtained experimentally at T = 270oC, P = 0.5 3.0 MPa

and H2/CO = 0.67 1.7.

Table 2.Operating conditions and reactor parameters.

Temperature [oC]Total Pressure [MPa]

Gas velocity [m/s]Catalyst apparent density [kg/m

3]

Reactor Length [m]Reactor Diameter [m]

Fixed Bed PorosityCatalyst Diameter [m]

2701.0 to 4.0

1.0 to 10.064710.00.025

0.6070.0 x10-6

B. Kinetic model

The kinetic model used to simulate the CO polymeri-zation and product distribution assumes that the alkyl

and alkenyl mechanism acts together in the FTS syn-thesis.

The alkyl mechanism can be represented by the fol-lowing reactions:

( )1RHCH 1ki2 + initiation

( ) ( )1nRCHnR 1kp2 ++ propagation

( ) ( )nPHnR

kpar+ reduction by surfacehydride giving alkanes

( ) ( )nPnR kolef = -hydride eliminationgiving a olefins

The alkenyl mechanism can be represented by the

following reactions:

( )2RCHCH 2ki2 + initiation

( ) ( )1n"RCHn"R 2kp2 ++ propagation

( ) ( )nPn"R 2kolef = reduction giving ole-fins

Methane and ethane are formed by the following

reactions:( ) ( )1PH1R kmet + reduction by surface

hydride giving meth-

ane

( )2PCHCH 2kO22= + methylene termination

The mass balance for the FTS is given by the fol-lowing set of equations (Fernandes, 2005):

( )p

2Hi

k

Pk1R

= , (11)

( )2p

FTS2i

k

Rk2"R

= , (12)


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L. C. A. MAZZONE, F. A. N. FERNANDES

143

( ) ( )1nRkPkRk

RknR

olef2HparFTSp

FTSp ++

= , (13)

( ) ( )1n"RkRk

Rkn"R

2olefFTS2p

FTS2p +

= , (14)

( ) ( )1RPkdt1dP 2Hmet = , (15)

( )( )2RPk

dt

2dP2Het = , (16)

( ) 2FTS2O Rk

dt

2dP=

=

, (17)

( )( )nRPk

dt

ndP2Hpar = , (18)

( )( ) ( )n"RknRk

dt

ndP2olefolef +=

=

. (19)

The development of the mass balances assumesthat the quasi-steady state is applied to the concentra-

tion of the propagating species (as assumed for thezero order moment of live polymers); the consumptionof methylene units is proportional to the global reac-

tion rate; and the concentration of hydrogen in thepolymerization site is proportional to the partial pres-sure of hydrogen in the reaction media. The kineticparameters for the CO polymerization are presented inTable 3.

The model has been validated using the data re-ported by Raje and Davis (1997) and Donnelly and

Satterfield (1989). Variance analysis was done usingthe software Statistica 5.0 which showed that themodel is significant within 99% of confidence (Fer-

nandes, 2005).

Table 3. Kinetic parameters for CO polymerization in ironcatalyst (at 270oC).

ki[MPa-1]

ki2[mol/h]kp[h/mol]kp2[h/mol]kpar[MPa

-1.h-1]kolef[h

-1]kolef2[h

-1]kmet[MPa

-1.h-1]

ket[MPa-1

.h-1

]kO2[h/mol]

0.4963

8.0540.35300.42060.023140.0034870.047920.06386

0.024210.09994

IV. RESULTS AND DISCUSSIONFischer-Tropsch synthesis in tubular reactors is acomplex system with many process variables thatshould be accounted for: gas velocity, catalyst density,total pressure, H2:CO ratio. Studies on how gas veloc-ity and pressure affects conversion and total produc-tion of hydrocarbons have been made by several au-thors (Maretto and Krishna, 1999; Krishna and Sie,2000; Krishna et al., 2001; Wang et al., 2003), butfew studies have been made on how these parameters

affect the product distribution.

In this work, several simulations were made to un-derstand the effect of pressure, gas velocity and hy-drogen to carbon monoxide ratio on the product distri-

bution, especially in the range of transportation fuelsand olefins. The simulation study assumes that the ratelaws for the FT and WGS kinetics are valid for the

entire range of the varied process parameters. Someextrapolations were done but kept near the experimen-tal regime of Raje and Davis (1997), and Donnelly

and Satterfield (1989). The extrapolation on pressurewas more significant, but in a related work Davis

(2003) has stated that for this catalyst the effect ofpressure (from 0.5 to 3 MPa) over the overall kineticrate is not significant. This information is also sup-ported by Dry (1996) and by Li et al.(2002). On theother hand, temperature has a great effect on the ki-netic rate laws and as we do not have information on

the effects of temperature over the kinetic rates, thetemperature was not subjected to variations in thisstudy and as such the system behavior was consideredat 270oC.

In general, conversion of syngas increases withH2:CO ratio. As the H2:CO ratio approaches 2.0 theamount of syngas converted to hydrocarbons (FTS)and water (WGS) increases. As conversion increases,the WGS reaction increases its rate due to the produc-tion of more water by the FTS reaction, and althoughCO conversion may be at 92% (40 atm, UG= 1.0 m/s,H2:CO=2.0), the hydrocarbon yield is at 88% (Fig. 1).

Hydrogen is responsible for the termination of hy-

drocarbon chains into paraffins. As such an increase inthe H2:CO feed ratio will increase the partial pressure

of H2in the reaction media and thus increase the ter-mination rate into paraffins, reducing the amount of

olefins produced by the reaction (Fig. 2). At lowH2:CO ratios, the fraction of olefins production is atits maximum since the amount of hydrogen is smallenough not to produce great quantities of paraffins. Asthe H2:CO ratio increases the termination into paraffinincreases and the ratio of olefin to paraffin tends tozero.

Figure 1.CO conversion as function of H2:CO ratio for twodifferent gas velocities (conditions: 40 atm, 270oC). Full

lines represent total syngas conversion. Dashed lines repre-sent hydrocarbon yield.


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Figure 2.CO yield into olefins as function of H2:CO ratio(conditions: 20 atm, 270oC, UG = 1.0 m/s). Full line repre-

sent total olefin yield. Dashed lines represent CO yield intoO2-4 and O5+.

Figure 3. Light olefins yield (C2-4) as function of H2:COratio and gas velocity (conditions: 270oC, 40 atm).

As the H2:CO ratio increases the production of lightolefins increases steeply, since chain termination oc-curs preferably towards paraffins, leading to the pro-duction of a greater quantity of light olefins and lightparaffins (Fig. 3). An increase in the gas velocity en-hances the production of olefins since the higher gasvelocity increases the concentration of the reagents asan effect of the residence time in the reactor. The in-

crease in the carbon monoxide partial pressure ishigher than the increase in the hydrogen partial pres-

sure, and as such the propagation rate increases morethan the termination rate (influenced by the hydrogenpartial pressure) leading to an increase in the averagehydrocarbon chain length (Figs. 3, 4).

The total pressure did not show any major influ-ence on CO conversion and hydrocarbon yield. An

increase in the total pressure in the system reduces COconversion and increases the hydrocarbon yield (about2 to 15% for each 10 atm increase). This happens be-cause the rate of the FT reaction is directly propor-tional to the total pressure; the rate of the WGS is notdirectly affected by the total pressure, but coupled tothe H2O partial pressure, which depends on the con-

version level. The H2O partial pressure also inhibitsthe FT reaction and its increase causes the conversion

to decrease. On the other hand, the productivity(ton/h) is favored by the increase in total pressuresince the reaction rate is proportional to the total pres-

sure.The effect on productivity however is significantand an 10 atm increase in pressure increases the pro-ductivity in approximately 50% due to the higher con-

centration of CO and H2in the reactor (Fig. 5).Lower pressures favor the WGS reaction and the

FTS reaction will be responsible only for 79% of theCO consumption (at UG= 1.0 m/s, H2:CO = 0.5; PT=20 atm), while higher pressures favors the FTS reac-tion and CO consumption by this reaction is as high as

98% (at UG= 10.0 m/s, H2:CO = 0.5; PT= 40 atm).

The yield of light olefins changes only slightly withgas velocity but is strongly influenced by pressurewhere an enhancement of up to 100% can be achievedby changing the operating pressure from 20 to 40 atm

(UG= 1.0 m/s; H2:CO = 2.0) (Fig. 6). The yield of C5+olefins is influenced both by gas velocity and totalpressure, where the maximum yield of C5+olefins is athigh gas velocities and high operating pressures (UG=10.0 m/s; PT = 40 atm) (Fig. 7). Gasoline production isfavored by high pressures and high gas velocities and

a maximum of 4.8% of gasoline (weight percentage)is produced in the reaction. The highest amount of

diesel obtained was 1.9% weight percentage, which isunsuitable for industrial applications.

Figure 4.C5+olefins yield as function of H2:CO ratio andgas velocity (conditions: 270oC, 40 atm).

Figure 5.Reactor productivity as function of pressureand gas velocity (conditions: 270oC, H2:CO = 2.0).


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Table 6. Optimal operating conditions for maximum pro-duction of gasoline, light olefins and higher olefins.

Optimal yield of H2:COratio

Pressure[MPa]

Gas veloc-ity [m/s]

GasolineLight Olefins (C2-4)

Higher Olefins (C5+)Higher Olefins (C12+)

1.180.88

1.732.00

4.04.0

4.04.0

10.010.0

10.010.0

When the maximization focuses on the mass pro-duction of the desired product the operating conditionsare different from the conditions for maximum yields.Pressure and gas velocity are maintained since maxi-mum production is also associated to higher gas con-

centrations. The H2:CO ratios for maximum produc-tion are higher than for maximum yield, existing atrade-off from reducing the average chain length to-wards a higher mass production associated to higherpropagation rates.

As shown in Table 7, when light olefins are the de-sired product, the production of heavy olefins (C5+) isat 7.4 kg/h per tube, but when the H2:CO ratio is in-creased, the average chain length of paraffins dimin-ishes and the average chain length of olefins increases,

producing 9.0 kg/h per tube of heavy olefins. As

H2:CO ratio is increased, the production of light paraf-fins increases, producing a greater quantity of methaneand ethane which has to be recycled back to the re-

former to produce syngas.

Decision on which optimum point to choose:

maximum production or maximum yield may dependon economical reasons. Running the system with the

operating conditions that favors maximum yield willlead to lower costs on recycling and burning of un-wanted products (paraffin light gases and LPG) butproduction will be lower for the same reactor size.While running the system with the operating condi-tions which favor maximum production will lead to

higher recycling costs which may be compensated bythe enhanced production rate.

V. CONCLUSIONS

Fischer-Tropsch synthesis can be used to produce

transportation fuels and olefins from natural gas andthe polymerization conditions can be set to maximizethe production of a certain product generated by theFTS reaction, such as light olefins, higher olefins andgasoline.

Table 5.Product distribution (weight fraction) of reactor operating at the optimum conditions for maximum yields of gasoline,

light olefins and higher olefins.

Total Paraffin Olefin

Paraffin Olefin

Light

Gases LPG Gasoline Diesel C2-4 O5+ O12+Maximum Gasoline Yield

0.44 0.56 0.31 0.07 0.05 0.01 0.33 0.22 0.00

Maximum Light Olefins Yield (C2-4)

0.42 0.58 0.34 0.05 0.02 0.00 0.52 0.06 0.00

Maximum Heavy OlefinsYield (C5+)

0.48 0.52 0.37 0.07 0.04 0.01 0.24 0.27 0.02

Maximum Higher Olefins Yield (C12+)

0.50 0.50 0.40 0.07 0.04 0.00 0.21 0.26 0.03

Table 7. Product distribution (weight basis) of reactor operating at the optimum conditions for maximum production of gasoline,light olefins and higher olefins (kg/h per tube).

Total Paraffin Olefin

Paraffin OlefinLightGases LPG Gasoline Diesel C2-4 O5+ O12+

Maximum Gasoline Yield

16.2 17.5 12.5 2.3 1.3 0.2 7.9 8.9 0.6

Maximum Light Olefins Yield (C2-4)

13.5 15.9 9.7 2.1 1.2 0.2 8.4 7.4 0.1

Maximum Heavy OlefinsYield (C5+)

16.7 17.4 13.0 2.3 1.2 0.2 7.6 9.0 0.7

Maximum Higher Olefins Yield (C12+)

17.1 17.1 13.7 2.2 1.2 0.2 7.3 8.9 0.8


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L. C. A. MAZZONE, F. A. N. FERNANDES

147

According to the simulations, the optimum operat-ing condition to maximize heavy olefins productionand yield needs high pressures and high gas velocityassociated to hydrogen to carbon monoxide ratios be-

tween 1.45 and 1.75. The optimum operating condi-tion to maximize light olefins production needs high

pressures and high gas velocity associated to hydrogento carbon monoxide ratios between 0.50 and 0.90. Theproduction of gasoline and diesel using this iron-basedcatalyst is not economically viable in this kind of reac-tor since their yields are lower than 5% in mass weightwhile some commercial catalyst presents yields higherthan 15% in mass weight.

ACKNOWLEDGMENT

The authors gratefully acknowledge the financial sup-port of the Brazilian research funding institutionCNPq/CTPetro (Conselho Nacional de Desen-volvimento Cientfico).

NOMENCLATUREA area [m2]Ci,j concentration of component iFi molar flow rate of component i[mol.h

-1]dP catalyst particle diameter [m]H reactor height [m]ket ethane formation rate constant [MPa

-1.h-1]

ki initiation rate constant for the alkyl mecha-nism [MPa-1]

ki2 initiation rate constant for the alkenyl mecha-nism [mol/h]

kmet methane formation rate constant [MPa-1

.h-1

]kO2 ethylene formation rate constant [h/mol]kolef termination by b-elimination rate constant for

the alkyl mechanism [h-1

]kolef2 termination rate constant for the alkenyl

mechanism [h-1

]kp propagation rate constant for the alkyl

mechanism [h/mol]kp2 propagation rate constant for the alkenyl

mechanism [h/mol]kpar termination rate constant for the alkyl mecha-

nism yielding paraffin [MPa

-1

.h

-1

]Ki equilibrium constant of reaction ior adsorp-tion coefficient of component i

Pi partial pressure [MPa]PT total pressure in the reaction zone [MPa]

P(n) paraffin containing ncarbons [mol]P

=(n) olefin containing ncarbons [mol]

Ri rate of reaction i[mol/s.kgcat]R(n) alkyl propagating species containing n car-

bons [mol]R(n) alkenyl propagating species containing ncar-

bons [mol]RFTS overall Fischer-Tropsch reaction rate

T temperature [K]UG gas velocity [m/s]

wi weight fraction of hydrocarbon with icarbonsin the product distribution

XCO carbon monoxide conversionY hydrocarbon yield

z axial position [m]

porosity stoichiometric coefficient gas mixture viscosity [N.s/m2] catalyst density [kg/m3]g gas mixture density [kg/m

3]

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Received: September 28, 2005.Accepted: December 27, 2005.

Recommended by Subject Editor G. Meira.

Modelling of Fischer Tropsch Reactor

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