reactor modeling of a slurry bubble column for fischer

Reactor Modeling of a Slurry Bubble Columnfor Fischer-Tropsch Synthesis

J.M. Schweitzer and J.C. Viguié

Institut français du pétrole, IFP, Process Design and Modeling Division, PO Box 3, 69390 Vernaison - Francee-mail: [email protected] - [email protected]

Résumé — Modélisation d’un réacteur à colonne à bulles pour la synthèse Fischer-Tropsch —Un modèle complet de réacteur à colonne à bulles pour la synthèse Fischer-Tropsch a été développé,prenant en compte les caractéristiques hydrodynamiques des trois phases (gaz de synthèse, mélangeliquide de paraffines linéaires et catalyseur solide) ainsi que la thermodynamique et les transferts dechaleur et de masse. Ce modèle est aussi capable de prendre en compte le recyclage du gaz après desétapes de condensation. Les résultats de simulation sont comparés aux données industrielles venant d’uneunité de démonstration.

Abstract — Reactor Modeling of a Slurry Bubble Column for Fischer-Tropsch Synthesis —A complete reactor model was developed for a slurry bubble column for Fischer-Tropsch synthesis intaking into account the hydrodynamic features of the three phases (syngas, liquid mixture of linearparaffins and solid catalyst) and including thermodynamics and heat and mass transfers. This model wasalso able to take into account the gas recycle after condensation steps. Simulation results were comparedwith industrial data coming from a demonstration unit.

Oil & Gas Science and Technology – Rev. IFP, Vol. 64 (2009), No. 1, pp. 63-77Copyright © 2009, Institut français du pétroleDOI: 10.2516/ogst/2009003

The Fischer-Tropsch ProcessLe procédé Fischer-Tropsch

D o s s i e r

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Oil & Gas Science and Technology – Rev. IFP, Vol. 64 (2009), No. 1

NOMENCLATURE

A total molar flow-rate (mol/s)ai, bi coefficients for Ki correlationsaw volumetric exchange area of the exchanger (m2/m3)b inhibition constant (bar-0.5)CCO CO concentration in the liquid (mol/m3)C*

CO CO concentration in the liquid at equilibrium (mol/m3)CH2

hydrogen concentration in the liquid (mol/m3)C*

H2hydrogen concentration in the liquid at equilibrium(mol/m3)

Cp slurry heat capacity (J/kg/K)Cg

p gas heat capacity (J/mol/K)Dax axial dispersion coefficient of the liquid (m2/s)E activation energy (J/mol)Fg

CO molar flowrate of CO in the gas (mol/s)Fg

H2molar flowrate of hydrogen in the gas (mol/s)

FgH2O molar flowrate of water in the gas (mol/s)

FgoCO initial CO flowrate in the gas (mol/s)

FgoH2

initial H2 flowrate in the gas (mol/s)Fg

i,p molar flowrate of paraffin i in the gas (mol/s)Fg

i,ol molar flowrate of olefin i in the gas (mol/s)Ftot

CO total CO flow-rate (mol/s)Ftot o

CO inlet total CO flowrate (mol/s)Ftot

H2total hydrogen flowrate (m/s)

FtotH2O total water flowrate (m/s)

Finert total inert flowrate (mol/s)Ftot

i,p total flowrate of paraffin i in gas and liquid phases (mol/s)Ftot

i,ol total flowrate of olefin i in gas and liquid-phases (mol/s)Fobj objective functionFo

syn initial syngas flow-rate (mol/s)g gravity constant (m/s-2)H reactor height (m)HCO Henry coefficient of CO (bar.m3/mol)HH2

Henry coefficient of hydrogen (bar.m3/mol)k kinetic constant ko kinetic frequency factorKi partition coefficient of compound iKL.a mass transfer coefficient (s-1)L liquid molar flow-rate (mol/s)Ml

m molecular weight of the wax (mol/m3)np

max maximum paraffin carbon numbernol

max maximum olefin carbon numbernp

mean mean paraffin carbon number of the equivalent paraf-fin/olefin

nolmean mean olefin carbon number of the equivalent paraf-

fin/olefinnH2

mean mean hydrogen molecule of the equivalent paraffinPCO CO partial pressure (bar)

Pe liquid Peclet numberPeT thermal Peclet numberPH2

hydrogen partial pressure (bar)Pvap

H2O vapor pressure of the water (bar)Pt total pressure (bar)Qg

NCPTsyngas flow-rate (Nm3/s)R constant of the ideal gas 8.314 (J/mol/K)rCO kinetic rate of CO conversion (mol/kg cat/s)Sol olefin weight selectivitySr reactor section (m2)T reactor temperature (K)Tcool cooling temperature (K)Tinj gas inlet temperature (K)Toutlet reactor outlet temperature (K)Tr kinetic reference temperature (K)Tx

inert inert ratioU heat transfer coefficient (W/m2/K)V vapor molar flow-rate (mol/s)vsg superficial gas velocity (m/s)vsl slurry superficial velocity (m/s)xCH4

methane selectivityxi

ol molar fraction of olefin ixi

p molar fraction of paraffin i xi molar fraction of compound i in the liquidyi molar fraction of compound i in the gasz vertical axisz* normalized axis to the total reactor heightzi total molar fraction of compound i

Greek letters

α1 Schultz-Flory parameter for paraffinsα2 Schultz-Flory parameter for olefinsβ stoechiometric coefficient of the equivalent paraffinΔHr reaction heat (J/mol)ζ H2/CO ratioεg gas holdupεs volumetric solid concentration in the slurryΦ Weisz criteriaλax axial thermal conductivity (W/m/K)ν vapor molar fractionμ stoechiometric coefficient of hydrogenρl wax density (kg/m3)ρs dry solid particle density (kg/m3)ρsl slurry density k(g/m3)τ slurry residence time (s)χ CO conversion

64

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INTRODUCTION

Fischer-Tropsch synthesis is a very important issue for thepetroleum companies because it is a way to produce cleanfuels from natural gas (Fischer et al., 1921). The slurry bub-ble column seems to be the most appropriate reactor for thisreaction (Mills et al., 1996). In fact, three phases are involvedin this reaction where the gas phase (syngas) is the reactant,the liquid phase (mixture of linear paraffins) is the reactionproducts and the solid phase is the catalyst on which the reac-tion occurs. This reaction is highly exothermic and fine parti-cles of catalyst are necessary to avoid internal diffusionallimitations.

A complete reactor model was developed taking intoaccount the hydrodynamic features of the three phases, thethermodynamics, the heat and mass transfers. This modelwas also able to take into account the gas recycle after con-densation steps. Then simulation results were compared withindustrial data coming from the demonstration unit in Italy.

1 FISCHER-TROPSCH REACTION

The reaction converts the syngas into a mixture of linearparaffins (Fischer et al., 1921).

ΔHr = -167093 J/mol

The syngas is a mixture of carbon monoxide and hydro-gen. This gas could be obtained from the partial oxidation (1)+ steam reforming (2) of the natural gas (methane), or byautothermal reforming (combined reactions (1) + (2) in a sin-gle reactor).

(1)

(2)

The Fischer-Tropsch reaction follows a polymeric kineticprocess, which can be decomposed, into 3 steps (simplifiedscheme):– initiation step: formation of the first CH2 group;– propagation step: chain length growing by addition of

other CH2 groups;– termination step: hydrogenation of the edge CH2 groups of

a given chain.The stoechiometry of the reaction is a little bit complicated

due to the termination step. The stoechiometric coefficient ofthe hydrogen is greater than 2 in order to satisfy this thirdstep. The determination of this coefficient is described in thefollowing paragraph. The stoechiometry is also depending onthe other product selectivities (olefins, which are in fact the

CH H O CO + 4 H4 2 2

natural gas syngas� � ��

+ →2

CH O CO + 2 H4 2

natural gas syngas� � ��

+ →1

22

CO + 2 H (CH ) +22

syngas n paraffin� ��

→ − − HH O2

primary products of the reaction by β- H abstraction fromCH2 growing -chain) by-products (alcohols, other oxy-genates) and methane selectivities. In the next step, onlyparaffins, olefins and methane are considered.

1.1 Stoechiometry

The stoechiometry of the reaction depends on the catalystselectivity. According to the experimental data from theliterature, the product selectivity follows a Schulz-Florydistribution (Schulz et al., 1988). Figure 1 shows a typicalSchulz-Flory distribution for paraffins obtained on Cobaltcatalyst for a given set of operating conditions.

Olefins are produced with a given weight selectivity Sol.Olefin molar selectivity follows a Schulz-Flory distributionas for paraffins. This Schulz-Flory distribution is based on achain-length-growing coefficient called α. Then we can dis-tinguished two distributions one for paraffins with a chainlength growing coefficient α1 and one for the olefins with acorresponding coefficient α2. Then, molar fraction of paraf-fins and olefins can be defined as follow:

(1)

This distribution is valid only for paraffins having atleast two carbon atoms. In fact, for methane, Schulz-Flory

α = − = +Schultz Flory parameter molar ratio

fo

CCn

n

1

rr paraffins

for o

x K i nip i

p= −( ) ≤ ≤−1 1 1

11 2. . maxα α

llefins

x K i niol i

ol= −( ) ≤ ≤−2 2 2

11 2. . maxα α

J-M Schweitzer et al. / Reactor Modeling of a Slurry Bubble Column for Fischer-Tropsch Synthesis 65

10 6020 30 40 500

Mol

ar c

ompo

sitio

n of

par

affin

s (%

mol

)

1.00%

0.00%

2.00%

3.00%

4.00%

5.00%

6.00%

Carbon number

CH4 = 48%

Schultz-Flory distributionα = 0.9

Figure 1

Schultz-Flory distribution.

04_ogst08055 13/03/09 19:05 Page 65


distribution is not followed. Then, it was shown in the litera-ture, that its selectivity is fixed by the catalyst and the operat-ing conditions and is independent on the distribution. Withthis Schulz-Flory distribution it is possible to calculate thestoechiometric coefficients for the hydrogen. Two equationsare necessary to find the values of coefficient K1 and K2.

(2)

(3)

With these distributions, it is interesting to have theaverage stoechiometric coefficient for hydrogen and equiva-lent paraffin/olefin. For this, consider the following reaction:

The average number of carbon atoms in the equivalentparaffin/olefin is given by:

(5)

The average number of hydrogen molecule contained inone molecule of equivalent paraffin/olefin is given by:

(6)

n i x i xmean

ip

i

n

iol

i

np ol

H2

1

1 2

= + += =

∑ ∑( ). .

max max

n i x i xmean

ip

i

n

iol

i

np ol

c= +

= =

∑ ∑. .

max max

1 2

CO H2

syngas equivalent paraffin/ol

+ →μ β� ��

Peq

eefin

2H O�� +

and S

x

x x

ol

i wol

i

n

i wp

i

n

ol

p

=

+

=

=

∑

∑

,

,

max

max

2

1

ii wol

i

n

iol

i

n

ol

ol

x i i

x

,

max

max

. . .

=

=

∑

∑

=

+( )

1

2

12 2

iip

i

n

iol

i

i i x i ip

. . . . . .

max

12 2 2 12 2

1

+ +( ) + +( )= =

∑11

nolmax

∑⇒

x K Kp i

i

ni

p

1 1 1 1

1

2

2 2 21 1+ −( ) + −( )−

=

−∑. . . .

max

α α α α 11

2

1

i

nol

=

∑ =

max

x xi

p

i

n

iol

i

np ol

= =

∑ ∑+ = ⇒1 1

1

max max

One mole of carbon monoxide produces β moles ofequivalent paraffin/olefin. The molar carbon balance leads to:

(7)

The molar hydrogen balance leads to:

(8)

By knowing the α coefficients and the methane selectivity,it is possible to determine the molar fraction of each paraffinand the stoechiometric coefficients of the reaction. Table 1shows the influence of the α values and olefin selectivity onthe stoechiometry. An increase of the α coefficient leads to aselectivity oriented towards the high chain lengths.

TABLE 1

Effect of selectivity on stoechiometry

Sol α1 α2 μH2

0.15 0.9 0.72 2.1688

0.05 0.9 0.72 2.1673

0.15 0.92 0.8 2.1389

1.2 Kinetics

Some kinetic studies were performed on a Cobalt basedcatalyst in autoclave reactors. There are many kinetic modelsin the literature (Yates and Satterfield, 1991; Sarup et al.,1989). It appears that the kinetic rate follows the Sarup-Wojciechowski kinetic model.

μ β= +12

hydrogen in water

H

hydrogen in

� �� .nmean

eequivalent paraffin/olefin

� ��

⇒ = +μ 1

(ii x i x

i x

ip

i

n

iol

i

n

ip

i

p ol

+ += =

=

∑ ∑1

1 2

1

). .

.

max max

nn

iol

i

n

ip

i

n

i

p ol

p

i x

x

i x

max max

max

. .∑ ∑

∑

+

= +

=

=

2

12

pp

i

n

iol

i

n

ip

i

n

p ol

p

i x

x

= =

=

∑ ∑+

⇒ = +

1 2

1

2

max max

.

.μ β

mmax

∑

β

β

.

. .

max

n

i x i x

cmean

ip

i

n

iol

i

np o

=

=

+= =

∑

1

1

1 2

Thenll

max

∑

66

S

K i i

ol

i

i

nol

=

−( ) +( )−

=

∑2 2 2

1

2

1 12 2

16

. . . . .

.

max

α α

xx K i ip i

i

np

1 1 1 1

1

2

1 12 2 2+ −( ) + +( ) +−

=

∑. . . . .

max

α α KK i ii

i

nol

2 2 2

1

2

1 12 2. . . . .

max

−( ) +( )−

=

∑α α

(4)

SeeEquation (4)

04_ogst08055 13/03/09 19:05 Page 66

(9)

In this kinetic expression, an inhibition term is taken intoaccount in order to represent the decrease of the number ofactive sites due to a high CO partial pressure. The activity istaken into account through a reference temperature. In fact,the kinetic coefficient can be written as follow:

where is the kinetic frequency factor, whichquantifies the intrinsic activity of the catalyst. This activitycan be adjusted by means of a kinetic reference temperatureTr. The higher reference temperature is, the lower activity is.

2 SLURRY BUBBLE COLUMN REACTORS

Slurry bubble column reactors are simple vertical cylindricalvessels with intense contact between the three phases: the gasreactant injected at the bottom of the column, the liquid prod-uct and the solid catalyst. The “liquid + catalyst” suspensionis called slurry. The gas phase is dispersed into the liquidphase using specific gas distributor at the bottom of the

k k eo r

ERTr= .

k k eo

ERT=

−.

rk P P

b PCO

CO H

CO

m=( ) ( )+ ( )⎛

⎝⎜

⎞

⎠⎟

. .

.

. .

.

0 5 0 5

0 52

2

1

ool/s/kg cat

.e mol/s/kg c- / . 1/ -1/

k krE R T Tr= ( )( )

aat/bar

in bar

reference temperature

bTr

−

=

0 5.

activation energyE =

column. A simplified representation of a slurry bubblecolumn is shown in Figure 2.

Most of dispersing energy in the bubble column isintroduced with the gas phase at the bottom of the column.Therefore, movement of fluids occurs by natural dynamicsof the phases: catalyst particles are in suspension in themixed liquid phase. It is well-known from literature that atsufficient gas throughput, in the churn-turbulent regime,the liquid is drawn upwards in the core region and whenthe bubbles disengage at the top, the liquid returns downnear the wall region (see Fig. 3). These results have beenoften observed but generally in small column (D < 0.2 m),without internals and with air-water systems. The center-line liquid velocity VL(0) measured along the axis of thecolumn is the maximum upward time averaged liquidvelocity (Miyauchi et al., 1970; Hills, 1974).

Due to specific hydrodynamics, slurry bubble columnstherefore possess many attractive features:– a high liquid mixing which provides homogeneous cata-

lyst concentration and temperature: thus an efficient heattransfer and temperature control is obatined;

– the use of small mean catalyst particles size diameters(about 50 μm) which avoid intra-granular diffusionnallimitations;

– easy catalyst addition and withdrawal.

These reactors present also some drawbacks:– large reactors are required because of the low catalyst con-

centration compared to fixed bed;– reliable scale-up and design criteria are still missing: for

instance a too high liquid recirculation could generatecatalyst attrition and internals abrasion;


Liquidphaseinlet

Internalheat-exchange

tubes

Liquid (slurry)phase outlet

Slurry(liquid + catalyst)

Gas phase outlet

Gas distributor

Gas phase inlet

Figure 2

Slurry bubble column reactors.

Gas holdupprofile

Liquid velocityprofile

Radial position r

Wall region

Wall

Core region

0 -R R

Figure 3

Liquid velocity profiles in churn turbulent regime.

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– the continuous separation of fine solid catalyst particlesfrom the liquid products is difficult;

– slurry handling requires careful design to avoid plugging.

2.1 Importance of Hydrodynamics

The reactor performance and volumetric productivity andselectivity are affected significantly by the fluid dynamicswhich are not yet well understood due to the complexity ofthe flow field in slurry bubble reactors.

Also, the success of the Fischer-Tropsch process (Krishna,2000) largely depends on the ability to achieve deep syngasconversions, approaching 90% or higher. But reliable designof the reactor to achieve such high conversion levels requiresreasonable accurate information on the following hydrody-namic, mass and heat transfer parameters: gas holdup, inter-phase mass transfer between the gas bubbles and the slurry,axial dispersion of the slurry and heat transfer coefficient tocooling tubes.

Slurry bubble columns are operated in either semi-batchmode (zero liquid throughput) or with liquid superficialvelocity lower than the gas superficial velocity by at least anorder of magnitude. As a result, the gas flow controls thefluid dynamics of each phase. It affects liquid mixing andinterface mass transfer, which subsequently controls conver-sion and selectivity.

2.1.1 Bubble Characteristics and Gas Holdup

In the literature, attention to gas holdup prevails because gasholdup affects mixing and mass transfer, and therefore, theperformance of the system. Gas holdup is influenced bymany parameters, including particle concentration, elec-trolyte concentration, liquid viscosity and surface tension.The residence time of a small bubble is longer than that of alarge bubble, because the rise velocity of a bubble increaseswith the square root of its size (Kluytmans, 2001). Hence, asmaller average bubble size leads to an increase in gasholdup. Also a swarm of bubbles rises much faster than sin-gle, isolated bubbles (Krishna et al., 1999). The trendobserved for a single bubble is the same than for a swarm ofbubbles: a swarm of smaller average bubble size leads to anincrease in gas holdup. Bubble diameters db and gas holdupare then intimately linked.

All published papers which deal with surface tensioneffect on gas holdup are consistent: as the surface tensionis a measure for the stability of the gas-liquid interface, asmaller surface tension leads to a less stable gas-liquidinterface and thus to a smaller average bubble size and anincrease of gas holdup. Adding even a small amount ofsurface-active material to water such alcohol or electrolytereduces surface tension and leads to a strong increase ofgas holdup. The higher gas holdup was attributed to adecrease in or suppression of coalescing tendencies (Keiteland Onken, 1982; Fan, 1989).

According to a lot of authors (Krishna et al., 2000; Kelkarand Shah, 1984; Bach and Pilhofer, 1978) an increase inliquid viscosity will decrease gas holdup. The increase inviscosity leads to larger stable bubbles and thus higher bub-ble rise velocities and lower gas holdup. Urseanu (2000) dis-tinguished the contribution of the large bubbles and the densephase (little bubbles dispersed in the liquid) to the total gasholdup: the difference in the large bubble holdup with liquidproperties is very small. However, the dense phase holdupdecreases dramatically with increasing viscosity of the liquidphase.

The fine catalyst particles are intimately mixed with theliquid and the slurry phase can be considered pseudo-homo-geneous (Krishna, 2000). In a slurry bubble column usingfine particles (< 100 μm), (Fan, 1989; Gandhi et al., 1999),the gas holdup decreases with an increase in solids concen-tration. The most plausible explanation for this seeminglyvaried behavior is that increasing solids concentrationincreases the “pseudo-viscosity” of the suspension which inturn promotes the bubble coalescence, resulting in anincrease in bubble size and a decrease in gas holdup.According to Krishna (2000), there is a deep decrease of thegas holdup when the solid concentration increases from 0 to15%; then, the gas holdup decreases more slightly when thesolid concentration varies from 20 to 30%. The concentrationof solid particles also affects the transition to the heteroge-neous flow regime, which occurs at a lower superficial gasvelocity when solid concentration increases.

According to Krishna et al. (1991), it does not matterwhether the increased gas density is a result of operation athigher pressure or due to the use of a gas with higher molarmass. The major effect of increased gas density is to stabilizethe regime of homogeneous bubble flow and, consequently, todelay the transition to the churn-turbulent flow regime. It wasobserved (Reilly et al., 1986; Idogawa et al., 1987; Wilkinsonand Van Dierendonck, 1990) that the gas holdup increaseswith gas density due to a reduction of bubble size. This wasattributed to a decrease in bubble stability and a decrease inthe coalescing rate with an increase in the gas density. Boththese factors favor into an increase in the gas holdup.

The fraction of large bubbles decreases with increasingpressure, and narrower bubble size distributions are observedat higher pressures (Jiang et al., 1995). The pressure mainlyaffects the fraction of large bubbles. Moreover, it has alsobeen observed (Clark, 1990; Letzel et al., 1999; Kemoun etal., 2001) that with an increase in pressure, bubble stabilityincreases and the transition to churn-turbulent regime charac-terized by the change of the radial gas holdup profile fromrelatively flat to almost parabolic, is delayed to highersuperficial gas velocities.

According to Joshi (1998) and Shah et al. (1982), in theheterogeneous regime, the average fractional gas holdup isindependent of the column diameter when.

68

04_ogst08055 13/03/09 19:05 8

Berg (1993) has performed gas holdup measurement inthree column diameters (0.290; 0.441 and 0.450 m) withdifferent internals configurations (open free area rangingfrom 70 to 100%, number of tubes up to 91 with a diameterof 25 mm with various arrangements). He reported that inter-nals do not affect the global gas holdup for superficial gasvelocity up to 0.60 m/s.

2.1.2 Liquid Flow Pattern Correlations

Most of the existing correlations for the axial dispersioncoefficient are developed and based on data with air-watersystem at atmospheric conditions.

An analogy between eddy diffusivity E and axial dispersioncoefficient Dax can be done (Baird and Rice, 1975). In thecase of eddy diffusivity, it can been shown by dimensionalanalysis that:

E = K l4/3 Pm1/3

It is assumed here that the largest eddies, which aremainly responsible for eddy diffusion, are related to a pri-mary length parameter l and to the specific energy dissipationrate Pm. The constant K is dimensionless and should have anuniversal value, provided the length parameter l is suitablydefined for different system geometries. If we consider aunit-sided cube of a gas-liquid dispersion in a bubble column,the vertical hydrostatic pressure gradient is – ρL g(1 – ε) andthe specific energy dissipation rate in the continuous phase isPm = Ug

.g. It is assumed that the energy dissipation in the gasbubbles is negligible. The liquid phase velocity is assumed tobe low enough not to have a significant effect on Pm. At verylow gas rates, the bubbles rise individually and are separatedby stagnant regions. The turbulence model does not apply tothis case. At high gas rates, the bubble wakes interact and theliquid phase is more uniformly turbulent. The bubbles them-selves can be carried out about in the eddies and the primarylength parameter l is obviously greater than the bubblesdiameter. In the simple case of a column without any baffles,packing or other internals, Baird and Rice (1975) assume thatthe primary length parameter l is the column diameter D.Hence, from the above equations: E = K D4/3 (Ug

.g)1/3.In general (Fan, 1989), the liquid axial dispersion

coefficient in a bubble column is proportional to the 0.3-0.5power of superficial gas velocity, proportional to 1.25-1.5power of column diameter, decreases slightly with anincrease of liquid viscosity and is essentially unaffected bythe liquid surface tension in the coalesced bubble regime.

So, the exponents of D and Ug for the eddy diffusivitiesand for the axial dispersion coefficient are very close,suggesting a correspondence between the model for eddydiffusivity E and the data for axial dispersion coefficientDax. It may be concluded that the simple relationshipDax ≈ 0.35 D4/3(Pm)1/3 can be used for “order of magnitude”estimates of the axial dispersion coefficient in unbaffled bub-ble columns under turbulent conditions. The correlation

should be used with particular caution in the case of smalldiameter columns where slug flow is a possibility, and inshort columns (H/D < 5). It should be noted that the turbu-lence in a bubble column is not necessarily isotropic. Reith etal. (1968) found that the axial dispersion coefficient consid-erably exceeded the radial dispersion coefficient.

2.2 Mass Transfer

The performance of a multiphase chemical reactor is linkedwith the exchange between phases. This is particularly truefor slurries reactors, where reactants are in the gas phase andwhere the reaction occurs in the slurry phase.

Due to the small size of catalyst particles in slurryreactors, intraparticle diffusion is not a limiting factor(Krishna, 2000). To confirm this point, a comparisonbetween the chemical production flux and the diffusion fluxin pores of the reactants is necessary. This is done by meansof the Weisz criteria (Froment et al., 1979).

Table 2 shows the values of the Weisz criteria obtained fora given catalyst (the present one) with two different sizes:one corresponding to the size for fixed bed reactor, an theother for the slurry bubble column reactor.

TABLE 2

Catalyst internal transport

Reactor Pressure Temperature Particle Weisz

type bar °C diameter (mm) criteria

SBC 20 225 0.06 0.026

Fixed bed 20 225 1 7.330

It is clearly shown that for the catalyst size used in theslurry bubble column, the Weisz criteria is far below 1(2 order of magnitude). This confirms that there are no inter-nal diffusionnal limitations of the reactants.

With catalysts of relatively low activity present in lowconcentration in bubble columns operated in the homoge-neous regime, gas-liquid mass transfer is unlikely to be a lim-iting factor either in view of the large surface area of thesmall bubbles or their long residence time in the liquid.However, for reactors of increased productivity, because ofthe use of more active catalysts at high concentrations andoperation in the heterogeneous regime, gas-liquid mass trans-fer can become a factor that needs serious consideration. Thegas-liquid mass transfer rate is determined to a large extent

Φ = =Chemical production flux

Diffusion flux

r s.ρ(( )⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎡⎣ ⎤⎦

>>

obspd

D

.

.

6

2

COCO

1 PerformancΦ ees governed by the diffusion in pores

1 PerformΦ << aances governed by the chemical reaction


04_ogst08055 13/03/09 19:05 Page 69


by the bubble diameter and gas hold-up. Quality and struc-ture of the interfacial area itself also affect the rate of masstransfer which is dependent upon it. Hence (Deckwer, 1992),a low mass transfer rate is found when bubbles are small andhave a relatively rigid surface, whereas bubbles with a largerdiameter and a mobile, oscillating surface encourage a highlevel of turbulence which results in high rates of mass trans-fer. Bubble rise velocity and hence gas phase residence timeare also a function of bubble size. The latter frequently havean extremely wide distribution pattern which may incorpo-rate several peaks. Non-uniform bubble size and the subse-quent difference in bubble rise velocity generate a wider gasphase residence time distribution. According to Nigam andSchumpe (1996), interfacial area a is one of the most impor-tant parameters for gas-liquid reactor design. It is the mostinfluential factor in determining reactor output, especially inthe region in which absorption is accompanied by fast chemi-cal reaction. In general, the gas-liquid interfacial area is afunction of the unit’s geometric size, operating parametersand the physical and chemical properties of specific materialsystems. In the case of absorption accompanied by slow orinstantaneous reaction, the mass transfer rate is determinedby the volumetric mass transfer coefficient kL·a which is afunction of the specific area a. The latter represents theamount of interfacial area with respect to the dispersion vol-ume. When mass transfer occurs from gas bubbles to the sur-rounding liquid in a bubble or slurry bubble column, the gas-side resistance can often be neglected in determining theoverall gas-liquid mass transfer resistance due to the low sol-ubility of gas in the liquid. Thus the gas-liquid mass transferrate per unit volume of aerated liquid (or slurry) can often bedefined in terms of the liquid-side volumetric mass transfercoefficient kL·a. As a general rule, absorption rate (local orintegral) can be described by :

All the effects shown above on bubble size affect directlythe interfacial area a and thus the mass transfer coefficientkL·a. A lot of parallels between gas holdup and kL·a cantherefore be made. The most accepted correlations for kL·a inthe literature are those of Akita and Yoshida (1973) andCalderbank and Moo-Young (1961), but these correlationswere obtained in bubble columns operating in the homoge-neous regime and are able to describe only mass transfer forsmall bubbles, which are considered as rigid spheres. Now,large bubbles continuously coalesce and break-up, while ris-ing along the column, at a very high frequency, between2 and 16 Hz (de Swart et al., 1996). This is very importantfor interface mass transfer, because the really large sizedbubbles have only a momentary existence. Hence, gas-liquidinterface renewal is very frequent and mass transfer charac-teristics of such large bubbles are better than those predictedby conventional theories.

Φ = ⋅ ⋅ −

⎛

⎝⎜⎜

⎞

⎠⎟⎟k a P

HCL

e0

2.3 Industrial Applications

Slurry bubble column reactors or three-phase fluidized bedreactors possess many attractive features which make them asuitable choice for carrying out highly exothermic reaction,for example in the Fischer-Tropsch conversion of syngas toliquid hydrocarbons.

The anticipated dimensions and operating conditions of anindustrial unit are given in Table 3.

TABLE 3

Anticipated Fischer-Tropsch large scale plant dimension and operating conditions

Diameter D (m) 5-10

Height H (m) 20-40

Pressure p (bar) 20-30

Temperature T (°C) 200-240

Superficial gas velocity Ug (m/s) 0.1-0.3

Volume fraction of catalyst εs (-) 0.15-0.3

3 REACTOR MODELING

The reactor model is shown in Figure 4. The general assump-tions are the following:– the flow pattern of the gas phase is considered to be plug

flow, which is an acceptable assumption according to thePeclet number measured by radioactive tracer test in coldmock-up (Peclet number for small bubbles = 6 and Pecletnumber for large bubbles = 41);

– the flow pattern of the slurry phase is considered to followthe dispersed-plug flow model, characterized by a slurryPeclet number measured by radioactive tracer test in coldmock-up;

– the reactants in the gas phase transfer to the liquid phase.This mass transfer is characterized by a gas/liquid masstransfer coefficient kL·a. The same mass transfer coeffi-cient is used for all the reactants;

– the dissolved reactants react in contact with the catalystto produce water, normal paraffins, olefins and heat.The reaction rate follows the Sarup and Wojciechowskikinetic law;

– the heat transport follows also the dispersed-plug-flowmodel by using the same Peclet number than the one usedfor the slurry phase;

– the temperatures in the solid, liquid and gas phases are thesame;

– the gas and the liquid composition profiles are calculatedby a two-phase flash calculation based on the Soave-Redlich-Kwong equation of state;

– the heat removal is taken into account by a heat transferterm representing the heat exchanger;

70

04_ogst08055 13/03/09 19:05 Page 70

– a three-phase flash calculation is performed at the reactoroutlet in order to estimate the liquid water, gas, condensateand wax production and corresponding compositionsgoing out of the unit.

3.1 Transient Material Balance of Reactant in the Gas Phase

3.1.1 Transient Material Balance for Carbon MonoxideCO in the Gas Phase:

(10)

where εg is the volume of gas per reactor volume, CCO theconcentration of CO in the liquid phase mol/m3 of liquidphase, a the interfacial area of gas in m2 of gas/m3 of slurry.

3.1.2 Transient Material Balance for Hydrogen H2in the Gas Phase:

(11)

∂

∂+ −( ) −

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟=

∂F

zk a S

P

HC

g

L r gH H

H

H2 2

2

2

1. . . .ε

FF

u

t

g

g

H2

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

∂

∂

∂+ −( )F

zk a S

PH

g

L r gCO

convective term

CO

C�. . . .1 ε

OO

CO

gas/liquid mass transfer term

−⎛

⎝⎜⎜

⎞

⎠⎟⎟C

� ��

=

∂⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

∂

Fu

t

g

g

CO

3.2 Transient Material Balance of Reactant in the Liquid Phase

3.2.1 Transient Material Balance for Carbon MonoxideCO in the Liquid Phase:

(12)

In a non-dimensional form:

(13)

with:

3.2.2 Transient Material Balance for Hydrogen H2in the Liquid Phase:

(14)


(15)

3.3 Transient Heat Material Balance

(16)

λ ρε

ax sl pslT

zC

v. . .∂

∂−

−

2

2 1

dispersion term

� �� ggs s

Tz

r( )

∂∂

−. . . .

convective term

CO

� ��

ε ρ ΔΔH

U aT T

r

w

gcool

production term

� �� +

−−(.

.1 ε

)) = ∂∂

transfer term

� ��

ρsl pC Tt

. .

1 1

1 1

2

2

2

2Pe

C

z

C

zg

s

ss. . . .

* *

∂

∂−

−( )∂

∂−

−H H

H2

εμ

ε

ερ .. .

.. . .

τ

ετ τ

r

k a P

HC

CL

s

CO

H

H

H

H

+

−−

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟=

∂

1

2

2

2

22

∂t

DC

z

v C

zrax

sl

g

s

ss. . . . .

∂

∂−

−( )∂

∂−

−

2

2

2 2

1 1

H H

εμ

ε

ερ

CCO

H

H

H

H

2

+

−−

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟=∂

∂

k a P

HC

C

tL

s

..

1

2

2

2

ε

Pe

v HD

Hv

z zH

sl

ax sl= = =

., , *τ

1 1

1 1

2

2PeC

z

C

zr

g

s

ss. . . . .

* *

∂

∂−

−( )∂

∂−

−CO CO

ε

ε

ερ τ

CCO

CO

CO

COCO

+

−−

⎛

⎝⎜⎜

⎞

⎠⎟⎟ =

∂

∂

k a PH

CC

tL

s

.. . .

1 ετ τ

DC

z

vax

sl

g

. .∂

∂−

−( )∂2

2 1

CO

dispersion term

� �� ε

CCz

rs

ss

CO

convective term

CO

pr

∂−

−� ��

ε

ερ

1. .

ooduction term

CO

CO

CO

� �� +

−−

⎛

⎝⎜

k a PH

CL

s

..

1 ε ⎜⎜⎞

⎠⎟⎟ =

∂

gas/liquid mass transfer term

� ��

CCtCO

∂


G/L mass transfer

Heat transferQ = U.aw.(T – Tcool)

kL.a.(C*CO – CCO)kL.a.(C*H2

– CH2)

Kinetics

Gasphase:plugflow

Slurry phase:dispersed plug flow

Heat transport:dispersed plug flow

Vapor and liquid compositionin the reactor are obtained by

2-phase flash calculations

Wax,condensate,water, gas

productions and compositions are

obtained by3- phase

flash calculations

PCO

PH2

CCO

CH2

C*H2

C*CO

rCO =

k.(HCO.CCO)0.5.(HH2.CH2

)0.5

(1+b.(HCO.CCO)0.5)2

Figure 4

Reactor model.

04_ogst08055 13/03/09 19:05 Page 71



(17)

with

The cooling temperature is constant along the reactorbecause the reaction heat is removed by water vaporization inthe cooling tubes. During the water vaporization, the temper-ature does not change.

3.4 Pressure Drop

In slurry bubble columns the pressure drop due to the frictioncan be neglected compare to the static height. Then, thepressure drop becomes:

(18)

where ρsl is the slurry density, kg/m3.

3.5 Two Phase Flash Calculation

For each elementary volume, the total composition of eachcompound (zi) is calculated. These compositions can bedetermined from the conversion and the total molar flowratesas follow:

This leads to:

total molar flowrate:

CO H H O2 2

F F F Ftottot tot t= + + oot

inert i ptot

i

n

i oltot

i

n

F F Fp ol

+ + += =

∑ , ,

max m

1 2

aax

∑

=total molar fraction of CO:CO

COzFF

tot

tot

conversion:

total mola

CO CO

CO

χ =−F F

F

tot o tot

tot o

rr flowrate of CO:CO CO C

F F v S Ctot gsl r s= + −( ). . .1 ε

OO

2 H Htotal molar flowrate of H : F F v Stot g

sl r2 2

= + . .. .12

−( )εs

tot

C

F

H

2 H Ototal molar flowrate of H O:

2

== F

F

tot o

i

CO

total molar flowrate of paraffin:

.χ

,,. . .p

tot tot oipF x=

CO

total molar flowrate of o

χβ

llefin :CO

i F F xi oltot tot o

iol

,. . .= χβ

∂

∂= − −( )P

zgt

g sl1 ε ρ. .

Pe

C v H Hv

z zHT

sl p sl

ax sl= = =ρ

λτ

. . ., , *

1 1

1

2

2PeT

zTz

r H

T g

s s r. .. . . .

* *

∂

∂−

−( )∂

∂−

ε

ε ρ τ

ρCO

Δ

ssl p

w

gcool

sl p

C

U aT T

CTt

.

.. .

..

+

−−( )

=∂∂

1 ετ

ρτ

The resolution of the gas/liquid equilibrium needs thevalues of the partition coefficients relative to each compound.These coefficients were determined using the Soave-Redlich-Kwong equation of state for different compositions andoperating conditions. It was shown that the compositiondoes not affect strongly these coefficients. Then, correla-tions were developed as a function of the operating condi-tions using an Antoine expression. The general form ofthese correlations is:

For each compound, coefficients ai and bi are determined.Then, it is possible to calculate the partition coefficients for agiven pressure and temperature. Figure 5 shows, for threedifferent temperatures, a good agreement between the corre-lations and the results coming from the equation of state.

Remark: The correlations were developed in order tosimplify the flash calculations an also to decrease the CPUtime needed for the convergence.

Now, by writing the molar balances, it is possible todetermine the flowrates and the compositions of the gas andthe liquid phases.

A is the total molar flowrate, L is the liquid molarflowrate, V is the vapor molar flowrate, xi is the liquid molar

A z L x V y

Kyx

A L V

i i i

ii

i

. . .= +

=

= +

⎧

⎨

⎪⎪

⎩

⎪⎪

log .

,

10P K

aT

b

Kyx

P T

t ii

i

ii

it

( ) = +

=with in bar, in KK

72

total molar fraction of H :

total m

2z

F

FHHtot

tot2

2=

oolar fraction of H O:

total mo

2z

F

FH OH Otot

tot2

2=

llar fraction of inert:

total m

zFFinertinert

tot=

oolar fraction of paraffins:

for zFFp

i ptot

tot= , ii n

z

p∈ ⎡⎣

⎤⎦1, max

total molar fraction of olefins:

ooli oltot

totol

FF

i n= ∈ ⎡⎣

⎤⎦

, max,for 2

04_ogst08055 13/03/09 19:05 Page 72

fraction of the ith compound and yi is the vapor molar flow-rate of the ith compound. This system of equations leads to:

Then, an objective function can be defined:

F y xobj i i

i

= −( ) =∑ 0

xzK

yK z

K

VA

ii

i

ii i

i

=+ −( )

=+ −( )

=

1 1

1 1

ν

ν

ν

.

.

.

where is the total vapor molar fraction

By adjusting ν, the flash calculation is solved in order tohave Fobj = 0.

Remark: the Henry coefficients for the CO and H2 arecalculated from the corresponding partition coefficients asfollow:

with:

3.6 Three-Phase Flash CalculationAt the reactor outlet, the gas phase is condensed at ambienttemperature and process pressure. Then, three phases are pre-sent in this system: gas phase, light liquid hydrocarbons andliquid water. To estimate the flowrates and the compositionsof the three phases, a three-phase flash calculation is needed.The vapor molar fraction of the water is determined from thevapor pressure of water at flash conditions. For this we usethe correlation given in the literature.

Then,

When the vapor molar fraction of the water is determined,a two-phase flash calculation is then performed on the othercompounds at the ambient temperature and at the pressure Pt

– PvapH2O (see Sect. 3.5).

3.7 Superficial Gas Velocity

Due to the reaction, the gas is consumed. Then, the superficialgas velocity decreases along the reactor. It is necessary tocalculate for each elementary volume the superficial gasvelocity going through. For this, the ideal gas law is used:

v

F F F F F F

sg

g g ginert i p

gi olg

i

n

=

+ + + + +=

CO H H O2 2

, ,

1

oolp

i

n

t r

R T

P S

maxmax

. .

.

∑∑=

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟1

y

P

P

vap

tH O

H O

2

2=

log ..

.105 11564

1687 537

230 17 273P

Tvap

H O2

( ) = −+ − ..15

with in bar, in KH O

2

P Tvap

Mml = molecular weight of the liquid phase kg/mol)(

ρρl

H

=

=

liquid specific gravity kg/m

Henrycoef

3( )

fficient bar.m /mol)

total pressure bar)

3(

(PK

t

i

=

== partition coefficient

H

K P MH

K P Mt m

l

l

t mCO

COH

H

2

2= =. . . .

ρ

ll

lρ


SRK at 100°Ccorrelation at 100°C



log(

Ki.P

t)

4

2

0

-2

-4

-6

-8

-10

-12

-14

-16

Carbon number

Partition coefficient for paraffins

0 20 40 60 80




log(

Ki.P

t)5

0

-5

-10

-15

-20

Carbon number

Partition coefficient for olefins

0 20 40 60 80

Figure 5

Comparison between SRK calculations and correlations forpartition coefficient of paraffins and olefins.

04_ogst08055 13/03/09 19:05 Page 73


Remark: Inert compounds are considered to be completelyin the gas phase.

3.8 Gas Holdup

The model for the gas holdup is based on the Krishnaapproach (Krishna et al., 1996; Krishna et al., 2000). Theequations of the model are summarized below:

Gas holdup in the homogeneous regime:

Gas holdup at the transition:

Gas holdup in the turbulent regime:

Gas holdup in the dilute phase:

Determination of the transition parameters (εtrans and Vsmall):

3.9 Gas/Liquid Mass Transfer

There are a lot of correlations in the literature, which gavedifferent values of kL·a. According to this wide range of pre-diction, it was decided to take the same value of kL·a for COand H2. For the moment this value is fixed at 0.6 s-1 (averagevalue determined from the numerous literature correlations)(Charpentier, 1981; Albal et al., 1984).

ε

ε

ρ

ρα

ρα

trans

transref

g

gref

=⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

1

2.exp .ln

gg

gref s

ρα ε

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟−

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟3

.

V

Vsmall

smallref

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟ = +1 4

α

VVsmallref s.ε

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

v U

D v U

sg trans

bsg trans

>

=⎛

⎝

⎜⎜

⎞

⎠

⎟⎟ −

⎛

⎝⎜ε α

α

8

1 16

. .⎜⎜

⎞

⎠⎟⎟ −( ) −( )

>

α

α ε

ε

7

0 8

10

0 1

. .exp .

.

.v Usg trans s

s

v U

D v U

sg trans

bsg trans

>

=⎛

⎝

⎜⎜

⎞

⎠

⎟⎟ −

⎛

⎝⎜ε α

α

5

1 16

. .⎜⎜

⎞

⎠⎟⎟ −( ) −( )

≤

α

α ε

ε

7

0 8

10

0 1

. .exp .

.

.v Usg trans s

s

ε ε ε εg g

transb b= −( ) +. 1

εg

trans trans

small

UV

=

εgsg

small

vV

=

3.10 Resolution of the Equations

A discretization of Equations (10, 11, 13, 15, 17) isperformed in order to define a system of non-linear equa-tions. An explicit numerical scheme is used and convergenceis achieved when accumulation terms are equal to zero.Atomic balances are controlled between the reactor inlet andoutlet.

3.11 Boundary Conditions

The boundary conditions for the reactant transport equationsin the liquid phase are (Danckwerts, 1951):

The boundary conditions for the heat transport equation inthe liquid phase are:

3.12 Reactor Temperature Regulation

In order to find the cooling temperature which is necessary toreach reactor temperature setpoint, a PID controller wereimplemented in the model.

3.13 General Reactor Scheme and CorrespondingAlgorithm

Figure 6 shows the general reactor scheme which wasmodeled. Fresh syngas can be mixed with gas coming fromreactor outlet after condensation. The reactor temperature iscontrolled by the vaporization of boiling feed water. Thepressure of the steam drum is adjusted thanks to a PIDcontroller link to the reactor setpoint. Figure 7 shows thecorresponding algorithm of the model.

4 MODEL VALIDATION

Table 4 gives a set of operating conditions of the demonstra-tion unit working in Sanazarro.

Table 5 shows the comparison of the reactor performancesbetween the model and the experimental data. Table 6 showsthe comparison of the outlet gas analysis between the modeland the experimental data. A good agreement is obtainedbetween the experimental data and the model.

−∂∂

= −∂∂

== =

λ λaxz

axz H

Tz

Tz

. , .

0

0 0

dispersion closeed at the reactor inlet and outlet

−∂

∂= −

∂

∂=

= =

DC

zD

Czax

zax

z H

. , .CO CO

dispersion

0

0 0

cclosed at the reactor inlet and outlet

H2−

∂

∂D

Cax .

zzD

C

zz

ax

z H= =

= −∂

∂=

0

0 0, .H

2

74

04_ogst08055 13/03/09 19:05 Page 74

TABLE 4

Operating conditions

Reactor geometry

Reactor diameter 0.5 m

Reactor height 10 m

Operating conditions

Pressure (bar) 21.5

Temperature (°C) 215

Syngas flow-rate (Nm3/h) 625

Syngas dilution (%vol) 23.5

Slurry characteristics

Volumetric solid concentration (%vol) 17

TABLE 5

Comparison of the reactor performances model/experience

SNZ Model

Conversion (%) 48 48.95

H2/CO out 2.07 2.07

Gas holdup (%vol) 24 21.06

Condensate (kg/h) 18.86 18.74

Wax (kg/h) 10.25 9.67

Water (kg/h) 57.38 58.17

T at 0.8 m (°C) 214.82 214.82

T at 3 m (°C) 215.01 214.96

T at 7 m (°C) 214.93 215.05

T at 13.5 m (°C) 215.65 215.02

T cooling (°C) not given 211.37

Wax and Condensate Analysis

Schulz-Flory parameters for paraffins and olefins wereobtained from experiments performed in lab scale. These val-ues lead to a good prediction of wax and condensate produc-tion. It is also interesting to compare condensate and waxanalysis with the ones predicted by the model. Figure 8shows the condensate composition obtained from the analy-sis and compared with the model prediction. A good agree-ment between the analysis and the model is obtained forparaffins and olefins.

Concerning the wax analysis, the agreement between themodel and the experiments is not so good (see Fig. 9).


Ambientpressure

gascondenser

Ambientpressure

waxcondenser

High pressure gas condenser

Steam drum

Reactor

Water

Condensate

Condensate

CO + 2.193208 H2 � 0.212156 P + H2O

Gas recycle

Fresh syngas

Gas outlet

Gas

Gas

Wax

Wax

Boilingfeed water

Figure 6

General reactor scheme.

Model inputsPressure

Cooling temperatureInlet Syngas flow-rate, temperature, H2/CO ratio and composition

Catalyst concentrationGeometrical data of the reactor

Slurry flow-rateMass and thermal Peclet number of the slurry phase

Kinetic reference temperatureVolumetric heat exchange area

Mass transfer coefficientSchultz-Flory parameter

Methane molar selectivity

KineticsCalculation

the reaction rate

Numericale resolutionDiscretisation and numerical resolution

of the 6 main equations usingthe modified Powell

hybrid method

2-phase flash calculationCalculation of the liquid and gas

compositions and flow-rates

Gas holdupCalculation

the gas holdup

3-phase flash calculationCalculation of the water, wax,

condensate and gas compositions and flow-rates Gas recycle

Model outputsConversion

Pressure profileTemperature profile

Superficial gas velocity profileGas holdup profile

Concentration profiles of each compound in the liquid phasePartial pressure of each compound in the gas phase

Wax production and compositionCondensate production and composition

Liquid water productionGas production and composition

Thermal stabilty diagram

Figure 7

Model algorithm.

04_ogst08055 13/03/09 19:05 Page 75


However, the wax analysis is not representative to the realcomposition of the wax produced. In fact, at the beginning ofthe run, the reactor was filled with a paraffinic mixture,which has a different composition than the one of the waxproduced. It takes a long time to remove the startup mixtureand to reach a representative composition of the wax pro-duced. Due to the low wax production and the high liquidholdup, the wax analysis is still modified because of the pres-ence startup mixture.

TABLE 6

Comparison of the outlet gas analysis model/experience

Gas composition %vol SNZ Model

CO 19.9 19.47

H2 41.22 40.3

H2O 0.09 0.56

Inert 36.12 36.42

C1 1.99 1.93

C2 0.129 0.176

C3 0.28 0.154

C4 0.206 0.134

C5 0.169 0.12

C6 0.08 0.09

C7 0.05 0.06

C8 0.01 0.03

C9 0.003 0.01

CONCLUSIONS

The reactor model is a useful tool to predict the reactorperformances. The validation of this model highlights that wewill be able with this tool to give a design of an industrialunit with a reasonable degree of confidence. Now, it is usedfor the reactor scale-up and gives support on the futuredesign of an industrial unit. At the present time, the mostimportant uncertainties are linked to the catalyst parameters,which are relative to the chosen catalyst and its range ofoperating conditions (Kinetic reference temperature andSchulz-Flory parameter). To determine these parameters, weneed validated results from catalytic tests in small reactors(Autoclave) giving the activity and the selectivity of the newcatalyst.

REFERENCES

Albal R.S., Shah Y.T., Carr N.L., Bell A.T. (1984) Mass transfercoefficients and solubilities for hydrogen and carbon monoxideunder Fischer-Tropsch conditions, Chem. Eng. Sci. 39, 5, 905-907.

Bach H.F., Pilhofer T. (1978) Variation of gas hold-up in bubblecolumns with physical properties of liquids and operating parame-ters of columns, Ger. Chem. Eng. 1, 270-275.

Baird M.H., Rice R.G. (1975) Axial dispersion in large unbaffledcolumns, Chem. Eng. J. 9, 171-174.

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76

Paraffin composition in condensate measured

Paraffin composition predicted by the model

Olefin composition in condensate measured

Olefin composition predicited by the model

80 1006040200

Wei

ght f

ract

ion

9.000

8.000

7.000

6.000

5.000

4.000

3.000

2.000

1.000

0.000

Carbon number

Condensate analysis

Figure 8

Condensate analysis.

Paraffin composition in condensate measured

Paraffin composition predicted by the model

60 8040200

Wei

ght f

ract

ion

6

5

4

3

2

1

0

Carbon number

Wax analysis

Figure 9

Wax analysis.

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Final manuscript received in December 2008Published online in March 2009


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