Residence time distributions with a radiotracer in a hydrotreating pilot plant: Upflow versus downflow operation

Chemical Engineering Science 57 (2002) 1859 – 1866

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Residence time distributions with a radiotracer in a hydrotreating pilot plant: Up(ow versus down(ow operation T. Burkhardta; ∗ , J. Verstraetea , P. Galtiera , M. Kraumeb a Institut

b Institut

Francais du Petrole, CEDI Rene Navarre, BP3, 69390 Vernaison, France fur Verfahrenstechnik, Technische Universitat Berlin, 10 623 Berlin, Germany

Received 18 October 2001; received in revised form 29 November 2001; accepted 14 February 2002

Abstract The objective of the present work is to determine the in(uence of the two-phase (ow direction in hydrotreating bench scale plants on the axial dispersion of the liquid phase. Residence time distribution experiments under ambient conditions in cocurrent up(ow and in cocurrent down(ow are carried out in a catalytic hydrotreating bench scale plant, which contains a thermowell. Particles that are representative of a commercial catalyst are used. The (uids and (ow rates are chosen in order to simulate deep desulfurization conditions of a straight-run gas oil. In order to determine the axial dispersion only within the bed of particles, a radioactive tracer is used. The hydrodynamic parameters are identi?ed using an axial dynamic piston dispersion model. The liquid axial dispersion is found to be signi?cantly higher in the down(ow mode than in the up(ow mode. The values of the up(ow liquid saturation are in a good agreement with the values found in the literature whereas the down(ow liquid saturation is lower. Simulations with a multiphase model indicate that the di@erence of the axial dispersion might have a signi?cant in(uence on the hydrodesulfurization performances. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: Hydrotreating; Hydrodynamics; Up(ow–down(ow; Residence time distribution; Dispersion; Scale-up

1. Introduction From the year 2005 onwards, both gasoline and gas oil in the European Union must contain less than 50 ppm of sulfur. In this context, laboratory reactors play an increasingly important role. A modi?cation of the operating conditions and new catalysts are tested in laboratory reactors before their application in industrial units. Hydrotreating (HDT) reaction kinetics are usually determined in this kind of installation. The laboratory reactors are chosen as small as possible in order to avoid the waste of raw material and to reduce the investment and operating costs. The volume ratio of a commercial unit and a pilot plant may be of the order of 100 000 (Sie, 1996). “Downscaling” leads to signi?cantly smaller (uid velocities in the pilot plant compared to the commercial unit. ∗ Corresponding author. Tel.: +33-4-78-02-20-20; fax: +33-4-78-02-20-09. E-mail addresses: [email protected] (T. Burkhardt), [email protected] (J. Verstraete), [email protected] (P. Galtier), [email protected] (M. Kraume).

Due to the low (uid velocities, (uid dynamics and mass transfer phenomena may have an impact on the obtained conversions. In this case, the pilot plant results do not re(ect the intrinsic kinetics alone. If these results are extrapolated without a correction, the prediction of the performances in the commercial unit may be incorrect and the severe product property constraints are possibly not ful?lled. Axial dispersion is one of these phenomena which are rate lowering and its importance is shown in the literature (see for example van Gelder & Westerterp, 1990; Papayannakos, Galtier, Bigeard, & Kasztelan, 1992; Giermann, 1988; van Klinken & van Dongen, 1980; Stiegel & Shah, 1977). The axial mixing occurs in both the liquid and the gas phase in a hydrotreating reactor. However, deviations from plug (ow in the gas phase are generally of minor interest in ?xed bed reactors (Froment & Bischo@, 1990). The capillary e@ects between the gas and the solid are signi?cantly less important than those between the liquid and the solid. Moreover, the concentration gradients are less important in the gas phase because hydrogen, the main component, is generally in large excess. Trambouze et al. con?rm that the axial dispersion coeLcients in the gas phase are about ten times lower than in

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the liquid phase (Trambouze, van Landeghem, & Wauquier, 1988). Mears states that the e@ect of axial dispersion in trickle-(ow is negligible if the following criterion for the minimum length of the catalytic bed Lmin is ful?lled (Mears, 1971): 20n Lmin C in ¿ ln out : dP Bo C

(1)

Commercial hydrodesulfurization ?xed bed reactors generally work in the down(ow mode. Yet it has been reported in the literature that small bench scale plants operating in the down(ow mode can have a poor conversion compared to the commercial units (Carruthers & Di Camillo, 1988; van Klinken & van Dongen, 1980; Montagne & Shah, 1975). A poor contact eLciency between the liquid and the catalyst was reported to be at the origin of this phenomenon. De Wind proposes to cope with this problem by operating the bench scale plant in the up(ow mode. The higher liquid holdup and a di@erent (ow regime (bubble (ow in up(ow and trickle (ow in down(ow) lead to a better utilization of the catalyst. It is reported that in this case the same performances were obtained as in commercial units (de Wind, Plantenga, Heinermann, & Homan Free, 1988). The objective of the present work is to determine in which (ow direction the liquid axial dispersion is more important— in cocurrent down(ow or cocurrent up(ow. In the literature, only qualitative statements are given. Shah simply states that the axial and radial mixing is higher in up(ow (Shah, 1979). In reaction systems where the axial dispersion represents a signi?cant rate lowering phenomenon, the (ow direction with the lower axial dispersion should be applied in pilot experiments in order to facilitate the extrapolation to commercial units, which are generally supposed to work—due to the important (uid velocities—in plug (ow conditions (Sie, 1991; Froment & Bischo@, 1990). 2. Experimental setup and procedure The residence time distribution (RTD) experiments are carried out in a typical hydrotreating bench scale plant. It is important to mention that the same reactor is used in the down(ow and in the up(ow con?guration. In order to measure the liquid axial dispersion in the catalytic bed only (and not in the reactor extremities), experiments with a radioactive tracer are carried out. By means of detectors in the bed inlet and outlet, the liquid axial dispersion and the liquid saturation are determined. The injection and detection of the radioactive tracer is carried out with the help of a team of the French Commissariat aQ l’Energie Atomique. The experimental setup is depicted in Fig. 1. A system of pneumatic 3-way-valves is installed to change the (ow direction between cocurrent up(ow and cocurrent down(ow (pneumatic valves 1, 2, 3 and 4 in Fig. 1).

Table 1 Characteristics of the bench scale plant used for the RTD experiments Internal reactor diameter Reactor length Diameter of the tube replacing the thermowell Length of the tube replacing the thermowell Free cross sectional area Bed length Distance between the detectors Particle diameter Particle length ⇒ equivalent particle diameter Bed void fraction

dR

A L dP

2:1 × 10−2 m 0:81 m 4 × 10−3 m 0:70 m 3:34 × 10−4 m2 0:68 m 0:63 m 1:2 × 10−3 m 3 × 10−3 m 1:5 × 10−3 m 0.37

By means of a second system of pneumatic valves the radioactive tracer is injected (valves 5 and 6 in Fig. 1): before the injection, the liquid feed crosses a bypass. Meanwhile the radioactive tracer is ?lled into a tank (valves 7 and 8). In the beginning of the experiment, the bypass is closed and the liquid feed (ows through the tank, thus injecting the tracer. The in(uence of the original thermowell (used to determine the axial temperature pro?le during catalytic experiments) in the axis of the reactor on the (ow pattern is not the same for up(ow and down(ow conditions: In down(ow, the entering liquid contacts immediately the thermowell. Hence, an important fraction of the liquid might then (ow down along this thermowell (see Fig. 2a). This preferential path would alter the results because a large fraction of the liquid would not be in contact with the bed of particles. On the contrary, in up(ow the entering liquid does not contact immediately the thermowell but is ?rst distributed. The risk of a preferential path caused by the thermowell is therefore signi?cantly smaller in up(ow. Since a preferential path would alter the results of the RTD experiments, the thermowell is replaced by a “pseudo-thermowell”, i.e. a tube with a diameter of 4 mm. It crosses the catalytic bed and ends just outside of it (see Fig. 2b). Consequently, the entering liquid in down(ow mode cannot immediately contact the tube and the risk of creating preferential paths is reduced. Aluminium extrudates are used to represent a typical commercial HDT catalyst. These extrudates are non-porous in order to avoid intraparticle di@usion e@ects that might affect the results and thus alter the determination of the axial dispersion. The distance between the two detectors corresponds to the bed length of typical hydrotreating experiments. The total bed length is superior to that distance in order that the detectors “see” only the bed of extrudates (and not the inert beads which are located before and after the bed). Table 1 shows the characteristics of the bench scale plant and of the bed of non-porous particles. For security reasons, the presence of a radioactive tracer makes it necessary to carry out the RTD experiments at ambient pressure and ambient temperature. Using gas–liquid equilibrium calculations, a (uid system is determined that

T. Burkhardt et al. / Chemical Engineering Science 57 (2002) 1859–1866

3

P pseudothermowell

detector 2 4

FT

1861

bed of nonporous extrudates

purge

detector 1 used liquid

P

Br82

air

2

1 7

N2 heptane 6

8 tank for tracer

W1 P2

5

« pseudo thermowell »

(a)

683 mm

228 cm 3 of non porous aluminium extrudates

detector 1 72 mm

good distribution

from bottom to 1st detector: 98 mm

preferential paths

inert beads

detector 2

from 1st to 2nd detector: 630 mm

thermowell

56 mm

from top to 2nd detector: 83 mm

Fig. 1. Experimental setup.

inert beads

(b)

Fig. 2. (a) Risk of preferential paths with the thermowell which is connected to one extremity. (b) Bed con?guration for radioactive tracer experiments.

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Table 2 Comparison of the gas–liquid systems at ambient and reaction conditions ((ash calculations with AspenTM )

Fluid system

Straight run gas oil =hydrogen

n-heptane=nitrogen

State Relative pressure (106 ) Temperature (◦ C) Thermodynamic method used in (ash calculation l (kg m−3 ) l (10−3 Pa s)  (10−3 N m−1 ) g (kg m−3 ) Vapor fraction (wt%) Ql (m3 s−1 )

Reaction conditions 5 613 K

Ambient conditions Ambient pressure Ambient temperature

Grayson streed

Redlich–Kwong–Soave

609

692

0.24

0.53

7.8 15 31% of SR GO 5:69 × 10−8 (usl = 0:2 × 10−3 m s−1 ) 1:33 × 10−6 (usg = 4 × 10−3 m s−1 )

20.6 1.3 0.5% of n-C7 —

Qg (m3 s−1 )

represents, at ambient conditions, the gas and liquid properties of a straight run gas oil=hydrogen system at reaction conditions. According to Euzen, Trambouze, and Wauquier (1993) density is the determining parameter of the gas phase and both density and viscosity are usually the determining properties of the liquid phase (Euzen, et al., 1993). Hence, n-heptane is chosen as liquid because its density and viscosity are close to those of the liquid phase at reaction conditions. Because of its higher density at ambient conditions, nitrogen is used as gas instead of hydrogen. Dibromobenzene, marked with radioactive Brome 82, is chosen as tracer substance for the liquid phase. Flash calculations are used to determine whether the vaporization of n-heptane and of the tracer at ambient conditions is negligible. The results indicate that the vapor fraction of n-heptane at these (ow rates is of about 0:5 wt%. Table 2 compares the properties of the nitrogen=heptane (uid system at ambient conditions to those of the gas oil=hydrogen (uid system at reaction conditions. The operating conditions for the RTD experiments are chosen to represent the following hydrotreating operating conditions: • a liquid hourly space velocity (LHSV) of 1=3600 s−1 and a ratio H2 =HC of 450 N m3H2 in the reactor outlet per m3 of liquid feed stock, • a pressure of 5:1 × 106 Pa, • a temperature of 613 K. In the case of a typical straight-run gas oil, these conditions result in a desulfurization degree of more than 99.9% (Burkhardt, 1999). At ambient conditions, the (ow rates of the gas oil=hydrogen system correspond to a liquid volume (ow

—

rate of 0:2 × 10−3 =3600 m3 s−1 and to a gas volume (ow rate of 106×10−3 =3600 m3 s−1 . The corresponding volume (ow rates at reaction conditions are determined by means of (ash calculations with AspenTM (see Table 2). These (ow rates are aimed at in the RTD experiments at ambient conditions with the n-heptane=nitrogen system. 3. Operating procedure The liquid (ow rate is veri?ed by measuring the loss of weight of the feed tank per unit time. The instant gas (ow rate is measured by a Brooks rotameter and the mean gas (ow rate by a mercury sealed displacement meter. Due to the presence of the radioactive tracer all the experiments have to be carried out within one day. A readjustment of the (ow rates between the experiments is not possible because it would take a too long time to wait for steady state after a change of the setpoint of the valves. At t = 0, the bypass is opened. The radioactive tracer is carried along by the liquid feed. When the liquid with the tracer passes in front of the two detectors, the radioactive counts are measured. Three experiments are carried out, two in up(ow and one in down(ow. Table 3 summarizes the gas and liquid (ow rates in the di@erent experiments. For the same setpoint of the pump, the liquid (ow rate in the down(ow experiment is by 20% higher than in the up(ow experiments. 4. Model equations and parameter identication A dynamic piston dispersion model is used to determine the liquid axial dispersion coeLcient and the intrinsic phase

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Table 3 Flow rates in radioactive RTD experiments

Experiment

Up(ow (1st expt.)

Up(ow (2nd expt.)

Down(ow

Ql (m3 s−1 ) Qg (m3 s−1 ) ⇒ usl (10−3 m s−1 ) ⇒ usg (10−3 m s−1 )

5:42 × 10−8 1:19 × 10−6 0.16 3.6

5:69 × 10−8 1:22 × 10−6 0.17 3.7

6:64 × 10−8 1:19 × 10−6 0.20 3.6

@Ct @ 2 Ct @Ct : = −ul + Dax; l @t @z @z 2

(2)

“Closed vessel” boundary conditions are used (Levenspiel, 1972). Their physical meaning is that the axial dispersion coeLcient in the inlet and in the outlet section of the catalytic bed is zero. The above equations are discretized according to a ?nite volume scheme for the axial coordinate and an explicit scheme for the time coordinate. It is supposed that the number of counts measured by the detectors is proportional to the tracer concentration Ct . For that reason, the concentration in the mass balance above is replaced by the number of counts that are detected. The di@erences between the experimental curve at the bed outlet and the simulation results are minimized by varying the numerical values of the liquid axial dispersion coeLcient and the liquid velocity in the equation above. There to an optimization program based on the Levenberg–Marquardt algorithm is used. In the beginning of the bed, the signal has not the form of a pulse because of mixing e@ects in the process equipment before the bed of particles (see Fig. 1). The exact form of the signal in the beginning of the catalytic bed is therefore determined by the inlet detector (detector 1 in up(ow mode and detector 3 in down(ow mode in Fig. 1). This signal is used as input of the model. The number of experimental data per experiment is quite high—about 6000 to 7000 per detector for a duration of about 90 min. It is not possible to use all these data points for the parameter identi?cation of the parameters due to the restrictions with regard to computation time and memory. Hence, the data set of the detector at the outlet is reduced to a set of about 50 data points which are used for the parameter identi?cation. In the region of the maximum of the response signal the time step between the data points is reduced by a factor three compared to the beginning and the end of the signal because the information contents there is much higher. It is veri?ed that smaller step sizes with regard to time and space result in only insigni?cant changes of the simulation results.

5. Results and discussion The following ?gures show the signal as determined by the inlet detector, the signal as determined by the outlet detector and the corresponding result of the mathematical model. Fig. 3 shows the experimental and the simulation results of the ?rst experiment in the up(ow mode. It can be seen that the agreement between the simulation and the measurement is quite good. This means that the assumed model describes well the backmixing e@ects in the considered reactor. The ?t is obtained for a liquid velocity ul of 0:67 × 10−3 m s−1 and for an axial dispersion coeLcient in the liquid phase Dax; l of 4:24 × 10−6 m2 s−1 . Fig. 4 shows the experimental and the simulation results of the second experiment in the up(ow mode. It can be seen that the agreement between the simulation and the measurement in up(ow is quite good, exactly as in Fig. 3. This ?t is obtained for a liquid velocity ul of 0:66 × 10−3 m s−1 and for an axial dispersion coeLcient in the liquid phase Dax; l of 3:86 × 10−6 m2 s−1 , which means that the reproducibility is very good.

-3

1

RTD

x 10

bed inlet exp bed outlet sim bed outlet exp 0.8

0.6 counts

average liquid velocity (named liquid velocity in the following). The tracer mass balance is the following:

0.4

0.2

0 0

1000

2000

3000

4000

5000

6000

time s

Fig. 3. RTD experiment with a radioactive tracer in up(ow (?rst experiment). Representation of the experimentally determined signals at the extremities of the catalytic bed and of the simulation result.

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1

-3

RTD

x 10

1.8 bed inlet exp bed outlet sim bed outlet exp

RTD

x 10

bed inlet exp bed outlet sim bed outlet exp

1.6

0.8

1.4 1.2 counts

counts

0.6

0.4

1 0.8 0.6 0.4

0.2

0.2 0

0 0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

time s

-3

RTD

x 10

detector 2 detector 1

1.6 1.4

counts

1.2 1 0.8 0.6 0.4 0.2 0 0

500

1000

1500

2000

500

1000

1500

2000

2500

3000

3500

4000

time s

Fig. 4. RTD experiment with a radioactive tracer in up(ow (second experiment). Representation of the experimentally determined signals at the extremities of the catalytic bed and of the simulation result.

1.8

0

2500

3000

3500

4000

time s

Fig. 5. Experimental results of the down(ow experiment.

Fig. 5 shows the experimental results of the down(ow experiment. The signal of the outlet detector (detector 1 in Fig. 5) shows a small shoulder peak before the main peak. This peak occurs even before the peak of inlet detector (detector 2). Consequently, the peak cannot be caused by a preferential path in the inner of the catalytic bed; in this case the small peak would occur after the peak of the inlet detector. The shoulder peak, which is detected by outlet detector, corresponds most probably to the pulse in the ascending tube next to the reactor (see Fig. 1)—in spite of the lead isolation around the detector—before the pulse enters the reactor. This is con?rmed by the time delay between the small peak and the peak of detector 2. This time delay is of about 2 min. At the actual operating conditions, these 2 min cor-

Fig. 6. RTD experiment with a radioactive tracer in down(ow. Representation of the experimentally determined signals at the extremities of the catalytic bed and of the simulation result.

respond to the mean residence time of the liquid in the ascending tube between the height of detector 1 and detector 2 in the bed of particles. This means that the pulse does not exclusively re(ect the behavior of the particle bed. Consequently the shoulder peak is removed from the curve for the parameter identi?cation. Fig. 6 shows the results of the optimization in down(ow. In Fig. 6, it can be seen that the agreement between the simulation and the measurement in down(ow is quite good. This ?t is obtained for a liquid velocity ul of 2:51 × 10−3 m s−1 and for an axial dispersion coeLcient in the liquid phase Dax; l of 1:24 × 10−4 m2 s−1 . Table 4 summarizes the results: The liquid saturation l is 3 times higher in up(ow than in down(ow. The values of the up(ow liquid saturation are in a good agreement with the correlations of Papayannakos, Thanos and Gotsis, as cited in Burkhardt (1999), and with that of Stiegel and Shah (1977), which are of 0.67 and of 0.77, respectively, at these conditions. The down(ow liquid saturation is somewhat lower than 0.31, the value given by the correlation of Midoux (Ramachandran & Chaudhari, 1983). The liquid velocity is about 4 times higher in down(ow than in up(ow and the gas velocity 2.5 times smaller. In up(ow the gas is about 40 times faster than the liquid and in down(ow 5 times faster. Clearly the higher liquid velocity in down(ow is due to the smaller liquid holdup. The liquid axial dispersion coeLcient in down(ow mode is about 30 times higher while the Peclet number of the liquid phase is about 9 times smaller. The higher liquid velocity in down(ow seems to cause a higher degree of turbulence and axial mixing. In the case of small dispersion degrees it is possible to determine approximate Peclet values by evaluating the mean times and variances of the signals, as described in Levenspiel

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Table 4 Results of the RTD experiments with a radioactive tracer in the U 208

Variable

Determination

Dax; l (m2 s−1 )

Param. identi?cation Param. identi?cation Ql = ul A l QG = ug A (1 − l ) Pel = ul L=Dax; l

ul (10−3 m s−1 ) l ug (10−3 m s−1 ) Pel

(1972). Applied to the obtained signals this method yields in the following Peclet numbers: 57 for the ?rst up(ow experiment, 59 for the second up(ow experiment and 10 for the down(ow experiment. These values are in agreement with those of Table 4. The fact that the axial dispersion is signi?cantly higher in down(ow than in up(ow, is not in agreement with the qualitative statement of Shah that axial and radial mixing are more important in cocurrent up(ow (Shah, 1979). With an extremely high conversion degree of more than 99.9% as observed in the catalytic experiments and a supposed reaction order of 1.2 with regard to the sulfur components (Burkhardt, 1999), the criterion of Mears is clearly not ful?lled in down(ow mode. According to this criterion the minimum bed length for the given particle size should be of about 10 m in the down(ow mode to neglect the in(uence of the axial dispersion on the HDS performance! Considering that the real bed length is of about 0:60 m, the axial dispersion should play, according to the criterion, an important role in down(ow. Mears developed his criterion for trickle-(ow conditions (Mears, 1971). But nothing in the derivation of the criterion prevents its application in up(ow because the same assumptions (one-dimensional plug (ow with superimposed longitudinal dispersion, form of the rate expression, etc.) can be used in up(ow conditions. In the up(ow mode, the minimum bed length is of about 1:2 m. In other words, neither in down(ow mode nor in up(ow mode Mears’ criterion is satis?ed. However, in up(ow mode the minimum bed length is signi?cantly smaller than in down(ow mode. In order to determine the impact of the axial dispersion coeLcients of Table 4 on the hydrodesulfurization performances, the coeLcients are entered in a three-phase reactor model that accounts for both the HDS reaction kinetics and the axial dispersion. The kinetic parameters are estimated with a series of up(ow hydrotreating experiments at very high conversion degrees (¿ 95%). A detailed description of this model may be found in Burkhardt (1999). The catalytic experiment mentioned above was simulated and the model indicates HDS conversions of 99.97% and 99.88% in up(ow and down(ow, respectively. In the case of a typical straight run gas oil, this may easily result in a di@erence of the residual sulfur content of more than 10 ppm, which is

Up(ow (1st expt.)

Up(ow (2nd expt.)

Down(ow

4:24 × 10−6

3:86 × 10−6

1:24 × 10−4

0.67 0.65 27.7 99.9

0.66 0.69 32.2 108.6

2.51 0.21 12.3 12.8

far from being negligible. Since the same kinetics is used in the up(ow and in the down(ow simulation, this di@erence is entirely due to the di@erent axial dispersion. According to these results, the conversion in up(ow mode might be less a@ected by the axial dispersion than in the down(ow mode. Therefore, pilot experiments should be carried out in up(ow in order to be as representative as possible of commercial units since the axial dispersion in commercial units is generally supposed to be negligible. 6. Conclusions Residence time distribution (RTD) experiments of the liquid phase are carried out in a hydrotreating bench scale plant, which contains a thermowell, in cocurrent two-phase up(ow and down(ow. Particles that are representative of a commercial catalyst are used. The (uids and operating conditions are representative of deep hydrodesulfurization operation. In order to determine the liquid axial dispersion and the liquid saturation only in the particle bed, a radioactive tracer is used. The values of the liquid velocity and of the liquid axial dispersion coeLcient are determined using a dynamic axial piston dispersion model with Danckwerts boundary conditions. The agreement between the experimental curves and the results of the dynamic axial piston dispersion model is quite good. At the chosen conditions, the liquid saturation is of about 0.67 in up(ow mode and of 0.21 in down(ow mode. The Peclet numbers of the liquid phase are of about 99 in up(ow mode and of 12 in down(ow mode. A higher degree of turbulence in down(ow mode due to the higher liquid velocity might be at the origin of this phenomenon. At the considered high desulfurization degrees, the Mears’ criterion is clearly neither satis?ed in up(ow mode nor in down(ow mode. Likewise, simulations with a three phase reactor model accounting for the HDS kinetics and for the axial dispersion indicate that the di@erence of the axial dispersion has a signi?cant in(uence on the desulfurization performance. These results are important for reaction systems where the axial dispersion represents a signi?cant rate lowering

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phenomenon. Then, since the axial dispersion is generally supposed to be negligible in commercial trickle (ow hydrotreating units, pilot experiments should be carried out in the up(ow mode in order to permit a correct extrapolation of the results. Notation A Bo C d Dax; l L LHSV n Pe Q ul ug usg usl V z

free cross sectional area of the reactor, m2 −1 Bodenstein number (ul dP Dax; l ), −3 −1 concentration (nV ), mol m diameter, m axial dispersion coeLcient based on the liquid phase volume, m2 s−1 distance in the particle bed between the two detectors, m −1 in −1 liquid hourly space velocity (Qfeed; 0 VB ), s reaction order, −1 Peclet number (ul LDax; l ); volumetric (ow rate, m3 s−1 intrinsic phase average liquid velocity, m s−1 intrinsic phase average gas velocity, m s−1 gas super?cial velocity (Qg A−1 ), m s−1 liquid super?cial velocity (Ql A−1 ), m s−1 volume, m3 distance from reactor inlet, m

Greek letters 

  ’

liquid saturation (Vl; external −1 VB−1 ) bed void fraction (Vvoid VB−1 ) dynamic viscosity, N s m−2 surface tension, N m−1 density, kg m−3

Subscripts ax B g l P R s t

axial bed gas liquid particle reactor super?cial tracer

Superscripts in out

variable at reactor inlet variable at reactor outlet

Acknowledgements The special thanks of the authors go to N. Papayannakos and to A. Cordier for their help during the experiments. They appreciated working with the team of the Commissariat aQ l’Energie Atomique and would like to thank Christophe Boyer for many helpful comments. References Burkhardt, T. (1999). Determination of the in:uence of the :uid-dynamics in hydrotreating bench scale plants. Ph.D. thesis, Technical University of Berlin and IFP. Carruthers, J. D., & Di Camillo, D. J. (1988). Pilot plant testing of hydrotreating catalysts: In(uence of catalyst condition, bed loading and dilution. Applied Catalysis, 43, 253–276. de Wind, M., Plantenga, F. L., Heinermann, J. J. L., & Homan Free, H. W. (1988). Up(ow versus down(ow testing of hydrotreating catalysts. Applied Catalysis, 43, 239–252. Euzen, J. P., Trambouze, P., & Wauquier, J. P (1993). Scale-up methodology for chemical processes. Editions Technip. Froment, G. F., & Bischo@, K. B. (1990). Chemical reactor analysis and design. New York: Wiley. Giermann, H. (1988). Design of laboratory hydrotreating reactors scaling down of trickle-(ow reactors. Applied Catalysis, 43, 277–286. Levenspiel, O. (1972). Chemical reaction engineering. New York: Wiley. Mears, D. E. (1971). The role of axial dispersion in trickle-(ow laboratory reactors. Chemical Engineering Science, 26, 1361–1366. Montagne, A., & Shah, Y. T. (1975). Backmixing e@ect in an up(ow cocurrent hydrodesulfurization reactor. Chemical Engineering Journal, 10, 99–105. Papayannakos, N. G., Galtier, P., Bigeard, P. H., & Kasztelan, S. (1992). Hydrodynamic e@ects in bench scale hydrotreaters operating in cocurrent gas–liquid up(ow mode. Chemical Engineering Science, 47, 2275–2280. Ramachandran, P. A., & Chaudhari, R. V. (1983). Three-phase catalytic reactors. London: Gordon and Breach Science Publishers. Shah, T. Y. (1979). Gas-liquid-solid reactor design. New York: McGraw-Hill. Sie, S. T. (1991). Scale e@ects in laboratory and pilot plant reactors for trickle (ow processes. Revue de l’Institut Francais du Petrole, 46(4), 501–515. Sie, S. T. (1996). Miniaturization of hydroprocessing catalyst testing systems: Theory and practice. A.I.Ch.E. Journal, 42(12), 3498–3507. Stiegel, G. J., & Shah, Y. T. (1977). Backmixing and liquid holdup in a gas-liquid cocurrent up(ow packed Column. Industrial Engineering Chemistry, Process, Design and Development, 16(1), 37–43. Trambouze, P., van Landeghem, H., & Wauquier, J. P. (1988). Chemical reactors: Design, engineering, operation. Editions Technip. van Gelder, K. B., & Westerterp, K. R. (1990). Residence time distribution and holdup in a cocurrent up(ow packed bed reactor at elevated pressure. Chemical Engineering Technology, 13, 27–40. van Klinken, J., & van Dongen, R. H. (1980). Catalyst dilution for improved performance of laboratory trickle (ow reactors. Chemical Engineering Science, 35, 59–66.