Catalyst Performance Testing in Multiphase Systems: Implications of

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Catalyst Performance Testing in Multiphase Systems: Implications of Using Small Catalyst Particles in Hydrodesulfurization Bandar H. Alsolami,†,§ Rob J. Berger,*,‡ Michiel Makkee,† and Jacob A. Moulijn† †

Catalysis Engineering, ChemE, Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands Anaproc, p/a ChemE, TU Delft, 2628 BL Delft, The Netherlands § R&D Center, Saudi Aramco, P.O. Box 62, Dhahran 31311, Saudi Arabia ‡

ABSTRACT: Three different gas−liquid−solid reactor configurations have been used to investigate the performance of a P-doped NiMo/Al2O3 catalyst in the hydrodesulfurization of dibenzothiophene. The commonly used millipacked bed reactor with 250−500 μm catalyst particles diluted with 125 μm inert particles, a micropacked bed reactor with 55−90 μm catalyst particles, and a slurry reactor with 150−250 μm catalyst particles were used in the catalyst performance testing program. It appeared that the inherently small particle size in the packed beds causes the hydrodynamics to be dramatically different compared to the industrially applied trickle-bed reactors. For particles smaller than typically 2 mm the capillary forces predominate over the viscous and gravitational forces, in sharp contrast to large-scale industrial reactors. Since the gas flow follows preferential pathways through beds consisting of small particles, the poor radial dispersion of the gaseous components can cause masstransport limitations, even for a rather slow reaction such as the hydrodesulfurization (HDS) of dibenzothiophene, as a result of the strong inhibition by the reaction product H2S. An adapted criterion is proposed for estimation of the contribution of poor radial dispersion in catalyst performance testing.

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2.2 mm using 55−90 μm catalyst particles, and a slurry reactor with 150−250 μm catalyst particles. The influence of diluting the catalyst bed with inert particles, which is often applied to improve the mass and heat transfer, the catalyst wetting, and the bed isothermicity,5−10 has been investigated. A relatively slow reaction, the hydrodesulfurization (HDS) of dibenzothiophene (DBT), a model sulfur compound, was chosen in order to focus on the hydrodynamics with the reactor scale rather than on the diffusion limitation inside the catalyst particles. Additionally, this reaction has already been extensively studied using different reactor configurations, i.e., reactor sizing, catalyst particle size, catalyst packing, diluents, etc., which may have affected the catalyst performance results in terms of activity, selectivity, and stability. In most cases the authors assumed that they directly measured the intrinsic kinetics, i.e., in the absence of any transport limitation, enabling a simple direct comparison of different catalysts and reactor types.11−18 The conclusions are put in perspective by comparing the two laboratory-scale flow reactors with a large-scale industrial reactor, and a new criterion for assessing the presence/absence of a contribution of poor radial dispersion is derived.

INTRODUCTION In the industry the hydrodesulfurization (HDS) of heavier types of naphtha is commonly performed in large trickle-bed reactors in which the naphtha and the hydrogen flow concurrently downward through a bed consisting of catalyst pellets.1,2 The liquid typically trickles down through the bed, allowing the gas to flow through all the voids in the bed. Although rather large catalyst pellets of about 1−3 mm are used, which may give rise to transport limitations inside the pellets, the dispersion on the reactor scale is pretty good. In order to investigate the catalyst performance for selecting the best catalyst and also to measure the reaction kinetics, facilitating a proper reactor design, it is highly preferred to use a small-scale reactor for reasons of safety, labor, equipment, and raw materials cost. Although it is to be expected that the hydrodynamic behavior of a small-scale trickle-bed reactor is not similar to that of a large-scale tricklebed reactor due to a strong increase of the effect of capillary forces when further scaling down,3 it is often assumed that these small-scale reactors follow a plug-flow behavior and the trickle-bed hydrodynamics. However, a priori, it is not to be expected that the trickle flow hydrodynamics regime is realistic and, in addition, the rule-of-thumb criterion that the ratio of reactor over particle diameter of >8,4 in order to guarantee plug-flow behavior, does not make sense for small particles, since there is no real trickle flow. This study was performed to investigate the behavior of small-scale gas−liquid fixed beds in more detail in order to see whether the predominant hydrodynamic phenomena are comparable to those at large scale and, if not, to map the phenomena causing the deviations. Three reactor configurations were used: a milliflow reactor having an internal reactor diameter of 15 mm using 250−500 μm catalyst particles diluted with 125 μm inert SiC particles, a microflow reactor having an internal diameter of © XXXX American Chemical Society

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EXPERIMENTAL SECTION Materials. The P-doped NiMo/γ-Al2O3 catalyst used in this study was prepared according to a European patent19 using different metal precursors: MoO3 and NiCO3 (Aldrich) were dissolved in a H3PO4 aqueous solution which was continuously stirred and refluxed with a final pH 2.5. The support, γ-Al2O3 Received: April 4, 2013 Revised: May 28, 2013 Accepted: May 29, 2013

A

dx.doi.org/10.1021/ie4010749 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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both reactors, the gas and liquid were separated using a level controller with a liquid lock. After neutralization of the H2S in a NaOH scrubber, the off-gas was sent to the vent and the liquid was sent to a computer-controlled autosampler. At the beginning of each run, the catalyst was sulfided in situ in the gas phase using 10 vol % H2S in H2 at atmospheric pressure. The temperature was held at 298 K for 1 h, raised at a 3 K min−1 rate, and held at 673 K for 2 h. Subsequently, the catalyst bed was cooled to 373 K and prewetted during 2 h at 373 K and 50 bar of H2. The liquid samples were analyzed off-line using a gas chromatograph equipped with a flame-ionization detector (FID). In the milliflow reactor the catalyst has been diluted with inert particles to achieve a certain bed height. In order to check if this amount is not causing a significant deviation of the conversion due to catalyst bypass, the criterion defined by Berger et al.23 was applied. The maximum allowed amount of inert bed dilution as a volume fraction of total solids (b) follows from the following correlation:

pellets (Ketjen 300), was added to this solution, mixed for 1 h, and dried at 393 K overnight. No calcination step was applied, and the final metal content obtained was 15 wt % Mo, 5 wt % Ni, and 4 wt % P.20 The catalyst pellets were crushed and sieved to particles in the desired sieve fraction (250−500 μm for the milliflow reactor and 55−90 μm for the microflow reactor). The catalyst particle density was 1650 kg m−3, the catalyst particle porosity was 0.67, and the pore volume was 0.41 m3 g−1. SiC with a particle size of 125 μm was used as diluent in catalyst packing in the milliflow reactor. A 0.2 wt % dibenzothiophene (DBT) (Sigma-Aldrich, 98%) sample was dissolved in hexadecane (Sigma-Aldrich, ≥99%) to obtain a concentration of 6.97 mol m−3, which corresponds to a feed sulfur content of 350 ppm. Activity Measurements. The milliflow reactor, depicted in Figure 1, was operated concurrently in a downflow regime,

Δ=

⎛ b ⎞ Xdild p ⎜ ⎟ ⎝ 1 − b ⎠ 2hb

(1)

With the maximum accepted deviation, Δ, set at the typical value of 0.05, it follows that b
1, which predicts trickle-flow behavior, in agreement with the hydrodynamic flow regime chart from Ng,35 as shown in Figure 5, which is drawn using the

the hydrodynamic regime and other characteristics are mostly invalid for small particles. In many cases this smaller size strongly influences the major physical phenomena that determine the hydrodynamics. Particularly the contribution of the capillary forces increases strongly. For a comparison of the two reactor configurations in our study with a typical industrial trickle bed, the main properties determining the hydrodynamics are collected in Table 4. De Santos et al.3 distinguish three force ratios (see Table 3): (i) the Reynolds number (ReL), (ii) the capillary number Table 3. Various Dimensionless Numbers Characterizing the Gas−Liquid Flow Regime in a Bed of Particles ReL =

ρL u0,Ld p μL

CapL = Eo ̈ = Oh =

μL u0,L σL

=

inertial force viscous force

(13)

=

viscous force capillary force

(14)

(ρL − ρG )gd p

2

σL μL d ρL σL confinement 2

=

gravitational force capillary force

(15)

viscous force = inertial and capillary forces

Figure 5. Hydrodynamic flow regime chart as a function of liquid and gas mass fluxes according to Ng35 using gas and liquid properties, liquid holdup, particle size, and bed voidage for the industrial tricklebed reactor (see Table 4). The large gray dot indicates the liquid and gas flow rate assumed. There is no reason to extend this flowchart to the conditions of the milliflow reactor and the microflow reactor since these reactors exhibit Eötvos numbers much smaller than 1 (see Table 4).

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(CapL), and (iii) the Eötvös number (Eö). At ReL < 1 viscous stress exceeds inertia and, therefore, liquid pockets will not break up. At CapL < 1 capillary forces exceed viscous stress, and if CapL < 0.001, liquid pockets will not break up. Eö gives direct information on the hydrodynamics; trickling behavior is obtained at Eö > 1, whereas Eö < 1 indicates that trickling will not occur since the capillary forces exceed the gravitational force. In most cases the critical particle size at which Eö becomes 1 lies around 1.5 mm. For significantly larger particles

conditions for the industrial reactor given in Table 4. Although the flow regime chart from Ng also predicts trickle flow hydrodynamics in the milli- and microflow laboratory reactors, this is very unlikely since in both laboratory reactors Eö < 0.01, which implies that correlations validated for the trickling regime are invalid. In this situation the actual hydrodynamics will probably E



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Table 4. Typical Conditions Applied in the Two Laboratory Reactor Types and a Typical Industrial Trickle Bed at 10 bar H2 Pressure and 200 °Ca parameter

units

microflow reactor

milliflow reactor

industrial trickle bed

catal particle diam (dp) diluent particle diam (dp) internal reactor diam (dt) amount of catalyst bed voidage (εb) catal bed height (hb) total packed bed height liquid weight flow rate liquid volume flow rate superficial liquid velocity (u0,L) WHSV gas flow rate (at NTP) gas flow rate (at NTP) gas flow rate (10 bar, 200 °C) superficial gas velocity (u0,G) H2/liquid ratio (at NTP) pressure drop liquid holdup (hL) ReLi CapLi Eöi Ohi

[mm] [mm] [mm] [g] [mvoid3 mbed−3] [mm] [mm] [g h−1] [m3 s−1] [m s−1] [h−1] [mL min−1] [m3 s−1] [m3 s−1] [m s−1] [m3 mliq−3] [bar] [m3 mvoid−3]

0.055 N.A. 2.2 0.694 0.35b 170 500 1.94 8.412 × 10−10 2.21 × 10−4 2.80 14.66 2.44 × 10−7 3.93 × 10−8 1.03 × 10−2 350 0.36 0.75g 0.0209 6.8 × 10−6 0.0016 0.036

0.4 0.125 15 4 (+4 g of SiC) 0.505c 42.0e 300 11 4.762 × 10−9 2.70 × 10−5 2.75 84 1.40 × 10−6 2.25 × 10−7 1.27 × 10−3 354 0.005 0.75g 0.0058j 8.3 × 10−7 0.0081j 0.024j

3 N.A. 1000 4 × 106 0.4d 5140 5140 11 × 106 4.762 × 10−3 6.06 × 10−3 2.75 8.3 × 107 1.38 0.222 0.283 350 0.066f 0.361h 31.2 1.86 × 10−4 4.66 0.0049

a

N.A. = not applicable. bValue estimated from the observed bed height. cVoidage estimated from the experimentally observed bed height of 4.2 cm; the relatively high value is probably due to cavities between the large catalyst particles of 0.4 mm which are only partly filled by the small diluent particles of 125 μm. dTypical value for large beds packed with whole pellets (or extrudates). eIncluding the SiC diluent between the catalyst particles. f Average value from several empirical correlations valid for trickle beds.43−50 gThe liquid holdup was estimated at 0.75, the typical value found by Marquez and co-workers in multiphase packed-bed microflow reactors with similar dimensions.51,52 hAverage value from several literature correlations valid for trickle-bed reactors at reactor conditions.53−60 iFor the physical properties of the liquid phase the properties of pure hexadecane liquid at 200 °C were used: density, 642 kg m−3;61 viscosity, 3.73 × 10−4 kg m−1 s−1;61 surface tension, 0.0121 N m−1.62 jBased on the particle size of the diluent.

be a combination of annular or bubbling flow through the wider channels and liquid flow through narrower channels through which there is no flowing gas. Obviously, for milli- and micropacked beds the hydrodynamic flow regime chart (and other parameters such as the axial dispersion, wetting, liquid holdup, and mass-transfer parameters) will be completely different compared to those of industrial trickle beds. No generally applicable flow regime charts and correlations for packed beds of small particles have been published up to now. This is not surprising. A major obstacle in determining generally applicable correlations and flow regime charts is poor reproducibility, mainly caused by the strong dependency of the capillary forces on the exact particle size, particle shape, surface properties, history, and packing details. The gas flow has a strong tendency to follow preferential relatively large diameter channels, either as large elongated bubbles or as a continuous phase surrounded by some annular liquid flow.36 The other parts of the bed are filled with liquid with, particularly at low flow rates, some stagnant gas bubbles in larger voids. This is in line with the observation of liquid holdups above 0.65 when using particles of 0.1 mm.37 A general recommendation when applying small particles is, therefore, to use particles of as much as possible equal size and shape and to develop a procedure to achieve a dense packing of the particles to suppress the formation of larger voids resulting in preferential gas-flow channels. The gas−liquid two-phase slug-flow regime in a bed of very small particles has been visualized in two dimensions using a bank of micropillars; e.g., see Krishnamurthy and Peles38 and

Wada et al.39 Vanapalli et al.40 investigated the pressure drop over various geometries of micropillar banks. Krishnamurthy and Peles distinguished four different flow patterns when going from low to high gas velocities (see Figure 6): (i) bubbly gas

Figure 6. Flow regimes for N2 in liquid water as a function of the superficial gas and liquid velocities distinguished by Krishnamurthy and Peles in a bank of 100 μm diameter micropillars, with pitch to diameter ratio of 1.5, located in a 1.5 mm wide and 100 μm deep channel (figure adapted from ref 38).

flow, (ii) gas-slug flow, (iii) bridged flow, and (iv) annular flow. In “bridged flow” the liquid tends to form bridges between the micropillars. The authors also plotted a hydrodynamic flow F



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supporting the conclusion that the gas flows along preferential channels. The very low liquid and gas flow rates (0.2 mm s−1 or less and 10 mm s−1 or less, respectively), extremely low Reynolds number (0.02 or less), and Eötvös number (0.008 or less) are by far insufficient to achieve anything other than a laminar viscous flow of the liquid in combination with gas flow along preferential channels. This conclusion was also drawn by Van Herk et al.,22 using identical microflow reactors.

regime map, which is, however, of little use for our laboratory reactors containing a bed of fines since that packing is much more irregular with the particles touching each other and since the flows in our reactors are much smaller than those the authors used (in the microflow reactor jg and jl are 0.0103 m s−1 and 0.000221 m s−1, respectively, and these are even smaller in the milliflow reactor). Olbricht41 showed that the pressure drop and the masstransfer rate were determined by the number of bubbles rather than the size of the bubbles. The tendency for breakup of bubbles is expressed using the Ohnesorge number (Oh); see eq 16 in Table 3. At Oh < 0.01 breakup of bubbles is likely to occur, whereas at Oh > 0.1 the flow is dominated by viscosity. The diameter of the confinement (dconfinement) was estimated as the particle diameter divided by 2. Since Oh in both laboratory reactors is around 0.03, it is not likely that much breakup of bubbles occurs. This indicates that the gas−liquid mass transfer is not enhanced. In the industrial trickle bed, however, Oh ∼ 0.005, which indicates that breakup of bubbles is very likely to occur there, thus enhancing the gas−liquid mass transfer. Visual observation using glass model reactor tubes of both reactors filled with the same catalyst bed as used in the experiments (in which a stainless steel reactor tube is used) shows that most of the gas seems to flow along the wall at one side of the bed,

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ASSESSMENT OF TRANSPORT LIMITATIONS AND AXIAL DISPERSION For the assessment of the influence of transport limitations and axial dispersion, standard experiment is used for which the conditions are given in Tables 4 and 5. For simplicity, the reaction kinetics is assumed to be first order with respect to DBT and hydrogen. The reaction order for the reaction product H2S lies between 0 and −3 (eqs 7 and 8). For simplicity an order of −1 is used. The H2S concentration is assumed to be equal to the initial DBT concentration. Note that this is the maximum H2S concentration that can be formed, thus yielding a conservative estimate. In reality, the H2S formed will be partly transferred to the gas phase. Table 5 gives an overview of the results of the assessment. For comparison, the values for a typical industrial trickle-bed

Table 5. Assessment of Transport Limitations and Other Phenomena in the Two Laboratory Packed-Bed Reactors and a Typical Industrial Trickle-Bed Reactorc phenomenon axial dispersion criterion liquid criterion gas external mass-transfer lim. criterion

parameter/equation

milliflow reactor

Pep,ax (liquid) Pep,ax (gas) hb dp

>

kLS,DBT =

Ca =

{ } (refs 65, 66)

8 n Pe p,ax

1 1 − Xi

ln

1.09Re1/3Sc1/3 DDBT,L εb dp

R v,obs i

84a 336 > 0.12a

0.10d 0.156f 3096 > 84a 3096 > 0.02a

0.44e 0.47e 1715 >19a 1715 > 0.006a

2.6 × 10−5 m s−1

4.2 × 10−5 m s−1

3.5 × 10−3 m s−1e

0.0053 < 0.05a

4.5 × 10−5 < 0.05a

0.00035 < 0.05a

1756 > 1

7.8 > 1

aLS = 6/dp wetting: Sie criterion internal diffusion lim. Weisz−Prater criterion (n ≥ 0.5) radial transport lim. in the bed

(dP / dh)flow (dP / dh)gravity

=

180μL μ0,L (1 − hLε b)2 hLε bd p2ρL g

(hLε b)3

> 1 (ref 42) 8.6 > 1 −9

1.3 × 10

DDBT,eff

Φ=

⎛ Vp ⎞ ⎜ ⎟ ⎝ Ap ⎠

2

( n +2 1 ) D

R v,obs i

i ,eff Ci ,s

(

Drad, i ,L = εb

Di,L τb

G−L mass-transfer lim. criterion

Φrad =

+ 0.137d p

2

u0,L hL

) (ref 72)

obs n + 1 (1 − ε b)(1 − b)R v, i 2 Drad, i ,LCi ,L,int

( )( ) hL aG

g

< 0.15

kGL

Ca =

R v,obs i (1 − ε b)(1 − b) k GLaGLCi ,L,b

0.15b H2S: 38 > 0.15b 1.0 × 10−4 m s−1 H2: 0.024 < 0.05a H2S: 0.157 > 0.05b

−9

1.3 × 10

2

−1

m s

1.3 × 10−9 m2 s−1

0.0001 < 0.08a

0.397 > 0.08b

H2: 6.8 × 10−9 m2 s−1 H2S:4.4 × 10−9 m2 s−1 185 m2 m−3 h H2: 0.51 > 0.15b H2S: 5.0 > 0.15b 2.0 × 10−4 m s−1 H2: 0.005 < 0.05a H2S: 0.033 < 0.05a

H2: 1.0 × 10−6 m2 s−1 H2S:2.8 × 10−6 m2 s−1 150 m2 m−3 e H2: 0.008 < 0.15a H2S: 0.020 < 0.15a 3.9 × 10−4 m s−1 e H2: 0.003 < 0.05a H2S: 0.021 < 0.05a

a

Criterion fulfilled. bCriterion not fulfilled. cThese results were obtained at standard test conditions and a typical DBT conversion of 0.65 and a H2 conversion of 0.038, which corresponds to an observed reaction rate of 8.7 × 10−6 mol kg−1 s−1 (at zero conversion, a DBT concentration of 6.97 mol m−3, and H2 and H2S solubilities in hexadecane of 45.263 and 0.61164 (mol mgas−3)/(mol mliq−3), respectively). dValue taken from Van Herk et al.36 obtained with N2/dye−ethanol (Sc ≈ 1.0 × 104) over a bed with particles of dp ≈ 0.1 mm in the range 0.02 < Re < 0.2. It is assumed that this value, obtained in a liquid−solid bed, applies in both reactors since the major part of the bed does not see any moving gas (bubbles). eAverage value from several literature correlations valid for trickle-bed reactors at reactor conditions.53−60 fObtained from Bischoff’s correlation:73 εb 1 0.45 = + Pep,ax τbReGScG 1 + 0.73(ReGScG) The bed tortuosity was estimated using the correlation from Puncochar and Drahos:74 τb = 1/εb1/2. hCalculated using aGL = εblch/[(1/4)πdt], where lch = chord length, being 0.915dt when hL = 0.75 (see Figure 7). g

G



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reactor are included. The results show that the criteria concerning axial dispersion are easily fulfilled in all reactors for both liquid and gas phase. This also applies for the criterion concerning external mass-transfer limitation, i.e., the mass-transfer limitation over the liquid film surrounding the catalyst particles. The assessment of external mass-transport limitation additionally requires a check of the wetting, i.e., the fraction of the external catalyst surface wetted by the liquid. Due to the small particle size used, less than 0.2 mm, complete wetting may be assumed at any flow rate in both laboratory reactors.5 Sie et al.42 indicated a minimum flow force/gravity force ratio above which liquid maldistribution is unlikely to happen in trickle beds. The data in Table 5 confirm that this industrial trickle-bed reactor is properly wetted. The influence of diffusion limitation within the catalyst particles is assessed using the Weisz−Prater criterion, assuming a typical catalyst pore tortuosity of 3 for calculating the effective diffusivity. Since both the concentration and the diffusivity of hydrogen are higher than that for DBT, and since the diffusivity of H2S is also higher than that of DBT, this assessment was done for DBT only. The results show that the internal diffusion limitation is completely negligible in both laboratory-scale reactors. The industrial-scale reactor, however, suffers from a significant internal diffusion limitation with Φ = 0.397, which corresponds to a catalyst efficiency of 0.82. Radial Mass-Transport Limitations. Unfortunately, there is no readily usable criterion for the radial mass-transport limitation caused by poor radial dispersion. It was, therefore, attempted to develop a criterion analogous to that for internal diffusion limitation by Weisz−Prater, based on the hypothetical worst-case scenario in which it is assumed that all the liquid flows through one side of the bed and that there is only gas flowing through the other side of the bed, as illustrated in Figure 7. Of course, the real situation will be less severe with gas flowing through several separate channels, allowing the assumption of complete catalyst wetting. In the worst-case scenario as described above, the gas components have to disperse in a radial direction through the liquid-filled part of the bed. This geometry can be modeled with a slab geometry, accessible from only one side, and with a slab thickness, dslab, equal to the ratio of the volume of the liquid-filled part of the bed and the gas−liquid interface area, i.e., hL/aGL. The gas− liquid interface area is assumed to be equal to the dashed red rectangle in Figure 7. Using eq 17 for the efficiency of a slab70 η=

tanh ϕ ϕ

Figure 7. Illustration of the worst-case scenario concerning radial mass-transport limitation, characterized by a completely segregated liquid and gas flow, in the laboratory reactors with a liquid holdup of 0.75. The chord length lch, used to calculate aGL, equals the width of the dashed red rectangle.

In the criterion we additionally use a radial dispersion coefficient instead of a diffusion coefficient and we correct for the presence of inert bed dilution, if present. This worst-case scenario criterion applies not only for H2, but also for H2S since this inhibiting reaction product needs to be transported from the catalyst into the gas flow. The results indicate that there is a significant radial dispersion limitation for H2 and an even stronger limitation for H2S in both laboratory reactors, particularly in the milliflow reactor, whereas there is no significant limitation in the industrialscale trickle bed due to the large effective radial dispersion. The high radial dispersion in the industrial-scale bed is mainly due to the much larger particle size. The main reason for the worse result for the milliflow reactor compared to the microflow reactor is the 7 times larger reactor diameter, which is only partly compensated by the about 2 times larger particle diameter of the dilution particles, which in fact determines the flow regime. Later in this paper we show that the situation is not as severe as in this worst-case scenario and that the criterion can be relaxed to a certain extent. Gas−Liquid Mass-Transfer Coefficients. For an estimation of the gas−liquid mass-transfer limitation, i.e., the limitation by mass transfer between the gas phase and the liquid phase which does not include the radial mass-transport limitation discussed in the section Radial Mass-Transport Limitations, we need estimates of the mass-transfer coefficients and the gas−liquid interfacial area. Typical ranges of mass-transfer coefficients and gas−liquid interfacial areas in (packed) bubble columns are shown in Table 6. Since the turbulence caused by

(17)

in which the Thiele modulus ϕ for an nth order reaction is defined as 1/2 ⎡ k(Ci ,L,int)n − 1(1 − εb)(1 − b)ρp ⎤ ⎛ ⎞ + n 1 ⎥ ⎟ ϕ = dslab⎢⎜ ⎢⎣⎝ 2 ⎠ ⎥⎦ Drad, i ,L

(18)

it follows that an efficiency of 0.95 is obtained at ϕ = 0.4. Since the Weisz modulus for radial dispersion, Φrad, can also be written as in eq 19 Φrad = ηϕ2

(19)

it follows that the critical value of Φrad amounts to 0.95(0.42) = 0.15. H



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as the dimensionless radius in the liquid-only cylindrical volume:

Table 6. Typical Values of Gas−Liquid Mass-Transfer Coefficients and Gas−Liquid Interfacial Areas in Bubble Columns75 (Taken from Ref 76)

packed columns cocurrent bubble columns packed bubble columns value selected for worst-case scenario milliflow reactor value selected for worst-case scenario microflow reactor

kGL [mbed3 m−2 s−1]

aGL [m2 mbed−3]

(0.4−6) × 10−4 (1−4) × 10−4 (1−4) × 10−4 1 × 10−4

10−1700 50−600 50−300 39

2 × 10−4

185

accumulation = radial dispersion − (axial) convection − catalytic reaction (all expressed per unit of bed volume) Drad, i ,L ∂ ⎛ Ci ,L ⎞ ∂Ci ,L ⎜ξ ⎟ − u0,L 2 ⎝ ⎠ ∂z rc ξ ∂ξ ∂ξ − ρp (1 − εb)(1 − b) ∑ νi , jrj

0 = εb

j

(21)

the gas bubbles is probably smaller in our two laboratory reactor configurations than that in bubble columns, the gas− liquid mass-transfer coefficient was conservatively estimated at 1 × 10−4 mbed3 m−2 s in the milliflow reactor and, considering the higher gas velocity, at twice this value in the microflow reactor. For both laboratory reactors the gas−liquid interfacial area was estimated to be that according to the worst-case scenario, explained with Figure 7. The results show that the gas−liquid mass-transport limitation is negligible in the microflow reactor and the industrial reactor whereas there is some limitation for H2S in the milliflow reactor, which is mainly due to the low aGL value of 39 m2 mbed−3. However, since this limitation is much smaller than that caused by the limitation due to radial dispersion, it can also be neglected for the milliflow reactor. Heat-Transport Limitations. In both laboratory reactors the heat-transport limitations are completely negligible due to the low reaction rate in combination with the small dimensions and the large heat capacity of the liquid. In the industrial-scale reactor, however, there is only some radial heat-transport limitation which causes a radial temperature difference between the center and the wall of about 7 °C (estimated using an effective radial thermal conductivity in the bed of 1.6 W m−1 K−1 and assuming a reaction enthalpy of 45 kJ molH2−1).

The following two boundary conditions are valid: left boundary equation (center liquid zone) (ξ = 0): ∂Ci,L

=0

∂ξ

(22)

right boundary equation (edge liquid zone) (ξ = 1): εb

⎞ ⎛ Ci ,G = k GL , i⎜ − Ci ,L⎟ ∂ξ ⎠ ⎝ Hi

Drad, i ,L ∂Ci ,L rc

(23)

In eq 21 the liquid velocity is assumed to be constant because of the low concentrations of the reactants and products. For simplicity it is also assumed that the liquid flow rate does not depend on the radial position in this “liquid-only” zone. Since the catalyst wetting is estimated to be complete in both laboratory reactors and since diffusion limitation inside the catalyst particles is negligible, all the catalyst particles are fully accessible for the liquid. For the components only present in the liquid phase, the continuity equation does not include the radial dispersion term and the two boundary conditions become equal; i.e., there is no radial gradient. It is noted that the continuity equation does not include the liquid holdup. This is due to the facts that the gas−liquid interfacial area is expressed per unit of reactor volume and that it is assumed that reaction takes place in all the catalyst particles. Since axial dispersion can be neglected, the steady-state continuity equation for H2 and H2S in the gas phase is given by the following equation:

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CONTINUITY EQUATIONS The results from the assessment of the transport limitations allow setting up a suitable reactor model. Axial dispersion, heat-transport limitations on both particle scale and reactor scale, mass-transport limitation on particle scale, and masstransfer limitation between gas and liquid phases can be neglected, but radial dispersion must be accounted for. The situation in practice is expected to be not as severe as the worst-case scenario shown in Figure 7 based on one big gas flow channel. It is assumed that the gas flows through several parallel channels and that they have the same radius. From a modeling point of view it is convenient to approach this situation with cylindrical volumes with liquid only, enclosing all the catalyst particles, surrounded by zones with only gas. This corresponds with the picture in which the gas channels are narrow and that all catalyst particles are wetted by the liquid. The radius of these liquid-only zones, rc, is unknown a priori and is estimated from the experimental results by treating it as a fitting parameter, which is directly linked with the gas−liquid interfacial area: 2πrc 2 = aGL = 2 r πrc (20) c

u0,G

∂Ci ,G ∂z

⎛ Ci ,G ⎞ = −aGLk GL , i⎜ − Ci ,L⎟ ⎝ Hi ⎠

(24)

Due to the much larger diffusivities in the gas phase compared to the liquid phase, radial gradients in the gas phase were not accounted for. The gas flow rate can be assumed constant because of the low hydrogen conversion (always less than 0.5%).

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RESULTS The results are shown in Figures 8−14. The symbols represent the experimental data, and the curves correspond to the profiles obtained with the optimal model obtained, which is discussed later. If not mentioned otherwise, the catalyst dimensions, catalyst bed dimensions, and standard conditions defined in Table 1 were used. Figures 8 and 9 show the results as a function of the reaction temperature in both reactors. The conversions are almost equal, and complete conversion is reached about 240 °C. The selectivities are similar: at low temperature the main product is BPh, at higher temperatures more of the hydrogenation products

The liquid-phase steady-state continuity equation for H2 and H2S is then given by the following equation with ξ defined I



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Figure 8. DBT conversion and product selectivity as a function of the reaction temperature in the milliflow reactor at standard reaction conditions (see Table 1).

Figure 12. DBT conversion and product selectivity as a function of WHSV in the milliflow reactor at 225 °C and standard reaction conditions.

Figure 13. DBT conversion and product selectivity as a function of WHSV in the microflow reactor at 225 °C and standard reaction conditions.

Figure 9. DBT conversion and product selectivity as a function of reaction temperature in the microflow reactor at standard reaction conditions (see Table 1).

Figure 14. DBT conversion and product selectivity as a function of the gas flow rate divided by the standard gas flow rate of 84 mLNTP min−1 in the milliflow reactor at 225 °C and standard reaction conditions.

Figure 10. DBT conversion and product selectivity as a function of reaction pressure at 200 °C in the milliflow reactor at standard reaction conditions.

Figures 10 and 11 show the results as a function of pressure in both reactors. The conversion is almost independent of the pressure in both reactors. Again the conversions are almost the same in both reactors. The selectivities depend on the pressure: at increasing pressure the selectivity to the hydrogenated products, CHB and BCH, increases, whereas the amount of BPh decreases. Since the hydrogenation equilibrium at 200 °C is entirely at the side of the BCH, this change in selectivity will have a kinetic cause. Additionally, the results show that the CHB selectivity is slightly higher in the milliflow reactor than in the microflow reactor. It is not yet clear what the underlying reason is. It is striking that at 275 °C the data suggest the opposite, i.e., that hydrogenation is more important in the microflow reactor than in the milliflow reactor. Apparently, this does not hold at 200 °C. Figures 12 and 13 show the results as a function of the liquid space velocity in both reactors. As expected, the conversion decreases at increasing WHSV, i.e., decreasing space time for

Figure 11. DBT conversion and product selectivity as a function of reaction pressure at 200 °C in the microflow reactor at standard reaction conditions.

CHB and BCH are formed, and after reaching full conversion the amount of BPh increases again. Around 275 °C the yields of CHB are different: in the milliflow reactor they are lower than those in the microflow reactor. J



Article

reaction. Both reactor systems exhibited similar behaviors. The selectivities to CHB slightly decrease with increasing WHSV, as expected for this serial reaction system. In agreement with Figures 8 and 9, the amount of BCH is low. Figure 14 shows the results as a function of the gas flow rate in the milliflow reactor. There appears to be a positive effect of the gas flow rate on the DBT conversion, particularly at flow rates lower than the standard gas flow rate of 84 mL min−1. The selectivities do not change significantly.

■

DISCUSSION AND PARAMETER ESTIMATION Parameter Fitting and Model Optimization. The initial estimates of the kinetic parameters are listed in Table 7. They

Figure 16. Optimal fit obtained when ignoring radial mass-transport limitation for the DBT conversion and product selectivity as a function of the WHSV in the milliflow reactor at 225 °C and standard reaction conditions (see Table 1).

Table 7. Initial Estimates of the Kinetic Parameters Used Using the Parameters from Our Slurry Reactor Study for the Values at 290 °C and the Temperature Dependencies from Vanrysselberghe and Froment29 value at 290 °C Ea or ΔH [kJ mol−1]

parameter

units

kDBT,dds kDBT,hyd kBPh kCHBKCHB,hyd KDBT,dds KH,dds KH2S,dds

[mol kgcat−1 h−1] [mol kgcat−1 h−1] [mol kgcat−1 h−1] [m3 kgcat−1 h−1] [m3 mol−1] [m3 mol−1] [m3 mol−1]

152.8 696 484 1.607 0.02768 1.092 × 10−3 0.0687

122.8 186.2 255.7 255.7 0 −113.2 −105.7

KBPh,dds KDBT,hyd KH,hyd KH2S,hyd

[m3 [m3 [m3 [m3

mol−1] mol−1] mol−1] mol−1]

0.0206 3.40 × 10−3 2.47 × 10−5 0.0162

−48.2 −76.8 −142.7 −105.7a

KBPh,hyd

[m3 mol−1]

0.112

Figure 17. Optimal fit obtained when ignoring radial mass-transport limitation for the DBT conversion and product selectivity as a function of the gas flow rate divided by the standard gas flow rate of 84 mLNTP min−1 in the milliflow reactor at 225 °C and standard reaction conditions (see Table 1).

−37.9

a

Value unavailable; for simplicity it is assumed to be the same as that for DDS.

of the parameter fitting with optimization of the same kinetic parameters in Table 7, but with ignoring the radial masstransport limitation. The poor fit of the conversion at low temperature (deviation i) could be improved by optimization of the activation energies and the adsorption enthalpies of the terms in the denominator having the largest impact on the reaction rates, which appear to be KH,dds and KH2S,dds, keeping the values of the rate and adsorption constants at 290 °C constant. The activation energies were estimated with the use of the modified Arrhenius equation in which the rate constant at the reference temperature, set at 653.15 K (290 °C), is decoupled from the activation energy:

were based on the results from our slurry reactor study together with the activation and adsorption energies from Vanrysselberghe and Froment. Using these initial estimates without any optimization, the fit is poor, as illustrated in Figures 15−17. The poor fit is

⎛ −Ea, j ⎧ 1 1 ⎫⎞ ⎨ − ⎬⎟⎟ kj = kj , Tref exp⎜⎜ Tref ⎭⎠ ⎝ R ⎩T

(25)

The same decoupling procedure is applied for the adsorption constants. The poor selectivities of the hydrogenated products above 250 °C (deviation ii) were improved by optimizing the rate constants of the hydrogenation reactions. This does not do much harm to the kinetic model fitted with the slurryreactor data at 290 °C since that experimental data set did not contain any data at full DBT conversion, where the (relatively slow) sequential hydrogenation reactions become important. The too-small influence of the liquid and gas flow rates on the conversion (deviation iii) was improved by introducing a simple nth order dependency of the effective gas−liquid

Figure 15. Simulation of DBT conversion and product selectivity as a function of reaction temperature in the milliflow reactor at standard reaction conditions using initial parameter estimates.

characterized by the following three main deviations: (i) a toolow conversion at temperatures below 200 °C, (ii) a too-low biphenyl selectivity and much too high bicyclohexyl selectivity at temperatures above 250 °C, and (iii) a too-small influence of the liquid and gas flow rates on the conversion. Deviations i and ii are clearly visible in Figure 15. Deviation iii is illustrated with Figures 16 and 17, which show the results K



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Table 8. Optimal Estimates of the Activation Energies, Adsorption Enthalpies, aGL’s, and Also the Flow Dependence Parameters nL and nG, Using All Experimental Data 95% conf range parameter

units

init est

opt est

value

relative

Ea(kDBT,dds) Ea(kDBT,hyd) kBPh at 290 °C Ea(kBPh) kCHBKCHB,hyd at 290 °C Ea(kCHBKCHB,hyd) ΔHads(KDBT,dds) ΔHads(KH,dds) ΔHads(KH2S,dds)

[kJ mol−1] [kJ mol−1] [mol kgcat−1 h−1] [kJ mol−1] [m3 kgcat−1 h−1] [kJ mol−1] [kJ mol−1] [kJ mol−1] [kJ mol−1]

122.8 186.2 484 255.7 1.607 255.7 0 −113.2 −105.7

15 181 93.7 128.9 1.61 92.7 fixed −101 −136

103 14 9.4 4.7 0.36 8.6 − 130 23

7.1 0.076 0.10 0.036 0.22 0.092 − 1.29 0.17

ΔHads(KBPh,dds) ΔHads(KDBT,hyd) ΔHads(KH,hyd) ΔHads(KH2S,hyd)

[kJ [kJ [kJ [kJ

−48.2 −76.8 −142.7 −105.7

fixed fixed fixed fixed

− − − −

− − − −

ΔHads(KBPh,hyd) aGLMilli(F0G,F0L) aGLMicro(F0G,F0L) nL nG obj function SSQ

[kJ mol−1] [m2 mbed−3] [m2 mbed−3]

−37.9 3900 18500 0 0 − 69269

fixed 441 1171 −0.71 0.54 1344 6240

− 116 331 0.26 0.28 − −

− 0.26 0.28 0.38 0.51 − −

mol−1] mol−1] mol−1] mol−1]

Table 9. Estimated Gas−Liquid Interfacial Areas (m2 mbed−3) and Comparison with the Worst-Case Scenario Illustrated in Figure 7

interfacial area, aGL, on the liquid and gas flow rate: aGL = a

⎛ F ⎞nL ⎛ F ⎞nG ⎜ L0 ⎟ ⎜ G0 ⎟ ⎝ FL ⎠ ⎝ FG ⎠

GL(FL0 , FG0)

(26) milliflow reactor microflow reactor

For the initial estimate of aGL, an arbitrary value of 100 times the value corresponding to the worst-case scenario defined with Figure 7 is used. With these adaptations the experimental data could be fitted successfully, yielding a much smaller sum of squared residuals (SSQ) of 6240 vs 69 269. Some of the parameters were not optimized (“fixed” in Table 8), since variation of these had hardly any influence on the fit. The simulations according to this fit are included in Figures 8−14. The fitted parameter values are, together with the initial estimates from Table 7 and the 95% confidence ranges, shown in Table 8. Table 8 shows that eight kinetic parameters could be estimated properly, although the activation energy of the DDS reaction and the hydrogen adsorption enthalpy in this reaction have rather large uncertainty ranges of about 100 kJ mol−1, which is due to the large correlation (see Table 10). Nevertheless, the statistics show that all parameters were significant. The results also show that the aGL values in both reactors as well as the aGL flow dependency parameters are statistically significant with relative errors of 50% or less. The estimated gas−liquid interfacial areas appear to be 6−10 times larger than those according to the worst-case scenario characterized by completely segregated flow as depicted in Figure 7; see Table 9. As might be expected because of its smaller scale, the aGL in the microflow reactor is about 3 times larger than that in the milliflow reactor. Table 9 also shows that the estimated interfacial areas are about 2 orders of magnitude smaller than the typically maximum achievable area, confirming indeed the rather poor gas−liquid contact in both reactors. The results of the parameter estimation show that the interfacial areas decrease with increasing liquid flow rate with a power of −0.71 and that they increase with increasing gas flow

estd

worst-case scenario

max possiblea

441 1171

39 185

15 000 109 000

a

The maximum possible gas−liquid interfacial area is assumed to be equal to the external particle surface area per volume reactor.

rate with a power of 0.54. The introduction of these flow dependency factors significantly improved the fit of the experiments in which the flow rate was varied. This gives additional confidence in the model regarding the effect of the limited radial dispersion. The negative power for the liquid flow is likely to be related to an increase of the liquid holdup and consequently a decrease of aGL. The effect of the gas flow is opposite. A closer look at the simulations of the experiments with the kinetic model including the radial mass-transport limitation shows that the component that causes the inhibition is clearly H2S: the slow transport of this reaction product from the catalyst through the liquid toward the gas flow causes accumulation of H2S in the liquid to concentrations which are about 1 order of magnitude higher than if there no radial mass-transport limitation. Since the value of KH2CH2 is about 3 and KH2SCH2S is about 13 at 65% conversion under typical conditions, this increases the denominator of the DDS rate equation (eq 7) by about a factor (3 + 13)/3 ≈ 5 since the DBT and BPh adsorption terms are both smaller than 1. It is noted that this is not predominantly the result of refitting of the H2S adsorption enthalpy in the DDS reaction since this value changed by only about 30 kJ mol−1. The strong inhibition of the DDS reaction by H2S is not surprising since it has been reported frequently.15,16,25,27,30,77 The model is unable to fit the higher selectivity to CHB and lower selectivity to BPh around 275 °C in the microflow reactor. Apparently, this difference is not directly related to the difference in radial mass-transfer limitation since the model L


1 −0.51

aGL,FL

1 0.49 −0.19

aGLMicro

0.35 0.23 0.62 −0.41 0.38 0.40 0.16 −0.03

0.70 0.71 0.41 −0.12

1 0.13 1 −0.00 0.29

1

1 0.93 0.48 −0.13

aGLMilli ΔHads(KH2S,dds) ΔHads(KH,dds) Ea(kCHBKCHB,hyd)

0.50 0.55 0.16 0.03

−0.12 −0.12 −0.04 0.01

For practical application of the radial mass-transport limitation criterion of eq 27, it is recommended to use the values of aGL in our study (eq 26 with the parameters in Table 9) as a first estimate. Our aGL values are about 1 order of magnitude higher than the values corresponding to complete segregation. Probably the flow pattern consisted of several parallel preferential tortuous gas channels as depicted in Figure 18. The radial dispersion coefficient Drad can be estimated using the equation from Delgado72 included in Table 5. A conservative estimate of the concentration at the interface, Ci,L,int, can be obtained by assuming thermodynamic equilibrium of the component between the gas and liquid phases. It is interesting to see the impact of this criterion in our results and to validate this criterion using the results of a study in a comparable packed-bed microflow reactor in which benzene hydrogenation over Ni/Al2O3 particles was investigated by Metaxas et al.78 The reactor, reaction, and catalyst characteristics are collected, together with those in our study, in Table 11. Although many characteristics are more or less comparable, ReL and the reaction rate are much higher in the case of Metaxas et al. The much higher ReL is mainly due to the much lower viscosity of the solvent used by Metaxas (pressurized hexane at 85 °C) compared to that of our solvent (hexadecane at 200 °C). The parameters were used to calculate the radial mass-transport criterion in eq 27. The results show that there is only a slight limitation concerning H2 in Metaxas’ study, whereas there is a strong limitation concerning H2S in our study, with Φrad values far above 1. The main difference between the radial masstransport limitation in our study and that of Metaxas et al. is the concentration of the rate-determining compound, being H2 in the benzene hydrogenation and the reaction-inhibiting H2S in

0.14 0.25 −0.31 0.30 aGLMilli aGLMicro aGL,FL aGL,FG

0.21 0.14 0.38 −0.28

−0.60 −0.59 −0.34 0.11

1 0.52 −0.00 −0.05 1 −0.24 0.11 −0.11 0.42 1 0.03 −0.22 −0.41 −0.22 −0.52 1 −0.12 −0.46 −0.00 −0.02 0.62 −0.10

kCHBKCHB,hyd at 290 °C Ea(kBPh) kBPh at 290 °C Ea(kDBT,hyd)

⎛ hL ⎞2 ⎛ n + 1 ⎞ (1 − εb)(1 − b)R v,obs i ⎟ =⎜ < 0.15 ⎟⎜ ⎝ ⎠ a 2 D C ⎝ GL ⎠ rad, i ,L i ,L,int (27)

1 −0.60 −0.12 0.38 −0.04 0.20 −0.83 0.44

Ea(kDBT,dds)

predicts almost exactly the same selectivity in both reactors, and it is thus probably the result of an aspect not accounted for in our kinetic rate expressions. Correlations between Estimated Parameters. The correlation matrix for the estimated parameters, presented in Table 10, shows that most correlations are small, indicating properly estimated independent parameters, but that there are two combinations of parameters with a rather high correlation coefficient: Ea(kDBT,dds) − ΔHads(KH,dds) and aGLMilli − aGLMicro. The first correlation is caused by the hydrogen-inhibition effect which dominates the denominator in the DBT DDS route reaction and the second correlation is caused by the good ability of the kinetic model to adapt the fit for the radial transport limitation. Evaluation of the Model with Radial Mass-Transport Limitation. Since the results obtained in our study yielded a clear proof of the existence of significant radial mass-transport limitations in the small gas−liquid packed bed used in our investigation, it is worthwhile to refine our rough worst-case scenario Weisz−Prater-type criterion on this phenomenon. Since our results show that the aGL values are about 1 order of magnitude larger than the value of the worst-case scenario in which the gas and the liquid are completely segregated, we conclude that our criterion (based on the worst-case scenario) can be relaxed accordingly. This then yields the following criterion for Φrad, the Weisz modulus for radial mass-transport limitation in small laboratory packed-bed reactors with particles of about 0.1 mm and low gas and liquid flows: Φrad

Ea(kDBT,dds) Ea(kDBT,hyd) kBPh at 290 °C Ea(kBPh) kCHBKCHB,hyd at 290 °C Ea(kCHB KCHB,hyd) ΔHads(KH,dds) ΔHads(KH2S,dds)

Table 10. Correlation Matrix between All the Parameters Estimated with the Optimized Kinetic Model

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aGL,FG


M



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is the case in our study since the DBT conversion rate via DDS is much larger than that via HYD and since the value of the term KH2SCH2S appears to be the largest term in the denominator of the rate equation, eq 7, under typical reaction conditions. It is noted that the transfer of the produced H2S to the gas phase is essential for the conversion. Without transfer the concentration would increase to 6.97 mol m−3 at complete DBT conversion, whereas it becomes about 0.75 mol m−3 in the presence of radial mass-transport limitation and about 0.13 mol m−3 in the absence of radial mass-transport limitation. Even the low concentration of 0.13 mol m−3 still has a significant inhibiting effect on the DDS reaction rate. It can thus be concluded that radial mass-transport limitation can be significant in small laboratory packed bed reactors with particles of about 0.1 mm and low gas and liquid flows and our refined Weisz−Prater type criterion of eq 27 can be used to estimate whether it is significant. The smaller microflow reactor in our study is slightly better concerning radial mass transport than is the milliflow reactor. The small but significant difference between both reactors can also be seen when looking carefully at the experimental data in Figures 10 and 11, in which the conversion in the microflow reactor is at all pressures about 3% higher than that in the milliflow reactor. Probably there are several possible experimental modifications that may help with increasing aGL and thus suppressing the radial mass-transport limitation in sensitive cases such as HDS with its H2S inhibition: increasing the gas flow rate and the liquid pressure drop by applying a longer bed (e.g., a spiralshape reactor tube) to achieve the same conversion or to apply external liquid recirculation.

Figure 18. Rough drawing of the real flow structure in the milli- and the microflow reactors used in this paper. The gas probably flows through several parallel preferential channels, whereas the other zones are always completely filled with liquid. This gas−liquid segregation is not as severe as in the worst-case scenario depicted in Figure 7; nevertheless it causes a significant radial mass-transport limitation.

■

CONCLUSIONS The investigation of the transport phenomena and the reaction kinetics of DBT HDS in laboratory-scale gas−liquid fixed beds showed that the small particle size used in these reactors has a

our study. The low H2S concentration largely magnifies the impact of the radial mass-transport limitation. Of course this only happens when there is indeed a significant H2S inhibition, which

Table 11. Comparison of Reaction and Reactor Aspects of Those in the Study of Metaxas et al. and Our Milliflow Reactor parameter

units

Metaxas et al.

milliflow reactor

microflow reactor

[kg m−1 s−1] [mol mparticle−3 s−1] [m2 s−1]

0.25 15 0.35 0.75a 0.81 0.09 0.87 1.3 × 10−7 0.031 0.0009 0.79 1.7 × 10−5 0.99 5.6 × 10−8

0.125 25.6 0.505 0.75 0.34 0.0027 1.27 8.3 × 10−7 0.0081 0.024 0.0058 3.7 × 10−4 0.0144 1.1 × 10−8

0.055 2.2 0.35 0.75 0 0.022 10.3 6.8 × 10−6 0.0016 0.036 0.0021 3.7 × 10−4 0.0144 1.1 × 10−8

[m2 s−1]

n.a.

6.0 × 10−9

6.0 × 10−9

dp (diluent) dt εb hL b uL uG CapL Eö Oh ReL μL Robs v,i Drad,H2,L

[mm] [mm]

Drad,H2S,L

[mm s−1] [mm s−1]

−3

CH2,L,int

[mol m ]

40.9

45.2

45.2

CH2S,L,int

[mol m−3]

n.a.

0.13b

0.13b

500 0.12

441 0.03

1171 0.008

n.a.

17.4

4.9

aGL Φrad,H2 Φrad,H2S

2

−3

[m mbed ]

c

Estimate. Concentration at the gas−liquid interface; in the presence of radial mass-transport limitation using the optimal fit of the kinetics and the aGL parameters the concentration of H2S in the bulk is about 0.75 mol m−3. cConservative estimate to facilitate the comparison with our results; due to the higher ReL, however, the real value will probably be higher. a

b

N



Article

dslab = thickness of the slab representing the liquid zone [m] dt = internal reactor tube diameter [m] dP/dh = pressure drop per unit of bed height [Pa m−1] Drad,i,L = effective radial dispersion component i in the liquid phase [m2 s−1] Di,eff = effective diffusivity inside the catalyst particles [m 2 s −1] Di,L = bulk diffusivity component i in the liquid phase [m2 s−1] Drad,i,L = effective radial dispersion component i in the liquid phase [m2 s−1] Ea,j = activation energy of reaction j [J mol−1 K−1] Eö = Eötvös number Fi = actual flow rate (i = L, liquid; i = G, gas) [mol s−1] Fi,0 = standard flow rate (i = L, liquid; i = G, gas) [mol s−1] g = acceleration due to gravity [m s−2] hb = catalyst bed height [m] hL = liquid holdup (i.e., fraction of bed voidage filled with liquid) [m3 mvoid−3] Hi = gas−liquid equilibrium distribution coefficient (Henry) [mol mgas−3/(mol mliq−3)] k = specific rate constant (expressed per catalyst weight unit) [unit depends on reaction] ki,j = rate constant of reactant i in reaction j [mol kgcat−1 h−1] kj,T = rate constant of reaction j at temperature T [mol kgcat−1 h−1] kj,Tref = rate constant of reaction j at the temperature Tref [mol kgcat−1 h−1] kGL,i = gas−liquid mass-transfer coefficient for component i [m s−1] kLS,i = liquid−catalyst mass-transfer coefficient for component i [m s−1] Ki,j = adsorption constant of component i in reaction j [mliq3 mol−1] Keqi−k = thermodynamic equilibrium constant between component i and k [mliq9 mol−3] lch = chord length of the G−L interfacial area in the worstcase scenario [m] n = reaction order Oh = Ohnesorge number ΔP = pressure drop [bar] Ptot = total pressure [bar] Pem,r = Péclet number for radial dispersion Pep,ax = particle Péclet number for axial dispersion rc = radius of the imaginary cylindrical liquid-only zone [m] rj = reaction rate of reaction j [mol kgcat−1 h−1] Re = particle Reynolds number Robs v,i = observed volumetric reaction rate of component i [mol mparticle−3 s−1] R = ideal gas constant [J mol−1 K−1] Sc = Schmidt number = μL/(ρLDi,L) T = temperature [K] Tref = reference temperature = 563.15 K [K] u0,G = superficial gas velocity [m s−1] u0,L = superficial liquid velocity [m s−1] Vp = particle volume [m3] WHSV = weight-hourly space velocity = ratio of liquid mass flow rate/catalyst weight [h−1] Xdil = conversion obtained in the diluted bed z = axial coordinate (in the bed) [m]

tremendous effect on the hydrodynamic phenomena compared to those in an industrial-scale trickle bed consisting of large catalyst particles. Small particles are intrinsically coupled with strong capillary forces, resulting in a poor radial dispersion in the reactor and thick liquid layers, making the gas transport through these layers often rate limiting. The gas tends to flow along preferential channels, causing the existence of larger zones in which there is only liquid. These issues apply particularly with reactions inhibited by reaction products, such as in HDS, since these products can easily accumulate in the liquid zones. Industrial-scale reactors, containing large particles, do not suffer from these issues. The effects are hardly influenced by applying dilution of the catalyst with inert particles. The modeling work in this study showed that the radial transport limitation of H2S has a significant influence on the conversion and that the effect decreases with increasing gas flow rate but increases with increasing liquid flow rate. By using the kinetic parameters obtained for the P-doped NiMo/Al2O3 catalyst at 290 °C in slurry reactor experiments in the absence of any transport limitations, the Langmuir− Hinshelwood−Hougen−Watson (LHHW) type rate expressions as a function of temperature could be fitted properly in the ranges 100−350 °C and 10−50 bar, if the effect of the radial limitation is accounted for. This radial mass-transport limitation, expressed using a Weisz modulus for radial dispersion (Φrad), could approximately be described with gas−liquid interfacial areas of about 400 and 1200 m2 mbed−3 for the milli- and microflow reactors in our study, respectively. These results were used to propose the Weisz−Prater-type criterion shown in eq 27 for the estimation of the contribution of poor radial dispersion in catalyst performance testing. This criterion shows that the reactor performance can be improved by increasing the gas−liquid interfacial area and the radial dispersion, which can be achieved by applying larger particles and/or both higher gas and liquid velocities.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.:+31-15-2784316. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

NOTATION aGL = effective gas−liquid interfacial area [m2 mbed−3] aLS = liquid−catalyst interfacial area = (1 − εb)(1 −b)aLS,p [m2 mbed−3] aLS,p = liquid−catalyst interfacial area per unit of particle volume [m2 m−3] aGL,FL,0,FG,0 = effective gas−liquid interfacial area at the standard flows [m2 mbed−3] aGL,FL = dependency factor of aG with the liquid flow rate aGL,FG = dependency factor of aGL with the gas flow rate Ap = particle external surface area [m2] b = volume of inert material as fraction of total solids [minert3 minert+cat−3] Ca = Carberry number CapL = capillary number Ci,L = liquid concentration of component i [mol m−3] Ci,G = gas concentration of component i [mol m−3] Ci,L,GL‑interface = liquid concentration at the G−L interface [mol mliq−3] dp = catalyst particle diameter [m]

Greek Symbols

Δ = maximum acceptable relative deviation εb = bed voidage [m3 mbed−3] εp = catalyst particle porosity [m3 mparticle−3]

O



Article

ϕ = Thiele modulus η = efficiency ξ = dimensionless radius (ξ = r/rc) μL = liquid viscosity [kg m−1 s−1] νi,j = stoichiometric coefficient in the reaction ρF = fluid density (with F = G, gas; F = L, liquid) [kg m−3] ρp = catalyst particle density (dry) [kg mparticle−3] σL = liquid surface tension [N m−1] τb = bed tortuosity Φ = Weisz modulus for internal diffusion limitation Φrad = Weisz modulus for radial mass transfer

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