Energy & Fuels 2002, 16, 647-652
647
Evaluation of Kinetic and Hydrodynamic Models in the Hydroprocessing of a Trickle-Bed Reactor Marı´a A. Callejas and Marı´a T. Martı´nez* Instituto de Carboquı´mica CSIC, Apartado 589, 50080 Zaragoza, Spain Received August 2, 2001. Revised Manuscript Received November 27, 2001
In this paper, the influence of the hydrodynamic effects on the plug flow model deviation in the hydrodesulfuration (HDS) and hydrodemetalation (HDM) reactions of a petroleum residue is evaluated. The study has been carried out in a small pilot scale trickle bed reactor in continuos operation at 375 °C and 10 MPa of partial hydrogen pressure with a commercial NiMo/alumina catalyst. The nickel removal reaction, a first-order liquid-limited reaction, was used to test the predictions of several models, which incorporate the influence of the hydrodynamics on the catalyst utilization. For this task, additional experiments in a stirred tank reactor at the same conditions were done in order to determine the value of the effectiveness factor for denickelation reactions. Comparison of model predictions and experimental data indicates that the use of a hydrodynamic parameter in the models improves the data fit.
Introduction For about 40 years, chemical engineers’ attention has been addressed to trickle-bed reactors (TBRs), owing to their suitability for many operations on chemical, oil refining, petrochemical, and biochemical processes. They have been also used in laboratory units in order to evaluate catalyst efficiency, study chemical kinetics and predict the behavior of industrial-scale reactors.1-3 Laboratory kinetic studies on desulfurization, denitrogenation, dearomatization, and cracking reactions occurring during hydrotreatment are mainly attempted by the use of bench-scale trickle-bed reactors operating at industrial conditions. Evaluation of kinetic data obtained in single phase, continuous stirred tank reactors are a comparatively simple task. The interpretation of the kinetic results in small pilot scale TBRs poses a number of relevant questions. In the analysis of data, one is faced with an assessment of the relative importance of the various mass transfer resistances (gas-liquid, liquid-solid, back-mixing, etc.) and flow behavior (e.g., holdup and incomplete catalyst wetting) effects, as well as the interaction of these effects with the conversion levels observed in the reactor. All these effects affect the behavior of the trickle bed reactors reducing its efficiencies, and therefore, these have to be considered and accounted for in the description of reaction kinetics. In the literature, we can find several “hydrodynamic” models, which incorporate the influence of the hydro* Author for correspondence. Instituto de Carboquı´mica, P.O. Box 589, Zaragoza, Spain. Fax: 34976733318. E-mail: mtmartinez@ carbon.icb.csic.es. (1) de Wind, M.; Plantenga, F. L.; Heinerman, J. J. L.; Homanfree, H. W. Appl. Catal. 1988, 43, 239-252. (2) Carrruthers, J. D.; di Camillo, D. J. Appl. Catal. 1988, 43, 253276. (3) Sie, S. T. Revue de L’Institut Franc¸ ais du Petrole 1991, 46, 501515.
dynamics on the catalyst utilization. Greenfield and Sudarmana4 presented an overview of models of trickle beds. The most important and applied models to isothermal kinetic hydrotreating data for petroleum derived feedstocks obtained in standard small scale pilot plant trickle bed units have been the following: Henry and Gilbert5 developed a reactor model that ignored axial dispersion and attributed the lower conversions in laboratory reactors to changes in the external liquid holdup. Mears6 developed a similar model, which replaced the liquid hold-up with the effective wetting of the external catalyst surface and catalyst effectiveness factor. This model, which ignored axial mixing, predicted plug-flow conversions in the pulsing-flow regime, in which the fractional wetting is unity. Dudukovic7 suggested that the effectiveness factor and partial surface-wetting effects were coupled and local phenomena and he incorporated both the external and internal partial wetting effects into the definition of Thiele modulus for nonvolatile, liquid-phase reactant-limited reactions, developing other model. The present study aims to examine the possibility of incorporating chemical and hydrodynamic complexity in the kinetic analysis of hydrotreating reactions in a pilot trickle-bed reactor. The removal of sulfur, vanadium, and nickel from a heavy residual oil was examined, using a commercial catalyst. We first briefly analyze the role of the hydrodynamic effects on these kinetics, and then we analyze the data derived from nickel removal reactions on the basis of Henry and Gilbert,5 Mears,6 and Dudukovic7 models. (4) Greenfield, P. F.; Sudarmana, D. Residence-Time Modeling of Trickle-Flow Reactors. In Encyclopedia of Fluid Mechanics; Cheremisinoff, N. P., Ed.; Gulf Publishing Co.; Houston, TX, 1986. (5) Henry, H. C.; Gilbert, J. B. Ind. Eng. Chem. Process Des. Dev. 1973, 12, 328-334. (6) Mears, D. E. Chem. Eng. Sci. 1971, 26, 1361-1365. (7) Dudukovic, M. P. AIChE J. 1977, 23, 940.
10.1021/ef010203o CCC: $22.00 © 2002 American Chemical Society Published on Web 02/19/2002
648
Energy & Fuels, Vol. 16, No. 3, 2002
Callejas and Martı´nez
Table 1. Properties of the Feedstock and of the Catalyst Used oil residue BP: 540 °C (vol %) sulfur (wt %) nitrogen (wt %) nickel (ppm) vanadium (ppm) asphaltenes (wt %) Conradson carbon (wt %) density g/mL (50 °C) kinematic viscosity, (cSt) 50 °C 100 °C 120 °C dynamic viscosity, (cP) 50 °C 100 °C 120 °C surface tension (kg s-2) BP > 540 °C cut properties asphaltenes (wt %) Ramsbottom carbon (wt %) sulfur (wt %) nickel (ppm) vanadium (ppm) catalyst NiO (wt %) MoO3 (wt %) Surface area (m2/g) Pore volume (cc/g) Pore diameter (Å) bulk density (kg/L) (sock loaded, 1/20 in. threelobes)
63.3 3.45 0.28 45.17 242.12 8.60 11.22 0.9245 111.5 16.5 9.2 103.1 14.73 8.11 31.04 10-3 15.39 30.4 4.84 142 562.4 2.0 6.0 140 0.60 150 0.58
Experimental Section The petroleum residue used as feed has a heavy nature as indicated by the high metal content (45.17 ppm of nickel and 242.12 ppm of vanadium), the sulfur content, 3.45 wt %, and the high dynamic viscosity (103.1, 14.73 and 8.11 cP at 50, 100, and 150 °C, respectively). Other feedstock properties are shown in Table 1. In this process, a commercial catalyst, Topsoe TK-711 (6 wt % MoO3 and 2 wt % NiO), supported on γ-Al2O3 and in the form of 1/20 in. diameter three-lobes particles was used. This catalyst was specially developed for pretreatment of residual oils for reduction of metals. Important physical properties of the catalyst such as surface area, pore volume, pore diameter and bulk density are listed in Table 1. Prior to HDS and HDM experiments, the catalyst was presulfided for 10 h at 350 °C at ambient pressure, under a hydrogen flow containing 10 vol. % of H2S. The temperature step increase to 350 °C was 25 °C/h. Experiments were carried out in a continuous way in a small pilot scale trickle bed reactor (1 in. inside diameter and 0.8 m in length). A flow sheet and more details have been reported elsewhere.8 The experimental conditions studied were at 375 °C, 10 MPa of hydrogen pressure, and 0.2 Kg/Kg ratio gas/ liquid. The liquid hourly space velocities, LHSV, ranged between 0.45 and 1.48 l/h gcat, the superficial liquid velocity was varied from 0.0197 to 0.066 kg/m2s, and the superficial gas velocity from 0.00223 to 0.00986 kg/m2s. To estimate the effectiveness factor for nickel removal reactions, additional experiments were carried out in a continuous stirred tank reactor (CSTR). The reactor has a capacity of one liter in which the catalyst is held in four baskets having a total volume of about 185 cm3. The details of the experimental setup have been reported elsewhere.9 The feedstock was passed through the reactor at the same conditions of (8) Martı´nez, M. T.; Ferna´ndez, I.; Benito, A. M.; Cebolla, V. L.; Miranda, J. L.; Oelert, H. H. Fuel Proc. Technol. 1993, 33, 159-173. (9) Trasobares, S.; Callejas, M. A.; Benito, A. M.; Martı´nez, M. T.; Severı´n, D.; Brouwer, L. Ind. Eng. Chem. Res. 1998, 37, 11-17.
temperature and pressure than the experiments in TBR and several values of LHSV, between 0.41 and 7.1 l/h gcat, were tested. In this study, two different sizes of catalyst were used. Three runs were conducted with a catalyst pellet size of 1.27 mm in the form of 1/20 in. diameter three-lobes particles, and another set of three runs were conducted with the catalyst crushed and sieved to a range of particle size between 53 and 530 µm. To ensure the kinetic data are free from the influence of the interphase gradients, two diagnostic tests have been done.10 The results indicated that the influence of external mass-transfer resistance on the reaction rate was negligible at 3500 rpm stirring speed and 0.2 Kg/Kg gas/liquid ratio. The contents of sulfur and metals of the feedstock and of the hydrotreated residue oil samples were determined in an analyzer Antek 7000 Elemental and by inductively coupled plasma optic emission spectrometry (Perkin-Elmer Model P-400), respectively. Conversions were determined from the disappearance of reactant.
Results and Discussion Specifically TBRs are used when a reaction catalyzed by a solid catalyst must be carried out between at least two components, one in a gas and the other in a liquid phase. Due to gas and liquid flowing concurrently through a catalyst bed, the behavior of this kind of reactor is rather complex, because fluid dynamics and reaction kinetics are closely interlinked and their effects on the conversions are inseparable. Therefore, to properly know the behavior of the trickle-bed reactors, hydrodynamic parameters such as the liquid holdup, the degree of catalyst wetting and the mixing of the fluids are important and must be considered. For this reason, values of these parameters in our experimental conditions have been estimated with correlations met in the literature. The liquid holdup, hL, and wetting efficiencies, ηCE, values have been estimated with Ring and Missen11 correlations since it is the only known study where measurements and correlations have been obtained at such high-severity conditions of temperature and pressure (hydrogenation of dibenzothiophene in a heavy oil at 10 MPa and 330-370 °C). The obtained values have been between 0.01 and 0.023 for the holdup and 0.12 and 0.24 for the wetting efficiencies. In trickle-flow hydrotreating in pilot scale reactors, it is observed decreases in reactor efficiency at low mass velocity which could not be attributed to transport limitations in the boundary layer or “film” around individual particles. It could exist the possibility that axial dispersion might be responsible. The present analysis applies different general criteria for predecting when such effects will be important. A criterion for liquid limiting reactions based on the minimum bed-length required to neglect axial dispersion effect on three-phase reactors behavior was early developed by Mears12 and was slightly modified later by Gierman.13 Later, Cassanello et al.14 formulated a (10) Martı´nez, M. T.; Callejas, M. A.; Trasobares, S.; Severı´n, D., Brouwer, L.; Kelemidou, K.; Ko¨necke, I.; Carbo´, E.; Jime´nez, J. M.; Go´mez, F. J.; Rial, C.; Herna´ndez, A.; Aguilar, C. Final Report Contract Nο. JOU2-CT92-0206, 1996. (11) Ring, Z. E.; Missen, R. W. Can. J. Chem. Eng. 1991, 69, 10161020. (12) Mears, D. E. Ing. Eng. Chem. Process Des. Dev. 1971, 10, 541. (13) Gierman, H. Appl. Catal. 1988, 43, 277-286. (14) Cassanello, M. C.; Cukierman, A. L.; Martı´nez, O. M. Chem. Eng. Technol. 1996, 19, 410-419.
Hydroprocessing of a Trickle-Bed Reactor
Energy & Fuels, Vol. 16, No. 3, 2002 649
Table 2. Concentration (ppm) and Conversions (%) of Sulfur, Nickel, and Vanadium in the Products Obtained from Kinetic Experiments in the TBR LHSV (l/h gcat)
S
Ni
V
XS
XNi
XV
0.45 0.71 1.11 1.48
15500 18100 20400 22300
23.27 26.39 29.45 30.79
82.09 104.12 123.61 134.06
55.1 47.5 40.9 35.4
48.5 41.6 34.8 31.8
66.1 57 48.9 44.6
general criterion, valid both for liquid and gaseous limited reactions, based on the development of an approximate solution of the axial dispersion model. By applying those criteria12-14 to our case, we found that the effects of axial dispersion could be considered significant. Hence, it was thought necessary to include the influence of the hydrodynamics in the kinetic expression and so to apply models, which took into account these effects. The consideration of these effects will improve the modeling in terms of data fit and therefore they need to be accounted. The holdup model of Henry and Gilbert5 and the catalyst wetting model of Mears6 account for the influence of the hydrodynamics in the kinetic expression adding 1 - R as exponent of the LHSV, R being 1/3 and 0.32, respectively, and defining a rate constant, K′, which includes a constant, b, dependent upon the catalyst dimensions and other fluid properties. The resulting expression for a first-order reaction was
ln
Co K′(L)R ) C (LHSV)1-R
(1)
where Co and C are the concentrations of metal or sulfur at the reactor inlet and the outlet, respectively; LHSV is the liquid hourly space velocity; and L is the length of the catalyst bed. In our experiments, L has been constant, and therefore, a new kinetic constant, K′′, has been defined
Co K′′ ) C (LHSV)1-R
ln
Table 3. Concentration and Conversions (%) of Sulfur, Nickel, and Vanadium in the Products Obtained from Kinetic Experiments in the CSTR catalyst/LHSV (pellets-crushed)/ (l/h gcat) crushed/2.4 crushed/4.8 crushed/7.1 pellets/0.41 pellets/1.22 pellets/1.64
S (wt %)
Ni (ppm)
V (ppm)
XS
XNi
XV
2.24 2.53 2.74 1.40 2.19 2.42
20.58 26.68 31.39 9.1 30.2 36.9
62.38 103.54 148.27 23.1 115.7 165.9
37.2 28.9 22.4 59.4 36.5 29.9
55.9 42.7 32.1 79.9 33.1 18.3
75.1 58.5 40.1 90.5 52.2 31.5
Table 4. Apparent Rate Constants, K′′, and Values of r Defined by Equation 2 element
K′′
1-R
R
S Ni V
2.1 × 10-5 (l/h gcat)0.67 (1/ppm) 0.46 (l/h gcat)0.47 9.34 ppm0.5 (l/h gcat)0.41
0.67 0.47 0.41
0.33 0.53 0.59
when hydrotreating oil from Kuwait, implied that, in a reacting system, the power-law coefficient might be dependent upon the reaction conditions (e.g., temperature) as well as the nature of the reaction. These authors obtained values of slopes between 0.532 and 0.922 for the HDS and HDM reactions, respectively. The nickel removal reaction, which is a liquid limited reaction system of known kinetics (first order in the liquid reactant15), was employed to test the ability of the models of Henry and Gilbert,5 Mears,6 and Dudukovic7 to predict the performance of a trickle bed reactor. While the models of Henry and Gilbert and of Mears have been utilized to correlate a limited number of industrial data, the intuitively appealing more general model of Dudukovic has been experimentally tested in few studies.17 Henry and Gilbert developed a reactor model, a modified plug flow model, that ignored axial dispersion and attributed the lower conversions in laboratory reactors to changes in the external liquid holdup, hL, which for a first-order reaction takes the form below:
(2)
where K′′ ) K′(L)R. In Table 2, the sulfur, nickel, and vanadium contents of the products and the conversions are shown. From the log-log plots of ln(Co/C), (1/C) - (1/Co), and 2(Co0.5 - C0.5) vs 1/LHSV for nickel-, sulfur-, and vanadiumremoval reactions, (first, second, and half intrinsic kinetic orders,15 respectively), the values of K′′ and R have been obtained. These plots are described in Figures 2-4, and the values of the parameters R and K′′ are indicated in Table 4. It can be observed in this table that the value of R for the HDS reaction is the same as that employed by Henry and Gilbert.5 However, for the HDM reactions, the values of the slopes (1 - R) are different and lower than those found by Henry and Gilbert5 for HDS and Mears,6 indicating that these reactions are more influenced by the hydrodynamics than the HDS reaction. A slight temperature dependence of the slopes and the nature of the reactions, observed by Paraskos et al.16 (15) Callejas, M. A.; Martı´nez, M. T. Energy Fuels 1999, 13, 629636. (16) Paraskos, J. A.; Frayer, J. A.; Shah, Y. T. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 315-322.
ln
K*ηhL
(1 -1 X) ) LHSV
(3)
where X is the conversion, K* is the intrinsic kinetic constant, and η is the effectiveness factor. Mears6 developed a similar model, which replaced the liquid holdup with the effective wetting of the external catalyst surface (i.e., the fraction of the external catalyst area wetted by flowing liquid), ηCE. His design equation is
ln
K*ηηCE
(1 -1 X) ) LHSV
(4)
An overall trickle bed effectiveness factor model was developed by Dudukovic.7 In this model, Dudukovic suggested that the effectiveness factor and partial surface wetting effects were coupled local phenomena. He incorporated both the external and internal partial wetting effects into the definition of the Thiele modulus for nonvolatile, liquid-phase reactant limited reactions and arrived at the following formulation for the overall (17) Wu, Y.; Al-dahhan, M. H.; Khadilkar, M. R.; Dudukovic, M. P. Chem. Eng. Sci. 1996, 51, 2721-2725.
650
Energy & Fuels, Vol. 16, No. 3, 2002
Callejas and Martı´nez
Table 5. Intrinsic and Apparent Rate Constants and Effectiveness Factor for Nickel Removal Reactions (in Parentheses, the Standard Errors of the Estimated Coefficients) η K* units correlation coefficient standard error of estimation Kapp units correlation coefficient standard error of estimation
3.2 (0.17) l/h gcat 0.99 8.5 × 10-2 1.46 (0.39) l/h gcat 0.93 1.04
0.45
effectiveness factor of a partially wetted pellet, ηTB, which accounts for both external (film) and internal effects.
( ) ( )
ηiφ ηCE tan h φ ηCE ηTB ) ηi φ φ 1+ tan h Bim ηCE
Figure 1. First-order kinetic plot based on eq 2 for the nickel removal reaction.
(5)
where ηi is the internal fractional wetting, φ is the Thiele modulus, and Bim is the Biot number for liquidsolid mass transfer. Due to capillary forces, ηi is commonly assumed to be unity18,19 and the reactor design equation for a first-order reaction based on assumed plug flow of the liquid is
ln
K*ηTB
(1 -1 X) ) LHSV
(6)
Figure 2. Second-order kinetic plot based on eq 2 for the sulfur removal reaction.
When the external mass transfer resistance is negligible and the Thiele modulus is large, the trickle bed effectiveness factor is closely approximated by the relationship
ηTB,∞ ) ηCEη
(7)
and the design eq 6 is reduced to eq 4, developed by Mears.6 To apply the different models mentioned above (eqs 3, 4, and 6), it was necessary to estimate the effectiveness factor experimentally for the nickel removal reactions. Therefore, additional experiments with two different sizes of catalyst were carried out in a continuous stirred tank reactor. The reactions in which the effects of intraparticle diffusion are important, for instance, for the kinetic experiments carried out with the catalyst in pellets, the simple mass action kinetic expression of the removal rate, rd, for first kinetic order is modified by the effectiveness factor,
rd ) ηK*CS
(8)
CS being the nickel concentration at the pore mouth of the catalyst. (18) Schwartz, J. G.; Weyer, E.; Dudukovic, M. P. AIChE J. 1976, 22, 894-905. (19) Ramachandran, P. A.; Smith, J. M. AIChE J. 1979, 25, 538.
Figure 3. Half-order kinetic plot based on eq 2 for the vanadium removal reaction.
Substituting the effectiveness factor in eq 8, the resulting expression is
rd ) hyp tan(Vp/Sx)
x
x
K/v /(V /S ) De p x
K/v K*CS De
(9)
Vp being the volume of the catalyst pellet, Sx the external surface area of the catalyst pellet, K/v the intrinsic rate constant defined in function of the cubic centimeters of oil and of porous structure, and De the effective diffusivity of the nickel-containing compounds in the catalyst pores.
Hydroprocessing of a Trickle-Bed Reactor
Energy & Fuels, Vol. 16, No. 3, 2002 651
Figure 4. Comparison of different model predictions and experimental data for nickel removal reactions.
If the eq 9 is expressed in two terms, a constant term and other one in function of the concentration, we can define an apparent rate constant
Kapp ) hyp tan (Vp/Sx)
x
K/v /(V /S ) De p x
x
K/v K* De
(10)
The calculus of the effectiveness factors, defined as the ratio of the actual rate of reaction, rd, to the rate which would occur with no resistance to heat and mass transfer inside the pellet, r, will confirm the effect of particle size on reaction rate in the hydrotreatment. From this definition, effectiveness factor for a first kinetic order removal reaction has the following form:
η)
rd ) (KappCS)/(K*CS) ) (Kapp/K*) r
(11)
The data of concentration at different LHSVs (Table 3) working with the crushed catalyst, assuming absence of intraparticle gradients, and with the catalyst in pellets were fitted with the equation corresponding to an heterogeneous perfectly mixed system working continuously and after steady-state conditions had been reached
Co - C )
K*C LHSV
(12)
Values of the intrinsic and apparent rate constants are shown in Table 5. The value of the effectiveness factor has been calculated according to the eq 11, and it is also indicated in Table 5. By substituting the value of the effectiveness factor, the liquid holdup and the wetting efficiency, the predictions based on eqs 3 and 4 could be made and these comparisons together with the experimental results are illustrated in Figure 4. To test the predictions from the eq 6, it was necessary to estimate the Biot number. The
Biot number required the knowledge of liquid-solid mass transfer coefficient, which was obtained at each liquid flow rate from the correlation of Dharwadkar and Sylvester20 and of the effective diffusivity, which was obtained experimentally from the value Kapp (eq 10). In addition, we tested the form of the effectiveness factor suggested by Beaudry et al.21 which has been successfully used to interpret the data for a gas limited reaction. These authors represented the catalyst particles as an assembly of externally half-wetted, totally wetted, and completely unwetted slabs and proposed the overall effectiveness factor for the assembly as
ηa ) (1 - ηCE)2ηd + 2ηCE(1 - ηCE)η1/2 + η2CEη
(13)
For a liquid limited reaction, ηd ) 0 and η1/2 is the overall effectiveness factor of a pellet of twice the actual modulus i.e., φ1/2 ) 2φ. By calculating ηTB (eq 5) and ηa (eq 13) with our experimental values, the reactor model represented by eq 6 has been tested and represented together with the predictions from Henry and Gilbert5 and Mears6 models in Figure 4. In Figure 4, it can be observed that eq 4 utilizing contacting efficiency of unity, ηCE ) 1, plug flow model, overpredicts the experimental data considerably clearly illustrating the need for properly accounting for incomplete particle wetting. However, all equations that have incorporated some hydrodynamic factors have underpredicted them. Equation 6 (Dudukovic model) with ηa from eq 13 predicts experimental results very similar to those from the eq 4 (Mears model). It is observed the same behavior with the eq 3 (Henry and Gilbert model) and the eq 6 (Dudukovic model), with ηTB from eq 5. The two first equations approach better to the experimental data than Henry and Gilbert and Dudukovic models confirming that both contacting efficiency and (20) Dharwadkar, A.; Silvester, N. D. AIChE J. 1977, 23, 376-378. (21) Beaudry, E. G.; Dudukovic, M. P.; Mills, P. L. AIChE J. 1987, 33, 1435.
652
Energy & Fuels, Vol. 16, No. 3, 2002
external transport resistance need to be accounted for liquid limited reactions at high Thiele moduli being less important the influence of the holdup. In general, the predictions of the models were superior at low levels of conversion. Conclusions The study outlined in this paper indicates that the hydrodynamic effects need to be accounted in the hydroprocess kinetics of desulfuration and demetalation of a petroleum residue in a small pilot scale trickle bed reactors. The slope of ln(Co/C) vs 1/LHSV (at otherwise constant reaction conditions) was assumed to be 2/3 by Henry and Gilbert5 and 0.68 by Mears,6 for sulfur removal reactions. In the present study, the values of the slopes were 0.66, 0.47, and 0.41 for the sulfur, nickel, and vanadium removal reactions, respectively, indicating that HDM reactions are more influenced by the hydrodynamics that HDS reaction. The comparison of predictions of the different models (Henry and Gilbert,5 Mears,6 and Dudukovic7) to the nickel removal reaction has confirmed that both contacting efficiency and external transport resistance need to be accounted for liquid limited reactions at high Thiele moduli being less important the influence of the holdup. The results using the correlation of Beaudry et al.21 in the Dudukovic7 model have been similar to those obtained with the model of Mears,6 and these are capable of predicting in a better manner the experimental results than the Henry and Gilbert5 model. Generally, the predictions of the models were superior at low levels of conversion. Acknowledgment. This work was sponsored by the UE contract No JOU2-CT92-0206 and the Spanish DGICYT project AMB93-1137-CE.
Callejas and Martı´nez
Nomenclature Bim ) Biot number for mass transfer (dimensionless) C, Co ) reactant concentration at the reactor inlet and the outlet, respectively, ppm CS ) reactant concentration at the pore mouth of the catalyst, ppm De ) effective diffusivity, m2/s hL ) external liquid holdup K* ) intrinsic rate constant K′ ) rate constant defined in eq 1, ) Kb K′′ ) rate constant defined in eq 2, ) K′(L)R K/v ) intrinsic rate constant defined in function of the cubic centimeters of oil and of porous structure. Kapp ) apparent kinetic constant (defined in eq 12) L ) length of the catalyst bed LHSV ) liquid hourly space velocity, l/h gcat rd) removal rate for first kinetic order ) ηK*CS Sx ) external surface area of the catalyst pellet, m2 Vp ) volume of the catalyst pellet, m3 X ) conversion, % Greek Letters R ) parameter defined in eq 1 η ) single fluid-phase catalyst pellet effectiveness factor ηCE ) fraction of external catalyst surface which is wetted with active liquid ηi ) fraction of internal catalyst void volume which is wetted (eq 5) ηa ) global (overall) effectiveness factor, defined by eq 13 ηTB ) global (overall) effectiveness factor, defined by eq 5 η1/2 ) overall effectiveness factor of a pellet of twice the actual modulus, eq 13 EF010203O
