Ind. Eng. Chem. Res. 1993,32, 1603-1609
1603
Restrictive Diffusion under Hydrotreating Reactions of Heavy Residue Oils in a Trickle Bed Reactor Ming-Chang Tsai and Yu-Wen Chen' Department of Chemical Engineering, National Central University, Chung-Li 32054, Taiwan
Chiuping Li Refining & Manufacturing Research Center, Chinese Petroleum Corporation, Chia- Yi 60036, Taiwan
The effect of the ratio of reactant molecular diameter to catalyst pore diameter on the restrictive diffusion under hydrotreating reactions of heavy residue oils over CoMo/alumina-aluminum phosphate catalysts was investigated. Hydrotreating reactions of residual oils were carried out in a trickle bed reactor a t 663 K and 7.6 MPa over a series of CoMo/alumina-aluminum phosphate catalysts. The results showed that the restrictive effect under reaction conditions is still severe. The values of the effective diffusivities and the relevant effectiveness factors for hydrodesulfurization (HDS) and hydrodemetalation (HDM) reactions were determined by applying the Thiele relation t o catalytic reactions. The effective diffusivities for the HDM reaction are always smaller than those for the HDS reaction. In addition, the effective diffusivity values decreased with increasing ratios of reactant molecular diameters to catalyst pore diameters for both HDS and HDM reactions, indicating a large restrictive diffusion effect.
Introduction Residual oils usually contain a high proportion of sulfur and metal contaminants. These not only contribute to the problem of air pollution but also cause catalyst deactivation in most refining processes such as hydrotreating and fluid catalytic cracking operation. Therefore, an upgrading process is required to remove most of the sulfur and metals for the effective use of residual oils as fuel oils or as charge stocks for cracking and hydrocracking operations. Hydrodesulfurization (HDS) and hydrodemetalation (HDM)reactions of residual oils involve the mass transport of large molecules into the catalyst pores. The molecular size distributions of these heavy feedstocks range from 2.5 to 15 nm, the majority being around 5 nm (Ohtsuka, 1977; Ruckenstein and Tsai, 1981; Dai et al., 1990). Therefore, the residue hydrotreating is strongly influenced by the intraparticle diffusion limitation since the dimension of the reactant molecules is comparableto that of the catalyst pores (Guin et al., 1986). This will result in the decrease of the diffusion rate or the effective diffusivity as the ratio of the molecular diameter to the pore diameter, A, increases. This phenomenon is referred to as hindered, restrictive, or configurational diffusion and is generally ascribed to steric exclusion a t the pore entrance and wall effect within the pore (Renkin, 1954; Beck and Schultz, 1972; Deen, 1987). Many researchers have extensively studied the restrictive diffusion effect under reactive or nonreactive conditions by the sorptive or kinetic method, and various theoretical or empirical correlations have been proposed to predict the restrictive effects for porous materials. A brief summary of the literature comparing these alternative expressions for the restrictive factor, F(X),is shown in Table I. All the experimental or theoretical results show that the restrictive diffusion effect is significant under ambient conditions. However, there is as yet no confirmed conclusion for the restrictive diffusion effect under reactive conditions analogous to nonreactive ones. This is in part because of the difficulty of obtaining effective diffusivity data from sorptive diffusion measurements at elevated
* To whom correspondence should be addressed.
temperature. Lee et al. (1991a,b) investigated the restrictive diffusion effect under reaction conditions by carrying out hydrogenation reactions of nitrogen- and nickel-bearingmodel compoundsand explicitlyevaluated restrictive factors. They found that their experimental results could be interpreted by the approximation of the theoretical restrictive factor, F(A) = (1 - AI4, without considering a temperature effect. However, several researchers (Galiasso and Morales, 1983; Seo and Massoth, 1985) studied the temperature effect under nonreactive conditions and reached the same conclusions that at high temperatures the effective diffusivity increases more than expected on the basis of temperature effects upon bulk diffusivity, since the extent of increase in effective diffusivities is higher than those in bulk diffusivities at elevated temperature. This indicated that the restrictive effect becomes less prominent under reaction conditions as compared to the nonreactive one. It is obvious that the above-mentioned two results are contradictory to each other. As such, a further study on the restrictive diffusion effect under reaction conditions is necessary. The aim of this study was to investigate the effect of the ratio of reactant molecular size to catalyst pore size on the restrictive diffusion under 7.6 MPa and 663 K by carrying out HDS and HDM reactions of Kuwait residual oils in a trickle bed reactor. The reason for choosing a cocurrent downflow trickle bed reactor mainly took into account the analogous performance to the commercial one. Since this type reactor possesses a relatively lower pressure drop and absence of flooding, it is by far the most common mode of operation in industrial practice (Ng and Chu, 1987). It is, therefore, anticipated to monitor more actual information relating to restrictive diffusion, in spite of its difficulty to unravel meaningful diffusion parameters from overall reaction rates of residue. In addition, the catalysts used in the most literature for restrictive diffusion study encompass micropores and macropores; i.e., they are bimodal catalysts (as shown in Table I). It was assumed that restrictive diffusion mainly occurs in the micropore region (Lee et al., 1991a). Accordingly, the restrictive diffusion correlation correlated from average micropore diameters will not reflect bidispersion of the porous
0888-5885/93/2632-1603$04.00/00 1993 American Chemical Society
1604 Ind. Eng. Chem. Res., Vol. 32, No. 8, 1993 Table I. Brief Summary of the Literature Comparing Alternative Expressions for Restricted Factor F ( X ) researchers systems conditions method conclusions Renkin (1954) idealized model ambient theoretics F(X)= (1 - X)2 (1 - 2.104X + 2.09~3- 0 . 9 6 ~ ) Beck and Schultz (1972) track-etchedmembrane ambient theoretics F(h) = (1 - A)' silica-alumina ambient sorption F(h) = exp(-4.6X) Satterfield et al. (1973) Prasher and Ma (1977) alumina ambient sorption F(X)= exp(ah3+ b); a = -3479.2 f 616.5, b = 0.863 f 0.19 ambient sorption F(h) = 1.03 exp(-4.5X) or Chantong and Massoth (1983) alumina F(X) = (1 - X)3.6 0.27 and 7 MPa, 298-333 K sorption F(X)= exp(-ah); Seo and Massoth (1985) alumina In CY = (1300/T) - 2.62 5.27 MPa,623 K kinetics F(h) = (1 - X)43 Lee et al. (1991a) NiMoIalumina sorption F(h) = (1 - V . 7 Tsai et al. (1991a) NiMoIalumina ambient CoMo/AAP 7.6 MPa,663 K kinetics F(h) = (1 - X)35 for HDS; this study F(N = (1 - X)x* for HDM
structure. For example, Philippopoulos and Papayannakos (1988) studied intraparticle diffusion for the hydrotreating of residue over CoMo/Al203 catalysts under 50 bar and 350-430 "C. They found that effective diffusivity for bimodal catalyst is approximately 3 times that of unimodal catalyst with the same micropore diameters. Alumina-aluminum phosphate (AAP) has been shown (Vogel and Marcelin, 1983; Chen et al., 1990) to have a narrow and monodispersed pore size distribution. By regulating the Al/P atomic ratio, one is able to prepare the samples with various average pore diameters of the supports. Therefore, this material is very suitable for studying the restrictive diffusion due to its uniform pore structure. Recently restricted configuration diffusion under hydrotreating reaction conditions has been studied (Lee et al., 1991a,b). Unfortunately, the published data were obtained with a noncontinuous batch reactor using model compounds as feeds. This makes it difficult to interpret the performance results and to correlate them to commercial operations. Therefore, it is our intention to describe the results obtained by using heavy residue oil as a feed in a continuous trickle be,dreactor, which closely mimics a commercial operation. Experimental Section Catalyst. A series of CoMo/AAP catalysts with various Al/P atomic ratios were prepared and used to investigate restrictive diffusion under catalytic hydroprocessing conditions. The detailed preparation procedure and characterization of these catalysts have been reported previously (Chen et al., 1990). The metal contents of the catalysts were determined by means of inductively coupled plasma-atomic emission spectroscopy (ICP-AES) performed on a Thermo Jarrell Ash 1100 spectrometer. The catalysts prepared in this study contain nearly constant amounts of Mo and Co. The metal loading in the catalyst is approximately 12 wt % Moo3 and 4 w t % COO. Surface areas and pore volumes of the catalyst samples were measured by nitrogen adsorption at 77 K (BET method) using a Quantasorb adsorption unit manufactured by Quantachrome Corp. The pore size distributions were measured by the mercury penetration method on an Autopore I1 9220 based on a contact angle of 140'. The sample powder was first pressed into a disk in a die and then crushed into granules for the penetration method. Pellet densities were obtained from the same instrument (Autopore I1 9220) by mercury displacement. The measurements, for convenience, were performed on the oxidic form of the catalyst samples. Sample weights of about 500 mg was used prior to BET surface area and desorption pore volume determinations. The samples were outgassed for 4 h at 573 K. In addition, two different pellet sizes of
x C0.5 C0.3 C0.5 CO.1
C0.4 C0.4 C0.5 C0.4 C0.3
Table 11. Physical Properties of CoMo/AAP Catalysts catalyst CoMoI CoMoI CoMoI CoMoI AAPl AAP2 AAF'3.5 AAP6 72 100 147 S, m2/g 37 0.55 0.58 0.64 V,, cm3/g 0.47 av d,: nm 50.8 30.6 23.2 17.4 1.15 1.13 1.06 P,, g/cm3 1.22 c 0.573 0.632 0.655 0.679 12.02 MOOa, wt % 11.75 12.49 12.68 c o o , wt % 3.78 3.94 4.01 4.03 The average pore diameter shown here was calculated from the common definition of 4VdS, for cylindrical pore.
catalyst extrudates with the same diameter of 1.5 mm and lengths of 1and 4 mm (i.e., the mean equivalent spherical diameters are 2.38 and 1.50 mm, respectively) were used in this study. The physical properties of the catalysts are listed in Table 11. As shown, BET surface area, S,, increases and average pore diameter decreases with increasing Al/P atomic ratio of the CoMolAAP catalysts, in agreement with the literature (Vogeland Marcelin, 1983; Chen et al., 1990). The pellet densities ranged from 1.06 to 1.22 g/cm3, and average pore diameters varied from 17.4 to 50.8 nm. HDS and HDM Activity Test. HDS and HDM experiments were carried out in a bench-scale trickle bed reactor. The feedback was passed through the reactor (0.5 mL/min) a t 663 K, 7.6 MPa, and LHSV = 1.8. The hydrogen flow rate was maintained at 300 mL/min at standard temperature and pressure (STP), sufficient to keep the H2S content of the exit gas low in the reactor and thus to minimize inhibition effect by H2S. All runs were conducted with catalyst pellet sizes of 2.38 or 1.50 mm. The flow pattern diagram presented by Charpentier and Favier (1975)was used to check the flow type. The analysis indicated that the flow pattern of the reactor in this work is indeed in the trickling flow mode. This can be identified from our previous paper (Chen et al., 1990). The details of the catalyst bed arrangement and design of a laboratory reactor have been reported elsewhere (Chen et al., 1990; Tsai et al., 1991b). In order to ensure the kinetic data are free from the influence of unwanted transport effects such as dispersion, wall effect, and channeling, several authors (Doraiswamy and Tajbl, 1974;Montagna and Shah, 1975; Satterfield, 1975)have presented many criteria to evaluate the minimum reactor length and diameter necessary to avoid a significant dispersion effect. Doraiswamy and Tajbl(1974) suggested that if the radial aspect ratio (ratio of bed diameter to catalyst particle diameter) is greater than 4, channeling and heat-transfer effects at the reactor wall can be neglected, and if the axial aspect ratio (ratio of catalyst bed length to catalyst particle diam-
Ind. Eng. Chem. Res., Vol. 32, No. 8,1993 1605
Results and Discussion KUWAIT RESIDUE
0.8
0.0 1
10 100 MOLECULAR DIAMETER (nm)
Figure 1. Molecular size distribution of Kuwait residue oil.
eter) is greater than 30, axial dispersion and axial heat conduction effects can be neglected. In this study, two different pellet sizes of catalyst extrudates (the mean equivalent diameters are 2.38 and 1.50 mm) were used. A stainless steel tube reactor of internal diameter 14.27 mm, outer diameter 25.40 mm, and length 430 mm was applied. From the above criteria, channeling, wall-transfer effects, axial dispersion, and axial heat conduction effects are negligible in this study. The authors have independently determined that they had no fluid distribution effect. Much effort was made to eliminate extraneous mass and heat effects and to produce more well-mixed surroundings during experiments. In addition, it should be emphasized that the small catalyst pellet size will result in a high pressure drop and the large pellet size will result in a wall effect and channeling in a trickle bed reactor. Therefore, the range of catalyst pellet sizes used in this study was narrower than those mentioned in the literature. Prior to HDS and HDM experiments, the catalysts were sulfided. There are three different routes in presulfiding, Le., presulfiding with nonspiked feedstock, presulfiding with hydrogen-hydrogen sulfide stream, and presulfiding with spiked feedstock. I t has been reported by Hallie (1982) that nonspiked presulfiding or hydrogen-hydrogen sulfide presulfiding of CoMo and NiMo catalysts results in lower activities than the spiked presulfiding method. Therefore, a spiked feedstock method was used for the presulfiding of the catalysts in this work, where dimethyl disulfide (DMDS) was used as a spiking agent. The diesel oil feedstock, which was doped to 1 w t 9% sulfur by addition of DMDS, was passed through the reactor with the following temperature program: heated from room temperature to 448 K and kept for 2 h; then increased to 523 K and held for 4 h; after that, increased to 598 K and retained until sulfiding completely. The LHSV was 2.8, the hydrogen flow rate was 300 mL/min at STP, and the operation pressure was maintained at 2.8 MPa. The feedstock used in this test was the atmospheric tower bottom (ATB) of Kuwait crude oil. This feedstock contained 3.72 w t % S, 0.21 wt % N, 14 ppm Ni and 53 ppm V; its gravity API was 16.8 and the Conradson carbon residue (CCR) content was 10.1 wt % The molecular size distribution of Kuwait residue oil was measured by gel permeation chromatography (GPC) under ambient conditions, where tetrahydrofuran was used as solvent. The results are presented in Figure 1. It shows that the average molecular size of residue oils is ca. 5 nm. At an appropriate time, the hydrotreated residue oil samples were withdrawn to measure sulfur and metal (Ni, V) contents by X-ray fluorescence spectrometry (Oxford, LAB-X 2000) and ICP-AES (Jarrell Ash Model 1100), respectively. All the details have been reported in the previous paper (Chen et al., 1990).
.
The chemical complexities of hydrotreating reactions in a trickle bed reactor in which several compounds with different chemical structures and molecular weights react simultaneously with different rates have been studied. Many researchers (Vrinat, 1983) have recognized that the HDS and HDM reactions of an individual compound may follow a first-order kinetics. However, as far as overall reaction kinetics is concerned, several parallel reactions which result in the apparent reaction rate may behave like a pseudo-second-order reaction (Schuit and Gates, 1973; van Dongen et al., 1980; Dai et al., 1990). This conclusion has been confirmed for CoMo/AAP catalysts in our previous paper (Chen et al., 1990). The generalized apparent pseudo-second-order rate equation for the trickle bed reactor, assuming bed isothermality and plug-flow pattern, is A Y k, = LHSV-CI ,l-XW -
where C, is the sulfur (or metal) concentration in the feed (wt 5% ), LHSV is the modified liquid hourly space velocity (cm3of oil/s.cm3of catalyst), Vis the catalyst volume (cm9, and Wis the catalyst weight (g). The conversion, X,refers to the percentage of sulfur (or metal) removal (wt 7%). For isothermal cylindrical pellets and a second-order irreversible reaction, the relationship between the effectiveness factor, 77, and the Thiele modulus, 4, is expressed as (Ruckenstein and Tsai, 1981) 1 II(24) 4 I,(24)
7=--
(2)
where (3)
The above expression of the Thiele modulus was reported by Froment and Bischoff (19901, where De is the effective diffusivity of the sulfur- or metal-containing compounds in the catalyst pores (cm2/s), ki is the intrinsic HDS or HDM rate constant (cm3/s.g.wt %), and C, is the sulfur (or metal) concentration at the pore mouth of the catalyst (wt %). The studies of hydrotreating in a laboratory- or pilot-scale trickle bed reactor generally confirm the predictions of mass-transfer correlation and show the absence of fluid-phase mass-transfer influence (Gates et al., 1979), although the interparticle diffusion resistance more or less exists due to nonidela flow pattern. Thereby, the external-phase resistance is assumed to be negligible, i.e., C, = C,. Figure 2 demonstrates the percentage of sulfur or metal removal in the initial period (40 h after reaction) as a function of average pore diameter of catalysts for different pellet sizes. All give a volcano plot. The optimum pore diameters in this case seem to be present at positions of about 10 and 20 nm for HDS and HDM reactions, respectively. This is inconsistent with those reported by Rajagopalan and Luss (1979). They found that the pore diameter which yields the optimal initial activity is never larger than 5 times the diameter of the diffusing species. Ruckenstein and Tsai (1981) also reached the same conclusion in a theoretical simulation. In addition, it can be seen that the percentage of sulfur or metal removal decreases with increasing catalyst pellet size, indicating that intraparticle diffusion effects are appreciable. In fact, small catalyst pellet not only reduces intraparticle diffusion resistance but also stacks densely in an integral reactor.
2-
A
, A \
1 .o --
HDS (pellet size 2.X)mm)
o HDS (pellet aim 1.mmm) A
:55-
ffl
0
A
A
HDM (pallet size 2.srnrn) HDM (pellet size t .mmm)
251 I "
-____--------- _ _ _ _ ,.-L
0.0
I
0
15
30
45
0
60
Average Pare Diameter, nrn
Figure 2. Effects of average pore diameter and pellet size of catalyst on HDS and HDM reactions.
pellet l@kws, l@kims, size, mm cmV(s-gwt %) cm3/(s-g.wt % ) 1.50 0.288 0.295 0.280 0.295 2.38 0.422 0.443 CoMo/AAP2 1.50 0.401 0.443 2.38 CoMotAAP3.5 1.50 0.772 0.848 2.38 0.702 0.848 1.344 1.653 CoMotAAP6 1.50 1.129 1.653 2.38
40
60
Figure 3. Relationship between effectiveness factor and average pore diameter of catalyst.
Table 111. Apparent and Calculated Intrinsic Rate Constants and Effectiveness Factors for HDS Reactions of Residue Oils at 663 K and 7.6 MPa catalyst CoMo/AAPl
20
Average Pore Diameter, nrn
1 .o L
0
q
0.975 0.948 0.953 0.904 0.910 0.827 0.813 0.683
z 0.8 ?I v)
0
5 0.6
.->
I
W
Lc
0.4 .
Table IV. Apparent and Calculated Intrinsic Rate Constants and Effectiveness Factors for HDM Reactions of Residue Oils at 663 K and 7.6 MPa
CoMotAAPl CoMotAAP2 CoMotAAP3.5 CoMotAAP6
1.50 2.38 1.50 2.38 1.50 2.38 1.50 2.38
0.287 0.270 0.437 0.390 0.734 0.612 1.209 0.922
0.303 0.303 0.493 0.493 0.916 0.916 1.875 1.875
0.947 0.892 0.887 0.790 0.802 0.668 0.645 0.492
The latter situation will somewhat reduce axial dispersion, wall effect, and channeling. This can, therefore, produce higher activity. Apparent second-order rate constants, as determined from eq 1, and the calculated intrinsic rate constants and effectiveness factors are summarized in Tables I11 and IV for HDS and HDM reactions, respectively. Examination of these two tables shows that the effectivenessfactor decreases with decreasing average pore diameter on the one hand. On the other hand, the extent of the decrease of effectiveness factor for HDS reaction is smaller than that for HDM one. These results not only indicate that the intraparticle diffusion resistance is significant for both HDS and HDM reactions, but also imply that the extent of the effect of pore diffusion on HDM reaction is greater than that on HDS reaction, especially for smaller pores. The variation of the effectiveness factor with average pore diameter at a reaction temperature of 390 "C is illustrated in Figure 3. In this figure, two cases of effectiveness factors from the literature (Kobayashi et al., 1987) were plotted and included for comparison, one for the lower reaction temperature (380 "C) and the other for the higher reaction temperature (420 "C). With a view to Figure 3, the effectiveness factors obtained in this study are substantially located within the range in the literature, as expected. Other information that can be extracted from
this figure is that the effectiveness factor decreases with increasing reaction temperature. This may be interpreted satisfactorily by the definition of the effectiveness factor. At higher temperatures, pore diffusion resistance becomes more important since a larger increase in the chemical reaction rate due to temperature rise occurs in comparison with that of pore diffusion phenomena. Therefore, smaller effectiveness factors were obtained at higher reaction temperature. In addition, it is worth mentioning that the effectiveness factor is related not only to catalyst pore size but also to reactant molecular size. However, we cannot understand the effect of reactant molecular size on the effectiveness factor from Figure 3. It is meaningful to draw the relation between the effectiveness factor and the ratio of reactant molecular size to average pore size of the catalyst (A). As can be seen from Figure 4, the experimental results indicate that the effectiveness factor decreases with increasing reactant size to pore size ratio, with values ranging from approximately 0.5 to 0.9 based on the calculated intrinsic rate constants. Kobayashi et al. (1987) carried out HDM reactions of residual oils over commercial CoMo/AlzOs catalysts at 673 K in a trickle bed reactor. The ratio of reactant size to catalyst pore size was estimated to be between 0.1 and 0.5 (incorporate reactant size of 5 nm, as described in their paper), a range slightly broader than the range of data in our study (reactant sizes of sulfurand metal-bearing compounds are estimated to be 5 nm from the GPC result, Le., X = 0.1-0.3). They obtained effectivenessfactors in the range of 0.2-0.7. It is, therefore, considered that the effectiveness factors obtained here are reasonable ones. Because the reaction temperature used in our work is lower than theirs, the somewhat higher effectiveness factors obtained in this work would be expected. Since the importance of diffusional limitations on HDS and HDM reactions has been recognized (Prasher et al.,
Ind. Eng. Chem. Res., Vol. 32, No. 8, 1993 1607 Table V. Effective Diffusivities of Residue Oils in HDS and HDM Reactions at 663 K and 7.6 MPa
0 HDS (Z=3.5)
WDe, cm2/s CoMo/AAF’l CoMo/AAF’2 CoMo/AAP6 CoMo/AAP8
HDS 17.88 12.96 11.94 9.03
HDM 14.75 9.80 8.88 6.91
1978; Johnson et al., 1986; Limbach and Wei, 1990), the availability of the active sites within the pores of the catalyst becomes critical for these reactions. Consequently, the effective diffusivity plays an important role in such reactions. The effective diffusivities of residual oils in HDS and HDM reactions at 663 K and 7.6 MPa are listed in Table V. As shown in Table V, the effective diffusivities for HDM reaction are always smaller than those for HDS reaction. The size of metal prophyrin is greater than the size of sulfur compound, which results in the difficulty of diffusion in HDM reaction. The effective diffusivityvalues decreased with decreasing average pore diameters for both HDS and HDM reactions, indicating a large restrictive diffusion effect. The order of magnitude of effective diffusivities is about 10-6 cm2/s, indicating that the diffusion of residue oils under hydrotreating reaction conditions lies in the “configurational”regime (Satterfield, 1991). The knowledge of kinetics and effective diffusivities as well as of the influence of the ratio of reactant size to catalyst pore size on restrictive diffusion permits the design of hydrotreaters and the selection of the proper catalysts. Therefore, an understanding of the restrictive diffusion effect under reaction conditions becomes very important. For restrictive diffusion in catalyst pores, a general form for expressing the restrictive diffusion effect is De = (DbE/7)(1- A)’ (4) where Db is the bulk diffusivity (cm2/s),t is the catalyst porosity, and 7 is the tortuosity factor. The value of the bulk diffusivity was determined from the Stokes-Einstein equation, even though this equation is based on the assumption of very large spherical particles and a continuous solvent (Laidler and Meiser, 1984)
kT
D, = (5) 61rur where k is the Boltzmann constant (1.38 X l t 2 3 J/K), T is the system temperature (663 K),Y is the viscosity (1.2 X 10-4 kg/(ms)), and r is the radius of diffusing solute (2.5 nm). Substituting these values into the above equation, the bulk diffusivity is approximately 1.6 X 106 cm2/s. Because the residue oils contain a molecular size distribution of sulfur-and metal-bearingmolecules,for purposes of simplicity, only an average molecule size, i.e., the molecule size for the maximum relative amount in the molecular size distribution (regardless of sulfur- or metalbearing compounds), was used to find the bulk diffusivity and restrictive diffusion correlation. This average molecule size is ca. 5 nm from the results of GPC conducted at ambient conditions because column packings will decompose under reaction conditions. There is very little information in the open literature on the molecular size distribution of the sulfur- or metal-bearing molecules at reaction conditions. Most of the reported molecular size distributions have been based on GPC and size-exclusion chromatographytogether with inductively coupled plasma spectrometry (SEC-ICP) measurements of feeds and products at room temperature (Pereira and Beeckman, 1989). It should be noted that thermal cracking under this reaction condition is negligible.
-3.0 -0.4
-0.2
-0.3
In
(1-3
-0.1
0.0
Figure 5. Determination of z from the experimental data.
0 O x W h M b l dab (HDM). ?-4.71
- F(h)=(l-h)4
...... F(a)=sxp(-4.6a)
LL
0.2-0.0 I 0.0
0.1
0.2
0.3
0.4
0.5
h
Figure 6. Comparison of experimental restrictive factor data with literature Correlations.
A logarithmic plot of D$Dbe vs (1- A) will yield a straight line with a slope of z and an intercept of -In 7. The best straight lines were determined by least-squares analysis, as shown in Figure 5. Two empirical correlations for restrictive diffusion during the course of HDS and HDM reactions are then given by De,HDdDbt= (1/3.86)(1-
(6)
De,HDM/Dbt= (1/4.71)(1 -
(7)
The values of z for HDS and HDM reactions are 3.5 and 3.8, respectively. The results once more implied that the restrictive diffusion for HDM reaction is more severe than that of HDS reaction even though their difference is finite. The results indicate that the restricted effect under catalytic hydrotreating reaction conditions is still severe and is substantially equal to the theoretical prediction for nonreactive diffusion, Le., z = 4. It should be noted that our results were obtained over a limited range of X (X < 0.3). Our results cannot be extended to high values of X (X > 0.3) with any certainty. There are probably different regimes for restrictive diffusion depending on the value of X (Prasher and Ma, 1977). A comparison of the values of restrictive factor obtained in this study with those in the literature is given in Figure 6; it can be seen that all the literature correlations give a satisfactory fit to our data. Our results are in accordance with those reported in the literature (Lee et al., 1991a,b)within a similar range of A. However, some literature (Galiasso and Morales, 1983; Seo and Massoth, 1985) give the opposite results. For instance, when the temperature-dependent restrictive factor presented by Seo and Massoth (1985) was extrapolated to our reaction temperature (663 K), a restrictive factor of 0.95 is predicted for X = 0.1 and a value of 0.86
1608 Ind. Eng. Chem. Res., Vol. 32, No. 8, 1993
for X = 0.3. Hence, the restrictive effect may not be important for X < 0.3 under our reaction conditions. Of course, one may note that their restrictive factors were obtained over a limited temperature range (298,313, and 333 K) and extrapolation to higher temperature is uncertain. In fact, because the diffusing moleculehas alarger kinetic energy at elevated temperature, it becomes easier to pass the energy barrier resulting from hydrodynamic drag within the pores, and the diffusion rate of the molecule would be greatly facilitated. One would also expect the restrictive effect should be less significant under reaction conditions based on hydrodynamic theory. The discrepancy may be attributed to the systems of dense (or concentrated) solutions used in this study in contrast with those very dilute solutions reported by sorption experiments under ambient conditions. This creates the difficulty of solute diffusion, in the dense solution system since the interaction between solutes is very appreciable in this situation, and, therefore, the restrictive effect is still significant even under reaction conditions. In addition, hydrodynamic theory for restrictive diffusion is developed for unidirectional diffusion under nonreactive conditions. However, the counterdiffusion phenomena of reactanta and products must occur simultaneously during the course of the hydrotreating process. This will result in a retarding effect on the diffusion rate and a larger restrictive effect due to interactions between the reactants and products. Consequently, it is doubtful that this theory can be applied to restrictive diffusion under reaction conditions. The counterdiffusion effect on restrictive diffusion is also studied by several workers (Satterfield and Cheng, 1972;Lee et al., 1991a). It is worth mentioning that typical hydrotreating reaction conditions are not only high temperature but also high pressure. However, pressure (up to 7 MPa) was found to have little effect on diffusivity (Seoand Massoth, 1985). Accordingly, the temperature effect was exclusively taken into account to contribute to diffusivity.
Conclusions In this paper, we investigated the effect of the ratio of reactant molecular size to catalyst pore size on restrictive diffusion under hydrotreating reactions of heavy residue oils over CoMo/AAP catalysts. The results are summarized as follows. 1. The restrictive diffusion correlations showed that the restrictive diffusion effect under reaction conditions for HDS and HDM reactions is still prominent for X < 0.3. 2. The values of the effective diffusivities for HDS and HDM reactions were determined by applying the Thiele relation to catalytic reactions. The results showed that the effective diffusivities for the HDM reaction are always smaller than those for the HDS reaction one for any specific A. In addition, the effective diffusivity values decreased with increasing X values for both HDS and HDM reactions, indicating a large restrictive diffusion effect. 3. For diffusion of sulfur- and metal-bearing compounds in CoMo/AAP catalysts at hydrotreating reaction conditions, the restrictive factors were correlated by F(X) = (1 - XI35 and F(X) = (1- X13.8, respectively. Acknowledgment This research is supported by the National Science Council (NSC-81-0402-E008-12)and Chinese Petroleum Corporation. Nomenclature C, = sulfur (or metal) concentration in the feed, wt %
C,= sulfur (or metal) concentration at the pore mouth of the
catalyst, wt % = bulk diffusivity, cm2/s De = effective diffusivity in the catalyst pore, cmVs IO,II = modified Bessel functions of order 0 and 1 k = Boltzmann constant, 1.38 X J/K k , = apparent rate constant, cm3/(s-gwt 7%) ki = intrinsic rate constant, cm3/(s.gwt %) LHSV = modified liquid hourly space velocity, cm3 of oil/ (s.crn3 of catalyst) r = radius of diffusing solute, nm 5, = internal surface area of the catalyst pellet, cm2/g 5, = external surface area of the catalyst pellet, cmYg T = temperature, K V = total catalyst volume in the reactor, cm3 V, = pore volume of the catalyst pellet, cm3/g V, = volume of the catalyst pellet, cmVg W = total catalyst weight in the reactor, g z = parameter in eq 4 Db
Greek Letters = particle porosity 7 = effectiveness factor X = ratio of reactant size to catalyst pore size u = viscosity, kg/(ms) pp = bulk density of the catalyst pellet, g/cm3 T = tortuosity factor 4 = Thiele modulus e
Literature Cited Beck, R. E.; Schultz, J. S. Hindrance of Solute Diffusion within Membranes as Measured with MicroporousMembranes of Known Pore Geometry. Biochim. Biophys. Acta 1972,255,273-303. Chantong, A.; Massoth, F. E. Restrictive Diffusion in Aluminas. AZChE J. 1983,29,725-731. Charpentier, J. C.; Favier, M. Some Liquid Holdup Experimental Data in Trickle-Bed Reactors for Foaming and Nonfoaming Hydrocarbons. AZChE J. 1975,21,1213-1218. Chen, Y. W.; Hsu, W. C.; Lin, C. S.; Kang, B. C.; Wu, S. T.; Leu, L. J.; Wu, J. C. Hydrodesulfurization Reactions of Residual Oils over CoMo/Alumina-AluminumPhosphate Catalysts in a Trickle Bed Reactor. Znd. Eng. Chem. Res. 1990,29,1830-1840. Dai, P. E.; Sherwood, D. E.; Martin, B. R. Effect of Diffusion on Resid Hydrodesulfurization Activity. Chem. Eng. Sci. 1990,45, 2625-2631. Deen, W. M. Hindered Transport of Large Molecules in LiquidFilled Pores. AZChE J. 1987,33,1409-1425. Doraiswamy,L. K.,Tajbl,D. G. Laboratory CatalyticReactor. Catal. Rev.-Sci. Eng. 1974,10,177-219. Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design, 2nd ed.; Wiley: New York, 1990;pp 160-163. Galiasso, R.; Morales, A.; Adsorption Mechanism of Boscan Porphyrins on HDM Catalysts. 111. Diffusion of Porphyrins. Appl. Catal. 1983,7,57-74. Gates, B. C.; Katzer, J. R.; Schuit, G. C. A. Chemistry of Catalytic Processes; McGraw-Hill: New York, 1979; pp 432-433. Guin, J. A,; Tsai, K. J.; Curtis, C. W. Intraparticle Diffusivity Reduction during Hydrotreatment of Coal-DerivedLiquids. Znd. Eng. Chem. Process Des. Dev. 1986,25,515-520. Hallie, H. Experience Reveals Best Presulfiding Techniques for HDS and HDN Catalysts. Oil Gas J. Technol. 1982,Dec. 20,69-74. Johnson, B. G.; Massoth, F. E.; Bartholdy, J. Diffusion and Catalytic Activity Studies on Resid-Deactivated HDS Catalysts. AZChE J. 1986,32,1980-1987. Kobayashi, S.; Kushiyama, S.; Aizawa, R.; Koinuma, Y.; Inoue, K.; Shimizu, Y.; Egi, K. Kinetic Study on the Hydrotreating of Heavy Oil. 2. Effect of Catalvst Pore Size. Znd. Enn. Chem. Res. 1987. 26,2245-2250. Laidler. K. J.: Meiser. J. H. Phvsical Chemistrv: ” , Beniamin/ Cummings: Taipei, 1984;pp 832-833. Lee, S. Y.; Seader, J. D.; Tsai, C. H.; Massoth, F. E. Restrictive Diffusion under Catalytic HydroprocessingConditions. Znd. Eng. Chem. Res. 1991a,30,29-38. Lee, S. Y.; Seader, J. D.; Tsai, C. H.; Massoth, F. E. Solvent and Temperature Effects on Restrictive Diffusion under Reaction Conditions. Znd. Eng. Chem. Res. 199Lb,30,607-613. I
Ind. Eng. Chem. Res., Vol. 32,No. 8,1993 1609 Limbach, K. W.; Wei, J. Restricted Diffusion through Granular Materials. AZChE J. 1990,36,242-248. Montagna, A. A.; Shah,Y. T. The Role of Liquid Holdup, Effective Catalyst Wetting, and Backmixingon the Performance of a Trickle Bed Reactor for Residue Hydrodesulfurization. Znd. Eng. Chem. Process Des. Deu. 1975,14,419-483. Ng, M.; Chu, C. F. Trickle-Bed Reactors. Chem. Eng. Prog. 1987, Nou, 55-63. Ohtsuka, T. Catalyst for Hydrodesulfurizationof Petroleum Residua. Catal. Rev.-Sci. Eng. 1977,16,291-325. Pereira, C. J.; Beeckman, J. W. Modeling of Hydrodemetalation Catalysts. Znd. Eng. Chem. Res. 1989,28,422-427. Philippopoulos, C.; Papayannakos, N. Intraparticle Diffusional Effects and Kinetics of Desulfurization Reactions and Aephaltenea Cracking during Catalytic Hydrotreatment of a Residue. Znd. Eng. Chem. Res. 1988,27,415-420. Praeher, B. D.; Ma, Y. H. Liquid Diffusion in Microporous Alumina Pellets. AIChE J. 1977,23,303-311. Praeher, B. D.; Gabriel, G. A.; Ma, Y. H. Catalyst Deactivation by Pore Structure Changes. The Effect of Coke and Metal Depositions on Diffusion Parameters. Znd. Eng. Chem. Process Des. Deu. 1978,17,266-269. Rajagopalan, K.; Luss, D. Influence of Catalyst Pore Size on Demetallation Rate. Znd. Eng. Chem. Process Des. Deu. 1979,18, 459-465. Renkin, E. M. Filtration, Diffusion and Molecular Sieving through Porous CelluloseMembranes. J.Gen. Physiol. 1954,38,225-227. Ruckenstein, E.; Tsai, M. C. Optimum Pore Size for the Catalytic Conversion of Large Molecules. AZChE J. 1981,27,697-699. Satterfield, C. N. Trickle-Bed Reactor. AZChE J.1975,21,209-228. Satterfield, C. N.Heterogeneous CataZyssia in Industrial Practice, 2nd ed.; McGraw-Hik New York, 1991;pp 240-241.
Satterfield, C. N.; Cheng, C. S. Liquid Counterdiffusion of Selected Aromatic and Naphthenic Hydrocarbons in Type Y Zeolites. AIChE J. 1972,18,124-728. Satterfield, C. N.; Colton, C. K.; Pitcher, W. H., Jr. Restrictive Diffusion in Liquids within Fine Pores. AZChE J. 1973,19,628635. Schuit, G. C. A.; Gates, B. C. Chemistry and Engineering of Catalytic Hydrodesulfurization. AZChE J. 1973,19,411-438. Seo, G.; Maesoth, F. E. Effects of Pressure and Temperature on Reetrictive Diffusion of Solutes in Aluminas. AZChE J. 1986,31, 494-496. Tsai, C. H.; Maesoth, F. E.; Lee, S. Y.;Seader, J. D. Effects of Solvent and Solute C d i a t i o n on Restrictive Diffusion in Hydrotreating Catalysts. Znd. Eng. Chem. Res. 1991a,30,22-28. Tsai,M. C.; Chen, Y. W.; Kang, B. C.; Wu, J. C.; Leu, L. J. Hydrodeaulfwization and Hydrodemetalation Reactions of Residue Oila over CoMo/Aluminum Borate Catalysts in a Trickle Bed Reactor. Znd. Eng. Chem. Res. 199lb,30, 1801-1810. van Dongen, R. H.; van der Eijk, D. B. H.; van Klinken, J. Hydrodemetallization of Heavy Residual Oile in Laboratory Trickle-Flow Liquid Recycle Reactors. Znd. Eng. Chem. Process Des. Deu. 1980, 19,630-635. Vogel, R. F.; Marcelin, G. Preparation of Stoichiometric Aluminum Phosphate. J. Catal. 1983,80,492-493. Vrinat, M. L. The Kinetica of the Hydrodesulfurization Process-A Review. AppZ. CataZ. 1983,6,131-158. Received for review October 20, 1992 Revised manuscript received March 30,1993 Accepted April 8,1993
