Ind. Eng. Chem. Res. 1991,30,607-613
607
KINETICS AND CATALYSIS
Solvent and Temperature Effects on Restrictive Diffusion under Reaction Conditions S. Y. Lee and J. D. Seader* Department of Chemical Engineering, University of Utah, Salt Lake City, Utah 84112
Chung H. Tsai and F. E. Massoth Department of Fuels Engineering, University of Utah, Salt Lake City, Utah 84112
The effects of decalin and mesitylene solvents and reaction temperatures of 573 and 623 K on restrictive diffusion were investigated for the catalytic hydrogenation of nickel porphyrins over three NiMo/y-A1203 catalysts, of average micropore sizes in the range 62-174 A. It was found that the solvents and temperatures used had little effect on restrictive diffusion under reaction conditions, except that less restrictive effect was observed when reaction temperature approached the solvent critical temperature. Because the adsorption strength of reactants under reaction conditions was relatively weak due to high temperature, the restrictive effect was not noticeably influenced by solvent and temperature. However, the effect was even less prominent when temperature approached the solvent critical temperature. It is proposed that the solvent behaved as a gaslike liquid when the reduced temperature was close to 1. Under such a condition, viscous drag on diffusing solutes was less important in comparison with inertial forces and, thus, a lower restrictive effect would be expected.
Introduction Effective diffusivity of a reactant molecule in a liquid solvent within a catalyst pore of comparable size is frequently found to be less than its value in free solution, and the effective diffusivity decreases as the ratio of the molecular diameter to the pore diameter, A, increases. This phenomenon, which has been termed restrictive diffusion, is caused by the combining effects of steric hindrance and hydrodynamic resistance (Deen, 1987). The effects of molecular size and shape on restrictive diffusion have been extensively studied, and various correlations have been proposed to predict the restrictive effects for porous materials (Satterfield et al., 1973;Chantong and Massoth, 1983;and Limbach and Wei, 1990). However, only limited studies regarding the effects of solvent and temperature on restrictive diffusion have been conducted, as summarized below. It is well-known that catalytic hydroprocessing is more or leas influenced by restrictive diffusion in hydrotreating catalysts. Considering the fact that hydrotreating is conducted at different reaction conditions, depending on the feedstock and the catalyst, it is important to know the dependence of the restrictive effect on the nature of the feed solution and temperature, especially under reaction conditions. Satterfield et al. (1973)and Prasher et al. (Prasher and Ma, 1977;Prasher et al., 1978a,b)used a wide variety of solute-solvent systems to investigate the solvent effect on restrictive diffusion in liquid-fded pores under nonreactive conditions at ambient temperature. Experimental results showed that the effective diffusivity was not only dependent on A, but also on the equilibrium partition coefficient, K p ,which is equal to the ratio of solute concentration within the porous material to that in the bulk
* Author to whom correspondence should be addressed.
solution. It was found that solvent mainly affected the restrictive diffusion rate by altering the adsorption behavior of solute in pores. For a particular value of A, effective diffusivity is smaller for a solute having strong adsorption strength than for a nonadsorbing solute, whereas the effective diffusivity of a solute would be higher in the case of strong adsorption of solvent. Therefore, a partition coefficient was incorporated into the correlation for the restrictive factor to take into account the adsorption effect. The theoretical basis to rationalize this phenomenon was developed (Anderson and Quinn, 1974;Deen, 1987)and experimentally verified (Malone and Anderson, 1978). The temperature effect under nonreactive conditions has been studied by several researchers. Galiasso and Morales (19831,who measured the diffusion rates of porphyrin compounds in several catalyst supports at different temperatures, found that the restrictive effect decreased with increasing temperature. They postulated that at low temperature the porphyrin molecules are strongly adsorbed on the pore wall and, thus, effective diffusivities of the diffusing molecules are reduced due to the smaller effective pore size. When temperature increases, adsorbed molecules desorb, thus increasing the effective pore diameter. Thus, a higher diffusion rate and a lower restrictive effect are achieved at higher temperature. Seo and Massoth (1985)also observed a decrease in the restrictive effect with increasing temperature. They suggested that because the diffusing molecule has a larger kinetic energy at elevated temperature, the molecule can more easily pass through an energy barrier resulting from hydrodynamic drag. In spite of the differences in these explanations, these investigators observed the same overall effect: at high temperatures the effective diffusivity increases more than expected on the basis of temperature effects upon bulk diffusivity. Accordingly, the restrictive effect should be
0888-5885/91/2630-0607$02.50/0 0 1991 American Chemical Society
608 Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991
less important under reaction conditions at high temperatures as compared to nonreactive, ambient-temperature conditions. Because of the difficulty of obtaining effective diffusivity data from sorptive diffusion measurements at elevated temperatures, some investigators have attempted to obtain such data in conjunction with catalytic reactions. For example, Spry and Sawyer (1975) and Pereira and Beeckman (1989) investigated the restrictive diffusion effect under reaction conditions by carrying out hydrodemetalation reactions of petroleum feedstocks and Boscan vacuum resid feedstock, respectively. Neither of the studies explicitly evaluated restrictive factors. However, both research groups found that their experimental results could be interpreted by the approximation of the theoretical restrictive factor, F(X) = (1- A)*, without considering a temperature effect. These results imply that the restrictive effect is still prominent under high temperature reaction conditions, which does not agree with those found in the sorptive diffusion studies at elevated temperatures. Clearly, a further study is necessary to better understand the differences among the above-mentioned results. We have recently reported the results of experimental studies of restrictive diffusion under catalytic hydroprocessing conditions in which a large restrictive effect was observed (Lee et al., 1991). An empirical correlation for restrictive diffusion showed that the effective diffusivity is strongly influenced by the ratio of the reactant molecular size to the average micropore size, taking into account changes in pore size due to coke deposition. To our knowledge, the effects of solvent and temperature on intraparticle diffusion of reactants under reaction conditions have not been reported by previous investigators. The study reported here is a continuation of our previous work on restrictive diffusion effects under reaction conditions. The same experimental method was used.
Experimental Section Three presulfided and aged NiMo/y-Al2O3 catalysts, containing 1.5% Ni and 4% Mo, with average micropore sizes of 62,83, and 174 A were used. These three catalysts were designated NiMo-325, NiMo-225, and NiMo-125, respectively, and each was crushed and screened to two average sizes, 0.01- and 0.17-0.18-cm radius. Other measured physical properties included particle density ranging from 1.28 to 1.32 g/cm3, particle porosity of 60%,and BET surface area varying from 112 to 291 m2/g. The model compounds used in the catalytic hydrogenation studies were nickel tetraphenylporphyrin (Ni-TPP) and nickel tetra(4-biphenyly1)porphyrin (Ni-TBP), both purchased from Mid-Century. Their critical molecular diameters are 15.7 and 21.8 A, respectively. Decalin (Aldrich, 99+%) and mesitylene (Aldrich, 99%) were employed as solvents because they have different strengths of adsorption on the catalyst surface, while having approximately the same critical diameter. Hydrogenation of the nickel porphyrin compounds over the aged NiMo catalysts of the two particle sizes was used to assess restrictive diffusion under reaction conditions. Reactions were carried out at two temperatures, 573 and 623 K, and 5.27-MPa hydrogen pressure with the two different solvents to investigate the effects of solvent and temperature upon restrictive diffusion rates. A Carberry-type spinning-basket reactor was used to eliminate external mass transfer resistances. Reactions under different conditions were achieved for batch operation using the same aged catalyst. After a batch reaction run, the liquid product in the reactor was drained and fresh feed solution containing Ni-TPP or Ni-TBP was charged into the re-
actor after the system had cooled down to room temperature. This draining and charging was carried out under hydrogen gas without exposure to air. By comparing the results with kinetic results from standard runs for hydrogenation of Ni-TPP in decalin at 623 K and 5.27 MPa, the catalyst in the reactor was found to maintain a steady-state activity during a sequence of batch runs under different conditions. When the solvent was changed from decalin to mesitylene, care was taken to replace the liquid product in the pores of catalyst. The change in solution concentration was measured by a Beckman Model 25 UV spectrophotometer. Duplicate runs using the same catalyst gave results within &3%. Effective diffusivities of the two nickel porphyrin compounds were determined from the kinetic data by employing the relationship between effectiveness factor and the Thiele modulus. Details of the experimental procedure and data treatment method were reported previously (Lee et al., 1991). Results and Discussion Catalyst Activities. Experimental results showed that hydrogenation of nickel porphyrins was well represented by pseudo-fist-order kinetics of porphyrin disappearance at 573-623 K and 5.27-MPa hydrogen pressure (Lee et al., 1991). Although the reaction occurs in a stepwise fashion involving hydrogenation and hydrogenolysis, only the rate of conversion of reactant was determined for the study reported here. The apparent first-order rate constants for hydrogenation of Ni-TPP and Ni-TBP over aged NiMo catalysts are summarized in Tables I and 11, respectively. For a given reactant and reaction condition, the apparent rate constant obtained from the large-sized catalyst is smaller than that for the small-sized catalyst, indicating that intraparticle diffusion substantially limits the rate of reaction with large catalyst particles. The intrinsic rate constants at different reaction conditions were calculated by the Thiele relation:
where
4 = (R2k,~,/&)0*5
(2)
where q and 4 are effectiveness factor and Thiele modulus, respectively,R is catalyst particle radius, and pp is particle density. Values of k,, intrinsic rate constant, and De, effective diffusivity of a reactant molecule in the catalyst, were evaluated by the “triangle method” using eqs 1and 2 (Satterfield, 1970). As shown in Tables I and 11, the intrinsic rate constants in decalin solvent are consistently smaller than those in mesitylene. Because the reaction rate is proportional to the concentration of hydrogen in the solvent (Hung and Wei, 1980) and the effect of hydrogen solubility was incorporated into the pseudo-first-order rate constant, differences in the rate constants for different solvents could have been due to different hydrogen concentrations in the solvents. Therefore, an attempt was made to estimate hydrogen sdubility. Radosz et al. (1982) improved the cubic equation of state of Soave for the prediction of hydrogen solubility in heavy hydrocarbons by using new mixing rules. Based on that method, mole fractions of hydrogen dissolved in decalin and mesitylene under conditions of 573K and 5.27 MPa were estimated to be 0.054 and 0.064, respectively, and 0.063 and 0.080, respectively, under conditions of 623 K and 5.27 MPa. Therefore, the lower rate constant in decalin solvent is attributed, at least in part, to the lower hydrogen solubility in the solvent.
Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991 609 Table I. Apparent and Intrinsic Rate Constants and Effectiveness Factors for Hydrogenation of Ni-TPP at 5.27-MPa Hydrogen Pressure and Elevated Temperatures solvent decalin mesitylene ~~~~~
temperature, K intrinsic rate const, cm3/(g.min) particle radius, cm rate const, cm3/(gmin) effectiveness factor
Case A. NiMo-125 Catalyst 573 623 0.61 2.02 0.01 0.18 0.01 0.18 0.61 0.22 1.98 0.60 0.99 0.36 0.94 0.29
temperature, K intrinsic rate const, cm3/(g.min) particle radius, cm rate const, cm3/(gmin) effectiveness factor
Case B. NiMo-225 Catalyst 573 623 0.81 3.24 0.01 0.18 0.01 0.18 0.76 0.14 3.00 0.48 0.94 0.17 0.93 0.15
temperature, K intrinsic rate const, cm3/(g.min) particle radius, cm rate const, cm3/(g.min) effectiveness factor
Case C. NiMo-325 Catalyst 573 623 0.62 3.83 0.01 0.17 0.01 0.17 0.57 0.10 3.28 0.42 0.93 0.17 0.86 0.11
573 0.64 0.01 0.64 0.99
623 2.34 0.18 0.34 0.54
0.01 2.34 0.98
0.18 0.96 0.40
573 1.18 0.01 1.15 0.98
623 7.89 0.18 0.33 0.28
0.01 7.30 0.93
573 1.03 0.01 0.97 0.94
0.18 1.19 0.15 623 6.97
0.17 0.20 0.19
0.01 6.10 0.88
0.17 0.87 0.12
Table 11. Apparent and Intrinsic Rate Constants and Effectiveness Factors for Hydrogenation of Ni-TBP at 5.27-MPa Hydrogen Pressure and Elevated Temperatures solvent decalin mesitylene ~
~~~~
temperature, K intrinsic rate const, cm3/(gmin) particle radius, cm rate const, cm3/(gmin) effectiveness factor
Case A. NiMo-125 Catalyst 573 623 1.08 4.06 0.01 0.18 0.01 0.18 1.04 0.22 3.81 0.66 0.96 0.20 0.94 0.16
temperature, K intrinsic rate const, cm3/(gmin) particle radius, cm rate const, cm3/(gmin) effectiveness factor
Case B. NiMo-225 Catalyst 573 623 0.93 3.78 0.18 0.01 0.18 0.01 0.13 3.21 0.37 0.85 0.91 0.14 0.85 0.10
573 1.34 0.01 1.32 0.98
623 6.28 0.18 0.39 0.29
0.01 5.99 0.95
573 1.10
623 7.43 0.18 0.23 0.21
0.01 1.06 0.96
0.18 1.17 0.19
0.01 6.67 0.90
0.18 0.92 0.12
Case C. NiMo-325 Catalyst 623 573 623 573 5.09 1.17 8.77 1.06 0.01 0.17 0.01 0.17 0.01 0.17 0.01 0.17 3.30 0.30 1.04 0.16 6.54 0.67 0.82 0.09 0.90 0.13 0.75 0.08 0.65 0.06 0.77 0.08 ... The effectiveness factors calculated from the ratios of Table 111. Effective Diffusivities (10sD,, cm2/s) of Nickel the apparent rate constants and the intrinsic rate constants Porphyrins at Hydrogen Pressure of 5.27 MPa are also included in Tables I and 11. At higher temperadecalin" mesitylene" tures, intraparticle diffusion resistance becomes more im573 K 623 K 573 K 623 K portant, since a larger increase in the chemical reaction NiMo-125 Catalyst rate due to temperature rise occurs in comparison with that Ni-TPP 8.49 17.9 24.4 43.8 of intraparticle diffusion phenomena. Therefore, smaller 11.2 20.5 Ni-TBP 4.14 9.76 temperature, K intrinsic rate const, cm3/(g.min) particle radius, cm rate const, cm3/(gmin) effectiveness factor
effectiveness factors were obtained at higher reaction temperature. Based on values of effectivenessfactors, the particle-size effect is more pronounced for Ni-TBP in decalin solvent, where a larger molecule diffuses in a more viscous bulk solution. The particle-size effect is also more significant with the NiMo-325 catalyst, which has a considerably lower average micropore diameter than the NiMo-225 and NiMo-125 catalysts. Restrictive Diffusion. The effects of particle size and pore size on reaction rate were quantified by use of the relation between effectiveness factor and Thiele modulus. Effective diffusivities of model compounds, determined by using eqs 1 and 2 in conjunction with kinetic results, are given in Table 111. For a given reactant and reaction condition, effective diffusivity decreases significantly with decreasing pore size. It is apparent that the mobility of the reactant was hindered by pore size, which implies that
a
Ni-TPP Ni-TBP
NiMo-225 Catalyst 2.32 6.36 9.10 1.57 3.24 4.88
Ni-TPP Ni-TBP
NiMo-325 Catalyst 1.26 3.39 2.78 0!52 1.23 1.57
15.7 10.4 7.59 3.63
Solvent.
restrictive diffusion occurred. For restrictive diffusion of a reactant in a catalyst, the effective diffusivity, De, may be expressed by (Lee et al., 1991) De
where
t
and
T
---F(X) T
EDb
-(1 T
- A)*
(3)
are the catalyst porosity and tortuosity
610 Ind. Eng. Chem. Res., Vol. 30, No. 4,1991
factor, respectively, Db is the bulk diffusivity, F(h) is the restrictive factor to account for the fractional decrease in reactant diffusivity due to the restrictive effect, and X is the ratio of critical reactant molecule diameter to average micropore diameter. The value of z is an indication of the magnitude of the restrictive effect; i.e., the larger the value of z , the more significant the restrictive effect. Values of X and porosity were obtained from the catalyst and reactant properties. Because tortuosity depends mainly on particle porosity (Wakao and Smith, 1962; Wang and Smith, 1983), the value of tortuosity was assumed to be the same for all three catalysts due to approximately the same values of porosity as reported previously by Lee et al. (1991). Bulk diffusivity, &, can be expressed by the Wilke-Chang equation (Wilke and Chang, 1955):
Db = B/ VA''~
Table IV. Data for Determination of z without the Correction of Pore-Mouth Size
reactant catalyst Ni-TPP NiMo-125 NiMo-225 NiMo-325 Ni-TBP NiMo-125 NiMo-225 NiMo-325
e
T
- A)'
0.090 0.189 0.253 0.125 0.263 0.352
(4)
where VAis the molar volume of the reactant at its normal boiling point and B is dependent on system temperature and,the solvent employed. Therefore, for a given solvent and reaction condition, B is a constant. Accordingly, the z value can be estimated by combining eqs 3 and 4 to give D,VAo'6 -- %I
decalin mesitylene 573 K 623 K 573 K 623 K 6.92 14.59 19.89 35.70 2.00 5.46 7.83 13.51 1.10 2.96 2.43 6.63 4.31 10.16 11.66 21.35 1.72 3.56 5.36 11.43 0.58 1.37 1.75 4.05
X
. .
-11'
.
.
'
.
'
.
'
.
'
1
(5)
Before applying eq 5, it was recognized that catalyst pore size and, thus, X could change under reaction conditions because coke formation or metal deposition occurred and was preferentially concentrated at the catalyst pore mouths, causing pore-mouth constriction. Lee et al. (1991) showed that this constriction reduced effective diffusivity and significantly increased the restrictive effect. The decrease in effective diffusivity, detected from sorptive diffusion measurements a t ambient conditions in aged catalyst, was accounted for by the reduction in pore-mouth size. A correction method was developed to estimate the true size of pore mouths, based on an assumption of constant tortuosity factor for both fresh and used catalysts. It appears that this assumption is a reasonable one because the porosities of fresh and aged catalysb are approximately the same. Accordingly, the pore-mouth sizes of the aged catalysts were calculated to be 117, 59, and 46 8, for NiMo-125, NiMo-225, and NiMo-325, respectively. A correlation was established between the restrictive factor and A', using the corrected pore-mouth diameter instead of average pore diameter. Alternatively, Prasher et al. (1978b) observed that the intraparticle diffusivities of solutes in used catalysts were much smaller than those in fresh catalysts, and the restrictive factor was correlated with average pore size. They found that the average pore diameter of used catalyst was either larger than or approximately equal to that of fresh catalyst depending on the mechanism of coke deposition. Therefore, it was concluded that the decrease in the intraparticle diffusivity in used catalysts was mainly due to the increase in catalyst pellet tortuosity factor. In view of the Prasher et al. (1978b) study, it is possible that both pore mouth size and tortuosity factor are affected by coke depositions, which in turn influence the restrictive diffusion process. In order to assess the restrictive effect, two approaches, correction of pore-mouth size or tortuosity factor for aged catalysts, were studied here. First, it was assumed that the average micropore size of fresh and used catalysts was the same, and only the tortuosity factor changed. Values of A, based on the pore sizes of fresh catalysts, and (D,VA0.6/t)are listed in Table IV. From eq 5, a logavs (1- A) will yield a straight rithmic plot of (DeVA0.6/e) line with slope equal to z. The value of z for each sol-
-10
'
I
.
-C
-9' -0.5
*
'
-0.4
*
'
-0.3
.
'
-0.2
.
'
-0.1
.
'
0.0
In (1 -A) Figure 1. Dbtermination of z from experimental data for hydrogenation of nickel porphyrins under different conditions (withoutthe correction of pore-mouth size).
vent-temperature combination was determined by a least-squares regression technique, as shown in Figure 1, where values of z are seen to vary from 6.0 to 7.0. Second, corrected pore diameters of the aged catalysts were used to correlate the restrictive factor, assuming the tortuosity factor to be the same for fresh and aged catalysts. The effective diffusivity was expressed by the following equation (Lee et al., 1991):
where the primed quantities re& to aged catalyst. Based on the corrected A' values, values of z under different conditions were obtained from the slope of the best fit of the data plotted as the logarithm of [D,(VAo.6)(X'2)/e(X2)]
Ind. Eng. Chem. Res., Vol. 30, No. 4,1991 611 0 (a)decalin,573K
A (b)decalin, 623 K 0.4
0
0
0
'
0.0
0.1
(c) medtylene, 573 K (d) medtylene,623K
I
0.2
0.3
0.4
0.5
Reactant critical diameter/Pore mouth diameter Figure 3. Decrease in effectiveness factor with increasing ratio of reactant diameter to pore-mouth diameter.
0" I C
-a
(c) mesitylene, 573 K, t
-9'.
'
'
-7 -e
'
'
.
'
'
'
.
(d) mrsitylene, 623 K,
= 5.1
'
1
'
z = 4.4
~~
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
In (1 - h') Figure 2. Determination of z from experimental data for hydrogenation of nickel porphyrins under different conditions (with the correction of pore-mouth size). Table V. Data for Determination of z with the Correction of Pore-Mouth Size 10'DeV~o~6A'a/cA2, (cm2/s)(cma/mol)o.s decalin mesitylene reactant catalyst A' 573 K 623 K 573 K 623 K Ni-TPP NiMo-125 0.135 15.57 32.85 44.78 80.33 NiMo-225 0.265 3.93 10.73 15.39 26.54 NiMo-325 0.344 2.03 5.47 4.49 12.26 Ni-TBP NiMo-125 0.187 9.65 22.83 26.18 47.89 NiMo-225 0.368 3.37 6.97 10.50 22.32 NiMo-325 0.477 1.12 2.65 3.39 7.84
vs [l - A'], as shown in Figure 2, using the data in Table V. The intercepts are equal to In ( B / r ) . As can be seen in Figures 1 and 2, the value of B / r increases with temperature for a particular solvent, and this value is larger in mesitylene solvent than in decalin solvent under the same reaction conditions. These trends are in agreement with the prediction of the Wilke-Chang equation, i.e., a higher temperature, a larger molecular-weight solvent, and a lower solvent viscosity all yield a larger value of B. As can be seen in Figures 1 and 2, these two different approaches yielded different values of z. Without considering poremouth constriction, the z values obtained are much larger than the theoretical prediction of 4.0. When considering the constriction, z values are in the range of 4.4-5.1. For diffusion in catalysts, it is believed that the change in pore-mouth size of aged catalysts must be taken
into account, and the tortuosity is by no means the only factor to account for this effect. Pereira and Beeckman (1989), who investigated restrictive diffusion in hydrotreating catalysts for the hydrodemetalation reaction, found that using a corrected pore size to correlate the restrictive factor yielded good agreement with experiment. Their approach is similar to the second approach used in this study. It is believed that the most plausible approach would be a correction method based on changes in both pore mouth and tortuosity due to coking. However, in view of the limited diffusion data obtained from fresh and aged catalysts, it was not practical, in the study reported here, to adjust both tortuosity and pore size simultaneously. The research reported here emphasizes the effects of solvent and temperature on restrictive diffusion under reaction conditions. Because the same catalyst was used for different reaction conditions, the effects of uncertainty about data treatment were the same for all cases, as shown in Figures 1and 2. Therefore, attention was directed to the relative z values obtained under different conditions and not to the absolute values. Despite the significant differences in z values, depending on data treatment, the slopes of the lines are approximately the same in each figure, except for reaction in mesitylene solvent at 623 K, where a lower z value signifies a significantly smaller restrictive effect. Effectiveness factor is a function of the ratio of intrinsic rate and diffusion rate of reactant. Experimental results indicate thqt the effectiveness factor is strongly dependent on the ratio of reactant molecule size to catalyst pore size due to the restrictive diffusion effect. The relationship is clearly illustrated in Figure 3, which is based on effectiveness factor data of Tables I and I1 and values of A' in Table V. As can be seen in Figure 3, effectiveness factor decreases with increasing reactant size to pore size ratio, with values ranging from approximately 0.1 to 0.6 based on the calculated intrinsic rate constants. Kobayashi et al. (1987) carried out hydrodemetalation reactions of residual oil over molybdenum 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, a range comparable to the range of data in our study. They obtained effectiveness factors in the range of 0.2-0.7, which is also about the same range as we observed. Because the reaction rates and catalyst pellet sizes dsed in our work are much larger than theirs, the somewhat lower effectiveness factors obtained in this work would be expected. Hung et al. (1986) reported that distribution factors, which are equal to run-average effectivenessfacton for fmt-order reactions, between 0.30 and 0.47 were obtained from their hydrodemetalation studies. However, since detailed information is not available from their study, a comparison with our work cannot be made. Taken together, all these studies
612 Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991
show that the values of effectiveness factors for hydroprocessing reactions can be very low, depending on the reaction system and catalyst properties. Therefore, an understanding of the restrictive diffusion effect under reaction conditions is very important to the design of efficient catalysts. Solvent and Temperature Effects. The two solvents used in this study are of two types. Mesitylene is an aromatic hydrocarbon that interacts strongly with NiMo/alumina catalysts by a *-bonding mechanism. Decalin is a naphthene without *-electrons. For example, the adsorption capacity of porphyrin on alumina in benzene solvent was found to be lower than that in cyclohexane solvent (Galiasso and Morales, 1983). Because reactants in the two solvents show different adsorption behaviors (partition coefficients), it was anticipated that different restrictive effects might be observed with these two solvents. Besides, the restrictive effect was predicted to decrease with increasing temperature, as observed in previous studies. However, our experimental results indicate that the effects of solvent and temperature are not significant under reaction conditions. This finding is different from that found by Satterfield et al. (1973) and Prasher et al. (Prasher and Ma, 1977; Prasher et al., 1978a,b) at ambient, nonreactive conditions. The concept of adsorption strength and hydrodynamic theory were explored here to elucidate the discrepancies among the different studies. According to the hydrodynamic theory of restrictive diffusion (Anderson and Quinn, 19741, the hydrodynamic resistance is a function not only of the ratio of solute size to pore size, A, but also radial position of the diffusing molecule within a pore. Therefore, the restrictive factor should be determined by averaging the local Stokes friction coefficient over available radial positions in conjunction with steric hindrance. However, this approach is difficult to apply because little is known of the distribution of solute within pores. The Stokes friction coefficient is easily obtained for a simplified case where the center of a diffusing solute molecule is restricted to the centerline axis of the pore. Accordingly, the widely used correlation is developed by assuming that the local Stokes coefficient is equal to the centerline value, i.e. the centerline approximation (Deen, 1987). This approach yields an acceptable prediction for the restrictive effect of a nonelectrolyte solute in an inert membrane. For the case here of liquid-filled catalyst pores, a radial variation in solute concentration can be present due to attractive forces between the solute and pore wall. Adsorption strength affects the radial distribution of solutes in a pore, which in turn can alter the hydrodynamic resistance of the solute within the pore. I t was shown by Malone and Anderson (1978) that if the solute is strongly adsorbed on the pore wall, restrictive effecb would be more important because the solutes close to the pore wall exhibit a greater drag force than those near the centerline, i.e., larger hydrodynamic resistance. Therefore, effective diffusivity is smaller than predicted by the centerline approximation and adsorption strength of reactants is crucial to assess the effects of solvent and temperature on diffusion rates under reaction conditions. The adsorption of metal porphyrins occurs through the *-electron of the porphyrin structure and the donor-acceptor interaction via the metal atom (Vielhaber and Knozinger, 1986; Cordischi et al., 1987). Since adsorption is an exothermic process, adsorption strength decreases with increasing temperature (Galiassoand Morales, 1983). Thus,as temperature increases, the concentration of solute near the pore wall should be reduced, resulting in lower
drag forces on the solutes and, correspondingly, a lower restrictive effect. Therefore, even though bulk diffusivity increases with temperature, the increase in effective diffusivity could be greater than the increase in bulk diffusivity. For diffusion studies at near-ambient temperatures, e.g., 298-333 K (Seo and Massoth, 1985), it is believed that the adsorption strength is sufficiently sensitive to temperature change due to greater adsorption at low temperature, within thiis limited temperature range, that a temperatwe effect on restrictive diffusion is observed. However, in our study, the effect of adsorption strength on restrictive diffusion might not be important because, at high temperature, reactants only weakly adsorb on the pore wall and the 50 K difference in temperature may not significantly change the adsorption strength at relatively high reaction temperatures. This explains why a significant temperature effect was not observed under our reaction conditions. Kobayashi et al. (1987) studied hydrodemetalation of residual oil, in a region of restrictive diffusion effect, to investigate the relationship between the optimum pore diameter and reaction temperature. Over a temperature range of 653-693 K, they found that using the same restrictive factor yielded a satisfactory prediction for their experimental results. This is basically in agreement with our finding. For the same reason, solvent used should have little effect on restrictive diffusion rates under reaction conditions because adsorption strength is so small that a partition coefficient is not an important factor. Based on the hydrodynamic theory, the restrictive factor is determined on the basis of the Stokes equation, which is derived from the Navier-Stokes equations by ignoring the inertial terms compared with the viscous term (Happel and Brenner, 1983). As temperature approaches the solvent critical temperature, the solvent behaves as a gaslike liquid, with a significant reduction in viscosity and, thus, an increasing importance of kinetic energy, i.e., inertial forces. The viscosity of the liquid solution under reaction conditions was estimated, taking into account hydrogen solubility, with a method developed by Ely and Hanley (1981). This method, based on an extended corresponding states principle, can predict the viscosity of hydrocarbons over the entire range of fluid states, from the dilute gas to the dense liquid. The viscosities of mesitylene at 5.27-MPa hydrogen pressure were calculated to be 0.099 and 0.055 cP at temperatures of 573 and 623 K, respectively, compared to corresponding values of 0.122 and 0.094 cP for the decalin solvent. For this low viscosity value of mesitylene at 623 K, the validity of the Stokes equation is questionable. Therefore, a lower restrictive effect may be possible in the case of hydrogenation of porphyrins in mesitylene solvent at 623 K because of less predominance of viscous drag. Restrictive (or configurational) diffusion is also observed for gases diffusing in zeolites, but it only occurs when the pore size is approximately equal to the molecular size. On the other liand, restrictive diffusion is significant in the liquid phase when pore size becomes less than 10 times the molecular size, due to the dominance of viscous forces in liquids. Reaction in near-critical fluid solvents is still poorly understood because only limited data are available. Paulaitis et al. (1983) found that the diffusion coefficient in the supercritical fluid state was about an order of magnitude larger than in the liquid state. Based on the study reported here, the restrictive diffusion effect is less prominent for reactions carried out in near-critical fluid state compared to that in ordinary fluid state. Also, because of improvement in transport properties, it was proposed by McHugh and Krukonis (1986) that reaction
Ind. Eng. Chem. Res., Vol. 30, No. 4, 1991 613
rates would be enhanced by carrying out reactions in supercritical fluids. Therefore, the potential advantages of using near-critical or supercritical fluid solvent instead of liquid solvent at subcritical conditions may be an important practical consideration to reduce a large restrictive diffusion effect under reaction conditions. Conclusions The following conclusions were drawn in this study: 1. A large restrictive diffusion effect was observed for a ratio of reactant critical diameter to average micropore diameter in the range of 0.09-0.35 ( t h e maximum ratio). 2. Temperature had little effect on restrictive diffusion for decalin solvent. However, the restrictive effect in mesitylene solvent was reduced when reaction temperature approached the critical temperature of mesitylene, i.e., a reduced temperature = 0.98. 3. It is believed that the change in adsorption behavior of a diffusing molecule has an important role in determining restrictive effect. A t the higher temperatures of reaction conditions, the effect appears to be negligible because the adsorption s t r e n g t h is relatively small. 4. It appears that effective diffusivity increases with temperature more than expected on the basis of the temperature effect on bulk diffusivity at near-ambient temperature due to a decrease in adsorption strength. The effective diffusivity increases with temperature at the same rate as the bulk diffusivity for reasonably h i g h temperatures due to a negligible effect of the decrease in adsorption strength. A further reduction in the restrictive effect due to temperature can occur at h i g h temperatures as the solvent critical temperature is approached. Near the critical temperature, the Stokes equation m a y no longer be valid because of much lower viscosity. 5. It is anticipated that the restrictive diffusion effect can be reduced b y employing a solvent with a relatively low critical temperature and operating the catalytic reactor at a temperature j u s t below the solvent critical temperature. Acknowledgment This work was sponsored by the Department of Energy under Contract No. DE-FG22-87PC79933. The alumina supports were kindly supplied by Aluminum Company of America.
Nomenclature
Db= bulk diffusivity, cmz/s De = effective diffusivity, cm2/s F(A) = restrictive factor
K, = equilibrium partition coefficient
k, = intrinsic pseudo-first-order rate constant, cm3/(g.s) R = radius of catalyst particle, cm V A = molar volume of reactant A at its normal boiling temperature, cm3/mol z = parameter in e q 3
Greek Symbols t
= particle porosity
7 = effectiveness factor A = ratio of reactant critical diameter to mean micropore
diameter of fresh catalysts A’ = ratio of reactant critical diameter to poremouth diameter of used catalysts pp = bulk density of catalyst particle, g/cm3 T = tortuosity factor 4 = Thiele modulus
Registry No. Ni-TPP, 14172-92-0;Ni-TBP, 129849-29-2;Ni, 7440-02-0;Mo,7439-98-7; decalin, 91-17-8; mesitylene, 108-67-8.
Literature Cited Anderson, J. L.; Quinn, J. A. Restricted Transport in Small Pores: A Model for Steric Exclusion and Hindered Particle Motion. Biophys. J . 1974,14, 130. Chantong. A,: Massoth, F. E. Restrictive Diffusion in Aluminas. A I C h g J . 1983,29,725. Cordischi, D.; Vielhaber, B.; Knozinger, H. Vanadyl Tetraphenyl PorDhvrin AdsorDtion on Oxides and on Mo/Al,02 . - - catalysts An ESR Study. Appl. Catal. 1987,30,265. Deen, W. M. Hindered Transport of Large Molecules in LiquidFilled Pores. AIChE J. 1987,33, 1409. Ely, J. F.; Hanley, H. J. M. Prediction of Transport Properties. 1. Viscosity of Fluids and Mixtures. Znd. Eng. Chem. Fundam. 1981, 20,323. Galiasso, R.; Morales, A. Adsorption Mechanism of Boscan Porphyrins on HDM Catalysts. 111. Diffusion of Porphyrins. Appl. Catal. 1983,7,57. Happel, J.; Brenner, H. Low Reynolds Number Hydrodynamics; Martinus Nijhoff Dordrecht, The Netherlands, 1983. Hung, C. H.; Wei, J. The Kinetics of Porphyrin Hydrodemetallation. 1. Nickel Compounds. Znd. Eng. Chem. Process Des. Dev. 1980, 19,250. Hung, C. H.; Howell, R. L.; Johnson, D. R. Hydrodemetallation Catalysts. Chem. Eng. Prog. 1986,March, 57. 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 Catalyst Pore Size. Ind. Eng. Chem. Res. 1987, 26,2245. Lee, S. Y.;Seader, J. D.; Tsai, C.H.; Massoth, F. E. Restrictive Diffusion under Catalytic Hydroprocessing Conditions. Znd. Eng. Chem. Res. 1991,30,29. Limbach, K. W.; Wei, J. Restricted Diffusion through Granular Materials. AZChE J. 1990,36,242. Malone, D. M.; Anderson, J. L. Hindered Diffusion of Particles through Small Pores. Chem. Eng. Sci. 1978,33,1429. McHugh, M. A,; Krukonis, V. I. Supercritical Fluid EztractionPrinciples and Practice; Butterworth: Stoneham, MA, 1986;pp 199-216. Paulaitis, M. E.; Kurkonis, V. J.; Kurnik, R. T.; Reid, R. C. Supercritical Fluid Extraction. Rev. Chem. Eng. 1983,1, 179. Pereira, C. J.; Beeckman, J. W. Modeling of Hydrodemetalation Catalysts. Znd. En& Chem. Res. 1989,28,422. Prasher, B. D.; Ma, Y. H. Liquid Diffusion in Microporous Alumina Pellets. AZChE J. 1977,23,303. Prasher, B. D.; Gabriel, G. A.; Ma, Y. H. Restricted Diffusion of Liquids in Microporous Catalysts. AZChE J. 19788,24, 1118. Prasher, 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. 1978b, 17, 266. Radosz, M.; Lin, H. M.; Chao, K. W. High-pressure Vapor-Liquid Equilibria in Asymmetric Mixtures Using New Mixing Rules. Ind. Eng. Chem. Process Des. Dev. 1982,21,653. Satterfield, C. N. Mass Transfer in Heterogeneous Catalysis; MIT Press: Cambridge, MA, 1970; ppi129-142. Satterfield, C. N.; Colton, C. K.; Pitcher, W. H. Restricted Diffusion in Liquids within Fine Pores. AIChE J. 1973,19, 628. Seo, G.; Massoth, F. E. Effects of Pressure and Temperature on Restrictive Diffusion of Solutes in Aluminas. AIChE J. 1985,31, 494. Spry, J. C.; Sawyer, W. H. Configurational Diffusion Effects in Catalytic Demetallization. Paper presented at the 68th Annual AIChE meeting, Los Angeles, Nov 16-20, 1975;paper 30c. Vielhaber, B.; Knozinger, H. In situ Preresonance Raman and Optical Spectra of Vanadyl Tetraphenylporphyrin Adsorbed on Mo/Al,OS Catalysts. Appl. Catal. 1986,26,375. Wakao, N.; Smith, J. M. Diffusion in Catalyst Pellets. Chem. Eng. Sci. 1962,17, 825. Wang, C.T.; Smith, J. M. Tortuosity Factors for Diffusion in Catalyst Pellets. AZChE J. 1983,29, 132. Wilke, C. R.; Chang, P. Correlation of Diffusion Coefficients in Dilute Solutions. AZChE J . 1955,1, 264.
Received for review August 8,1990 Accepted November 5,1990
