Ind. Eng. Chem. Process Des. Dev. 1984, 23, 515-522
515
Hydrodemetalation of Nickel and Vanadium Porphyrins. 2. Intraparticle Diffusion Rakesh Agrawalt and James Wel' DepHment of Chemical Enginewing, Massachusetts Institute of Technology, Cambrklge, Massachusetts 02 139
Metal deposition profiles in catalyst extrudates were studied at various reactor bed positions. At the entrance of the bed, the maxima in the metal deposition occurred Inside the catalyst, so that the metal depositlbn profiles resembled the letter M. I n the middle and the exit sections of the bed, the maxima moved to the external surface, and the metal deposition profiles assumed the classical U-shaped profiles. These metal profiles have been successfully simulated by diffusion coupled with the consecutive kinetic model of part 1. From the theoretical simulations, it is inferred that both the nlckel and vanadyl etloporphyrins and their reaction intermediates have cm2/s. diffuslvities of the Order of
Introduction Most investigators have found that catalysts in an HDS reactor deactivate in two steps: a rapid decline in activity due to coke formation and a slow decline in activity due to metals deposition. Beuther and Schmid (1963) observed that of the total carbon deposited on the HDS catalyst in 16 days of operation, one half deposited in the fiist 12 h. The nearly stable value of coke on the catalyst is explained by a dynamic equilibrium between the hydrocracking rate and the hydrogenation rate on the catalyst surface (Beuther and Schmid, 1963; Kwan and Sato, 1970). Unlike coke deposition, metals deposition rate is nearly constant in time. Oxenreiter et al. (1972) reported the amount of deposited vanadium to be as high as 56 wt % and nickel 17 w t %. It has been proposed that pore mouth plugging is the major cause in limiting the total catalyst life (Dautzenberg et al., 1978; Kwan and Sato, 1970; Oxenreiter et al., 1972). Arey et al. (1967), Audibert and Duhaut (1970), Kwan and Sato (1970), Oxenreiter et al. (1972), and Sato et al. (1971) studied the metals deposition on the catalyst with a scanning electron X-ray microanalyzer. All these investigators found that vanadium deposita in the thin outer shell of the catalyst, whereas nickel tends to be more uniformly distributed across the diameter of the catalyst. Sat0 et al. (1971) applied classical diffusion analysis to the metals deposition and concluded that the effective diffusivity for vanadium has ts be less than 10% of that for nickel. However, Todo et al. (1971) reported that the concentration profiles for both nickel and vanadium were U-shaped. Inoguchi et al. (1971), Kwan and Sato (1970), Oxenreiter et al. (1972), and Sat0 et al. (1971) have investigated the metals deposition profiles along the length of the reactor. All the investigators have observed that the maximum deposition of the metals occurred near the inlet of the reactor and decreased toward the reactor outlet. Another important observation is the distribution of the metals profile inside the catalysts at various bed locations. Tamm et al. (1981) observed that at the entrance of the bed, the maximum in the metal deposition occurs inside the catalyst, so that the metal deposition profiies resemble the letter M. A t the exit section of the bed, the maximum moved to the external surface, and the metal deposition profiles assumed the classical U-shaped profiles. The internal maxima in the metals deposition have also been +AirProducts and Chemical, Inc., Allentown, PA 18105. 0196-4305/84/1123-0515$01.50/0
observed by Hardin et al. (1978) and Oxenreiter et al. (1972). Audibert and Duhaut (1970) observed more than one internal maximum for nickel deposition in thk catalyst. T a " et al. (1981) suggested that hydrogen sulfide is necessary for the hydrodemetalation and the internal maxima in metal deposition is coupled with the concentration of hydrogen sulfide in the reacting stream. Apart from the speculation of Tamm et al. there is no published explanation for these internal maxima in the metal deposition ptofies and the role of the catalyst location in the bed. The objective of this paper is to address these questions about the nickel and vanadium deposition profiles in the hydrodemetalation process. Experimental Section The details of the experimental equipment, materials, and procedure are given in part 1of this series (Agrawal and Wei, 1982) and by Agrawal (1980). In this study nickel etioporphyrin I (Ni" Etio I) and vanadyl etioporphyrin I (VO'" etio I) were used as model metal compounds. A mineral oil (Nujol) was used as solvent; it is free of sulfur, nitrogen, and any metal compounds. Both nickel and vanadyl etioporphyrins are solids at room temperature and have limited solubility in the mineral oil of about forty parts per million by weight of metals (ppm). The catalyst used is a typical hydrodesulfurization Co0-Mo03/A1203 catalyst, supplied by American Cyanamid Company as 1.6 mm ( 1 / 1 6 in.) extrudates. A continuous flow reactor was used. The liquid solution was saturated with hydrogen gas at room temperature (-25 "C) and the desired hydrogen pressure in an autoclave, and was then pumped through the packed bed reactor. There was no other gas source to the reactor. It is estimated that under typical operating conditions, the approximate ratios of the moles of the dissolved hydrogen to the moles of metal would be 200-450 (Chao and Seader, 1961). Since in paraffins and naphthenes the solubility of hydrogen increases with temperature, heating up to the reactor temperatures would not cause hydrogen gas to leave the solution phase (Cukor and Prausnitz, 1972; Prather et al., 1977). One of the central problems in the design of laboratory reactors is to ensure that the data are free from the influence of unwanted transport effect (Anderson, 1968; Doraiswamy and Tajbl, 1974). In order to ensure that channeling and wall heat transfer effects at the reactor wall are not limiting, the radial aspect ratio (ratio of the bed diameter to the catalyst particle diameter) should be 0 1984 American Chemical Society
518
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 3, 1984 -
-..
-
I
1.6
b
I
1.6
1
C
t
1.0 .8 .6 .4
rlR
rlR
-! 4
.2
0 .2 .4
.6 .8 1.0
rlR
Figure 1. Vanadium deposition profiles in catalyst, run VE-4; (X) catalyst 1; ( 0 )catalyst 2; (A) catalyst 3; calculated lines: (- - -) D A= D B = 1.6 X 10" cm2/s; (-) D A= 1.8 X lp cm2/s; DB= 6.0 X 10" cm2/s; (a) location at reactor entrance; (b) location at reactor middle; (c) location at reactor exit.
greater than 4-5 (Doraiswamy and Tajbl, 1974). For the cylindrical catalyst of diameter 1.52 mm and length 4.32 mm, the equivalent spherical diameter is 2.8 mm (Mears, 1971a,b). In order to satisfy the above criterion, the internal diameter of the reactor should be greater than 14 mm. Doraiswamy and Tajbl (1974) have also suggested that if the axial aspect ratio is greater than 30, then axial dispersion and axial heat condition effects can be neglected. For our system, the length of the catalyst bed should be greater than 84 mm. A reactor tube of internal diameter 17.5 mm, outer diameter 25.4 mm, and length of 305 mm was used. It satisfied both the radial and axial aspect ratios. In a typical run, the reactor was packed with about 5 g of 1.6 mm (1/16 in.) catalyst extrudates. Each of the catalyst extrudates was carefully hand-picked to make sure that there were no cracks or broken ends. The length of catalyst used was controlled within the range of 5 to 7 mm. The catalyst bed was diluted with an inert solid to a catalyst to inert volume ratio of 1:2.5. The reactor was first purged with helium at 370-390 "C for about 3 h and then was raised in temperature and hydrogen pressure to the desired values. Through the reactor, the metal solution was passed at the flow rates of 10 mL/h to 40 mL/h (0.5-2.0 h-' LHSV). In any single run, the total amount of the solution pumped was about 1500 mL, and the total number of hours on stream was 35-100 h. The catalyst was not sulfided. During the run the liquid samples from the reactor outlet solution were collected at various time intervals. As described in part 1of this series, the total metal content of the liquid samples was analysed by atomic absorption spectrophotometry. For nickel etioporphyrin and vanadyl etioporphyrin analysis, peaks at 517 and 534 nm, respectively, in the visible spectrum were used. Beer's law was used to correlate the intensity of absorption with the concentration. At the end of the run, the flow of solution through the reactor was stopped; the reactor was cooled down rapidly by allowing hydrogen and helium to flow from the reactor in the purge. Then the catalyst from various reactor positions was collected and analyzed for the internal metal deposition profiles. The spent catalyst from the reactor was first cleaned of oil and the unreacted metal compounds in a Soxhlet extractor for 24 h with chloroform. The cleaned catalyst was dried under vacuum. A wood disk of 25 mm diameter was covered with a 2 mm thickness of liquid epoxy mixture, and several cylinders of catalysts were completely immersed in this liquid with their major axes parallel to the disk surface. The epoxy was cured. Coarse emery papers were used to polish and remove the flat epoxy surface, so that the cylinders of catalysts gradually emerged. When the top halves of the cylinders were removed, the polishing coninued with 5 stages of finer
emery papers to 4-5-pm papers. Carbon coating with an arc under vacuum was performed to make the samples conducting. A scanning electron X-ray microanalyzer was used to scan the concentration of deposited vanadium or nickel across the minor axis of the catalyst at several positions of the major axis. A few cleaned catalyst samples were sent to Galbraith Laboratories Knoxville, TN, to analyze for carbon, nitrogen, hydrogen, and nickel.
Results For the first 30 h on stream, there was a transience of catalyst activity for both the vanadium and nickel runs, which was discussed in part 1. There was a rapid deactivation of the catalyst for the first 15 h; then the catalyst activity increased again and finally stabilized. The rapid deactivation may be due to rapid coke buildup on the catalyst. The spent catalyst from the reactor had coke as high as 3 to 4%. A period of 15 h may be sufficient to build up almost all the coke formed during the total course of the reactor operation. The second phase of the increase in the activity may be due to metal deposition in the catalyst. As the catalyst activity increased, the concentration of the hydrogenated intermediate in the solution also increased. This simultaneous increase in both the hydrogenation and demetalation activities is in agreement with the observation of Bridge and Green (1979) that the metal deposited is catalytically active for hydrogenation and demetalation. Seven experiments were performed with vanadium etioporphyrin and seven with nickel etioporphyrin. The operating conditions for vanadium are given in Table I. Metal deposition profiles for three of the vanadium runs are plotted in Figures 1 to 3. In Figure la, two extrudates from the reactor entrance were examined and showed clear internal mslxima in weight of metals at r / R of 0.7 to 0.8; in Figure lb, three extrudates from the reactor middle showed that the maxima have moved to the edge to form the classic Ushape; in Figure IC,a single extrudate from the reactor exit showed edge maxima and a lower level of metal concentration. The same pattern is repeated in Figures 2 and 3 where the pressure has increased from 6.9 to 9.7 MPa. The experimental conditions for the nickel experimenta are given in Table 11. Figure 4a shows a similar internal maxima at the reactor entrance, where the nickel concentration at the pellet center is much higher than for vanadium. This is in agreement with Sat0 that nickel profiles tend to be more nearly uniform. Figures 4b and 4c show that for pellets from the reactor middle and exit, the concentration maxima moved to the extrudate edge. In all of these runs,the low metal loading on the catalyst led to large uncertainties in measurements. The scanning electron X-ray microanalyzer is much more sensitive to
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 3, 1984 517 -
Table I. The Vanadium ExDenments'
D A = DB OA # DB DA X lo6 DA X lo6 & x
run no.
T
P
Q
W
CA,
VE-1 VE-2 VE-3 VE-4 VE-5 VE-6 VE-7
343 343 315 34 3 288 343 343
9.65 9.65 9.65 6.89 9.65 9.65 9.65
19.5 19.5 19.5 19.5 19.5 19.5 40
4.998 4.997 5.003 5.005 4.991 2.999 4.999
19.1 25.7 27.1 28.4 29.3 26.6 27.5
1.6 1.6 1.2 1.6 0.9 1.6 1.6
1.9 1.9 0.9 1.8 0.8 1.9 1.9
lo6
6.0 6 .O 4.5 6.0 4.2 6 .O 7.0
T = temperature in "C. P = pressure in MPa. Q = flow rate of solution in mL/h. W = amount of catalyst in reactor, g. CAD inlet concentration of vanadyl etioporphyrin, ppm. Inlet concentration of B is zero. DA, DB = calculated diffusion coefficients of A and B from the theoretical model, cm2/s. Table 11. The Nickel Experimentsa outlet solution concn exptl
T 343 343 343 343 315 343 343
run no. NE-4 NE-5 NE-6 NE-7 NE-8 NE-9 NE-10
Q
CAO
c,
19.5 19.5 19.5 30 19.5 14.7 30
26.4 25.8 28.1 28.6 27.2 27.5 16.8
7.5 6.9 7.6 11.1 10.6 5.5 5.1
DA = DB6
calcd
CM
CB
DA X 10cm2/s
7.5 6.8 7.7 11.0 10.6 5.7 5.0 5.1
0.92 0.84 0.94 1.33 2.04 0.7 0.62 0.62
1.1 1.3 1.2 1.6 2.5 1.0 1.5 2.7
CB
__
-_ 0.93 1.33 1.64 0.97 0.62
T = temperature in "C. Q = flow rate of solution in mL/h. CAD= inlet concentration of nickel etioporphyrin, ppm. = sum of the concentrations of nickel etioporphyrin and nickel etiochlorin. CB = concentration of nickel etiochlorin, ppm. DA, DB = calculated diffusion coefficients of A and B from the theoretical model, cm2/s. For all the runs the pressure is 9.65 MPa and the amount of catalyst in the reactor is about 5 g. These calculations are done with the rate constants which are not corrected for the lower inlet concentration. a
C, = C, + C,
LOCotlOn
2'o
:E n l r o n c e
Locotian :Maddlo
F
-
2.0
Locat son
-
E x ,t
:
1.6
-
-
E
-
1.2 -
1 I I.
I
I
1.0 .D .6 4
.2
0 .2
.4
.6 .B 10
r / R
rlR
r l R
Figure 2. Same as Figure 1 for run VE-7; calculated lines: (---) DA = DB = 1.6 X 10" cm2/s; (-) D A= 1.9 X 10" cm2/s;DB = 7.0 cm2/s. 3.2-
Lo~ol~on:M~ddie
2.8 I
r
2.4 1
1 2.0 i
10"
cm2/s;DB = 6.0 X
lo4
-
,
I 1
t
b
X
-
2.0
-I I
1I-
LOCOt8On
i
-
Eilt
-
7I
1.6
-
\
-1
E
I
I
JI
1-
I
1 0 6 6 4 2 0 2 4 6 8 1 0 rlR
1.0.8 6 .4 . 2 O .2 4 .6 .8 1.0 r l R
1.08 .6 , A
2
0 .2 4 r l R
Figure 3. Same aa Figure 1 for run VE-6; calculated linea: (---) DA = DB = 1.6 X 10" cm2/s; (-) DA = 1.9 X cmz/s.
vanadium than to nickel. When the same spot on the catalyst surface was analyzed several times in succession, the variation was k0.07 wt % in the vanadium readings and as high as *0.13 wt % for the nickel. Therefore, the magnitude of the error involved near the center of the
.6
lo*
.8 1.0
catalyst, due to the low metal loadings, is fairly high. The second kind of error is due to the uncertainty of the catalyst position in the reactor bed. Since the metal porphyrins are expensive, low flow rates and small catalyst bed heights must be used. The catalyst bed height was
518
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 3, 1984
i-
-1
0 1 0 8 6 4 2 0 2 4 6 8 1 . 0 r l R
riR
r 1 R
Figure 4. Nickel deposition profiles in catalyst, run NE-8. Same as in Figure 1: (0) experimental values; (-) calculated lines for DA = D B = 2.5 X lo4 cm2/a; (a) reactor entrance; (b) reactor middle; (c) reactor exit.
limited to 10 cm by the fact that at reasonable flow rates, less than 100% conversion is desired, so that the reactor outlet solution concentration may be monitored. Since the average length of the catalyst extrudate used is about 6 mm, it is difficult to specify the exact location of the catalyst sample. The best way to analyze the samples would be to analyze for the metal deposition on more than one catalyst extrudate at the same axial position, and then take statistical average of all the readings. However, the cost and the time involved in the analysis prohibited such an elaborate procedure. Therefore, in most cases, only one catalyst extrudate at the center of its axial position was scanned. Sometimes more than one catalyst at a particular axial position was scanned. The general magnitude of the reproducibility involved can be seen in Figures la, lb, 2b, and 2c. The analysis of the carbon, nitrogen, and nickel on the used catalyst from the nickel runs was made by Galbraith Laboratories (Knoxville, TN). The size of the samples required for this analysis was fairly large; therefore, the exact location of the samples in the bed was not known. Within each sample collected, there was a variation in the concentration of the above species from one catalyst particle to the other. On the average, the nitrogen and carbon contents of the catalyst seem to be functions of temperature, whereas the hydrpgen content is not. At 9.65 MPa and 343 OC,the values were 1.56 f 0.39 for % C and 0.33 f 0.05 for % N. At 9.65 MPa and 315 "C,the values were 2.49 f 0.54 for 70C, and 0.41 f 0.04 for 7O N, whereas 5% hydrogen at both the telqperatures was 0.78 f 0.09. The nickel deposition valves agreed with those found by the scanning electron X-ray microanalyzer. Discussion The hydrodemetallation kinetics from part 1were used to develop a consecutive kinetic model (Agrawal and Wei, 1984). In the hydrodemetalation of both the vanadium and nickel etioporphyrin, three major kinetic steps are involved k
A &B
k3
metal depostiop on catalyst and organic residue in solution where A is the model metal etioporphyrin in the solution and B is the reaction intermediate in the solution. The first kinetic step is hydrogenation to the reaction intermediate with a first-order dependence on the metal etioporphyrin concentration in the solution. The other two steps are dehydrogenationand demetalation of the reaction intermediate-both with first-order dependence on the reaction intermediate concentration in the solution. The reaction orders of hydrogenation, dehydrogenation, and demetalation rates on the hydrogen pressure are first, zero, and second, respectively. k2
The main assumptions involved in the development of the model are the following: (i) There are no axial and radial dispersion effects. (ii) The interphase resistance between the catalyst particle and the solution is negligible. (Si) The end effects in the catalyst particle can be neglected. This assumption would allow the treatment of the catalyst particle as a cylinder of infinite length. (iv) The diffusivities of A and B inside the catalyst do not change with time. For our runs the metal loadings on the catalyst particles were not large and this assumption is justified. If the metal loadings were large, then the change in the diffusivities as a function of loading would have to be considered. The criteria of Mears (1971a,b) were used to justify the assumptions (i) and (ii) (Agrawal, 1980). From the Fick's law, steady-state diffusion with the hydrodemetalation reactions inside an infinite cylinder can be described by the following equations
PC
Where V2 is the Laplace operator for the cylinderical coordinates. Ca and Cb are the concentrations of A and B inside the catalyst particle respectively, pc is the bulk density of the catalyst extrudates, and DA and DB are effective diffusivities of A and B. k l , k2,and k, are the rate constants for the hydrogenation, dehydrogenation, and demetalation kinetic steps, respectively. The boundary conditions for eq 1 and 2 are
where CA and CB are the concentrations in the solution at the outside of the catalyst. This set of equations can be solved analytically (Wei, 1962a,b). Once the concentration profiles inside the catalyst are known, the flux of each species per unit mass of the catalyst can be easily calculated from the following equations (4)
(5)
Ind. Eng. Chem. Process Des. Dev., Vol. 23,No. 3, 1984 519 Table 111. Comparison of the Experimental and the Calculated Reactor Outlet Solution Concentrations for Vanadium Runs
XI+
* - B h 4 y k 2 1 3 +
calcd deposit
The parameters kl+,k2+, k3+,and k4+ are functions of the kinetic rate constants, the extrudate radius, the density of the catalyst, and the diffusivities, and are called "diffusion-disguised rate parameters". In the intrinsic kinetic scheme, there is no direct path from A to deposit. Due to the interaction of diffusion and reaction, the global kinetics contains the diffusion-disguisedconstant k4+ that appears to be a direct step from A to deposit. Therefore, given the diffusivities and solution concentration at the outer surface of the catalyst, the flux per unit mass of the catalyst can be easily calculated. The mass balance over a differential section of the bed gives
--
-Q&A
dW
- fA
(8)
-Q&B
(9) dW = f B where dW is the weight of the catalyst in a differential length of the bed. Since in our runs only pure A enters the reactor, the initial conditions for these equations are at W = 0, CM = CA = CAO; CB = 0 (10) The above set of equations can also be solved analytically. Thus, we have the set of governing equations for the reactor. The kinetic rate constants have already been determined in part 1, and the only unknowns are the diffusivities. Experimental efforts to measure the diffusivities of nickel and vanadyl etioporphyrin8 were made with various techniques with required modifications (Komiyama and Smith, 1974; Satterfield et al., 1973; Weisz, 1966). In all these techniques it is necessary to have the equilibrium a h r p t i o n isotherm. Unfortunately, when the catalyst was left in the metal solution even at the low temperature of 60 "C, adsorption continued without attaining equilibrium. A chloroform extract of the spent catalyst showed new peaks in the visible spectrum range, which showed that reaction had occured on the catalyst surface. Therefore, in order to uncouple the diffusion effect, it was necessary to know the rate of the reaction on the surface. Furthermore, there was not a sufficient quantity of pure reaction intermediate for diffusion experiments. Due to these problems, the direct measurement of diffusivities was not successful. Instead, a theoretical estimate of the order of magnitude of diffusivities was made. The diameter of the metalloporphyrins is about 14.2 A. From the Stokes-Einstein equation it was estimated that the bulk diffusivity of a molecule of diameter 14.2 A in the white oil (Nujol) at 315 "C is 1 X lo4 cmz/s. To estimate the effective diffusivity in the catalyst, the configurational correction of Spry and Sawyer (1975) along with the tortuosity factor of 8 suggested by Shah and Paraskos (1975) was used. Catalyst porosity and void fraction were taken from Table I of part 1. The effective diffusivity thus calculated is 2.5 X lo4 cm2/s. In addition, the values of the diffusivities were calculated from eq 6 1 0 using the experimental values of the solution concentrations at the inlet and the outlet of the reactor. The amount of the catalyst in the reactor was known; therefore, for a given inlet solution concentration, the values of DA and DB were adjusted so that the outlet
run no. VE-3 VE-4 VE-5 VE-6 VE-7
equal diffusivity
exptl
c,'
cBb
10.8 6.5 16.8 8.4 9.6
1.62 1.05 2.82 1.16 1.5
C, 9.2 5.9 16.8 7.1 9.6
C, 2.63 1.55 4.04 1.76 2.26
unequal diffusivity cM
10.5 5.0 16.5 5.7 8.0
cB
1.75 1.04 3.45 1.11 1.45
' C, = total metal concentration. It is the sum of the vanadyl etioporphyrin and the reaction intermediate concentrations (in ppm). CB = reaction intermediate concentration (in ppm). concentrations calculated from eq 6-10 matched the experimental values. If the model applied above is accurate, then the values of the calculated diffusivities should be very reliable, since the bulk solution concentrations are analytically very reliable. Finally, the most critical test of the above set of equations is on the prediction of the metal deposition profiles inside the catalyst at various bed locations. Once the diffusion coefficients are known, then the concentrations C, and CBin the solution phase at any point in the reactor can be calculated from eq 6-10. These values of CA and CBalong with eq 1-3 give the concentration profile of the reaction intermediate B in the catalyst, and in time TR, the metal deposition profile, can be calculated as md = (k3c,,27@)io-4
(11)
The calculated metal deposition profiles were compared with the experimental profiles. The net weight average metal deposited in the catalyst can be calculated from the equation
Now resulta of the theoretical calculations will be compared with the experimental ones. 1. Vanadyl Etioporphyrin I. In the first model, it was assumed that at the reaction temperatures, the diffusivities of the vanadyl etioporphyrin I and the reaction intermediate are equal. However, no value of the diffusion coefficient can simultaneously match both the total metal concentration and the intermediate concentration in the outlet solution of the reactor. The experimental and the best calculated values of the outlet solution concentrations are summarized for some of the runs in Table 111. In the second model, the assumption of the equal diffusivities was relaxed. A remarkable agreement for both the total vanadium and the reaction intermediate concentrations at reactor outlet were obtained. A range of the diffusion coefficients which would match the outlet total metal concentrations from the use of eq 6-10 within f 2 ppm was accepted. In this range, the maximum variation in the values of the diffusivities was 40%. It should be pointed out that the error in the analysis of vanadium in solution atomic absorption can be easily as large as 1.5 ppm. As a next step from this range, the diffusivities which gave the best match to the location and the magnitude of the internal maxima in the metal deposition profile of the catalyst at the entrance of the reactor bed were accepted as the derived values of the diffusivities. Because of the magnitude of the error involved in the
520
Ind. Eng. Chem. Process Des. Dev., Vol. 23,No. 3, 1984
analysis of the total vanadium concentration in the reador outlet solution, this method of the search for the diffusion coefficient is justified. Once again, the calculated values of the reactor outlet solution concentrations are listed in Table 111. Good agreement for both the total vanadium and the intermediate concentrations was obtained. The calculated values of the diffusion coefficient for the various vanadium runs are tabulated in Table I. From this table we can draw the following observations. (a) The theoretically estimated value of the diffusion coefficient for the metal etioporphyrin in the white oil (Nujol) at 315 OC is 2.5 X lo* cm2/s. The calculated v a l u ~ are of the Same order of magnitude as the estimated values. This is an encouraging result. (b) The values of the diffusivities do increase with the increase of temperature and are independent of the operating pressure. This is, again, in agreement with the expected trend for the diffusivities in the liquid phase. (c) For a given temperature, the variations in the other operating parameter do not change the value of the diffusion coefficient. In Table I, all the runs at 343 “C have about the same diffusivities despite the fact that CAO,P, and W/Qhave changed. (d) For unequal diffusivities of A and B, the relative ratio of DBto D A is about 3-5. It is not clear why the diffusion coefficient for the reactor intermediate should be so much higher than the VO-etioporphyrin. VO-etioporphyrin is strongly adsorbed on the catalyst surface, but perhaps chlorins are not strongly adsorbed on the surface and diffuse on the surface. In the separation column, the VO-etioporphyrin adsorbs as a thin ring at the entrance of the alumina bed, but the reaction intermediate traveled far down in the column (Agrawal and Wei 1982). Therefore, it is possible that even under reaction conditions, the adsorption of the reaction intermediate is less strong than that of the VO-etioporphyrin. For surface diffusion to be significant, the adsorption on the surface should be strong, but not too strong as to immobilize the molecules on the surface. It is possible to have surface diffusion contribution in the liquid filled pores to be three to five times higher than the pore volume diffusion contribution. Komiyama and Smith (1974) studied the diffusion of benzaldehyde in hydrophobic polymeric porous amberlite particles and found that with water as the solvent, the surface diffusion flux was about 5 to 14 times the pore volume diffusion flux. Once the values of the diffusion coefficients were calculated, the next test of the model was to predict the metal deposition profiles inside the catalyst extrudates at various catalyst bed locations. It should be pointed out that most of the runs were made for 70-100 h, while the transient activity of the catalyst lasts for about 25-40 h. Since we are using the steady-state kinetics in the model, metals deposited during the transient would interfere with a good agreement between the calculated and the experimental metal deposition profiles. The calculated profiles are also plotted in Figures 1 to 3. Equations 6-10 were used to get the concentrations of A and B in the solution at the outer surface of the catalyst and then eq 1-3 were used to calculate the concentration of B inside the catalyst particle and finally eq 11was used for the metal deposition profile calculation. The dotted curves are the result of the assumption of equal diffusion coefficients while the continuous curves are obtained by the relaxation of this assumption. Just l i e the concentrations of the metal in the exit stream, the unequal diffusivities gave better agreement with the experimental deposition profiles. As Figures la, 2a, and 3a show, a t the entrance of the reactor the assumption of equal diffusivities predicts too
V O -Et10 Unoqual
01 0
Diffus v ~ N P S
I
,
I
I
02
04
06
06
RE-IZTIVE
HElGHl
I
i
343’C
P
965MPo
2
1
343’C,
P.
689qPo
3
1
315”C,
P
965
IC
‘ N BED
MPo
’ 286’C P 5 8 9 M P D Figure 5. Calculated average vanadium deposition profiles in the reactor for unequal diffusivities of reactant and intermediate. The values of the parameters used in calculations are Q = 19.5 mL/h, w = 5 g, CAo = 28 ppm, and total time on stream = 68 h; (1) T = 343 O C , P = 9.65 MPa; (2) T = 343 O C , P = 6.89 MPa; (3) T = 315 “C, P = 9.65 MPa; (4) T = 288 OC, P = 6.89 MPa. 4
much metal deposition at the internal peaks, and too little deposition at the center of the catalyst. This trend of higher predicted metal deposition at the edge and lower deposition near the center of the catalyst continues over the whole reactor bed as seen in Figures lb, IC, Zb, 2c, 3b, and 3c. At the entrance of the bed, the assumption of the unequal diffusivities improves the agreement between the calculated and the experimental values. This can be observed from the “a” series of the Figures 1to 3. However, the effect is more dramatic at the middle and exit catalyst bed locations. As seen from the “b” and “c” series of the Figures 1to 3, the agreement between the calculated and the experimental metal deposition profiles is remarkably good. Changes in the inlet solution concentration, LHSV, catalyst to inert ration, and the operating hydrogen pressure do not affect the agreement between the calculated and experimental profiles. The model not only predicts the metal deposition profiles inside the catalyst particles at various bed locations, but it also predicts the average metal deposit in the catalyst particle, given by eq 12, along the length of the bed. If a catalyst extrudate was dissolved in a suitable acid and the concentration of the metal analyzed, the wt 70 metal obtained could be compared to this prediction. For the case of unequal diffusivities of reactant and intermediate, the calculated results for three different temperatures and two pressures are plotted in Figure 5. It is seen that along the reactor bed length, the total metal deposition profiles have maxima which are not at the entrance. At high temperatures, the maximum is very high and near the entrance of the reactor. As the temperature is lowered, the maxima become more flat and move toward the exit of the reactor. Under the assumption of equal diffusivities, Figure 6 shows that the maxima are nearer the entrance of the bed, and the metal deposition profiles are not as steep as they were for Figure 5. In the middle and the exit sections of the reactor bed, the profiles in the Figures 5 and 6 are very close to being identical. 2. Nickel Etioporphyrin I. The same calculations were performed for nickel. The calculated profiles, along with the experimental values, are shown in Figure 4. There is a good qualitative agreement between the calculated and the experimental profiles, but it is not as good as the vanadium runs. A t low metal loadings, the error in the
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 3, 1984 521 Ni-Etio
0.8 "O
1 r ' l
L
2 -6,00.4
Li
I
. 5
0.6 6
5
ol 0
O Z
1
I
I
I
J
0.2
0.4
0.6
0.8
1.0
RELATIVE
0
02
04
06
0 8
0
R E L A T I V E HEIGH? IN BED I
I
343'c
F
0 6 5 MPO
2
1
343'C
P
689 M P o
3
1 1
315°C 288'C
P
9 6 5 MPa 689 M P a
4
F
Figure 6. Calculated average vanadium deposition profiles in the reactor for equal diffusivities of reactant and intermediate. Same as Figure 5.
analysis of nickel from the scanning X-ray microanalyzer is about twice that of vanadium. The results are tabulated in Table 11. The following observations are made. (a) Unlike the vanadium runs, the assumption of equal diffusivities for reactant and intermediate gives good agreement between the calculated and the experimental outlet concentrations. (b) Runs NE-4, NE-5, and NE-6 were made at the identical temperature, pressure, and flow rate and also about the same inlet concentration. The only difference between them was that for the runs NE-5 and NE-6, prior to the solution flow through the reactor, the catalyst was pretreated by purging with hydrogen for a half hour at the temperature of 370 "C. For the run NE-4, the catalyst pretreatment was similar to all other runs. The values of the diffusivities calculated for runs NE-4, NE-5, and NE-6 are nearly identical, and this proves that the pretreatment of the catalyst with hydrogen does not influence the catalyst performance. Moreover, it gives confidence in the reproducibility of runs. (c) Except the flow rate, Q, all other operating conditions were the same for the runs NE-7, NE-6, and NE-9. Within some scatter, the value of the diffusivity for all the three runs at 343 "C is 1.3 f 0.3 X 10* cm2/s. This magnitude of the error is not significant. In the literature, even under nonreacting conditions, the normal errors in the diffusivities measured for liquids in porous solids have been reported to be 50-100% (Copeland, 1978; Pitcher, 1972). (d) For nickel, one of the most critical tests for the suggested diffusion model would be to study the impact of the change in the inlet solution concentration on the diffusivity. For run NE-10, the inlet concentration was lower than NE7; otherwise, all the conditions were identical for both the runs. A t 343 "C, 9.65 MPa, and for the inlet concentration of 27 ppm, the rate constants kl,k2, and k3 measured are: 39.75, 153.5, and 146.2 mL/g-h, respectively. The model of the Langmuir isotherm with equally strong adsorption by nickel porphyrin, nickel chlorin, and the organic residue would predict that the rate constants are inversely proportional to inlet nickel porphyrin concentrations. The estimated rate constants k,, k2, and k3 for the run NE-10 are 63.9, 246.7, and 235.7 mL/g-h, respectively (Agrawal, 1980). With these estimated values of the rate constant, the value of the diffusion coefficient is calculated to be 1.5 X lo4 cm2/s. This is in excellent agreement with the values found for the other runs at 343 "C.This again suggests that within the concentration range of nickel etioporphyrin used in this study, the kinetic model with first-order rate constants and Langmuir isotherm is reasonably good.
H E I G H T lh
1
T = 343"C,
2
T:
BED
P.965
MPo
3 ' 5 " C , P = 9.65 M F o
Figure 7. Calculated average nickel deposition profiles in reactor: Q = 19.5 mL/h, w = 5 g, CAo= 27 ppm, and time on stream 68 h; (1) T = 343 O C , P = 9.65 MPa; (2) T = 315 O C , P = 9.65 MPa.
If in run NE-10 the rate constants are not corrected for the inlet concentration, the calculated value of the diffusion coefficient is 2.7 X lo4 cm2/s, which is much higher than the expected value of 1.3 f 0.3 X 10* cm2/s. (e) In Table 11,the high value of the diffusivity for runs NE-8 is anomalous. For this run,the temperature was 315 "C, but the value of the diffusion coefficient calculated is higher than the one at 343 "C. The calculated reactor outlet value of nickel etiochlorin is about 25% off from the experimental value. (f) All the diffusion coefficients listed in Table I1 have an order of magnitude agreement with the theoretical estimated value of 2.5 X lo* cm2/s. In Figure 7, the calculated averaged nickel deposits along the length of the reador are plotted. This figure is similar to Figures 5 and 6 for vanadium. The nickel deposit profile along the reactor is not as steep as that of vanadium. Conclusions Metal deposition profiles in 1.52-mm catalyst extrudates at various reactor bed positions have been studied. At the entrance of the bed, the maximum in the metal deposition occurs inside the catalyst and not at the external surface. In the middle and the exit sections of the bed, the maxima moved to the external surface, and the metal deposition profiles assumed the classical U-shape profiles. At the entrance of the bed, the location of the internal maximum inside the catalyst depends on the temperature and the pressure of the operation. Low temperature and low hydrogen pressure lead to lower Thiele moduli and the inward movement of the maximum. Theoretical calculations to simulate continuous plug flow reador operation with catalyst intraparticle mass transport limitations led to nickel and vanadyl etioporphyrin diffusivities of the order of lo4 cm2/s. This order of magnitude agrees with the theoretically estimated values of the diffusion coefficients. For vanadium, the reaction intermediate appears to have three to five times higher diffusivity than the vanadyl etioporphyrin. For nickel, both the etioporphyrin and etiochlorin appear to have the same diffusivities. Acknowledgment The authors are grateful to the National Science Foundation for support of the work under Grant No. ENG 75-16456. R.A. is also grateful to Raymond R. Cwiklinski of Massachusetts Institute of Technology for useful discussions. Nomenclature A = model metal etioporphyrin in the solution B = reaction intermediate in the solution CA = concentration of model metal etioporphyrin in solution, parts per million by weight, ppm
522
Ind. Eng.
Chem. Process Des. Dev. 1984, 23,522-528
CAP= concentration of the model metal etioporphyrin in the inlet solution to the reactor, ppm C, = concentration of model metal etioporphyrin inside the catalyst, ppm C B = concentration of the reaction intermediate in the solution, ppm Cb = concentration of the reaction intermediate inside the catalyst, ppm CM = total metal concentration in the solution, (CA + CB) DA = effective diffusivity of A in the catalyst extrudate, c m z / s DB = effective diffusivity of B in the catalyst extrudate, cmz/s fA = flux of A per unit mass of the catalyst f~ = flux of B per unit mass of the catalyst kl = first-order rate constant for hydrogenation step, (mL of solution)/ (g of cat. h) k , = first-order rate constant for dehydrogenation step, (mL of solution)/(g of cat. h) k3 = first-order rate constant for the demetallation step, (mL of solution)/(g of cat. h) kl+, k2+,k3+,k4+ = diffusion disguised rate parameters md = weight % metal deposition on the catalyst m d = net weight averaged metal deposition on the catalyst, %
P = hydrogen pressure of the reactor, MPa Q = solution flow rate to the reactor, mL/h R = radius of the catalyst extrudate r = radial length coordinate from the center of the catalyst extrudate T = temperature of the reaction, "C TR = time on stream, h W = weight of the catalyst, g p = solution density, g/mL pc = bulk density of the catalyst, g/mL Registry No. COO, 1307-96-6; MOO3, 1313-27-5;Ni, 7440-02-0; V, 7440-62-2;nickel etiochlorin, 89922-68-9; vanadyl etiochlorin I, 89922-69-0.
Literature Cited
Anderson, R. E. "Experimental Methods in Catalytic Research", Academic Press; New York, 1968; Chapter 1. Arey, W. F., Jr., Blackwell, N. E., 111; Reichie. A. D. Seventh World Petroleum Congress, Mexlco, 1967; p 167. Audibert, F.; Duhaut, P. Paper at the 35th Mklyear Meeting of the American Petroleum Instltute Dhrlsion of Reflnlng, Houston, TX. May 13-15, 1970. Beuther, H.; Schmld, E. K. Proceedings. 6th World Petroleum Congress, Sec. III, FrankfurtlMain, 1963, Paper 20, p 1-11. Bridge. A. G.; Green, D. C. Paper., Dlv. Pet. Chem., Am. Chem. Soc. 1979, 24, 791. Chao, K. C.; Seader. J. D. A I M J. 1861. 7 , 598. Copeland, T. M. Ph.D. Thesis, MIT, Cambridge, MA, 1978. Cukor, P. M.; Prausnk, J. M. J. Phys. Chem. 1972, 76, 598. Dautzenberg, F. M.; Van Kilnken, J.; Pronk, K. M. A.; Sie. S. T.; Wijffels, J. 8. ACS Symp. Ser. 1978, 65, 254. Docalswamy, L. K.; Tajbl, D. 0.Catal. Rev. Sci. Eng. 1974, IO, 177. Hardin, A. H.; Packwood, R. H.; Ternan, M. Prepr., Div. Pet. Chem., Am. Chem. SOC.1978, 23, 1450. Inoguchi. M.; Kagaya, H.; D a m , K.; Sakurade, S.; Satomi, Y.; Inaba, K.; Tate, K.; Nishiyama, R.; Onishi, S.; Nagai, T. Bull. Jpn. Pet. Inst. 1971, 13, 153. Komiyama, H.; Smb, J. M. A I C M J. 1974. 20. 728. Kwan, T.; %to, M. Nlppon Kagaku ZessM 1970, 91, 1103. Loev, E.; Goodman. M. M. "Progress In Separation and Purification"; Perry, E. S.; Van Oss, C. J., Ed.; Wliey: New Ywk, 1970; Vol. 3, p 73. Mears, D. E. Chem. Eng. Scl. 1971a. 26, 1361. Mears, D. E. Id. Eng. Chem. Process Des. Dev. W7lb, IO, 341. Oxenrelter, M. F.; Frye, C. G.; Hoekstra, G. E.; Sroka, J. M. Paper presented at the Japanese Pet. Inst., Nov 30, 1972. PNcher, W. H., Jr. Sc.D. Thesis, MIT, Cambridge, MA, 1972. Prathef, J. W.; Ahangar, A. M.; Pltts, W. S.; Heniey, J. P.; Tarrer, A. R.; Guin. J. A. I d . Eng. Chem. ProcessDes. Dev. 1977, 16, 287. Sato, M.; Takayoma, N.; Kurka, S.; Kwan, T. Nippon Kagaku Zasshi 1971, 9 2 , 834. Satterfield, C. N.; Coiton, C. K.; Pitcher, W. H.. Jr. A I C M J. 1973, 79, 628. Shah. Y. T.; Paraskos, J. A. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 388. Spry. J. C., Jr.; Sawyer, W. H. Paper presented at 68th annual AIChE Meeting, Lo8 Angeles. CA, Nov 16-20, 1975. Tamm, P. W.; Harnskger, H. F.; Bridge, A. G. Ind. Eng. Chem. Process Des. Dev. 1981. 20. 262. Todo, N.; Kabe, T.;.Ogawa, K.; Kurka, M.; Sato, T.; Slhmada, K.; Kurikl, Y.; Oshima, T.; Takematsu, T.; Kotera, Y. Kogyo Kagaku Zesshi 1971, 74, 563. Wel, J. J . Catal. 1982a, 1 , 526. Wei, J. J . Catal. 1962b, 1 , 538. W e k , P. E. Doctoral Dissertation, Swiss Federal Institute of Technology, Zurlch, 1966.
Agrawai. R. Sc.D. Thesls, MIT, Cambrldge, MA, 1980. Aqawai, R.; Wei, J. Ind. Eng. Chem. Process Des. Dev. 1984, Preceding article In this issue.
Received for review March 28, 1983 Accepted August 4, 1983
Design of Regenerative Noncontinuous Processes via Simulation F. Carl Knopf,'t 0. V. Reklaltlr,' and M. R. O k o d L b w f i m t of Chemlml E m , Lordslena Stet8 Unhrslty, Baton Rouge, Loulsiana 70803, Lbpartment of Chemlcal Englnwing, and Depafimnt of Agicuttwal Enghwing, pvro'ue Untverslty, West Lafayene, Indiana 47907
A generalized noncontinuous system ccmsisting of M parallel semicontinuous trains and their input queues, followed first by N parallel intermediate storage units and then by another stage of P parallel semicontinuous trains, is c-onsbred. A SLAM si" model is devekped which incorporates both multiproduct scheduting via dispatching rules as we# as optimal selection of processing rates and Hermediate storage volumes for regenerative processes, i.e., those that operate with cyclically reoccurring shutdown periods. A response surface strategy is used for executing the design optimization. An application with a fluid milk plant is described.
Introduction to Noncontinuous Processes Noncontinuous processes are representative of a considerable segment of the processing industry and are used to produce some of the highest unit price products. Department of Chemical Engineering, Louisiana State University. * Department of Chemical Engineering, Purdue University. 9 Department of Agricultural Engineering, Purdue University. 0196-4305/84/1123-0522$01.50/0
Noncontinuous operations are particularly prevalent in the food, pharmaceutical, polymer, and fine chemicals processing industries in which virtually all operations are of the batch semicontinuous type. Such operations are used in these industries because of the flexibility that they provide in accommodating the variable nature of the feed stock materials, the large number of products produced using similar recipes, the nature of the processing steps (e.g., bacterial culture), the inherent variability and seasonality of the market demand, as well as the short al0 1984 American Chemical Society
