533
Ind. Eng. Chem. Prod. Res. Dev. 1980, 19, 533-537
CATALYST SECTION Catalyst Pore Structures by Constrained Nonlinear Optimization L. Louis Hegedus' General Motors Research Laboratories, Warren, Michigan 48090
The COMPLEX method of Box was employed to optimize the pore structure and impregnation characteristics of pelleted catalysts for applications in automobile emission control. The activity of the catalyst after a fixed time period of poisoning was chosen as the objective function. The explicit floating variables included the macro- and micropore volumes and volume-integralaveraged pore radii, while implicit variables were introduced to control the surface area and pellet density. Various constraint strategies were employed to contain the variables within physically attainable bounds. The resutts strongly favor bimodal, bwdensity catalyst pellet structures. With respect to current catalysts, specific parametric improvementsare suggested which should be explored in experiments. The calculations indicate a potential for significant further improvement of catalyst performance.
Introduction Ever-strengthening emission control requirements have resulted in a steady improvement in the design of catalyst supports. In the case of pelleted catalysts, we have shown (Hegedus and Summers, 1975, 1977a,b, 1978a) that an intelligent restructuring of the pores of the support, together with choosing appropriate impregnation strategies (Summers and Hegedus, 1978; Hegedus and Summers, 1978b; Summers and Hegedus, 1979; Hegedus et al., 1979) should result in significant improvements in performance and durability. Such low-density catalyst structures have now been widely adopted, with notable success (Adomaitis et al., 1980). Even though significant progress occurred in this area, there is still room for further improvement. For example, even slight improvements in catalyst performance may lead to replacing the current dual-bed system by a single-bed system (Zemke and Gumbleton, 1980), with the potential of significant savings in hardware and complexity. As part of our efforts in developing improved catalysts, we undertook this analysis to investigate the possibilities of obtaining global optima for the pore structure of the pellets. The pore structure primarily affects poison resistance and lightoff characteristics, and thus the findings of this paper do not obviate the need to continue work on other catalyst characteristics such as thermal stability and performance under cycled conditions. Design Equations The pore structure of a catalyst pellet can be conveniently characterized by its pore size distribution, determined, e.g., by ultrahigh-pressure Hg porosimetry. For bimodal pore structures, the relevant quantities are Vmaao
(macropore volume)
(1)
Vmiao
(micropore volume)
(2)
* W. R. Grace & Co., Washington Research Center, Columbia,
Md. 21044.
0196-4321/80/1219-0533$01.00/0
f;,,,, =
1 x v m r du
(macropore radius)
(3)
Vmacro
f;nicro =
v,,1,,lv,rv,
(micropore radius) (4)
du
(solid density) (5) The following properties can be derived from these 1 (pellet density) (6) pP= 1 pa
Ps
+
Vmacro
emacrO= tmicro
+
Vmacro
Vmacrdp (macroporosity)
= Vmicropp
nmicroporositye
(7) (8)
The surface area of the catalyst is directly related to its pore structure. For bimodal pore structures, integral properties allow a reasonably good correlation s=- 2Vmacro Fmacro
2vmiao
+-
rmiao
(9)
For typical automobile exhaust catalysts, surface areas calculated from Hg porosimetric curves using the above formula agree surprisingly well with N2BET measurements, suggesting that only a very small fraction of the surface area is generated by pores smaller than about 15 A in radius, which is the lower limit of pores detected by ultrahigh-pressure Hg porosimetry. When typical numbers are substituted into eq 9, it will also become evident that the surface area is dominated by the micropores. Beyond the surface area, the pore structure also determines the diffusive characteristics of the support. We will employ the random pore model of Wakao and Smith (Smith, 1970) in these calculations, since we found it to correlate very well with diffusivity measurements and diffusion-influenced reactivity measurements (e.g., Oh et al., 1978). The random pore model considers both Kundsen diffusion (very small pores) and molecular diffusion (very 0 1980 American Chemical Society
534
Ind. Eng. Chem. Prod. Res. Dev., Vol. 19, No. 4, 1980
large pores) and accounts for the transition region. We will compute both the diffusivity of our reactant (in this case, propylene) and the poison precursor (H3P04),so that we can follow the rate of poison accumulation and the associated changes in catalyst activity at the diffusion h i t . These diffusion-limited calculations are relevant to both ends (rich and lean) of the A/F scale: NO is often diffusion limited at the rich end, and propylene and CO at the lean end (Hegedus et al., 1979). The following equations will be needed for the random pore model
N, is the saturation concentration of the poison in the poisoned shell. It was experimentally determined from electron microprobe measurements (Hegedus and Baron, 1978),and, for phosphorus poisoning, its value is 2.2 X 1015 molecules/cm2 support. cp,o is the time-averaged, gas-phase poison precursor concentration to which our catalyst pellet is exposed. Ita value depends on numerous variables, such as the phosphorus content of the fuel and oil, fuel and oil consumption, and the volumetric flow rate of the exhaust gas. Using eq 20 we can obtain resonable estimates of cpp if everything else is measured in a real-time experiment. Bip is the Biot number of the poisoning process
The mass transfer coefficient km was determined from the correlation of DeAcetis and 'rhodos, given in Smith (1970). The Newton-Raphson numerical inversion technique was used to compute 5 from eq 20. Once f has been determined, we can calculate the conversion performance of our poisoned reactor by first computing the diffusion-limitedreaction rate per catalyst pellet and integrating it for the reactor. The derivations are not shown here, but the result is = 1 - e-a
(22)
where 1
-1
Again, B ~ is A the Biot number of the main reaction krn,AR
1-l
(17)
The molecular diffusivities are computed separately. For DA, the Slattery-Bird model (Bird et al., 1960) was used while the Chapman-Enskog model (Bird et al., 1960) was found suitable to calculate Dp (see also Hegedus and Baron, 1978). With all these, the effective diffusivities are computed from
Since on the time scale of the poisoning process the converter is well mixed (i.e., the pellets move around), it is sufficient to characterize the poison penetration into a single catalyst pellet. We have ample evidence (e.g., Hegedus and Baron, 1978) that the poisoning process is diffusion limited, and thus the shell-progressive model of Carberry and Gorring (1966) can be employed, giving the following implicit function for the fractional poison penetration f after an elapsed time, t
BiA = 7 Ueffa
where kmA was determined from the correlation of DeAcetis and Thodos (Smith, 1970). Optimization Technique and Strategy The COMPLEX method of Box (1965) was employed. Our version is based upon its interpretation by Kuester and Mize (1973). The method is a sequential search technique which effectively finds global optima for problems involving nonlinear objective functions subject to explicit and implicit nonlinear inequality constraints. In our use, these constraints were a convenient means to bracket the range of variables within physically attainable boundaries. The calculations proceeded as follows: Vmacro,Vmicro, F-, and F~~ were the independent variables, their values to be optimized such that the conversion performance of the reactor after a predetermined time on stream (eq 22) is maximized. Initial guesses were placed on the independent variables, and the calculations proceeded through eq 6 to 24. The value of a (eq 23) served as the objective function. Besides explicit boundaries (constraints) placed on the independent variables, we also employed two implicit constraints. One of these was placed on the pellet density pp (eq 6); experience indicates that excessively low pellet densities may result in physical erosion and mechanical crushing. We also bracketed the surface area (eq 9); again, experience shows that it is not possible to stabilize arbitrarily high surface areas at the operating conditions of automobile exhaust catalysts.
Ind. Eng. Chem. Prod. Res. Dev., Vol. 19, No. 4, 1980 535 "macro
/'J
7'
\
iicro
Figure 1. Snowflake diagram of an optimized catalyst structure s, and , pp as a current low-density placing the same bounds on i ~ c m structure. The parameters were normalized against those of the current support and these normalized values are shown in Figures 1 to 5. Table I. Constant Parameters cp
(mol/cm3)
T '(K) MA MP
vr (em3) A (em2) R (em) E
P (torr) Q (cm3/s) P s (g/cm3) t (SI
0.4 x 773 42 (propylene) 98 (H,PO,) 2622 (type 160 converter) 516 0.16 0.36 760 92133 3.52 (alumina) 5.76 x lo6 (1600h )
Results a n d Discussion Table I shows the parameters which were kept constant in the calculations, while the constraints are listed in Table 11. The inlet poison concentration (cP& was evaluated by observing the poison penetration into a typical commercial, low-density catalyst after dynamometer aging. The properties of this reference catalyst are shown in Table 111, together with the results of the optimization calculations
Figure 2. Relaxing the lower bound on Fmicro.
employing different constraint strategies. If liberal constraints are employed, the pore structure tends to converge toward very low densities and very high surface areas. In run no. 1 (Tables I1 and 111),we limited the minimum value of the micropore radius, the maximum value of the surface area, and the minimum value of the pellet density to those of the reference catalyst. The results (shown normalized against the properties of the reference catalyst, Figure 1) indicate that a better performance can be obtained if the bimodality of the catalyst is increased (larger macropore volume and radius, smaller micropore volume). The results suggest to trade some of the surface area for macropores. The required impregnation depth (indicated by the fractional poison penetration depth 5) will have to be larger. If these changes are made, the catalyst would improve its conversion performance as reflected in the increased value of CY, without interfering with its density. Let us now gradually relax some of these restrictions. Run no. 2 (Tables I1 and 111, Figure 2) keeps the production catalyst's constraints on pellet density and surface area, but allows the micropore radius to converge to the lower bound of 50 A. Further significant improvement in performance is noted resulting from a restructuring of the
Table 11. Constraints -
run Vmacro, cm3/g Vmicro, cm3/g rmaw, A no. lower upper lower upper lower upper 1 >O 2 >O 2 500 100000 2 >O 2 >O 2 500 100000 3 >O 2 >O 2 500 100000 4 >O 2 >O 2 500 100000 5 >O 2 >O 2 500 100000
-
rmiao, A
6,
lower
upper
lower
110.5 50 50 50 50
500 500 500 500 500
>O >O >O >O >O
mZ/g upper
Pp,
lower
114.5 114.5 150 150 150
0.783 0.783 0.783 0.700 0
g/cm3 upper
3.52 3.52 3.52 3.52 3.52
Table 111. Results run no. ref a 1
Vmacro,
cm3[g 0.366 0.569 0.707 0.629 0.770 1.154
Vmicro,
cm3/g
0.627 0.424 0.286 0.364 0.375 0.374
-
rrnacro, A
6 962 99 327 98 435 96 574 99 991 99 631
-
rmicro, A
110.5 110.5 50.0 50.0 50.0 50.0
S, m'/g
114.5 75.6 114.5 149.6 150.0 150.0
PP,
g/cm3
0.783 0.783 0.783 0.783 0.700 0.552
5
0.0396 0.0666 0.0559 0.0443 0.0493 0.0645
cy
2.69 3.12 2 4.28 3 4.35 4 4.48 5 4.57 a Catalyst used as a reference (current low-density, production design). The N, BET surface area of this catalyst is 113.0 m2/g, in good agreement with the value computed from the Hg porosimetric curve and listed above (114.5m'/g).
536
Ind. Eng. Chem. Prod. Res. Dev., Vof. 19, No. 4, 1980 “macro
iz
/3
Figure 3. Relaxing the lower bound on P~~~ and the upper bound on s.
Figure 4. Relaxing the lower bound on T s, and the lower bound on pp.
“macro
~ the~upper ,
bound on
pores as indicated (again, favoring bimodality). (Note that this catalyst still has the same density and surface area as the production catalyst!) Making further advances, we can now relax the upper bound on the surface area, from 114.5 to 150 m2/g (run no. 3, Tables 11and 111, Figure 3). The system immediately converges to nearly 150 m2/g surface area, but again a restructuring of the pores is suggested as indicated. This catalyst will have a slightly further improved performance, still at the pellet density of the commercial support. Let us now also loosen the restriction on the pellet density, allowing it to go to, say, 0.700 g/cm3 (run no. 4, Tables I1 and 111, Figure 4). The result is a further incremental performance improvement, and, again, a more pronounced bimodal pore structure than possessed by the production catalyst. Finally, disregarding possible mechanical problems, we removed the lower bound on the pellet density by simply confining it to positive values. Since the pore structure has to simultaneously satisfy both diffusivity and surface
Figure 5. Relaxing the lower bound on idm, the upper bound on s, and removing the lower bound on pp.
area requirements, we expected that the optimum pellet density will converge to some finite value. Indeed (Tables TI and 111, Figure 5 ) , an “ultimate” pellet density of 0.552 g/cm3 was computed for the conditions of run 5. Although the conversion performance improved only marginally with respect to runs 2 to 5, such ultralight pellets would, of course, possess significantly lower thermal inertia and thus excellent warmup characteristics. The value of a is indicative of the performance of the individual catalyst pellets. For the particular operating conditions and converter size employed in these calculations, even the reference catalyst provided a conversion of 93.2% after aging, which was improved from runs 1 through 5 to 95.6%, 98.6%, 98.7%, 98.9%, and 99.0%, respectively. Since the catalytic converter was sized to perform well using the reference catalyst, the computed incremental conversion improvements for the optimization runs are small. Note, however, that the intrinsic activity of the poisoned catalyst pellets improved by a factor of up to 1.7 upon restructuring their pores; this improvement may allow a significant reduction in the size of the catalytic converter at constant final conversion. The optimization results suggest rather large macropore radii. In practice, such structures can be obtained by, e.g., the embedding of polymeric microspheres into the pellets, which are subsequently destroyed by air calcining (Bedford and Berg, 1977). Beyond the detailed properties of the support, the calculations also show the expected penetration depth of the poison; this information is, of course, useful in determining the corresponding noble metal impregnation strategies. Nomenclature A = reactor frontal cross-section, cm2 Bi = Biot number (see text) cPg = poison precursor concentration, mol/cm3 e = conversion of reactant after aging D = molecular diffusivity, cm2 s Deff= effective diffusivity, cm /s DK = Knudsen diffusivity, cm2/s k, = mass transfer coefficient, cm/s M = molecular weight, g/mol N A = Avogadro’s number N p = number of catalyst pellets in reactor
1
537
Ind. Eng. Chem. Prod. Res. Dev. 1980, 19, 537-541
N , = saturation concentration of poison, molecules/cm2 P = Pressure, torr Q = volumetric gas flow rate, cm3/s 7 = volume-averaged pore radius, cm or A R = pellet radius, cm s = surface area, cm2/g or m2/g t = time, s T = temperature, K V = pore volume, cm3/g V , = reactor volume, cm3 a = constant in eq 22 e = porosity 6 = fractional poison penetration depth into a catalyst pellet pa = solid density, g/cm3 pp = pellet density, g/cm3
Literature Cited
Bird, R. B.; Stewart, W. E.; Llghtfoot, E. N. “Transpat phenomena”, Wlley: New York. 1960. BOX, M. J. Comput. J . 1965, 8 , 42. Carberry, J. J.; Gorring, R. L. J. Catal. 1966, 5, 529. Hegedus, L. L.; Summers, J. C., 4th North American Meeting of The Catalysis Society, Toronto, Ont., Canada, Feb 18, 1975. Hegedus, L. L.; Summers, J. C. J. Catal. 1977a, 48, 345. Hegedus, L. L.; Summers, J. C. US. Patent 4051 073, Sept 27. 1977b. Hegedus, L. L.; Baron, K. J. Catal. 1978, 54, 115. Hegedus, L. L.; Summers, J. C. U.S. Patent 4 119571, Oct 10, 1978a. Hegedus, L. L.; Summers, J. C. U.S. Patent 4 128 506, Dec 5, 1978b. Hegedus, L. L.; Summers, J. C.; Schlatter, J. C.; Baron, K. J. Catal. 1979, 56, 321. Kuester, J. L.; Mize, J. H. "Optimization Techniques wtth Fortran”, McGrewHiii: New York, 1973. Oh, S. H.; Baron, K.; Cavendish, J. C.; Hegedus, L. L. ACS Symp. Ser. 1978, 65, 461. Smith, J. M. “Chemical EngineeringKinetics”, M&aw-HIiI: New York, 1970. Summers, J. C.; Hegedus, L. L. J. Catal. 1978, 51, 185. Summers, J. C.; Hegedus, L. L. U.S. Patent 4153579, May 8 , 1979. Zemke, B. E.; Gumbieton, J. J. Society of Automotive Engineers, Paper No. 800398, Detroit, Mich., Feb 28, 1980.
Adomaitis, J. R.; Smith, J. E.; Achey, D. E., Society of Automotive Engineers, Paper No. 800084, Detroit, Mich., Feb 25, 1980. Bedford, R. E.; Berg, M. US. Patent 4051 072, Sept 27, 1977.
Received for review July 31, 1980 Accepted August 26, 1980
Chloriding of Pt-AI2O3 Catalysts. Studies by Transmission Electron Microscopy and X-ray Photoelectron Spectroscopy Francls Delannay, Camille Defosse,’ and Bernard Delmon Groupe de Physico-Chlmle Minerale et de Catalyse, Universit6 Catholique de Louvaln, B- 1348 Louvain-la-Neuve, Belglum
P. Govlnd Menon and Gllbert F. Froment Laboratorlum voor Petrochemische Techniek, Rijksuniversiteit Gent, 8-9000 Gent, Belgium
The changes occurring to R-Al2O3 catalysts on chloriding them with CCI4 in H2 or dry HCI gas were studied by X-ray photoelectron spectroscopy (XPS or ESCA) and transmission electron microscopy (TEM). The TEM results show that R crystallites grow in size and the clusters of the crystallites are dispersed on chloriding with CCI4, but not with HCI. The XPS data support the observation on the crystallie size from TEM. They also indicate that coke laydown during the CCI4 treatment occurs preferentiallyon the surface of Pt crystallites. These results account for the decrease in H2 chemisorption capacity and the strong attenuation of the hydrogenolysis activity of the CC14-chloridedcatalyst. The coke content and CI content of the catalyst calculated from XPS data are of the same order as the values determined independently from direct combustion of the coke and electron-probe microanalysis of CI, respectively.
Introduction In bifunctional Pt-A1203-typecatalysts used for catalytic reforming of naphtha to produce higher-octane-number gasoline or aromatics for the petrochemical industry, a careful balance has to be maintained between the hydrogenation-dehydrogenation function of Pt and the acid function of A1203. If the metal function is too strong, excessive hydrogenolysis to C1-CI gases and dehydrogenation to polyolefinic coke precursors can occur; if it is too weak, then the catalyst also gets deactivated very soon due to excessive coking. If the acid function is too strong, it leads to excessive hydrocracking, coke lay-down on the catalyst, and consequent catalyst deactivation; if it is too weak, the rate-determing carbonium-ion reactions involved in dehydroisomerization and dehydrocyclization do not proceed fast enough, which in turn leads to an increase in
’ChargB de Recherches FNRS (Belgium). 0198-4321/80/1219-0537$01 .OO/O
C1-CI gas production and a decrease in the yield of liquid reformate. Moisture in the naphtha feed and chlorine in the catalyst are the two main factors which control the acidity of the catalyst under actual reforming conditions. While water enhances the Bronsted acidity of A1203 at the reforming temperature of 490-520 OC, above 20 ppm levels it also strips off the chlorine from the catalyst, thereby lowering its acidity at the same time; the net result in such cases is sometimes the acute corrosion in downstream equipment due to the wet HC1 gas at high temperatures. More often, however, the chlorine stripped off from the catalyst, particularly during catalyst regeneration, has to be replenished by addition of an organic halide such as CCL, either in one lot at the start of the cycle after the regeneration or continuously at ppm levels in the feed. In the patent literature (for a review, see Birke et al., 1979) such additons of chloride to the catalyst have been claimed to enhance the stability of Pt crystallites on the alumina surface and 0 1980 American Chemical Society
