390
Ind. Eng. Chem. Prod. Res. Dev. 1982, 21, 390-397
(415) Sallmgareeva, F. G.; Davidovlch, B. V.; Ivanova, M. F.; Kalechlts, I. V. Tr. Vostoch. a i r . Fib&, Akad. Neuk SSSR, Ser. Khhn. 1959, (18). 87; Chem. Absf. 1060. 54. 14636. (416) Jelinek, J. F. Chem. Rumysl1956, 8 , 397. (417) Jellnek, J. F. Chem. PTUmysl 1961, 72, 4. (418) Jellnek, J. F. Sb. R . Vyzk. Chem. Vyuzffi Uhli, Dehfu R q y 1962, 2, 70; Chem. Abstr. 1965, 62, 5117. (419) Jellnek, J. F. qollect. Czech. Chem. Commun. 1963, 28, 504. (420) Wells, 0. L.; Long, R. British Patent 999 472, July 28, 1965; Chem. Abstr. 1965, 63,9711. (421) Mllnes, M. H. Coal Tar Research Association (CTRA) Report No. 0283, 1961. (422) Milnes, M. H.; Dean, R. E. J . Appl. Chem. Blofechnoi. 1971, 27, 287. (423) Mllnes, M. H.; Dean, R. E. J . Appl. Chem. Biofechnol. 1972, 22(10), 1095. (424) Wells. G. L.; Long, R. Ind. Eng. Chem. Prod. Res. Dev. 1962, I , 73. (425) Davies, G. A. Report on Gas Council Research Scholarships 1963; Res. Commun. QC 95. (426) Davles, G. A.; Long, J . Appl. Chem. 1965. 75, 117. (427) Moghul, Y. A.; Yamazakl, Y.; Kawai, T. Bull. Jpn. Pet. Inst. 1973, 15(1), 23. (428) Kawase,'T.; Arai, H.; Tominaga, H.; Kunigl. T. Kogyo Kageku Zasshi 1970, 73(5)959; Chem. Abstr. 1971, 7 4 , 12437. (429) Kubicka, R. Czech. Patent 103744, May 15, 1962; Chem. Absfr. 1964, 60, 2832. (430) Beranek, L.; Kraus, M.; Bazant, V. Collect. Czech. Chem. Commun. 1964, 29, 239.
(431) Jost, F.; Bazant, V. Collect. Czech. Chem. Commun. 1961, 26, 3020. (432) Jost, F.;Kadlec, J.; Bazant, V. Czech. Patent 99012, Mar 15, 1961; Chem. Absf. 1982, 57,13680. (433) Jost, F.; Klyachko Gwvlch, A. L.; Rubinshtein, A. M. Izv. Akad. Nauk SSSR, Ser. Khlm. 1963. (12), 2105. (434) Jost, F.; Tomanova, D.; Banner-Volgt, A.; Collect. Czech. Chem, Commun. 1964, 29(7), 1626. (435) Kadlec, J.; Bazant, V. Coltect. Czech. Chem. Commun. W61, 26, 1201. (436) Kadlec, J.; Jost, F.; Bazent, V. Collecf. Czech. Chem. Commun. 1961, 26, 818. (437) Bakelite Ltd. British Patent 519721, Apr 4, 1940; Chem. Absfr. 1942, 36,97. (438) Good, G. M.; Holzman, G. U.S. Patent 2678337, May 11, 1954; Chem. Abstr. 1955, 49, 9038. (439) El'bert, E. I.; Kostyuk, L. B.; Panfiiov, I . A,; Biryukova, M. E. Pererab. Tverd. Top/. 1970, (2), 146. (440) Bovkun, R. A.; El'bert, E. I.; Morozova, S. N.; Usenko, L. L. Pererab. Tverd. Topl. 1970, (2), 130. (441) El'bert, E. I.; Katsobashvili, Ya. R.; Smirnov, V. K., Barino, G. I . , Splglazova, E. V. Pererab. Tverd. Topl. 1970, (2), 99. (442) Rutkowskl, M. Zesqfy Nauk. Mitech. Wroc&w., Chem. 1965, (12), 3; Chem. Abstr. 1966, 64, 17301.
Received for review December 10, 1981 Accepted March 22, 1982
CATALYST SECTION Deactivation by Carbon of Nickel, Nickel-Ruthenium, and Nickel-Molybdenum Methanation Catalysts A. Douglas Moeller and Calvin H. Bartholomew' &pami"
of Chemlcal Engineeringr Brigham Young University, Rovo, Utah 84602
The deactivation of Ai,03-support6d Ni, Ni-Ru, Ni-Mo, and Ni-Mo-Cu catalysts during high-temperature, combined shift/methanatlon was investigated. Activii-time measurements were conducted for each catalyst over a period of 24 h at 723 K, 138 and 2600 kPa in a fixed bed reactor and at 138 kPa in a fluidized bed reactor. Effects of carbon deposits and regeneration treatments in air or oxygen on metal surface area and specific intrinsic activii were measured for each catalyst. The results establish that Ni and Ni-Ru are significantly more resistant to deactivation by carbon deposits than Mo-containing catalysts. Ni-Mo-Cu deactivates more rapidly than Ni-Mo in a fluidized bed at 138 kPa and in a fixed bed at 2600 kPa. Regeneration of these catalysts in air at 573 K restores specific intrinsic activity but causes signiflcant loss of metal surface area. A model for deactivation is proposed which c a n be used to estimate catalyst life under carbondepositing conditions. Mechanisms of deactivation are discussed.
Introduction
A serious problem in the catalytic methanation of coal synthesis gas is fouling of the catalyst by carbon deposits (Bartholomew, 1982). This problem can be avoided by increasing the hydrogen content of the feed stream so that kinetics or thermodynamic equilibria are unfavorable toward carbon deposition (Gardner and Bartholomew, 1981a; Whalen, 1976); however, process economics favor minimizing hydrogen usage. Since most gasifiers produce a hydrogen-deficient gas, the application of a methanation catalyst which deposits carbon at negligible rates would be highly desirable since it would eliminate the need for the shift reactor prior to methanation. Except for a few recent studies in this laboratory (Weatherbee et al., 1980; 0196-4321/82/ 1221-0390$01.25/0
Bartholomew, 1977, 1980; Gardner, 1979; Gardner and Bartholomew, 1981a), there has been very little research to determine the effects of carbon deposits on adsorption and activity/selectivity properties of methanation catalysts or to understand the kinetics and mechanisms of catalyst deactivation by carbon during methanation. Such information is needed to establish catalyst types which resist deactivation by carbon and to determine optimum operating conditions for methanation of hydrogen-poor synthesis gas mixtures in combined shift/methanation processes. A previous study in this laboratory (Fowler and Bartholomew, 1979) showed that Ni-Mo catalysts are promising for use in the BI-GAS since they are as active as Ni 0 1982 American Chemlcal Society
Ind. Eng. Chem. Prod. Res. Dev., Vol. 21, No. 3, 1982 391 Table I. Catalyst Compositions and Suppliers metal compn, w t %
a
cat.
Ni
Ni Ni-Mo Ni-Mo-Cu Ni-Ru
14 10.9 10 10
Mo 19.8 9“
cu
Ru
bulk density, g/cm3
0.5
0.54 0.91 0.86 0.84
3
support y -A1,0,
A1,O,SiOzd A1Z03
A1203
supplier BYUe Catalysis Lab Climax Moly. Corp. Harshaw Chem. Co. Matthey-Bishop Inc.
Powder form. Kaiser SAS medium; 0.32-cm spheres used in preparation; ultimately crushed t o a Harshaw A1-1605P (91% AlZ0,, 6% SiO,). e Brigham Young University; Le., this laboratory.
W t % MOO,.
powder.
but more resistant to sulfur poisoning. Ni-Ru catalysts show promise in terms of their resistance to deactivation by carbon (Weatherbee et al., 1980) and sintering (Pannell, 1978) as well as their high activity and stability in fluidized bed methanation (Tucci and Streeter, 1980). The present study was undertaken to determine the behavior of Ni, Ni-Mo and Ni-Ru catalysts under reaction conditions characteristic of combined shift/methanation and thermodynamically favorable for carbon formation. The objectives of this study were (1)to determine the effects of carbon deposition on the metal surface areas and activity/selectivity properties of these catalysts under high temperature conditions (both low and high pressures) which favor carbon formation, and (2) to determine if the carbon-fouled catalysts could be regenerated by treatment in air or O2at moderately high temperatures. The results of activity, adsorption, carbon deposition, and regeneration tests to accomplish these objectives are presented and discussed in this paper.
Experimental Methods Materials. Catalyst compositions and suppliers are listed in Table I. Catalyst preparation and pretreatment were the same as described previously (Fowler and Bartholomew, 1979). Hydrogen gas (99.99%, Whitmore) was purified using a Pd catalyst followed by a molecular sieve trap. Gases for the reaction mixtures, N2 (99.99%, Whitmore), CO (99.99%, Matheson), CHI (99.97%, Matheson), and C02 (99.8%, Whitmore) were used as delivered. The reaction mixture for the carbon deposition runs was passed through an activated charcoal trap heated to 473 K and a ZnOl molecular sieve trap heated to 353 K to remove any iron carbonyl and sulfur impurities before undergoing methanation. Catalyst presulfiding treatments were carried out using a 66 ppm H2S in H2 mixture prepared in this laboratory and diluted to 9 ppm with hydrogen. Procedure. H2 Chemisorption. Prior to each test series, small samples (0.2-0.6 g) of each catalyst (previously reduced overnight in large batches at 773 K) were rereduced at 773 K as previously described (Fowler and Bartholomew, 1979). H2 adsorption isotherms were then measured at 298 K following procedures reported previously (Bartholomew, 1975; Bartholomew and Farrauto, 1976; Bartholomew and Pannell, 1980). H2chemisorption measurements were also performed following each series of tests to detect any changes in the catalyst surface area, and in the case of catalysts analyzed for carbon content, Hzchemisorption measurements were made directly after carbon deposition. Specific Rate Measurements. Specific rates were measured in the same differential manner as in our previous study (Fowler and Bartholomew, 1979) using 0.5 to 1mL samples in a Pyrex, fixed-bed reactor a t 498 K and 138 kPa before and after low-pressure steady-state carbon deposition runs and after low- or high-pressure regeneration or in a stainless steel, high-pressure reactor described previously (Fowler and Bartholomew, 1979) before and
CARBON
A REGION
HYDROGEN
OXYGEN
Figure 1. Equilibrium diagram at 723 K and 138 kPa showing BI-GAS and test feed gas compositions: (A) BI-GAS; (B) fluidized bed runs; (C) high and low pressure runs plus some differential runs; (D) differential runs. Curve 1 is the equilibrium curve based on graphite. Curve 2 is based on “nonideal” carbon as reported by Rostrup-Nielsen (1972).
after high-pressure carbon deposition runs. Specific rate measurements for catalysts deactivated in a fluidized bed reactor (Fowler and Bartholomew, 1979) were performed in the Pyrex, fixed bed reactor after regeneration. The reactant mixture used for catalysts tested at low pressures was 1%CO, 4% H2 and 95% N2 while that used in activity measurements before and following high-pressuretats was 4.3% CO, 5.6% H2, and 90.1% N2 The latter composition was chosen to simulate combined shift/methanation conditions in the BI-GAS process and to determine the effects on specific activity of changing gas composition. Steady-State (24 h) Carbon Deposition Runs. After initial specific rate measurements, each catalyst was tested in a fixed-bed reactor (Pyrex or stainless steel) for approximately 24 h under steady-state conditions at 723 K and pressures of 138 kPa or 2600 &Pa to observe its behavior under severe carbon depositing conditions representative of combined shift/methanation. Two samples of each catalyst were run at the lower pressure. One was used for regeneration tests and one was analyzed for carbon content. The space velocity for all fixed bed, steady-state carbon depositing runs was 100000 h-l, a space velocity sufficiently high to maintain a high partial pressure of CO at the surface thereby ensuring measurable rates of carbon deposition (Weatherbee et al., 1980). Operation under carbon depositing conditions as predicted by equilibrium calculations was ensured by using a 4.2% CO mixture (in a N2diluent) and a H2/C0 ratio of 1.3. Figure 1shows this composition on a carbon-hydrogen-oxygen triaxial equilibrium composition diagram (point C) along with the 1 % CO mixture having H2/C0 = 4 (point D) and the nominal BI-GAS feed gas composition having Hz/CO = 1.4 (point A). Sample sizes were again 0.2-0.6 g for lowpressure runs and 1mL for high-pressure runs. Reactant and product sampling was performed chromatographically in the same manner as in our previous in situ deactivation measurements (Fowler and Bartholomew, 1979). Samples of Ni-Mo-Cu and Ni-Mo (0.5 g each) were tested in a fluidized bed reactor (Fowler and Bartholomew, 1979) for 24 h at 723 K, 45000 h-’ and 138 kPa in order
392
Ind. Eng. Chem. Prod. Res. Dev., Vol. 21, No. 3, 1982
Table 11. Results of Differential Reactor Tests (498 K and 138 kPa) low pressure carbon depositionu H2
cat. Ni pre-carbon deposition post-carbon deposition post-regeneration f post-regeneration + 20 h at 623 K Ni (presulfided) pre-carbon deposition post-carbon deposition post-regeneration
uptake,c pmol/g 163 142 135
_.-
___89 99
NCH $ s-1 ~
~
1
0
high-pressure carbon deposition
yield, % e CH, CO,
3
2.4 2.6 2.1
69 43 68
0 0 0
2.0 1.9 2.4
66 42 85
19 0 0
___
H* uptake, Mmol/g
NCH s - 1 ~ 1’03
yield, %
CH,
CO,
1.5 0.8 2.7 2.7g
14 1 14
___ ___
___ ___
_-_
--_
Ni-Ru pre-carbon deposition post-carbon deposition post-regeneration
89.4 147.2h 66.2
2.4 1.5 2.1
52 91 81
0 0 0
1.1 0.7 0.7
0 0 0
Ni-Mo pre-carbon deposition post-carbon deposition post-regeneration post-regeneration FBR
83 51 24 41
2.8 0.16 2.5 2.2
53 13 23 43
3 26 21 9
0.35 0.04 2.6
20 71 42
Ni-Mo-Cu pre-carbon deposition post-carbon deposition post-regenerat ion post-regeneration FBR’
52 37 30 25
0.11 0.15
28 27 21
31 46 3y
0.11 0.01 0.31
69 73 34
25 _-
1;
___ _-_ ___
__
Ni-Mo-Cu (presulfided) pre-carbon deposition post-carbon deposition post-regenerat ion
20
__
18
0.11
...I
0.22 ___I
___ j
.I
___ i
__
1
___
a Steady-state deactivation test conditions: 773 K, 138 kPa, 4.2% CO, H,/CO = 1.3; specific rate measurement conditions: 498 K, 138 kPa, 1% CO, H,/CO = 4. Steady-state deactivation test condition: 773 K, 2600 @a, 4.2% CO, H,/ CO = 1.3; specific rate measurement conditions: 498 K, 138 kPa, 4.3% CO, HJCO = 1.3. Total H, adsorption uptake at 298 K. N C H (turnover number) is the number of methane molecules produced per site per second. e Yield is percent CO converted d h i c h goes to CH, or CO,. f Regeneration in 1-3% air/N, at 573 K , 138 kPa o r 1-4% OJN, at 573 K, 2600 kPa. Specific rate measurement conditions same as in footnote a . Measured at 373 K ;H, uDtake of fresh catalvst at 373 K is i39.9 Mmol/g. FBR: Fluidized Bed Reactor run. i TOO low to measure accuritefy.
to simulate more closely the BI-GAS process. The reaction mixture, a dilute versidn of the BCR process mixture, was of the following composition: 5.3% CO, 6.5% H2, 1.6% CH4, 3.6% C02,and 83.0% N2 These runs were repeated using fresh samples (0.5-0.6 g) and a 4.2% CO, 5.5% H2, 90.3% N2 mixture to obtain samples for carbon analysis. Regeneration Tests and Passivation. Regeneration tests were performed using a 1-3% air in N2 mixture at 138 kPa for catalysts deactivated a t low pressure and a 1-4% O2 in N2 mixture at 2600 kPa for those dewtivated at high pressure. In both cases the temperature was 573 K. Catalysts deactivated in a fluidized bed were also regenerated in a fluidized bed using dilute air at 573 K. During regeneration CO and C02 concentrations in the product stream were monitored continuously with the chromatograph for 15 to 30 min. Generally, after 30 min the COz concentration was negligible, indicating completion of carbon removal. The catalysts which had undergone either high-pressure regeneration or low-pressure fluidized bed regeneration were transferred to the fixedbed Pyrex reactor cell to facilitate subsequent specific rate and H, chemisorption measurements. Presulfiding Runs. Samples (0.5 mL) of the Ni and Ni-Mo-Cu catalysts were loaded into the Pyrex fluidized bed reactor and re-reduced as discussed previously. The fluidized bed was used to assure uniform poisoning of the catalyst particles. These catalysts were then exposed to 375 mL/min of a gas mixture of 9 ppm H2S in H2 at 725
K for sufficient time to sulfide 50% of the catalyst surface (Fowler and Bartholomew, 1979). After exposure for the required time, the catalysts were cooled to room temperature and passivated in dilute air. Activity testa were then run as described below. Results Specific Rate and H2 Chemisorption Measurements. Reaction rates per active site of catalyst, i.e., and product yields methane turnover numbers (NCH,), (fractions of converted CO occurring as various products) obtained in specific rate measurements of Ni, Ni-Mo, Ni-Mo-Cu, and Ni-Ru catalysts before and after carbon deposition and following regeneration testa are presented in Table I1 along with H2chemisorption uptakes. The data in Table I1 show that all catalysts except Ni-Ru suffered significant decreases in metal surface area measured by Hzadsorption after carbon deposition at either low or high pressure. However, there were significant variations in the magnitude of changes observed for turnover numbers after carbon deposition at low pressure. The CHI turnover numbers of Ni and Ni-Mo-Cu did not change significantly while those of Ni-Ru and Ni-Mo dropped by about 38% and 94%, respectively. CH4yield dropped for Ni and Ni-Mo, increased for Ni-Ru but remained unchanged for Ni-Mc-Cu. Ni-Mc-Cu and Ni-Mo exhibited significant increases in C 0 2 yield after carbon deposition, whereas the C 0 2yields of Ni and Ni-Ru were negligible before and after carbon deposition.
Ind. Eng. Chem. Prod. Res. Dev., Vol. 21, No. 3, 1982 393
Table 111. Results of Steady-State (24 h ) Carbon Deposition Tests (723 K,138 or 2 6 0 0 kPa, 4 5 000 or 100 000 h - I ) initial CH, rate, pmol/ final (cm3 cat. s) Low Pressure
normalizeda activity after 2 4 h
% CO conversion
cat.
initial
fixed bedC Ni Ni (P)d Ni-Ru Ni-Mo Ni-Mo-Cu Ni-Mo-Cu (P)d
41 33 59 43 33 13
43 34 49 31 27 2
14 11 17 9.0 9.6 3.6
1.05 0.93 0.80 0.67 0.81 0.10
fluidized bed Ni-Mo Ni-Mo-Cu
61 32
23 0
7.7 4.6
0.38 0
Ni Ni-Ru Ni-Mo Ni-Mo-Cu
94 100 81 81
91 100 83 52
High Pressure 36 28 21 25
0.99 1.02 1.05 0.63
half-life,b C content h after 2 4 h , w t %
170 134 80 50 107 13
0.6
___
2.4 16.8 1.7
_--
33 2f
7.2 0.6
___ .____ ___
-__
___ __. ___
Normalized activity = rate of CH, production divided by initial CH, production rate. Half life = time at which nor. malized activity equals 0 . 5 ; estimated from eq 2 and 4 . Space velocities of about 100 000 h - ' . (P) refers to sample partially poisoned with H,S in a fluidized bed. e Space velocities of about 45 000 h - ' . N o activity after 15 h .
The catalysts also responded differently to regeneration (after low-pressure treatment). Ni, Ni-Mo, and Ni-Ru regained activity after regeneration having CHI turnover numbers near those for the fresh catalysts; CH4yield was almost completely restored for Ni but only in part for Ni-Mo. Regeneration did not improve the activity or selectivity of Ni-Mo-Cu, but rather caused small decreases in CH4 and C02 yields. All of the sulfur-free catalysts apparently suffered a decrease in surface area after regeneration. Catalysts subjected to carbon deposition at high pressure, suffered, with the important exception of Ni-Ru, substantial losses in specific activity and selectivity for methane (see Table 11). Indeed, the methane turnover number decreased by a factor of 10 for Ni-Mo-Cu and Ni-Mo, a factor of 2 for Ni, but only 30-40% for Ni-Ru. Despite a decrease in surface area, the regeneration treatment at high pressure with a dilute O2mixture seemed to greatly improve catalyst performance for all catalysts except Ni-Ru. Indeed, CHI turnover numbers for the other three catalysts ranged from 1.5 to 8 times the value before carbon deposition and CHI yields were 37 to 66% higher than pre-carbon deposition values. To determine if this effect was lasting, the Ni catalyst was tested for an additional 20 h at 623 K and space velocity of 100000 h-' with 1%CO and H2/C0 = 4, during which the turnover number reverted to the pre-carbon deposition value. The behavior of Ni-Ru after high-pressure testing in the carbonizing environment was unique. In fact, when subjected to the same regeneration treatment as the other catalysts, the product stream from Ni-Ru contained no CO or C02 as in the regeneration of the other catalysts, even when the flow of O2 was increased. Table I1 also shows the results of differential tests on two catalysts, Ni-Mo-Cu and Ni, which were presulfided and exposed to carbon depositing environments at low pressure. These results show that carbon deposition is extremely detrimental to Ni-Mo-Cu when it has been previously exposed to H2S. On the other hand, Ni is relatively unaffected, showing similar activity performance to the non-sulfided catalyst. Both catalysts showed little change in H2uptake as a result of carbon deposition and/or regeneration. However, regeneration apparently caused a significant increase in CH4yield for pre-sulfided Ni.
9 G
0.1 0.0
1
1
1
10
5
15
J
20
25
TIME (HRS)
Figure 2. Variation of normalized activity with time at low pressure: (0) Ni; (0) Ni (presulfided); (A) Ni-Mo-Cu; (A) Ni-Mo-Cu (presulfided); (m) Ni-Mo. Solid lines represent correlation of data by expression: a = a,J(l + exp(-kaor)[exp(k~[C0],t)- 11).
0.4
D
0.3 !0.2
1
0
oo
\
't
0.0 10
15
20
TIME (HRS)
Figure 3. Variation of normalized activity with time: ( 0 )Ni-Mo Ni-Mo low-pressure fluidized bed run; ( 0 ) high-pressurerun; (0) Ni-Mo-Cu high-pressurerun; (A) N i - M d u low-pressure fluidized bed run. Fluidized bed data after 5 h are correlated by the expression a = a, exp(-kdt).
Steady State (24 h) Carbon Deposition Tests. Values of CO conversion, rates of methane production, and normalized activities are listed in Table III for all catalysts before and after 24-h steady-state deactivation tests at 773 K and 100000 h-l. Typical plots of normalized activity vs. time are shown in Figures 2 and 3. Normalized activity is defied aa the ratio of the instantaneous rate of methane production (mass basis) to the initial rate; the half-life
394
Ind. Eng. Chem. Prod. Res. Dev., Vol. 21, No. 3, 1982
corresponds to a normalized activity of 0.5. Based on the normalized activity after 24 h treatment at low pressure the order of decreasing resistance to carbon deposition was Ni, Ni (presulfided), Ni-Mo-Cu, Ni-Ru, Ni-Mo, Ni-Mo-Cu (presulfided). The order of increasing content of carbon deposited after 24 h followed this same trend. However, when the Ni-Mo and Ni-Mo-Cu catalysts were operated in a fluidized bed, Ni-Mo maintained an activity of 0.38 compared to zero for Ni-Mo-Cu after the 24-h c a r h n deposition test, even though 10 times more carbon was deposited on Ni-Mo compared to Ni-Mo-Cu. In fact, the Ni-Mo-Cu catalyst lost all measurable activity within 15 h in the fluidized bed. The presulfided NiMo-Cu also deactivated very rapidly as shown in Figure 2. Figure 3 shows fairly significant fluctuations in the data at 8 h for the Ni-Mo fluidized bed run. Maintenance of a steady flow during this run required constant attention, and this fluctuation can be attributed to flow variations during the evening and night hours when the run was unattended. Data in Table I11 obtained at high pressure show that neither Ni-Mo nor Ni-Ru lost activity during the 24-h period. Only a slight decrease in activity was observed for Ni, whereas the activity for Ni-Mo-Cu decreased by almost 40 % A simple ion-exchangetype deactivation model was used to fit the activity vs. time data (see detailed description of model in Discussion section). Decreases in normalized activity with time during the low-pressurefmed-bedcarbon deactivation runs were fitted by the expression
.
Un
u =
1 + exp(-k~~~)[exp(k~[CO]~t) - 11
(1)
where a = normalized activity at time t , a. = normalized activity at t = 0 (generally unity although could be different from unity if new sites are created by reduction or if deactivation occurs by other mechanisms during long term tests), k = reaction rate constant (h-l), k d = decay constant (L mol-' h-l), t = time (h), [CO], = concentration of CO at bed entrance (mol L-I), and T = inverse space velocity (h). An expression for the half life (tl12)was obtained from eq 1 by setting a l a o = 0.5 and rearranging
Equations 1 and 2 were used to plot the solid lines in Figures 2 and 3 and to calculate the half lives shown in Table 111. The data from the fluidized bed runs were correlated fairly well by the following expression after about 5 h a =
~~e-k'd(t-5)
(3)
where u5 = normalized activity at t = 5 h and where k $ = kd[CO]. From eq 3 the half-life was obtained tl,z = 0.693(kh)-'
(4)
This expression was used to calculate the half-lives of Ni-Mo and Ni-Mo-Cu in the fluidized bed tests (Table 111). Discussion Effects of Carbon Deposits O n Methanation Activity. Effects on Intrinsic Activity Properties. The decreases in catalytic activity observed in this study were clearly due to carbon deposits in the catalyst and were not the result of poisoning by sulfur or iron carbonyl or of sintering, since necessary precautions were taken to avoid
these other forms of deactivation. Indeed, the reactant gases were carefully purified of any contaminants such as H2S or Fe(C0)5,and the catalysts were reduced 12-20 h at 773 K to ensure thermal stability in the later tests at 723 K. In addition, the presence of large amounts of carbon in several of the most severely deactivated catalysts (Table 111) and the presence in the gas stream of CO and C02 during regeneration strongly suggest that carboncontaining species were responsible for the observed losses in activity. Moreover, in previous studies in this laboratory (Gardner and Bartholomew, 1981a; Erekson et al., 1981) filamentous carbon deposits were observed by TEM after methanation under conditions similar to the steady-state tests of this study (723-773 K, H2/C0 = 2). The results of this study show that the rate and extent of deactivation due to carbon vary with catalyst composition and reaction conditions. Mo-promoted nickel catalysts, for example, are readily deactivated at low pressures and moderately low conversions, Ni-Mo most readily in a fixed bed, and Ni-Mo-Cu in a fluidized bed. All of the catalysts, except Ni, lose activity under low pressure, moderately low conversion conditions, while except for Ni-Ru, all of the catalysts suffer much greater losses in activity after the 24-h test under high-pressure, highconversion conditions. The results obtained for Ni-Ru are unique and exciting. This catalyst was not only the most active, consistent with the earlier work of Tucci and Streeter (1980), but also the most resistant to carbon deposition under high-pressure, high-conversion conditions. The absehce of CO and C02 in the gas phase products during regeneration provides strong evidence that no carbon was formed on Ni-Ru during 24 h of methanation at a H2/C0 ratio of 2. Thus, Ni-Ru is clearly the most promising of the catalysts tested as a candidate for combined shiftlmethanation or service in low H2/C0 environments. These results are consistent with the earlier work of Weatherbee et al. (1980), who found that Ni-Ru and especially Ni-Pt were more resistant than Ni to deactivation by carbon. What accounts for the differences in resistance to deactivation by carbon as a function of different reaction conditions and catalyst composition? Product selectivity, i.e., catalytic activity for the shift reaction relative to methanation and for various elementary steps in methanation which produce and remove carbon, is probably the governing factor. High activity for the water-gas shift (WGS) reaction results in a larger H2/C0 ratio, thereby preventing or attenuating the formation of inactive carbon species. The WGS reaction rate is enhanced at high conversion conditions since the reaction rate is a positive function of the partial pressure of water (Grenoble et al., 1981) and since the product water concentration from methanation is highest at high conversions. Moreover, greater quantities of C 0 2 are experimentally pbserved at higher CO conversions (Bartholomew, 1977, 1980). Previous work showing that Ni-Mo catalysts are more active than Ni for the WGS (Ference, 1978) and that Ru catalysts are less active than Ni for the WGS during methanation (Tucci and Thomson et al., 1979) are consistent with the data from this study showing C02 yields of 3-70% and 0% for Ni-Mo and Ni-Ru, respectively (see Table 11). Hence the resistance of Ni-Mo to deactivation by carbon at high pressures is explained by its ability to catalyze the water-gas shift reaction, whereas the reason for the resistance of Ni-Ru must lie elsewhere. Several recent investigations of methanation over Ni and Ru catalysts (Araki and Ponec, 1976; McCarty and Wise,
Ind. Eng. Chem. Prod. Res. Dev., Vol. 21, No. 3, 1982 395
1979; Ponec, 1978; Gardner and Bartholomew, 1981b) have provided evidence that adsorbed carbon is an active reaction intermediate and a precursor to inactive forms of carbon. McCarty and Wise (1979) reported three types of carbon which are adsorbed on the Ni surface after,exposure to CO. Atomic or a-carbon was easily removed by H2 at a relatively low temperature while j3-carbon (polymerized carbon) was removed at a significantly higher temperature and was about 1/100 as active toward H22 Graphitic carbon, the third type, was apparently formed by high-temperature conversion of the @-form. McCarty and Wise indicated that a-carbon (C,) is slowly transformed to j3-carbon (C,) at temperatures above 600 K. Thus, carbon fouling of methanation catalysts at 600-700 K is likely the result of C, formation from C, (Pederson et al., 1980; Sughrue, 1980;Bartholomew 1982). The formation of a fourth carbon species, vermicular or filamentous carbon, has also been observed during methanation at higher reaction temperature (2' > 700 K) (Weatherbee et al., 1980; Bartholomew, 1982). This species, which is presumably formed by bulk diffusion of carbon through the metal lattice, can cause deactivation of the catalyst above 700 K at low H2/C0 ratios by means of metal crystallite encapsulation (Weatherbee et al., 1980; Bartholomew, 1982). Assuming that carbon is an active intermediate in methanation, the deactivation rate is then determined by the relative contributions of the rates of active carbon formation, gasification of C, or C,, and dissolution of carbon in the bulk metal. The relationship between rates of carbon formation and gasification determines how much of a C, or graphitic film.is formed on the surface and whether complete encapsulation occurs, while the relative rates of carbon gasification and dissolution, in the bulk determine how much filamentous carbon is formed (Bartholomew, 1982). The formation of C, or an encapsulating film is difficult to confirm experimentally since these films are difficult or impossible to observe by TEM (Sughrue and Bartholomew, 1982) and the weight increase is typically not more than 0.1 to 0.2 wt 5% (generally about the same magnitude as the error involved in the measurement of catalyst weight). Filamentous carbon, on the other hand, is easily observed by TEM and contributes to easily measurable increases in the percent carbon of a sample. Accordingly, the significant carbon contents after lowpressure deactivation tests (Table 111)are consistent with formation of filamentous carbon forms, especially in the case of Ni-Mo. However, formation of a C, film on the catalyst surface which transforms to a graphitic film may also occur since some of these catalysts (particularly NiMo) were severely deactivated. Moreover, the significant decreases in H2 adsorption on Ni-Mo and Ni-Mo-Cu suggest the presence of carbon films which block adsorption on these metal surfaces. Nevertheless, the rate of C, gasification on nickel under these conditions (1atm, 723 K) is known to be significant (McCarty and Wise, 1979) and may explain why unpromoted nickel was not measurably deactivated in the low-pressure tests. The absence of deactivation and of any measurable carbon species during the high-pressure deactivation test of Ni-Ru can be explained by (i) the ability of Ru-promoted nickel to gasify C, and C, forms as rapidly as they are formed and/or (ii) the low solubility of carbon in Ru compared to Ni (Baker and Harris, 1979), preventing formation of carbon filaments. This desirable behavior of Ni-Ru may be typical of noble metal-promoted nickel catalysts and the above explanations may also account for the superior resistance to deactivation by carbon of Ni-
Pt/A1203observed earlier in this laboratory (Weatherbee et al., 1980). Although considerable quantities of carbon were formed during the steady-state deactivation test and although significant losses of specific activity (measured under differential conditions) were evident for most of the catalysts (Ni and Ni-Ru excepted) after the steady deactivation tests, relatively little deactivation was observed during steady state deposition tests for most catalysts except Ni-Mo-Cu (see Figures 2 and 3); high activity maintenance was particularly apparent at high pressure. This apparent contradiction is easily explained by the integral nature of the data obtained during the steady-state tests. In an integral reactor test at high conversions only a portion of the active sites are necessary to maintain a high reaction rate. It is further well known that in a fixed bed reador most of the reaction takes place in a small zone at the entrance to the bed, creating a large concentration gradient over a small portion of the reactor. In this small zone, the CO partial pressure is large and the rate of formation of inactive carbon forms is high; further downstream the catalyst is subjected to lower CO partial pressures and less carbon is formed. Thus an active reaction zone is present in the integral bed which gradually moves downstream as the catalyst becomes fouled. Therefore, at high temperature, high conversion conditions and especially at high pressure, we would expect to observe very little deactivation until the reaction zone reaches the end of the bed. The slow "breakthrough" observed at low pressures was apparently fitted reasonably well by the ion-exchange deactivation model (at least after 5-10 h), whereas breakthrough did not appear to occur during the 24-h accelerated deactivation tests at high pressure and thus could not be modeled. Accordingly, the importance of differential activity tests to determine effects of deactivation is emphasized by this experience. Effects of Carbon on Selectivity Properties. The changes in selectivity observed for all catalysts after lowpressure carbon deposition suggest some type of modification of the active sites. It is also reasonable to expect that a partially or completely carbon-covered surface will behave catalytically more like a metal carbide than a clean metal surface. This is supported by previous work of McCarty and Madix (1975,1976) and Sexton and Somorjai (1977). In addition, filamentous carbon forms have been shown by previous workers to separate metal crystallites from the support (Baker and Harris, 1979). Thus formation of large quantities of carbon filaments may place the metal crystallites in a new support environment, the subsequent change in metal-support interactions inducing changes in activity/selectivity properties. In the case of bimetallic catalysts, metal-carbon interactions may induce changes in surface composition which affect selectivity. Ponec (1978), for example, presents evidence for the surface modification of a Ni-Cu film by repeated adsorption and temperature-programmed desorption of CO. Effects of Presulfiding. In previous work it was found that presulfiding inhibits carbon formation on nickel catalysts in steam reforming at moderately high carbonforming potentials (Rostrup-Nielsen, 1974), while rates of carbon formation during methanation were actually greater on presulfided nickel catalysts after the carbon-deposition process had been initiated at very high carbon forming potentials (Gardner and Bartholomew, 1981a). Gardner and Bartholomew (1981b) found that presulfiding of Ni/A1203 reduced its carbon hydrogenation rate to a greater extent than the rate of carbon deposition, causing increased C, formation during methanation. Based on
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similar results, Wentrcek et al. (1980) concluded that adsorbed sulfur catalyzes the transformation of C, to C,. In this study, the partially presulfided Ni catalyst did not behave much differently than the fresh nickel catalyst after the low-pressure deactivation tests (see Tables 11and 111). Presulfided Ni-Cu-Mo, however, was 2-3 times less active than fresh Ni-Cu-Mo before the steady-state deactivation test and 20-30 times less active afterwards. The differences in behavior for Ni and Ni-Mo-Cu are difficult to explain on the basis of the limited data in Tables I1 and 111. The complete loss of activity after the steady-state run may have resulted from sulfur-catalyzed formation of C, films on the active surface. However, the almost complete restoration of H, surface area but negligible recovery of activity after regeneration suggests that an additional deactivation effect such as Cu enrichment of the surface (Araki and Ponec, 1976) may operate in the case of Ni-Mo-Cu. Obviously, additional research involving more sophisticated techniques such as TEM, TPD, and ESCA is needed to understand this behavior and more generally the interactions between poisoning by H2S and deactivation by carbon. For the present however, it is clear that an interesting but unfortunate synergism operates for deactivation of Ni-Mo-Cu in the presence of both sulfur ahd carbon, making it unsuitable as a candidate for combined shift/methanation. Carbon Deposition in a Fluidized Bed. As might be expected, Ni-MoCu and Ni-Mo deactivated more rapidly in a fluidized bed than in a fixed bed due to more uniform exposure to the reaction mixture. However, Ni-Mo-Cu deactivated more rapidly than Ni-Mo, a result opposite to that obtained in the fixed bed. This can be accounted for by the lower space velocities and lower conversions associated with the fluidized bed reactor. Since the rate of carbon formation is proportional to the partial pressure of CO, the lower conversion (especially in the case of Ni-Mo-Cu) would translate to a higher CO partial pressure at the catalyst surface which would affect each catalyst differently because of their different compositions. Since large concentration and temperature gradients are absent in the fluidized bed, the results obtained in the fluid bed experiments in this study are much more indicative of the true deactivation behavior in fluid bed processes such as the BI-GAS process. Regeneration of Carbon Fouled Catalysts in Air/ Oxygen. The restoration of activity following regeneration for most of the catalysts was very gratifying; these results show that carbon fouled methanation catalysts can be regenerated with a mild treatment at 573 K in dilute mixtures of air or oxygen. In fact, this may be the most practical aproach (at least in fluid bed systems) since in industrial equipment the regeneration temperature is usually limited to 700 K, whereas carbon gasification by steam, H2, or CO, does not occur at significant rates below 800 K (Figueirdo and Trimm, 1975; Trimm 1977). Regeneration of methanation activity by oxygen is not without a disadvantage, however. The results of this study (Table 11) show overall decreases in surface area after carbon deposition and regeneration of 18 to 71% . This loss of catalytic surface area is undoubtedly a consequence of sintering and even loss of the catalyst crystallites themselves. Rostrup-Nielsen (1972) reports that deposited carbon grows in long hollow filaments with the Ni crystallite at the end. Transmission electron microscopy studies in this laboratory (Gardner and Bartholomew, 1981a) confirm this observation. The Ni crystallite is thus removed from the support by the carbon filament and when the carbon is removed by oxidation the crystallite
is probably carried out of the reactor with the gas stream. In fact, chemical analysis of fresh and regenerated Nil A1203samples revealed a 7% loss of nickel. Accordingly, it may be impractical to regenerate carbon-fouled catalysts with air or oxygen more than 2-3 times since after a few cycles of deactivation and regeneration a large part of the active surface of the catalyst will be gone. It depends, of course, on how much Ni is removed per treatment and the frequency and severity of treatment. The increase in CHI turnover number for the catalysts after the high-pressure dilute O2treatment was more than could be accounted for by simple removal of the deposited carbon. This could be the result of a surface modification by the O2 treatment and/or a modification which occurred during reaction. Palmer and Vroom (1977) showed that methanation activity of nickel is increased by high-temperature treatment with O2 as a result of incorporating dissolved 0, just below the surface. Sexton and Somorjai (1977) reported similar results. Unfortunately, this effect appears to be only temporary, since the specific activity of regenerated Ni/A1203returned to the same value as the fresh catalyst after 24 h of reaction at 623 K and H2/C0 = 4, a condition chosen to ensure that deactivation by carbon did not occur. A Model for Deactivation by Carbon. One of the difficult problems in industrial methanation has been the modeling of deactivation by carbon and the prediction of catalyst life. We propose a model to account for deactivation of nickel by @-carbonor encapsulating graphitic carbon in a fixed bed during methanation and which can be used to estimate catalyst life if the appropriate constants are obtained under conditions representative of the process. The proposed model for deactivation is a modification of an ion-exchange type model proposed for interaction of sulfur with Ni (Wise et al., 1977; Wentrcek et al., 1980; Fowler and Bartholomew, 1979). The reaction mechanism involves five elementary steps, H2 and CO adsorptions, CO dissociation, hydrogenation of adsorbed C, and the transformation of C, to C,
+ 2s 2H-S co + s co-s co-s + s c,-s + 0-s
+ c,-s - c,-s H2
C,-S
H-S
(CH,), stepwise
(5) (6)
(7) (8)
(9)
where the S denotes a surface site. Adsorption of H,and CO are assumed to be in quasiequilibrium; steps 7 and 8 are rapid relative to step 9 and approximately in balance. Accordingly, the rate of deactivation is controlled by reaction 9. Based on this model and the above assumptions it can be shown that the rate of deactivation is proportional to the partial pressure of CO and the active site concentration of the catalyst. Thus by assuming first-order dependence on both of these variables and assuming that normalized activity is proportional to the active site concentration, an expression for the deactivation rate can be written as daldt = -kd[CO]a where kd = the deactivation rate constant, [CO] = concentration of CO, and a = normalized activity at time t. Simultaneous solution [the solution assumes a quasi-static (deactivation slow compared to reaction), isothermal, isobaric system of constant density] of the deactivation rate expression and the equation of continuity in the z direction (direction of flow; reaction rate is assumed to be first order in CO) yields eq 1 (Moeller, 1979). Solution of these equations for CO conversion at the outlet
Ind. Eng. Chem. Prod. Res. Dev., Vol. 21, No. 3, 1982 397
results in the following expression (Moeller, 1979), where V is the velocity in the z (axial) direction and z = L at the outlet. In [(1/(1- XCO))- 11 = In [exp(lza&/V) - 11 -k,[CO],t
(10)
(Note that L/V = r , the inverse space velocity or residence time.) By plotting In [ ( l / ( l - Xco))- 11 vs. time t , values of It and lzd can be determined from the intercept and slope, respectively. Equation 1 is plotted as a solid line in Figure 2 using these parameters. It fits the data fairly well in the case of the low-pressure fixed bed runs, especially at t > 10 h. A similar development assuming no concentration gradient in the z direction leads to the exponential relationship of eq 3 for fluidized beds which also provides a good fit of the data after 5 h (Figure 3). Using eq 1and 3 we estimate that half of the active sites for Ni-Mo would be fouled in 151 h in a fixed bed and only 5 h in a fluidized bed based on industrial process conditions of H2/C0 = 1.4,25% CO, 1 atm, and a space velocity of 3000 h-l. The higher rate of deactivation in the fluidized bed occurs because the surface CO concentration is maintained at higher levels uniformly throughout the bed compared to the fixed bed. While the proposed model appears to be consistent with the experimental data and provides in our experience a better fit than several other possible mechanisms (e.g., zero or second order in Pco or zero or second order in active site concentration), this does not prove that the proposed mechanism is correct. It is possible that other rate expressions based on the same mechanism or other mechanisms may be found which fit the data just as well. Nevertheless the proposed mechanism is consistent with recently proposed models for carbon deposition (Bartholomew, 1982) and thus this approach may be instructive. Conclusions 1. Nickel and molydenum-promoted nickel catalysts suffer significant and relatively rapid losses in activity due to formation of carbon deposits under conditions representative of combined-shift methanation (H2/C0 = 1.3) in either fixed or fluidized beds. The rate of deactivation is first order in CO concentration and fmt order in catalyst activity. Typical half-lives for these catalysts determined from a deactivation model range from 13 to 170 h at atmospheric pressure. 2. Rates of deactivation are only apparently lower for Ni and Ni-Mo catalysts at high pressure. That is, during 24 h of reaction in a fixed bed at high temperatures and pressures, essentially no deactivation is observed, as the true effects of deactivation are masked by the fast rate of reaction occurring in a small portion of the bed. However, the turnover numbers determined thereafter under reaction-limited conditions reveal that Ni and Ni-Mo catalysts suffer significant losses of activity which are more serious than at low pressure. 3. Ni-Ru is extremely resistant to carbon deposition under high-pressure, combined-shift methanation conditions; apparently no measurable quantities of carbon deposit on the catalyst during 24 h of reaction. Ni-Ru is therefore highly recommended for combined-shift methanation applications or other similar applications where deactivation by carbon may be a problem. 4. Under conditions favorable for deactivation due to carbon deposits, a given catalyst is generally longer-lived in a fixed bed relative to a fluidized bed since the deactivation rate is proportional to the CO concentration and since uniformly high reactant concentrations are main-
tained in a fluidized bed, while sharp concentration gradients are present in fixed beds. 5. Presulfiding of Ni/A1203neither improves nor lowers its tolerance to carbon deposition, while presulfiding of Ni-Mo-Cu severely degrades its performance under severe carbon depositing conditions. In general, sulfur is believed to poison the hydrogenation of active carbon leading to a buildup and transformation to inactive carbon species. However, in the case of Ni-Mo-Cu, an additional effect such as Cu enrichment of the surface may play a role in the deactivation. 6. Dilute air or oxygen regeneration of carbon-fouled catalysts at 573 K is apparently successful in restoring activity for methanation. Regeneration using air results in a significant loss of surface area, but it may be the most practical method due to temperature limitations of industrial equipment. Regeneration at high pressures results in CH, turnover numbers and CHI yields which are temporarily higher than for fresh catalysts. Acknowledgments The authors gratefully acknowledge financial support from Bituminous Coal Research, Inc., under their Contract No. EF-76-C-10-1207, U S . Department of Energy; permission to publish catalyst data from Climax Molybdenum Company of Michigan, the Harshaw Chemical Co., and Matthey-Bishop Inc.; and technical assistance from Dr. Robert Streeter of BCR. Literature Cited Araki, M.; Ponec, V. J. Catal. 1976, 4 4 , 439. Baker, R. T. K.; Harris, P. S. Chem. Phys. Carbon 1979, 14, 83. Bartholomew, C. H. "Alloy Catalysts with Monolith Supports for Methanation of Coal-Derived Gases"; Quarterly Technical Progress Report to ERDA, FE-1790-1, Aug 6, 1975. Bartholomew, C. H. Final Report to DOE, FE-1790-9, Sept 6, 1977. Bartholomew, C. H. Catal. Rev.-Scl.-€ng. 1982, 24(1), 67. Bartholomew, C. H.; Farrauto, R. J. J. Catal. 1976, 45, 41. Bartholomew, C. H.; Pannell, R. B. J. Catal. 1880, 65, 390. Erekson, E. J.; Sughrue, E. L.; Bartholomew, C. H. FuelProc. Techno/. 1981, 5,91. Ference, R. A., Climax Molybdenum Corp., private communication, 1978. Figuelrdo, J. L.; Trlmm, D. L. J. Catal. 1975, 40, 154. Fowler, R. W., Jr.; Bartholomew, C. H. Ind. €na. Chem. Prod. Res. D e v . 1978, 18, 339. Gardner, D. C. M.S. Thesis, Brlgham Young University, 1979. Gardner, D. C.; Bartholomew, C. H. Ind. Eng. Chem. Prod. Res. D e v . 1981a, 20, 80. Gardner, D. C.; Bartholomew, C. H. Ind. Eng. Chem. Fundam. lQElb, 2 0 , 229. Grenoble, D. c.; ~stadt,M. M.; oilis, D. F. J. cats/. 1881, 6 7 , go. McCarty, J. G.; Madix, R. J. J. Catal. 1975, 38, 402. McCarty, J. G.; Madix, R. J. Surf. Scl. 1978, 54, 121. McCarty, J. G.; Wise, H. J. Catal. 1979, 57, 406. Moeller, A. D., M.S. Thesis, Brigham Young University, 1979. Palmer, R. L.; Vroom, D. A. J. Catal. 1977, 50, 244. Pannell, R. B. Ph.D. Dissertation, Brigham Young University, 1978. Pederson, K.; Skov, A.; Rostrup-Nlelson, J. R. Prepr. Am. Chem. SOC.Div. Fuel Chem. 1980, 25(2) 89. Ponec, V. Catal. Rev. Scl. Eng. 1978, 78(1), 151. Rostrup-Nielsen, J. R. J. Catal. 1972, 27, 343. Rostrup-Nielsen, J. R. J. Catal. 1974, 33, 184. Sexton, B. A.; Somorjai, 0. A. J. Catal. 1877. 46, 167. Sughrue, E. L. Ph.D. Dissertatlon, Brigham Young University, Provo, UT, 1980. Sughrue, E. L.; Bartholomew, C. H., paper in preparation, 1982. Trimm, D. L. Catal. Rev. Scl. Eng. 1977, 16(2), 155. Tucci, E. R.; Thomson, W. J. Hydrocarbon Process. Feb 1979, 123. Tucci, E. R.; Streeter, R. C. Hydrocarbon Process. Apr 1980, 107. Weatherbee, G. D.; Jarvi, G. A.; Bartholomew, C. H. Chem. Eng. Commun. 1980,5, 125. Wentrcek, P. W.; McCarty, J. G.; Ablow, C. M.; Wise, H. J. Catal. 1980, 61, 232. Whalen, M. J. "Carbon Formation in Methanators"; Final Report to ERDA, FE-2240-10, July 1976. Wise, H.; Gikls, 8. J.; Isakson, W. E.; McCarty, J. G.; Sancier, K. M.; Schechter, S.; Wentrecek, P. R.; Wood, B. J., SRI, Final Report PERC0060-8 (ERDA), Sept 30, 1977.
Received for review July 31, 1981 Revised manuscript received March 11, 1982 Accepted April 21, 1982
