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Kinetics and mechanism of the fischer tropsch hydrocarbon synthesis on a cobalt on alumina catalyst
Catalysis, 1 (1981)247-272 ElsevierScientificF'ublishmgCompany,Amsterdam-RintedinBelgium
Applied
247
KINETICS AND MECHANISM OF THE FISCHER TROPSCH HYDROCARBON SYNTHESIS ON A COBALT ON ALUMINA CATALYST A. Outi I. RAUTAVUOWand
Hessel S. van der BAAN
Laboratory for Chemical Technology, Eindhoven University of Technology, Eindhoven, The Netherlands. *Present address: Neste Oy Research Center, Kullo, Finland. (Received 4 April 1981, accepted 15 May 1981) ABSTRACT The kinetics of the Fischer Tropsch reaction have been studied on a cobalt on alumina catalyst. The kinetics can be explained satisfactorilyby a model in which the initiation proceeds via carbon monoxide dissociation and formation of a CHBsurface intermediate.The formation of this intermediate is the rate determining step. The chain growth is thought to proceed via the addition of the same CH3 groups to the growing molecule. The model also explains the influence of the hydrogen and carbon monoxide partial pressures on the olefin/paraffinratio as determined experimentally for the C3 fraction, and on the methane selectivity. For high ratios of hydrogen to carbon monoxide, the methane selectivity is higher than predicted, while at the same time a correspondingdeficit in the ethene yield is noticed. These two facts are tentatively ascribed to an ethene hydrocracking reaction. The experimental data show that the Schulz Flory (S.F.) "constant" a has a tendency to increase from C3 to C7. An analysis on the basis of our model shows that the S.F. constant is a complex function of the partial pressures of hydrogen and carbon monoxide. INTRODUCTION The overall kinetics of the Fischer Tropsch (F.T.) synthesis have been the subject of a number of experimental studies during the past years (l-3). The results are generally described by power laws, resulting in a more or less exact first order behaviour in hydrogen and a low or even negative order in carbon monoxide. It is generally accepted that hydrogen enters the F.T. reactions via dissociative adsorption. For carbon monoxide, dissociative adsorption is supported by the more recent OlSS-9834/81/000@-0000/$02.50 @1981Ekvier6cientificPubli&ingComp~y
248
results of a number of investigators (14-19). For the chain growth, a number of models have been suggested. Fischer's original model, the polymerization of CH2 groups (4) has largely been neglected in later years as many arguments were put forward against it, e.g. by Anderson et al (5,6). The latter described the chain growth as the dehydrocondensationof alcoholic intermediates.This mechanism has been supported by Kiilbel(7). Pichler and Schulz (8) were the first to suggest propagation to proceed via carbon monoxide insertion. Barneveld and Ponec (9) and Kitzelmann et al (10) have used this model also. Recently Biloen et al (11) have presented data indicating that the chain growth proceeds via CHx entities. The possibility that a carbene group can be inserted into a metal-carbon bond has also been demonstrated by Yamamoto (12) and Young and Whitesides (13). Our interest in the F.T. reaction is directed towards the manufacture of small olefins by this process. Consequently the reaction mechanism, and especially the factors that influence the olefin/paraffinratio and the molecular mass distribution, are our main concern. Although iron is the most appropriate catalyst for small olefin manufacture (20) we have used cobalt in this study as its greater stability facilitated our obtaining reproducible kinetic data. EXPERIMENTAL All experiments were carried out in a plug-flow fixed bed reactor at atmospheric pressure at 523 K, under differential conditions (conversion below 2%). The reactants, hydrogen (Hoekloos, purity > 99.9%), carbon monoxide (Matheson, purity > 99.5%) and helium (Hoekloos, purity > 99.995%) were purified separately over BTS reduced copper catalyst and molecular sieve 5A. For the analysis, three 8LC instruments were used with the following columns: C4-C8 hydrocarbons; 5% squalane on Chromosorb W-AW DMCS Cl-C4 hydrocarbons; two columns, phenyl isocyanate on Poracil-C and n-octane on Poracil-C water; Porapak-Q. The water data proved to be rather inaccurate, partly due to the peak shape and partly due to adsorption of water on the alumina support. Carbon dioxide was determined with a Maihak VNOR CO2 I.R.
absorption monitor
The cobalt on alumina catalyst (6.2% by weight Co) Co/A1203 was prepared by impregnation of Ketjen 0.6-1.5 E alumina (0.3-0.5 mn particles) with an aqueous cobalt (II)
nitrate solution, drying at 395 K, calcination at 575 K and reduction
with hydrogen at 675 K for 58 ks.
3 -1 After 12 ks, with a gas flow of 1.4 cm s over 1 g catalyst at 523 K and atmos-
pheric pressure, steady synthesis conditions are obtained as shown in Figure 1 for a representative run. The experimental data are the average of three determinations spread over the next three ks. As there is still some drift in catalyst activity after prolonged synthesis, we have taken a new quantity of catalyst for each data set.
249
FIGURE 1
Rate of formation of various products as a function of time: typical
example. 0, CH4;o. C2H6;0, C2Hq (x10);&, C3H8. Calculations according to Satterfield and Sherwood (21) show that no MSS
or heat
transfer limitations are to be expected under our experimental conditions. The value found by us for the apparent energy of activation of 106 kJ IIWB~-~ (22) checks with the results found by Yang (23) and confirms that little or no diffusional lifflitation occurs.
In tqtal 38 experjments have been run, with hydrogen pressures from 5 to 60 kPa and carbon monoxide pressures of 10 to 80 kPa. The experimental results are shown in Table 1. The rate of formation of each hydrocarbon fraction is expressed as r!
J
IC’
EL%! W
pmol/kg cat s
and the total.rate of hydrocarbon formation is given as
rtit = F CI (Cj)
utnolcarbon/kg cat s
W A nunber of repeat experiments (not all shown) indicates a standard deviation of about 6% with a minimum of about 0.1 umol/kg cat s for the lower rates. The data showed that always less than 10% of the oxygen of converted carbon monoxide is converted to carbon dioxide. At the higher conversions this was even less than 5%. A MOUEL FOR THE OVERALL KINETICS Introduction For the description of the network of the Fischer Tropsch synthesis reactions we
250 TABLE
1
Experimental no
1
PH pco /kFa /kPa 5
2 3 4
results
5
c1
AC'
c; c3 Cj C4 c2 rates in pmol/kg cat s
C5
C6
C,
a
10
10.3
0.5
0.2
0.6
0.05
0.7
0.3
0.2
0.2
0.2
0.82
10
10.0
0.5
0.1
0.7
0.05
0.7
0.4
0.2
0.2
0.2
0.75 0.69
20 10
tot
16.7
0.6
0.1
0.8
0.1
0.9
0.6
0:3
0.2
0.4
5
28
2.9
1.3
0.9
0.8
1.8
1.0
0.6
0.4
0.3
0.65
7.5
32
2.6
1.1
1.3
0.6
2.2
1.1
0.7
0.4
0.4
0.65
6
10
28
2.0
0.8
1.3
0.4
2.0
1.1
0.6
0.4
0.3
0.63
7
10
31
2.2
0.9
1.5
0.5
2.2
1.1
0.7
0.5
0.4
0.68
8
20
29
1.5
0.6
1.3
0.3
2.0
1.3
0.9
0.6
0.5
0.68
9
30
24
1.2
0.3
1.5
0.2
1.7
1.0
0.6
0.4
0.3
0.65
10
40
23
1.1
0.2
1.4
0.1
1.5
0.9
0.5
0.4
0.3
0.68
11
15
20
57
1.4
1.7
1.0
3.3
2.0
1.4
0.9
0.8
0.69
12
20
5
90
24
6.9
0.4
4.8
3.5
2.5
1.6
0.8
0.7
0.62
7.5
85
18
6.0
0.7
4.3
4.1
2.6
1.3
0.8
0.4
0.53
14
13
3.5
14
10
79
5.6
1.7
3.3
4.6
2.6
1.5
0.9
0.4
0.57
15
15
69
8.6
4.0
1.4
2.7
3.1
2.7
1.5
1.2
0.9
0.68
17
20
59
6.5
2.7
2.2
1.6
4.1
5.7
3.4
2.1
1.1
0.70
18
30
53
3.8
1.5
2.2
1.0
3.0
2.2
1.5
1.0
1.1
0.62
19
40
46
3.7
1.1
2.6
0.6
3.5
2.1
1.3
0.9
0.4
0.69
20'
50
41
2.4
0.6
2.2
0.3
2.7
1.8
1.2
0.9
0.8
0.61
21
60
38
2.0
0.4
2.0
0.2
2.6
1.5
1.1
0.9
0.9
0.71
22
70
37
1.8
0.4
2.0
0.2
2.4
1.7
1.1
0.9
0.8
0.77
23
80
43
1.9
0.3
2.1
0.1
2.3
2.1
1.5
1.1
1.0
0.74
10
134
10.0
1.1
7.1
6.7
4.0
1.9
1.3
0.7
0.76
25
20
79
7.3
3.5
1.2
2.5
3.9
3.0
1.5
1.3
0.8
0.56
26
40
77
6.3
2.2
3.3
1.3
5.6
3.0
2.0
1.2
0.6
0.64
24
30
29
10
141
41
0.6
7.6
5.3
3.7
1.6
0.9
0.5
0.60
29
20
134
19
8.4
1.3
6.2
5.6
4.7
2.6
1.5
1.0
0.48
30
30
104
13
31
40
96
27
40
5.0
2.7
3.3
7.2
3.7
2.1
1.4
1.1
0.56
9.3
3.3
3.0
2.2
6.7
4.0
2.3
1.5
0.8
0.63
2.4
3.8
1.5
6.7
3.5
2.2
1.5
0.9
0.60
32
50
90
7.7
33
60
87
6.9
34
50
10
187.5
16 11
35
20
161
30
40
111
13
20
197
46
40
143
19
37
60
1.8
62
36
38
12
4.8 15 7.0
3.9
1.1
6.5
3.7
2.2
1.3
0.8
0.63
0.6
9.8
6.7
4.6
1.9
1.1
0.6
0.59
1.1
6.7
7.2
5.3
2.9
1.7
1.1
0.49
3.3
3.2
8.1
4.0
2.5
1.3
0.8
0.57
1.1
9.5
7.9
5.8
2.5
1.7
1.1
0.57
3.2
4.8
9.7
5.3
2.9
2.0
1.0
0.54
251
Kt par
t2 H”
(7)
C2H4 4 kt olef
kt par
(7)
-
CzH6
-
C3H8 ( 9 1
t2 H” (9)
C3H6
FIGURE 2
=
kt olef
kt par
Reaction network for the Fischer Tropsch reaction on a cobalt on alumina
catalyst. will use the scheme presented in Figure 2.
Although a number of details are shown
that will be discussed later, the diagram is useful for an explanation of the main features of the reaction network. We will assume that on the catalyst surface carbon monoxide dissociates (step 2), forming adsorbed carbon atoms (C*) that are the basis of at least the initiation step 3. As we have differential conditions in all of our experiments, we may assume the reaction rates to be constant throughout the reactor. We can then express rj and t-jwith the following formulae:
rj
=
k j(Cj)
rj ={
(cj)
(2)
262
and write for the initiation rate = r; + r+ + ri + ........ r. =r in 3 or r. in
(3)
Reverting to Figure 2, we will further assume that there is a building block (Gins*) that contains one carbon atom and that chain growth occurs by insertion of this species in an initiated chain, fonsing on the catalyst surface a series of adsorbed species C2*, C3*
...... Cj*. Thus a surface species C.* is fonsed by
one initiation step and j-l insertion steps. These surface spec:es will desorb with or without further hydrogenation fran the catalyst and form the hydrocarbons that are the products of F.T. synthesis.
FIGURE 3
Rate of conversion of carbon monoxide to total hydrocarbons as a function
of the hydrogen pressure.
253
FIGWE 4
Rate of formation of all products as a function of the hydrogen partial
pressure. PartiaT pressure of carbon monoxide = 20 kPa. The initiation and the rate determining steps From Figure 3, where the total rate of hydrocarbon fonaation
is plotted as a function of the hydrogen partial pressure for three carbon monoxide partial pressures, we see that the rate is exactly first order in hydrogen. To explain this we will have to find the step that is rate determining or a number of steps that together govern the overall rate of hydrocarbon formation, rtot. A first assumption in this respect might be that all termination reactions together would be rate determining. In Figure 4 we show the rates of the individual.tennination reactions as a function of the hydrogen pressure at 20 kPa carbon monoxide pressure. Corresponding curves am
obtained for other carbon amnoxide pressures. As it is
difficult to visualize how such a bundle of different curves would add up to a straight line if they were independent,we rule out the possibility that the termination reactions together are rate determining.The same argua#nt applies to the assunption that the rates of the initiation step rins (= r4) together would be rate determining. When these two rates are plotted for a given carbon monoxide partial pressure according to equations (3) and (4)
254
r. = i I:(j-l) (Cj) ins as a function of the hydrogen pressure again two pronounced curves are obtained for which it is difficult to conceive that, if these two curves were independent, they would add up to the linear first order relation shown in Figure 3. We therefore conclude that the rate determining step that is first order in hydrogen is cotnson to the formation of Cl* and of Gins*. As hydrogen is dissociativelyadsorbed on cobalt, the first order dependence in hydrogen then strongly suggests that in the rate determining step two adsorbed hydrogen atoms react simultaneously,or that a reversible addition of one adsorbed hydrogen atom is followed by the addition of a second adsorbed hydrogen atom. Of such reactions, those shown in Table 2 have been mentioned in the literature as rate determining steps. A choice between the possibilities shown there will be based on the influence of the carbon monoxide partial pressure on the overall reaction rate. We would then reject hydrogen adsorption as the rate determining step because the F.T. reaction has a positive order in carbon monoxide for low carbon monoxide pressures. Moreover, we have obtained orders in hydrogen higher than one for a pure cobalt catalyst, on which we would expect to have a rate determining step that is related to the one for the catalyst used in this study. The next three reactions, (II)-
have the same rate expression: (5)
if we assume fast equilibriun adsorption for carbon monoxide on one site, low coverage with hydrogen and Langmuir-Hinshelwoodkinetics. Reaction (III)
follows
this rate expression, on the further assumption that the oxygen complex is formed according to reaction (II).
For a constant hydrogen pressure this equation is
plotted in its linearized form l/3 pco A, + 6, pco = r ( )
(6)
as curve a of Figure 5. The nonlinear result excludes any of these reactions as being the rate determining step. If we assume two site undissociated adsorption of carbon monoxide for these reactions, we obtain a complicated relation because we derive, again under the assumption of low hydrogen coverage, for the equilibrium co + 2* + co** the expression
(7)
TABLE 2 Rate detemlining steps mentioned in the literature for the Fischer Tropsch reaction.
(I)
Hz + 2* * 2H*
Hydrogen adsorption
Schonbye (29)
(II)
Formation of an oxygen
Co* + 2H* + COH2 + 2*
containing complex
or CDlr*+ 2H* + COH l * + * Vlasenko et al (224)
(III)
Hydrogenation of
COH2* + 2H* + Cl* + Hz0 + 2*
such a complex
COH2** + 2H* + C,* + Hz0 + 3* Vannice (25), van Hemijnen et al (26). Bond and Turnham (27) Co* + 2H* + C* + Hz0 t 2*
(IV) The hydrogen assisted dissociation of CO
or CO*
+ 2H* + C* t Hz0 t 3*
Palmer and Vroom (28) (V)
C* t 2H* + CH * t 2* 2 or
The hydrogenation of surface carbon
C* t H* * CH* t * CH* t H* + CH2* t * Rautavuoma (22)
%o =
+ l-d4 KCopCo + 2 KCOpCO
1
2 .KCOpCO
and for the rate
r = k2 eCO (1.- eco)2
(9)
To check this equation we have for the same set of data as used in Figure 5 adjusted KC0 and k2 in such a way that equation '(9)fits two experimental data points exactly. If we choose pco = 5 kPa and pco = 80 kPa (both p = 20 kPa) as the two Hz data points we find KC0 = 1.2 x 10m4 Pa-l and k2 = 610 umol/kg catalyst s. But, as shown in Figure 6. with this set of constants relation (9) does not fit the other experimental data. This is also the case for any other set of constants KC0 and k2. We therefore also reject reactions (Z)-(4) with two site adsorption of undissociated carbon monoxide.
If reaction (V). the hydrogenation of surface carbon, is the rate determining
0
[PC&) l/3
0.6
1 0.4
O.! 0.2
l/2,p,1/3 (PC0
0 I-
I
50 FIGURE 5
Checks for linearity: a) equation (6). b) equation (16).
V 0
25 aalculated
FIGURE 6
0
100
PC0
50 rate/wnl/kq
Check for linearity: equation (9).
I
t
75
100
cat s
257 step, and the preceding dissociative carbon monoxide adsorption is a fast equilibrium, i.e. if we have the set of reaction steps 11(a)-(c): Co+2*
f
c*+o* -3
(114
C* + 2H* t4 CH2* + 2*
(llb)
O* + 2H* t5 H20 + 3*
(llc)
we obtain from the steady state requirement that the'rates of (llb) and (11~) must be equal: k4 e. = 1;-; sc
(‘2)
The equilibrium (lla) then,yields:
k3
lq
e2* - lqk4 ec2
PC0
or eC =
(13)
KCpco a*
and with (llb) as the rate determining step we find
ktot pH2&l (14) '&It=
('+%/%I
+JF2
3,
Note (1). It would also be conceivable that the kinetically equivalent reaction (11~) would be the rats determining step. If that were the case, D* would be the most abundant surface species and not C*. We find however that during F.T. synthesis on our catalyst that the amounts of hydrocarbons and water formed are almost stoichianetricallyequivalent, whereas the mnount of carbon dioxide formed is very small. If we now stop the carbon monoxide flow to the reactor we can strip off a quantity of hydrocarbon that is much larger than the amount of water. Recently we obtained further information supporting the low 0*/t? ratio during F.T. synthesis on our catalyst. Van Oijk (34) found in our laboratory that, when after synthesis on a cobalt catalyst ( that gave during synthesis almost equivalent quantities of hydrocarbons and water and almost no carbon dioxide) the catalyst was
268
stripped with helium, the production of hydrocarbons and water decreased but that the quantity of carbon dioxide formed increased. If thereafter hydrogen was passed over the catalyst the carbon dioxide production dropped to zero and a short high water production peak was observed. In our opinion the carbon dioxide production during helium stripping shows the formation of free surface oxygen from adsorbed carbon monoxide which, in the absence of hydrogen, can build up to a level that allows the higher carbon dioxide rate. The introduction of hydrogen again reduces the surface oxygen concentration to such a low level (by water formation) that the carbon dioxide production stops completely. Note (2). According to the findings reported in the next section, it is not unlikely that the CH2* adspecies of equation (llb) is double bonded to the surface, i.e. CH2**. This would not change the kinetic relations derived above.
FIGURE 7
Rates of conversion of carbon monoxide to hydrocarbons as a function of the
carbon monoxide partial pressure. Drawn curves calculated according to equation (14). Hydrogen pressure/kPa:O, GO;&, 5D;O, 4O;V. 30;0, 20;+,
15;A, 10;m. 5.
If we assume
hi 2 pH2 << 1 +J k. pco the linearized version of equation (14) becomes
(15)
259
PC0 l/3
f-1
A2+52&=
(‘6)
)"
Curve b of Figure 5 shows that the data follow this relation very well. On the strength of this result we have applied a computer prograssne(30) to find the best fit for ktot, KC0 and KH2 for the data in Table 1. Figure 7 shows that for the values = 7.9 mol/kg cat s kPa3" k tot KO
= 0.27
kPa"*
(i1.0) (kO.02) (kO.002)
a good fit for all the conditions is obtained. The value found for KH2 justifies the assumption (15) of low hydrogen coverage. Note. If we omit the constraint that all constants must be positive, the best value found for KH2 is -5 x 10-4 l/kPa"*. This result regrettably does not give an indication of the value of the hydrogen adsorption equilibrium constant under F.T. conditions. Consequently,we will have to treat KH2 as a small but unknown constant in further modelling. From these results we conclude that: (i) the rate determining step in the F.T. reaction on cobalt on alumina catalysts is the formation of a surface compound by hydrogenation of a surface carbon species (ii) the initiating species and the insertion species are formed according to the same rate expression and can therefore be assumed to be the same. This means that basically the mechanism suggested by Fischer, the "polymerization" of CH2 species (4) is supported by our results. APPLICATIONS OF THE MODEL TOWARDS SELECTIVITIES Introduction Rate equation (14). with the data found for the constants in that equation, imply that the surface fractions of C*, H* and empty sites are
ec =
eH =
O.*7Jpco 1 + 0.276
KHPKP 1 + 0.27Ko
(174
(‘7b)
260
e*=,TT&&
(17c)
We have assumed that the surface fraction of oxygen is so small that it does not materially affect the e*, and with reaction (llb), i.e. reaction (3) of Figure 2, as rate determining step we have further assuned that the surface fraction of the surface compounds formed further down in the reaction network are also so small that they do not influence the value of the surface fraction of the empty sites, a*. The olefin/paraffin ratio For a study of the olefin/paraffin ratio we can use the data for either the C2 or the C3 fraction. As the C2 fraction shows an abnormal behaviour in the SchulzFlory relation (see the following two sections) we have used in the first instance the C3 data. As shown in Figure 2, the paraffin fraction is assumed to be formed according to C3* + 2H* + C3Hg t 3*
(13)
with the rate expression
r3,p =
kt,par %3
e2 . H
As it is well known that olefins, when added to the feed of the F.T. process, readily take part in that process, we have assumed that the olefin production step is in fact reversible and has to be expressed by C3*
$
CH
36
t n*
(20)
where n indicates the number of empty sites required to bind one C3* adspecies. In cases where this equilibrium is established we can write K 01 sc3 (C3$j) =
e*"
(21)
which leads-to the rate expression
riol=
9
F Kol ac3
W
e*n
(22)
If however the reverse rate of equation (20) is low we have only the rate of the
261
forward reaction
‘i .01 =
kt,ol ac3
From equations (19) and either (22) or (23) we find for the ratio of the paraffinic and olefinic rates
r3.par
' =k6_
412
(24)
F (1 + 0.27Eo)n+2
'3.01
or '3,par _E
k7
pH2
(25)
(1 + o.~~JPED)~
'3.01
respectively. In Figure 8 we have plotted this ratio as a function of the hydrogen pressure for partial pressures of carbon
monoxide ranging from 5 to 60 kPa. We see
that the first order in hydrogen, predicted by either equation (24) or (25). corresponds to the experinmntal results. The best fit for the carbon monoxide influence is found for n = 2. The straight lines of Figure 8 are drawn with n
I
2
and k6 W/F = 0.42 kPa-'. This indicates an olefinic termination reaction with a rate as given in equation (22). The fact that we find n = 2 suggests that the c3 adspecies is double bonded to the surface. The correspondingequation (24) further predicts that the propane/propene ratio is proportional to W/F. One of us (22) has measured this ratio on a stabilized cobalt on alumina catalyst as a function of W/F. Her results are shown in Figure 9 and indicate that in that respect equation (24) describes the experimental results. The methane selectivity For the derivation of an expression for the methane selectivity sm we have assumed that for constant reaction conditions the Schulz-Flory (S.F.) constant Q
a_+ J
(26)
is constant for all j > 1. We exclude j - 1 because the Cl termination can only proceed via a route that gives the paraffinic product methane (hydrogenation),as can be concluded from the data of Table 1, whereas for the higher hydrocarbons
262 2
1.5
1.0
0.5
c
0
10
hpdrogen
FIGURE 8
partial
60 pr.mmure/kPa
Ratio of the rates of formation of propane and propene as a function of
the hydrogen partial pressure for various carbon monoxide partial pressures.
FIGURE 9
Ratio of the rates of formation of propane and propene as a function of
space time.
263 a paraffinic and an olefinic termination route are always available. In fact the assumption of a constant a also deviates from reality.for j = 2 and is not perfect for j > 2. On the average, the ratio r!&
is about twice the a
calculated from
(27)
Further, we often notice within one experiment the tendency for the ratio ri+,/r; to increase with j for j * 3. Nevertheless we have applied the concept of the idealized S.F. constant to the network of Figure 2 and obtained, as shown in the appendix, a relation for eC, and from that an expression for the methane selectivity sm. We find (equation 1,lO) l-a S
p"2
m=
l/2
(28)
pCo(l + 0.27 pCo) J/Figure 10 shows that this relation between sm and the right hand side of equation (28) can reasonably be presented by a straight line passing through the origin for values of sm not higher than 0.16. We will revert to the deviation at high methane selectivities in the next section. Taking into account the rather sweeping assumptions made in the derivation of equation (28) (see appendix), the fit is satisfactory. The ethene-ethane fraction The ethene-ethane fraction differs from the propene-propanefraction on two accounts: (i) the rate of formation of the total C2 fraction is well below the value predicted by the S.F. relation (ii) the olefinicity of the C2 fraction is much lower than for the C3 fraction.
If we look at the paraffinic parts of the C2 and C3 fractions we see from Figure 11 that there is a reasonable agreement between the ethane/propane ratio and l/a. This suggests that for the C2 and C3 surface compounds the relation
ec2 ’ -=Bc3 a
(29)
is approximately right. However the same figure shows that the ethene/propene ratio is much lower than l/a, and a pronounced function of the hydrogen pressure. This
264
FIGURE 10 Comparison between the experilRenta1 mathane selectivity and the right hand side of equation (28). The straight line gives a value for k8 - 0.118 kPaf. A, uncorrected data;LIsasm data, but corrected for ethane cracking (equation 30). discrepancy is also noticeable when the rates of formation of ethene and propene are compared. The comparison suggests that at the higher hydrogen pressure ethene is converted in a reaction that does not occur with propene. If we compare the rates of the ethane and ethene formation, as is done in Figure 12, we see that the ratio of these two rates is a very strong function of the hydrogen partial pressure. This z+2.5 pCo, suggests that ethene hydrogen influence, which becomes pronounced for p "2 is converted via a reaction that requires much hydrogen, such as the hydrocracking reaction: C2Hq + 2H2 *
2@,
not directly related to the F.T. mechanism. This suggestion is supported by the following: one could reduce the values in Figure 12 to the levels of Figure 8 by increasing the observed ethene levels to (ethene) corrected = -#$$
(propene)
(31)
To keep the mass balance straight, we have, if equation (30) describes what actually happens, to decrease the methane levels with the correspondingquantities. If we do this for all values for which
pH2
* 2.5pCo, the triangle data points in Figure 10
265
3-
l/a;
l-
(P;/P;)~_;
(F;/P;)~~
.
A v
l I
.
Q Q
A A
I
Q A I
1
0
l
Q A
A
I
I
. Q I
60
40
20
hydrogen partial pressure/kPa FIGURE 11 Comparison of l/a and the ethane/propane ratio and the ethene/propene ratio. (C2/C3)paraffinic
(C2/C3)0lefinic
pCO/kPa
l/a
10
0
0
A
20
+
0
V
40
n
cl
0
are replaced by the squares, showing that the excess quantities of methane observed in Figure 10 correspond to the large ethene deficits indicated by Figure 12. The Schulz-Flory distribution As discussed before, in our experiments the S.F. relation is only approximately followed, although for C3 and higher the deviations from linearity are not too great. From equations (1.4) and (1,8) of the appendix we can derive the relation
(l-a)3'2
l/2
pH2 6
a(2-a)1’2 =
kg
(1 + 0.27&)3
>
(33)
This equation predicts a linear relation (through the origin) when the a containing function is plotted against the function of the partial pressures. But instead of that, some hyperbolic type of curve is obtained. This means that the assumptions used in the appendix cannot be all correct. From the discussion in a previous section, we have seen that for the C2 and heavier fractions the termination reaction
266
FIGURE 12 Ethane/ethene ratio as a function of the hydrogen partial pressure for various carbon monoxide partial pressures. pCO/kRa; 5 (v). 7.5 (0). 10 (0). 20 @)S 40 (0). consists of two parts. This means that the termination rate constant kt applied in the appendix is in fact a complex function of the partial pressures of hydrogen and carbon monoxide. It is also conceivable that the propagation rate constant kp as used in the appendix is dependent on the hydrogen and carbon monoxide partial pressures, because the CH2 adspecies may have to be transported from the active center where it was formed to the growing chain in which it is going to be inserted. This transport may require empty sites, or may be hydrogen assisted. If we rewrite equation (33) to make it an explicit function of kt and k,,we obtain
-
kt
Ikp
=
k,O
l/2
pH2Jpc0 1 + 0.27&
3
(1-u)3'2 (34) a(2-a)"2
An analysis of the product data calculated according to this expression indicates that
kt
-
%
= k,, (eH)3'2
=
k,,
J”H2 (1 + 0.275~)
3/2 (35)
267
3k k?
2-
1-
I 10
0
FIGURE 13
20
Relation between a function of the rate constants for propagation and
termination and the partial pressures of hydrogen and carbon monoxide (see equation 37). as follows from Figure 13, where the straight lines are drawn according to this expression. The only rather weak conclusion one might draw from this result is that presumably the influence of the hydrogen and carbon monoxide partial pressures on (Iis for an important part caused by the influence of these partial pressures on kt. We base this on the consideration that according to the discussion of a previous section, kt can be expressed as
kt=
k; par OR* + k; ol . l/e** (
.
(36)
DISCUSSION The model discussed in the previous sections offers an explanation for a number of experimental data observed for the F.T. reaction on a cobalt on alumina catalyst. In equation (lla), which is the basis for the overall rate equation (14). we have assumed that as far as the kinetically active surface ensembles are concerned, carbon monoxide is only dissociatively adsorbed. This does not exclude that carbon monoxide can be adsorbed as such on sites that are not active in the F.T. reaction, nor that a small amount of undissociated carbon monoxide is present on kinetically active centres. As the dissociative adsorption presumably begins with the carbon and oxygen
being adsorbed with a C-O distance comparable to that distance in carbon monoxide, followed by surface diffusion of the two adspecies away from each other, there need not be a very clear distinction between undissociated two site adsorption of carbon monoxide and the dissociative adsorption of that compound. In the kinetics, the rate determining step and the propagation reactions have been described as irreversible.There is, however, evidence that these reactions may be reversible to some extent under certain conditions. We have found that on a pure cobalt catalyst the order in hydrogen is around 1.4.
If we assume that
basically the same reaction network applies, this indicates that the hydrogenation of surface carbon must be a reversible step, that, together with the hydrogen consuming termination steps, leads to a hydrogen order above one. The reversibilityof the propagation step may thus explain the results of Pichler and Schulz (a), who found that when 14CH2=CH-C14H2gwas added to a reacting F.T. system, 80% of the 14 C ended up in hexadecane but that part of the remaining 14C (70%) ended up in hydrocarbons smaller than C16. As far as the manufacture of small olefins is concerned, this study gives cause for the following remarks. In order to obtain a high olefin content of the F.T. product the olefinic termination rate must be high compared to the paraffinic termination rate. This may be caused by: (i) a weakening of the metal-carbon bond strength. This gives an increased olefin production and an increased overall termination rate, or (ii) a decrease of the hydrogenation rate which, at a constant olefinic termination rate, decreases the overall termination rate. Case (i) entails, at a constant propagation rate, a decrease in the S.F. constant a and thus results in a high percentage of small olefins in the product. Case (ii), on the other hand, would lead to an increased a, i.e. the product would be olefinic but would have a wider molecular weight distribution. Catalysts of type (i) are to be preferred for the manufacture of CB-C4 olefins. Catalysts that behave like type (i) catalysts have been described by Biissemeieret al (31,32) and by Kieffer (33). ACKNOWLEDGEMENTS The authors wish to thank Mr. V.M.G. Matthey for his careful experimental work and Mr. R. Jansen for his numerous computer simulations. The financial assistance to the first author by Neste Oy Foundation, Finland, and the Board of the Eindhoven University of Technology is gratefully acknowledged. NOMNCLATURE Symbols used 'j F
hydrocarbon with j carbon atoms feed rate/m3 s-'
269
KA k
(pseudo)adsorptionequilibrium constant for species A (varying) reaction rate constant (varying)
P r'
partial pressure/kPa
r
reaction rate/(Pmol CO.converted to hydrocarbons/kgcat s)
W
mass of catalyst/kg
a
Schulz-Flory constant
eA * (A)
reaction rate/(runolhydrocarbon formed/kg cat s)
fraction of surface sites covered with species A (unoccupied) surface sites concentration of species A/(~mol/m~)
Subscripts in
initiation
ins
insertion
j
number of carbon atoms per molecule
01
olefinic
P
propagation
par
paraffinic
t
termination
tot
total
APPENDIX Derivation of an expression for 8, and the methane selectivity s -1 We will assume: (i)
pIJ+1 rlj
for each experimant a constant a determines the ratio
forallj
>l
(ii) the termination rate for the Cj fraction can be written as r Lj except for j = 1 when we have rt,, = kt,, 8 Cl (iii) the propagation rate from eC
can be written as rp,j =kp eCj eC1
= kt scj in which
the propagation rate constani kp is constant for all j are constant (iv) a steady state, i.e. the values of all e cj differential conversion only.Thus there is a constant ratio between (Cj) (v) at the reactor exit and ec We then have, see Figure 2.
'tot = '1.t + r2,t
i
"
t r3,t + ,......
everywhere on the catalyst.
= kt,l
2, 2 kt ec2 +
eH
%,
= kt,l %,
'H2 +
= kt,l eC, 'H2,
3 kt eC3 +
.......
kt eC, (2a+ 3a2 t .....) 2 .a kt ec,
(1.1)
a g
From the steady state mass balance for Cj+,*
decjtl dt
=O=k
P
8
'1
-
(kp
eC
"'j
1
+
kt)
eC
jtl
(1.2)
we find with
(1.3)
a
l-a
kP eC, =-
(1#4)
kt
Substitution into equation (1.1) gives 2 'tot= kt,l eC, eH + kp ec,2 g
(1.5)
From which 2 eH4 t 4 "c1
V.7
2-a pl-a
_ia
rtot
(1.6)
2k
Substituting equation (14) we obtain 2 kt,l eH ac, =
2-a 2 kpI_a
1
271 With eH << 1 we assume the second term in the square root fom
to be much larger
than 1, and we then obtain kp(2-a) 31.6 -
kt,l e"2 eC1 = 2 k 2-a p=
Q, =
I
l-a
41, &%O (1+0.27 Eo)3
2.&z!z$
1 2 4 kt,l eH
(1*7)
(1.8)
We can now evaluate the methane selectivity 5,
'1.t
2 kt,l 'Cl 'H
'tot
2 ktot eC eH
'rn=-=
(1.9)
or with equations (13) and (1.8) we find
REFERENCES M.A. Vannice, Catal. Rev. Sci. Eng., 14 (1976) 153. M.E. Dry, T. Shingles and L.J. Boshoff, J. Catal., 25 (1972 99. R.A. Dalla Betta, A.G. Piken and M. Shelef, J. Catal., 40 1975) 173. F. Fischer and H. Tropsch, Ber. Deutsch. Chem. Ges., 59 (1626) 830. H.H. Starch, H.Golumbic and R.B. Anderson, The Fischer-Tropschand Related Syntheses, John Wiley and Sons, New York, 1961. R.B. Anderson, Catalysis, Vol. IV, ed. P.H. Ennet. Reinhold Pub. Corp., Baltimore, 1956. H. Kolbel, Chemische Technologie. Band 3, ed. K. Winnacker and L. KDchler. Carl Hansen Verlag, Munchen, 1959. H. Pichler and H. Schulz, Chem. Ing. Tech., 42 (1970) 1162. W.A.A. van Bameveld and V. Ponec, J. Catal., 51 1978) 426. D. Kitzelmann and W. Vielstich, Z. Phys. Chem., 112 (1978) 215. P. Biloen, J.H. Helle and W.M.H. Sachtler, J. Catal., 58 (1979) 95. T. Yamamoto, J. Chen Sot., Chem. Coam~.,(1978) 1003. G.B. Young and G.M. Whitesides, J. hr. Chem. Sot.. 100 (1978) 5808. P.R. Wentrcek, B.J. Wood and H. Wise, J. Catal., 43 (1976) 363. M. Araki and V. Ponec, J. Catal., 44 (1976) 439. B.A. Sexton and G.A. Somorjai, J. Catal., 46 (1977) 167. J.A. Rabo, A.P. Risch and M.L. Poutsma, J. Catal., 53 (1978) 295. D. Kitzelmann, Dissertation, Bonn (1978). J.W.A. Sachtler, J.M. Koo and V. Ponec, J'.Catal.. 56 (1979) 284 B. BUssemeier. C.D. Frohning and 8. Cornils, Hydrocarbon Proc.. 55 (1976)105.
212 C.N. Satterfield and T.K. Sherwood, The Role of Diffusion in Catalysis. AddisonWesley Publ. Co. Inc., Reading, 1963. A.O.I. Rautavuoma, Dissertation,Eindhoven (1979). C.H. Yang, F.E. Massoth and A.G. Oblad, Amer. Chem. Sot., Anaheim Meeting 1978, preprints, p. 538. 24 V.M. Vlasenko, L.A. Kukhar, M.T. Rusov and N.P. Sachenko, Kinet. Catal. (Eng. trans.), 5 (1964) 301. MA. Vannice, J. Catal., 37 (1975) 462. T. van Herwijnen, H. van Doesburg and W.A. de Jong, J. Catal., 28 (1973) 391. G.C. Bond and B.D. Turnham, J. Catal., 45 (1976) 128. R.L. Palmer and D.A. Vroom, J. Catal., 50 (1977) 244. P. Schonbye, J. Catal., 14 (1969) 238. Miniquad progrananewith Marquardt search method. Computer prograsmm?library, Eindhoven University of Technology. 8. Bussemeier, C.D. Frohning, G. Horn and W. Kluy, Gemmn Pat., 25.18.964 6. Bussemeier, C.D. Frohning, G. Horn and W. Kluy, German Pat., 25.36.448 E.P. Kieffer, Dissertation,Eindhoven (1981). W.L. van Dijk, private comnunication.
21
Applied
247
KINETICS AND MECHANISM OF THE FISCHER TROPSCH HYDROCARBON SYNTHESIS ON A COBALT ON ALUMINA CATALYST A. Outi I. RAUTAVUOWand
Hessel S. van der BAAN
Laboratory for Chemical Technology, Eindhoven University of Technology, Eindhoven, The Netherlands. *Present address: Neste Oy Research Center, Kullo, Finland. (Received 4 April 1981, accepted 15 May 1981) ABSTRACT The kinetics of the Fischer Tropsch reaction have been studied on a cobalt on alumina catalyst. The kinetics can be explained satisfactorilyby a model in which the initiation proceeds via carbon monoxide dissociation and formation of a CHBsurface intermediate.The formation of this intermediate is the rate determining step. The chain growth is thought to proceed via the addition of the same CH3 groups to the growing molecule. The model also explains the influence of the hydrogen and carbon monoxide partial pressures on the olefin/paraffinratio as determined experimentally for the C3 fraction, and on the methane selectivity. For high ratios of hydrogen to carbon monoxide, the methane selectivity is higher than predicted, while at the same time a correspondingdeficit in the ethene yield is noticed. These two facts are tentatively ascribed to an ethene hydrocracking reaction. The experimental data show that the Schulz Flory (S.F.) "constant" a has a tendency to increase from C3 to C7. An analysis on the basis of our model shows that the S.F. constant is a complex function of the partial pressures of hydrogen and carbon monoxide. INTRODUCTION The overall kinetics of the Fischer Tropsch (F.T.) synthesis have been the subject of a number of experimental studies during the past years (l-3). The results are generally described by power laws, resulting in a more or less exact first order behaviour in hydrogen and a low or even negative order in carbon monoxide. It is generally accepted that hydrogen enters the F.T. reactions via dissociative adsorption. For carbon monoxide, dissociative adsorption is supported by the more recent OlSS-9834/81/000@-0000/$02.50 @1981Ekvier6cientificPubli&ingComp~y
248
results of a number of investigators (14-19). For the chain growth, a number of models have been suggested. Fischer's original model, the polymerization of CH2 groups (4) has largely been neglected in later years as many arguments were put forward against it, e.g. by Anderson et al (5,6). The latter described the chain growth as the dehydrocondensationof alcoholic intermediates.This mechanism has been supported by Kiilbel(7). Pichler and Schulz (8) were the first to suggest propagation to proceed via carbon monoxide insertion. Barneveld and Ponec (9) and Kitzelmann et al (10) have used this model also. Recently Biloen et al (11) have presented data indicating that the chain growth proceeds via CHx entities. The possibility that a carbene group can be inserted into a metal-carbon bond has also been demonstrated by Yamamoto (12) and Young and Whitesides (13). Our interest in the F.T. reaction is directed towards the manufacture of small olefins by this process. Consequently the reaction mechanism, and especially the factors that influence the olefin/paraffinratio and the molecular mass distribution, are our main concern. Although iron is the most appropriate catalyst for small olefin manufacture (20) we have used cobalt in this study as its greater stability facilitated our obtaining reproducible kinetic data. EXPERIMENTAL All experiments were carried out in a plug-flow fixed bed reactor at atmospheric pressure at 523 K, under differential conditions (conversion below 2%). The reactants, hydrogen (Hoekloos, purity > 99.9%), carbon monoxide (Matheson, purity > 99.5%) and helium (Hoekloos, purity > 99.995%) were purified separately over BTS reduced copper catalyst and molecular sieve 5A. For the analysis, three 8LC instruments were used with the following columns: C4-C8 hydrocarbons; 5% squalane on Chromosorb W-AW DMCS Cl-C4 hydrocarbons; two columns, phenyl isocyanate on Poracil-C and n-octane on Poracil-C water; Porapak-Q. The water data proved to be rather inaccurate, partly due to the peak shape and partly due to adsorption of water on the alumina support. Carbon dioxide was determined with a Maihak VNOR CO2 I.R.
absorption monitor
The cobalt on alumina catalyst (6.2% by weight Co) Co/A1203 was prepared by impregnation of Ketjen 0.6-1.5 E alumina (0.3-0.5 mn particles) with an aqueous cobalt (II)
nitrate solution, drying at 395 K, calcination at 575 K and reduction
with hydrogen at 675 K for 58 ks.
3 -1 After 12 ks, with a gas flow of 1.4 cm s over 1 g catalyst at 523 K and atmos-
pheric pressure, steady synthesis conditions are obtained as shown in Figure 1 for a representative run. The experimental data are the average of three determinations spread over the next three ks. As there is still some drift in catalyst activity after prolonged synthesis, we have taken a new quantity of catalyst for each data set.
249
FIGURE 1
Rate of formation of various products as a function of time: typical
example. 0, CH4;o. C2H6;0, C2Hq (x10);&, C3H8. Calculations according to Satterfield and Sherwood (21) show that no MSS
or heat
transfer limitations are to be expected under our experimental conditions. The value found by us for the apparent energy of activation of 106 kJ IIWB~-~ (22) checks with the results found by Yang (23) and confirms that little or no diffusional lifflitation occurs.
In tqtal 38 experjments have been run, with hydrogen pressures from 5 to 60 kPa and carbon monoxide pressures of 10 to 80 kPa. The experimental results are shown in Table 1. The rate of formation of each hydrocarbon fraction is expressed as r!
J
IC’
EL%! W
pmol/kg cat s
and the total.rate of hydrocarbon formation is given as
rtit = F CI (Cj)
utnolcarbon/kg cat s
W A nunber of repeat experiments (not all shown) indicates a standard deviation of about 6% with a minimum of about 0.1 umol/kg cat s for the lower rates. The data showed that always less than 10% of the oxygen of converted carbon monoxide is converted to carbon dioxide. At the higher conversions this was even less than 5%. A MOUEL FOR THE OVERALL KINETICS Introduction For the description of the network of the Fischer Tropsch synthesis reactions we
250 TABLE
1
Experimental no
1
PH pco /kFa /kPa 5
2 3 4
results
5
c1
AC'
c; c3 Cj C4 c2 rates in pmol/kg cat s
C5
C6
C,
a
10
10.3
0.5
0.2
0.6
0.05
0.7
0.3
0.2
0.2
0.2
0.82
10
10.0
0.5
0.1
0.7
0.05
0.7
0.4
0.2
0.2
0.2
0.75 0.69
20 10
tot
16.7
0.6
0.1
0.8
0.1
0.9
0.6
0:3
0.2
0.4
5
28
2.9
1.3
0.9
0.8
1.8
1.0
0.6
0.4
0.3
0.65
7.5
32
2.6
1.1
1.3
0.6
2.2
1.1
0.7
0.4
0.4
0.65
6
10
28
2.0
0.8
1.3
0.4
2.0
1.1
0.6
0.4
0.3
0.63
7
10
31
2.2
0.9
1.5
0.5
2.2
1.1
0.7
0.5
0.4
0.68
8
20
29
1.5
0.6
1.3
0.3
2.0
1.3
0.9
0.6
0.5
0.68
9
30
24
1.2
0.3
1.5
0.2
1.7
1.0
0.6
0.4
0.3
0.65
10
40
23
1.1
0.2
1.4
0.1
1.5
0.9
0.5
0.4
0.3
0.68
11
15
20
57
1.4
1.7
1.0
3.3
2.0
1.4
0.9
0.8
0.69
12
20
5
90
24
6.9
0.4
4.8
3.5
2.5
1.6
0.8
0.7
0.62
7.5
85
18
6.0
0.7
4.3
4.1
2.6
1.3
0.8
0.4
0.53
14
13
3.5
14
10
79
5.6
1.7
3.3
4.6
2.6
1.5
0.9
0.4
0.57
15
15
69
8.6
4.0
1.4
2.7
3.1
2.7
1.5
1.2
0.9
0.68
17
20
59
6.5
2.7
2.2
1.6
4.1
5.7
3.4
2.1
1.1
0.70
18
30
53
3.8
1.5
2.2
1.0
3.0
2.2
1.5
1.0
1.1
0.62
19
40
46
3.7
1.1
2.6
0.6
3.5
2.1
1.3
0.9
0.4
0.69
20'
50
41
2.4
0.6
2.2
0.3
2.7
1.8
1.2
0.9
0.8
0.61
21
60
38
2.0
0.4
2.0
0.2
2.6
1.5
1.1
0.9
0.9
0.71
22
70
37
1.8
0.4
2.0
0.2
2.4
1.7
1.1
0.9
0.8
0.77
23
80
43
1.9
0.3
2.1
0.1
2.3
2.1
1.5
1.1
1.0
0.74
10
134
10.0
1.1
7.1
6.7
4.0
1.9
1.3
0.7
0.76
25
20
79
7.3
3.5
1.2
2.5
3.9
3.0
1.5
1.3
0.8
0.56
26
40
77
6.3
2.2
3.3
1.3
5.6
3.0
2.0
1.2
0.6
0.64
24
30
29
10
141
41
0.6
7.6
5.3
3.7
1.6
0.9
0.5
0.60
29
20
134
19
8.4
1.3
6.2
5.6
4.7
2.6
1.5
1.0
0.48
30
30
104
13
31
40
96
27
40
5.0
2.7
3.3
7.2
3.7
2.1
1.4
1.1
0.56
9.3
3.3
3.0
2.2
6.7
4.0
2.3
1.5
0.8
0.63
2.4
3.8
1.5
6.7
3.5
2.2
1.5
0.9
0.60
32
50
90
7.7
33
60
87
6.9
34
50
10
187.5
16 11
35
20
161
30
40
111
13
20
197
46
40
143
19
37
60
1.8
62
36
38
12
4.8 15 7.0
3.9
1.1
6.5
3.7
2.2
1.3
0.8
0.63
0.6
9.8
6.7
4.6
1.9
1.1
0.6
0.59
1.1
6.7
7.2
5.3
2.9
1.7
1.1
0.49
3.3
3.2
8.1
4.0
2.5
1.3
0.8
0.57
1.1
9.5
7.9
5.8
2.5
1.7
1.1
0.57
3.2
4.8
9.7
5.3
2.9
2.0
1.0
0.54
251
Kt par
t2 H”
(7)
C2H4 4 kt olef
kt par
(7)
-
CzH6
-
C3H8 ( 9 1
t2 H” (9)
C3H6
FIGURE 2
=
kt olef
kt par
Reaction network for the Fischer Tropsch reaction on a cobalt on alumina
catalyst. will use the scheme presented in Figure 2.
Although a number of details are shown
that will be discussed later, the diagram is useful for an explanation of the main features of the reaction network. We will assume that on the catalyst surface carbon monoxide dissociates (step 2), forming adsorbed carbon atoms (C*) that are the basis of at least the initiation step 3. As we have differential conditions in all of our experiments, we may assume the reaction rates to be constant throughout the reactor. We can then express rj and t-jwith the following formulae:
rj
=
k j(Cj)
rj ={
(cj)
(2)
262
and write for the initiation rate = r; + r+ + ri + ........ r. =r in 3 or r. in
(3)
Reverting to Figure 2, we will further assume that there is a building block (Gins*) that contains one carbon atom and that chain growth occurs by insertion of this species in an initiated chain, fonsing on the catalyst surface a series of adsorbed species C2*, C3*
...... Cj*. Thus a surface species C.* is fonsed by
one initiation step and j-l insertion steps. These surface spec:es will desorb with or without further hydrogenation fran the catalyst and form the hydrocarbons that are the products of F.T. synthesis.
FIGURE 3
Rate of conversion of carbon monoxide to total hydrocarbons as a function
of the hydrogen pressure.
253
FIGWE 4
Rate of formation of all products as a function of the hydrogen partial
pressure. PartiaT pressure of carbon monoxide = 20 kPa. The initiation and the rate determining steps From Figure 3, where the total rate of hydrocarbon fonaation
is plotted as a function of the hydrogen partial pressure for three carbon monoxide partial pressures, we see that the rate is exactly first order in hydrogen. To explain this we will have to find the step that is rate determining or a number of steps that together govern the overall rate of hydrocarbon formation, rtot. A first assumption in this respect might be that all termination reactions together would be rate determining. In Figure 4 we show the rates of the individual.tennination reactions as a function of the hydrogen pressure at 20 kPa carbon monoxide pressure. Corresponding curves am
obtained for other carbon amnoxide pressures. As it is
difficult to visualize how such a bundle of different curves would add up to a straight line if they were independent,we rule out the possibility that the termination reactions together are rate determining.The same argua#nt applies to the assunption that the rates of the initiation step rins (= r4) together would be rate determining. When these two rates are plotted for a given carbon monoxide partial pressure according to equations (3) and (4)
254
r. = i I:(j-l) (Cj) ins as a function of the hydrogen pressure again two pronounced curves are obtained for which it is difficult to conceive that, if these two curves were independent, they would add up to the linear first order relation shown in Figure 3. We therefore conclude that the rate determining step that is first order in hydrogen is cotnson to the formation of Cl* and of Gins*. As hydrogen is dissociativelyadsorbed on cobalt, the first order dependence in hydrogen then strongly suggests that in the rate determining step two adsorbed hydrogen atoms react simultaneously,or that a reversible addition of one adsorbed hydrogen atom is followed by the addition of a second adsorbed hydrogen atom. Of such reactions, those shown in Table 2 have been mentioned in the literature as rate determining steps. A choice between the possibilities shown there will be based on the influence of the carbon monoxide partial pressure on the overall reaction rate. We would then reject hydrogen adsorption as the rate determining step because the F.T. reaction has a positive order in carbon monoxide for low carbon monoxide pressures. Moreover, we have obtained orders in hydrogen higher than one for a pure cobalt catalyst, on which we would expect to have a rate determining step that is related to the one for the catalyst used in this study. The next three reactions, (II)-
have the same rate expression: (5)
if we assume fast equilibriun adsorption for carbon monoxide on one site, low coverage with hydrogen and Langmuir-Hinshelwoodkinetics. Reaction (III)
follows
this rate expression, on the further assumption that the oxygen complex is formed according to reaction (II).
For a constant hydrogen pressure this equation is
plotted in its linearized form l/3 pco A, + 6, pco = r ( )
(6)
as curve a of Figure 5. The nonlinear result excludes any of these reactions as being the rate determining step. If we assume two site undissociated adsorption of carbon monoxide for these reactions, we obtain a complicated relation because we derive, again under the assumption of low hydrogen coverage, for the equilibrium co + 2* + co** the expression
(7)
TABLE 2 Rate detemlining steps mentioned in the literature for the Fischer Tropsch reaction.
(I)
Hz + 2* * 2H*
Hydrogen adsorption
Schonbye (29)
(II)
Formation of an oxygen
Co* + 2H* + COH2 + 2*
containing complex
or CDlr*+ 2H* + COH l * + * Vlasenko et al (224)
(III)
Hydrogenation of
COH2* + 2H* + Cl* + Hz0 + 2*
such a complex
COH2** + 2H* + C,* + Hz0 + 3* Vannice (25), van Hemijnen et al (26). Bond and Turnham (27) Co* + 2H* + C* + Hz0 t 2*
(IV) The hydrogen assisted dissociation of CO
or CO*
+ 2H* + C* t Hz0 t 3*
Palmer and Vroom (28) (V)
C* t 2H* + CH * t 2* 2 or
The hydrogenation of surface carbon
C* t H* * CH* t * CH* t H* + CH2* t * Rautavuoma (22)
%o =
+ l-d4 KCopCo + 2 KCOpCO
1
2 .KCOpCO
and for the rate
r = k2 eCO (1.- eco)2
(9)
To check this equation we have for the same set of data as used in Figure 5 adjusted KC0 and k2 in such a way that equation '(9)fits two experimental data points exactly. If we choose pco = 5 kPa and pco = 80 kPa (both p = 20 kPa) as the two Hz data points we find KC0 = 1.2 x 10m4 Pa-l and k2 = 610 umol/kg catalyst s. But, as shown in Figure 6. with this set of constants relation (9) does not fit the other experimental data. This is also the case for any other set of constants KC0 and k2. We therefore also reject reactions (Z)-(4) with two site adsorption of undissociated carbon monoxide.
If reaction (V). the hydrogenation of surface carbon, is the rate determining
0
[PC&) l/3
0.6
1 0.4
O.! 0.2
l/2,p,1/3 (PC0
0 I-
I
50 FIGURE 5
Checks for linearity: a) equation (6). b) equation (16).
V 0
25 aalculated
FIGURE 6
0
100
PC0
50 rate/wnl/kq
Check for linearity: equation (9).
I
t
75
100
cat s
257 step, and the preceding dissociative carbon monoxide adsorption is a fast equilibrium, i.e. if we have the set of reaction steps 11(a)-(c): Co+2*
f
c*+o* -3
(114
C* + 2H* t4 CH2* + 2*
(llb)
O* + 2H* t5 H20 + 3*
(llc)
we obtain from the steady state requirement that the'rates of (llb) and (11~) must be equal: k4 e. = 1;-; sc
(‘2)
The equilibrium (lla) then,yields:
k3
lq
e2* - lqk4 ec2
PC0
or eC =
(13)
KCpco a*
and with (llb) as the rate determining step we find
ktot pH2&l (14) '&It=
('+%/%I
+JF2
3,
Note (1). It would also be conceivable that the kinetically equivalent reaction (11~) would be the rats determining step. If that were the case, D* would be the most abundant surface species and not C*. We find however that during F.T. synthesis on our catalyst that the amounts of hydrocarbons and water formed are almost stoichianetricallyequivalent, whereas the mnount of carbon dioxide formed is very small. If we now stop the carbon monoxide flow to the reactor we can strip off a quantity of hydrocarbon that is much larger than the amount of water. Recently we obtained further information supporting the low 0*/t? ratio during F.T. synthesis on our catalyst. Van Oijk (34) found in our laboratory that, when after synthesis on a cobalt catalyst ( that gave during synthesis almost equivalent quantities of hydrocarbons and water and almost no carbon dioxide) the catalyst was
268
stripped with helium, the production of hydrocarbons and water decreased but that the quantity of carbon dioxide formed increased. If thereafter hydrogen was passed over the catalyst the carbon dioxide production dropped to zero and a short high water production peak was observed. In our opinion the carbon dioxide production during helium stripping shows the formation of free surface oxygen from adsorbed carbon monoxide which, in the absence of hydrogen, can build up to a level that allows the higher carbon dioxide rate. The introduction of hydrogen again reduces the surface oxygen concentration to such a low level (by water formation) that the carbon dioxide production stops completely. Note (2). According to the findings reported in the next section, it is not unlikely that the CH2* adspecies of equation (llb) is double bonded to the surface, i.e. CH2**. This would not change the kinetic relations derived above.
FIGURE 7
Rates of conversion of carbon monoxide to hydrocarbons as a function of the
carbon monoxide partial pressure. Drawn curves calculated according to equation (14). Hydrogen pressure/kPa:O, GO;&, 5D;O, 4O;V. 30;0, 20;+,
15;A, 10;m. 5.
If we assume
hi 2 pH2 << 1 +J k. pco the linearized version of equation (14) becomes
(15)
259
PC0 l/3
f-1
A2+52&=
(‘6)
)"
Curve b of Figure 5 shows that the data follow this relation very well. On the strength of this result we have applied a computer prograssne(30) to find the best fit for ktot, KC0 and KH2 for the data in Table 1. Figure 7 shows that for the values = 7.9 mol/kg cat s kPa3" k tot KO
= 0.27
kPa"*
(i1.0) (kO.02) (kO.002)
a good fit for all the conditions is obtained. The value found for KH2 justifies the assumption (15) of low hydrogen coverage. Note. If we omit the constraint that all constants must be positive, the best value found for KH2 is -5 x 10-4 l/kPa"*. This result regrettably does not give an indication of the value of the hydrogen adsorption equilibrium constant under F.T. conditions. Consequently,we will have to treat KH2 as a small but unknown constant in further modelling. From these results we conclude that: (i) the rate determining step in the F.T. reaction on cobalt on alumina catalysts is the formation of a surface compound by hydrogenation of a surface carbon species (ii) the initiating species and the insertion species are formed according to the same rate expression and can therefore be assumed to be the same. This means that basically the mechanism suggested by Fischer, the "polymerization" of CH2 species (4) is supported by our results. APPLICATIONS OF THE MODEL TOWARDS SELECTIVITIES Introduction Rate equation (14). with the data found for the constants in that equation, imply that the surface fractions of C*, H* and empty sites are
ec =
eH =
O.*7Jpco 1 + 0.276
KHPKP 1 + 0.27Ko
(174
(‘7b)
260
e*=,TT&&
(17c)
We have assumed that the surface fraction of oxygen is so small that it does not materially affect the e*, and with reaction (llb), i.e. reaction (3) of Figure 2, as rate determining step we have further assuned that the surface fraction of the surface compounds formed further down in the reaction network are also so small that they do not influence the value of the surface fraction of the empty sites, a*. The olefin/paraffin ratio For a study of the olefin/paraffin ratio we can use the data for either the C2 or the C3 fraction. As the C2 fraction shows an abnormal behaviour in the SchulzFlory relation (see the following two sections) we have used in the first instance the C3 data. As shown in Figure 2, the paraffin fraction is assumed to be formed according to C3* + 2H* + C3Hg t 3*
(13)
with the rate expression
r3,p =
kt,par %3
e2 . H
As it is well known that olefins, when added to the feed of the F.T. process, readily take part in that process, we have assumed that the olefin production step is in fact reversible and has to be expressed by C3*
$
CH
36
t n*
(20)
where n indicates the number of empty sites required to bind one C3* adspecies. In cases where this equilibrium is established we can write K 01 sc3 (C3$j) =
e*"
(21)
which leads-to the rate expression
riol=
9
F Kol ac3
W
e*n
(22)
If however the reverse rate of equation (20) is low we have only the rate of the
261
forward reaction
‘i .01 =
kt,ol ac3
From equations (19) and either (22) or (23) we find for the ratio of the paraffinic and olefinic rates
r3.par
' =k6_
412
(24)
F (1 + 0.27Eo)n+2
'3.01
or '3,par _E
k7
pH2
(25)
(1 + o.~~JPED)~
'3.01
respectively. In Figure 8 we have plotted this ratio as a function of the hydrogen pressure for partial pressures of carbon
monoxide ranging from 5 to 60 kPa. We see
that the first order in hydrogen, predicted by either equation (24) or (25). corresponds to the experinmntal results. The best fit for the carbon monoxide influence is found for n = 2. The straight lines of Figure 8 are drawn with n
I
2
and k6 W/F = 0.42 kPa-'. This indicates an olefinic termination reaction with a rate as given in equation (22). The fact that we find n = 2 suggests that the c3 adspecies is double bonded to the surface. The correspondingequation (24) further predicts that the propane/propene ratio is proportional to W/F. One of us (22) has measured this ratio on a stabilized cobalt on alumina catalyst as a function of W/F. Her results are shown in Figure 9 and indicate that in that respect equation (24) describes the experimental results. The methane selectivity For the derivation of an expression for the methane selectivity sm we have assumed that for constant reaction conditions the Schulz-Flory (S.F.) constant Q
a_+ J
(26)
is constant for all j > 1. We exclude j - 1 because the Cl termination can only proceed via a route that gives the paraffinic product methane (hydrogenation),as can be concluded from the data of Table 1, whereas for the higher hydrocarbons
262 2
1.5
1.0
0.5
c
0
10
hpdrogen
FIGURE 8
partial
60 pr.mmure/kPa
Ratio of the rates of formation of propane and propene as a function of
the hydrogen partial pressure for various carbon monoxide partial pressures.
FIGURE 9
Ratio of the rates of formation of propane and propene as a function of
space time.
263 a paraffinic and an olefinic termination route are always available. In fact the assumption of a constant a also deviates from reality.for j = 2 and is not perfect for j > 2. On the average, the ratio r!&
is about twice the a
calculated from
(27)
Further, we often notice within one experiment the tendency for the ratio ri+,/r; to increase with j for j * 3. Nevertheless we have applied the concept of the idealized S.F. constant to the network of Figure 2 and obtained, as shown in the appendix, a relation for eC, and from that an expression for the methane selectivity sm. We find (equation 1,lO) l-a S
p"2
m=
l/2
(28)
pCo(l + 0.27 pCo) J/Figure 10 shows that this relation between sm and the right hand side of equation (28) can reasonably be presented by a straight line passing through the origin for values of sm not higher than 0.16. We will revert to the deviation at high methane selectivities in the next section. Taking into account the rather sweeping assumptions made in the derivation of equation (28) (see appendix), the fit is satisfactory. The ethene-ethane fraction The ethene-ethane fraction differs from the propene-propanefraction on two accounts: (i) the rate of formation of the total C2 fraction is well below the value predicted by the S.F. relation (ii) the olefinicity of the C2 fraction is much lower than for the C3 fraction.
If we look at the paraffinic parts of the C2 and C3 fractions we see from Figure 11 that there is a reasonable agreement between the ethane/propane ratio and l/a. This suggests that for the C2 and C3 surface compounds the relation
ec2 ’ -=Bc3 a
(29)
is approximately right. However the same figure shows that the ethene/propene ratio is much lower than l/a, and a pronounced function of the hydrogen pressure. This
264
FIGURE 10 Comparison between the experilRenta1 mathane selectivity and the right hand side of equation (28). The straight line gives a value for k8 - 0.118 kPaf. A, uncorrected data;LIsasm data, but corrected for ethane cracking (equation 30). discrepancy is also noticeable when the rates of formation of ethene and propene are compared. The comparison suggests that at the higher hydrogen pressure ethene is converted in a reaction that does not occur with propene. If we compare the rates of the ethane and ethene formation, as is done in Figure 12, we see that the ratio of these two rates is a very strong function of the hydrogen partial pressure. This z+2.5 pCo, suggests that ethene hydrogen influence, which becomes pronounced for p "2 is converted via a reaction that requires much hydrogen, such as the hydrocracking reaction: C2Hq + 2H2 *
2@,
not directly related to the F.T. mechanism. This suggestion is supported by the following: one could reduce the values in Figure 12 to the levels of Figure 8 by increasing the observed ethene levels to (ethene) corrected = -#$$
(propene)
(31)
To keep the mass balance straight, we have, if equation (30) describes what actually happens, to decrease the methane levels with the correspondingquantities. If we do this for all values for which
pH2
* 2.5pCo, the triangle data points in Figure 10
265
3-
l/a;
l-
(P;/P;)~_;
(F;/P;)~~
.
A v
l I
.
Q Q
A A
I
Q A I
1
0
l
Q A
A
I
I
. Q I
60
40
20
hydrogen partial pressure/kPa FIGURE 11 Comparison of l/a and the ethane/propane ratio and the ethene/propene ratio. (C2/C3)paraffinic
(C2/C3)0lefinic
pCO/kPa
l/a
10
0
0
A
20
+
0
V
40
n
cl
0
are replaced by the squares, showing that the excess quantities of methane observed in Figure 10 correspond to the large ethene deficits indicated by Figure 12. The Schulz-Flory distribution As discussed before, in our experiments the S.F. relation is only approximately followed, although for C3 and higher the deviations from linearity are not too great. From equations (1.4) and (1,8) of the appendix we can derive the relation
(l-a)3'2
l/2
pH2 6
a(2-a)1’2 =
kg
(1 + 0.27&)3
>
(33)
This equation predicts a linear relation (through the origin) when the a containing function is plotted against the function of the partial pressures. But instead of that, some hyperbolic type of curve is obtained. This means that the assumptions used in the appendix cannot be all correct. From the discussion in a previous section, we have seen that for the C2 and heavier fractions the termination reaction
266
FIGURE 12 Ethane/ethene ratio as a function of the hydrogen partial pressure for various carbon monoxide partial pressures. pCO/kRa; 5 (v). 7.5 (0). 10 (0). 20 @)S 40 (0). consists of two parts. This means that the termination rate constant kt applied in the appendix is in fact a complex function of the partial pressures of hydrogen and carbon monoxide. It is also conceivable that the propagation rate constant kp as used in the appendix is dependent on the hydrogen and carbon monoxide partial pressures, because the CH2 adspecies may have to be transported from the active center where it was formed to the growing chain in which it is going to be inserted. This transport may require empty sites, or may be hydrogen assisted. If we rewrite equation (33) to make it an explicit function of kt and k,,we obtain
-
kt
Ikp
=
k,O
l/2
pH2Jpc0 1 + 0.27&
3
(1-u)3'2 (34) a(2-a)"2
An analysis of the product data calculated according to this expression indicates that
kt
-
%
= k,, (eH)3'2
=
k,,
J”H2 (1 + 0.275~)
3/2 (35)
267
3k k?
2-
1-
I 10
0
FIGURE 13
20
Relation between a function of the rate constants for propagation and
termination and the partial pressures of hydrogen and carbon monoxide (see equation 37). as follows from Figure 13, where the straight lines are drawn according to this expression. The only rather weak conclusion one might draw from this result is that presumably the influence of the hydrogen and carbon monoxide partial pressures on (Iis for an important part caused by the influence of these partial pressures on kt. We base this on the consideration that according to the discussion of a previous section, kt can be expressed as
kt=
k; par OR* + k; ol . l/e** (
.
(36)
DISCUSSION The model discussed in the previous sections offers an explanation for a number of experimental data observed for the F.T. reaction on a cobalt on alumina catalyst. In equation (lla), which is the basis for the overall rate equation (14). we have assumed that as far as the kinetically active surface ensembles are concerned, carbon monoxide is only dissociatively adsorbed. This does not exclude that carbon monoxide can be adsorbed as such on sites that are not active in the F.T. reaction, nor that a small amount of undissociated carbon monoxide is present on kinetically active centres. As the dissociative adsorption presumably begins with the carbon and oxygen
being adsorbed with a C-O distance comparable to that distance in carbon monoxide, followed by surface diffusion of the two adspecies away from each other, there need not be a very clear distinction between undissociated two site adsorption of carbon monoxide and the dissociative adsorption of that compound. In the kinetics, the rate determining step and the propagation reactions have been described as irreversible.There is, however, evidence that these reactions may be reversible to some extent under certain conditions. We have found that on a pure cobalt catalyst the order in hydrogen is around 1.4.
If we assume that
basically the same reaction network applies, this indicates that the hydrogenation of surface carbon must be a reversible step, that, together with the hydrogen consuming termination steps, leads to a hydrogen order above one. The reversibilityof the propagation step may thus explain the results of Pichler and Schulz (a), who found that when 14CH2=CH-C14H2gwas added to a reacting F.T. system, 80% of the 14 C ended up in hexadecane but that part of the remaining 14C (70%) ended up in hydrocarbons smaller than C16. As far as the manufacture of small olefins is concerned, this study gives cause for the following remarks. In order to obtain a high olefin content of the F.T. product the olefinic termination rate must be high compared to the paraffinic termination rate. This may be caused by: (i) a weakening of the metal-carbon bond strength. This gives an increased olefin production and an increased overall termination rate, or (ii) a decrease of the hydrogenation rate which, at a constant olefinic termination rate, decreases the overall termination rate. Case (i) entails, at a constant propagation rate, a decrease in the S.F. constant a and thus results in a high percentage of small olefins in the product. Case (ii), on the other hand, would lead to an increased a, i.e. the product would be olefinic but would have a wider molecular weight distribution. Catalysts of type (i) are to be preferred for the manufacture of CB-C4 olefins. Catalysts that behave like type (i) catalysts have been described by Biissemeieret al (31,32) and by Kieffer (33). ACKNOWLEDGEMENTS The authors wish to thank Mr. V.M.G. Matthey for his careful experimental work and Mr. R. Jansen for his numerous computer simulations. The financial assistance to the first author by Neste Oy Foundation, Finland, and the Board of the Eindhoven University of Technology is gratefully acknowledged. NOMNCLATURE Symbols used 'j F
hydrocarbon with j carbon atoms feed rate/m3 s-'
269
KA k
(pseudo)adsorptionequilibrium constant for species A (varying) reaction rate constant (varying)
P r'
partial pressure/kPa
r
reaction rate/(Pmol CO.converted to hydrocarbons/kgcat s)
W
mass of catalyst/kg
a
Schulz-Flory constant
eA * (A)
reaction rate/(runolhydrocarbon formed/kg cat s)
fraction of surface sites covered with species A (unoccupied) surface sites concentration of species A/(~mol/m~)
Subscripts in
initiation
ins
insertion
j
number of carbon atoms per molecule
01
olefinic
P
propagation
par
paraffinic
t
termination
tot
total
APPENDIX Derivation of an expression for 8, and the methane selectivity s -1 We will assume: (i)
pIJ+1 rlj
for each experimant a constant a determines the ratio
forallj
>l
(ii) the termination rate for the Cj fraction can be written as r Lj except for j = 1 when we have rt,, = kt,, 8 Cl (iii) the propagation rate from eC
can be written as rp,j =kp eCj eC1
= kt scj in which
the propagation rate constani kp is constant for all j are constant (iv) a steady state, i.e. the values of all e cj differential conversion only.Thus there is a constant ratio between (Cj) (v) at the reactor exit and ec We then have, see Figure 2.
'tot = '1.t + r2,t
i
"
t r3,t + ,......
everywhere on the catalyst.
= kt,l
2, 2 kt ec2 +
eH
%,
= kt,l %,
'H2 +
= kt,l eC, 'H2,
3 kt eC3 +
.......
kt eC, (2a+ 3a2 t .....) 2 .a kt ec,
(1.1)
a g
From the steady state mass balance for Cj+,*
decjtl dt
=O=k
P
8
'1
-
(kp
eC
"'j
1
+
kt)
eC
jtl
(1.2)
we find with
(1.3)
a
l-a
kP eC, =-
(1#4)
kt
Substitution into equation (1.1) gives 2 'tot= kt,l eC, eH + kp ec,2 g
(1.5)
From which 2 eH4 t 4 "c1
V.7
2-a pl-a
_ia
rtot
(1.6)
2k
Substituting equation (14) we obtain 2 kt,l eH ac, =
2-a 2 kpI_a
1
271 With eH << 1 we assume the second term in the square root fom
to be much larger
than 1, and we then obtain kp(2-a) 31.6 -
kt,l e"2 eC1 = 2 k 2-a p=
Q, =
I
l-a
41, &%O (1+0.27 Eo)3
2.&z!z$
1 2 4 kt,l eH
(1*7)
(1.8)
We can now evaluate the methane selectivity 5,
'1.t
2 kt,l 'Cl 'H
'tot
2 ktot eC eH
'rn=-=
(1.9)
or with equations (13) and (1.8) we find
REFERENCES M.A. Vannice, Catal. Rev. Sci. Eng., 14 (1976) 153. M.E. Dry, T. Shingles and L.J. Boshoff, J. Catal., 25 (1972 99. R.A. Dalla Betta, A.G. Piken and M. Shelef, J. Catal., 40 1975) 173. F. Fischer and H. Tropsch, Ber. Deutsch. Chem. Ges., 59 (1626) 830. H.H. Starch, H.Golumbic and R.B. Anderson, The Fischer-Tropschand Related Syntheses, John Wiley and Sons, New York, 1961. R.B. Anderson, Catalysis, Vol. IV, ed. P.H. Ennet. Reinhold Pub. Corp., Baltimore, 1956. H. Kolbel, Chemische Technologie. Band 3, ed. K. Winnacker and L. KDchler. Carl Hansen Verlag, Munchen, 1959. H. Pichler and H. Schulz, Chem. Ing. Tech., 42 (1970) 1162. W.A.A. van Bameveld and V. Ponec, J. Catal., 51 1978) 426. D. Kitzelmann and W. Vielstich, Z. Phys. Chem., 112 (1978) 215. P. Biloen, J.H. Helle and W.M.H. Sachtler, J. Catal., 58 (1979) 95. T. Yamamoto, J. Chen Sot., Chem. Coam~.,(1978) 1003. G.B. Young and G.M. Whitesides, J. hr. Chem. Sot.. 100 (1978) 5808. P.R. Wentrcek, B.J. Wood and H. Wise, J. Catal., 43 (1976) 363. M. Araki and V. Ponec, J. Catal., 44 (1976) 439. B.A. Sexton and G.A. Somorjai, J. Catal., 46 (1977) 167. J.A. Rabo, A.P. Risch and M.L. Poutsma, J. Catal., 53 (1978) 295. D. Kitzelmann, Dissertation, Bonn (1978). J.W.A. Sachtler, J.M. Koo and V. Ponec, J'.Catal.. 56 (1979) 284 B. BUssemeier. C.D. Frohning and 8. Cornils, Hydrocarbon Proc.. 55 (1976)105.
212 C.N. Satterfield and T.K. Sherwood, The Role of Diffusion in Catalysis. AddisonWesley Publ. Co. Inc., Reading, 1963. A.O.I. Rautavuoma, Dissertation,Eindhoven (1979). C.H. Yang, F.E. Massoth and A.G. Oblad, Amer. Chem. Sot., Anaheim Meeting 1978, preprints, p. 538. 24 V.M. Vlasenko, L.A. Kukhar, M.T. Rusov and N.P. Sachenko, Kinet. Catal. (Eng. trans.), 5 (1964) 301. MA. Vannice, J. Catal., 37 (1975) 462. T. van Herwijnen, H. van Doesburg and W.A. de Jong, J. Catal., 28 (1973) 391. G.C. Bond and B.D. Turnham, J. Catal., 45 (1976) 128. R.L. Palmer and D.A. Vroom, J. Catal., 50 (1977) 244. P. Schonbye, J. Catal., 14 (1969) 238. Miniquad progrananewith Marquardt search method. Computer prograsmm?library, Eindhoven University of Technology. 8. Bussemeier, C.D. Frohning, G. Horn and W. Kluy, Gemmn Pat., 25.18.964 6. Bussemeier, C.D. Frohning, G. Horn and W. Kluy, German Pat., 25.36.448 E.P. Kieffer, Dissertation,Eindhoven (1981). W.L. van Dijk, private comnunication.
21