Ind. Eng. Chem. Res. 1989, 28, 659-664 Snel, R. Rationalizing Activity Patterns in the Catalytic Hydrogenation of Carbon Monoxide. C1 Mol. Chem. 198613,1, 427-447. Snel, R. On-Line Gas Chromatographic Analysis of Light FischerTropsch Synthesis Products. Chromatographia 1986c,5,265-268. Snel, R. Olefins from Syngas. Catal. Rev.-Sei. Eng. 1987a,29(4), 361-445. Snel, R. Control of the Porous Structure of Amorphous Silica-Alumina 4. Nitrogen-Bases as Pore Regulating Agents. Appl. Catal. 1987b,33,281-294. Snel, R. Catalytic Hydrogenation of Carbon Monoxide to Alkenes Over Partially Degraded Iron Complexes I. Unsupported Catalysts. Appl. Catal. 1988,37, 35-44.
659
Snel, R. The Nature of the Hydrocarbon Synthesis by Means of Hydrogenation of Carbon Monoxide on Iron-Based Catalysts I. Hydrogenation-Strength Distribution of Surface Sites. J . Mol. Catal. 1989,in press. Vanhove, D.; Zhuyong, Z.; Makambo, P.; Blanchard, M. Hydrocarbon Selectivity in Fischer-Tropsch in Relation to Textural Properties of Supported Cobalt Catalysts. Appl. Catal. 1984,9, 327-342.
Received for review August 26, 1988 Revised manuscript received February 6, 1989 Accepted February 17, 1989
Fischer-Tropsch Reaction Mechanisms and a Posteriori Probabilistic Treatment of Product Distribution Luca Basini SNAMPROGETTI S.p.A. Research Laboratories, Via Maritano 26, 20097 S a n Donato Milanese, Milano, Italy
Fischer-Tropsch synthesis can be considered a structure-sensitive polymerization process over solid surfaces and its product distributions can be described by adopting a statistical approach. This is done here assuming that common intermediates originate three classes of compounds: alcohols, alkanes, and alkenes. A break zone instead of a sharp break in Anderson-Shultz-Flory plots is considered and is represented as the result of competition between two different reaction mechanisms. Growth and termination probabilities for the intermediates are defined and related t o the experimental molar fractions of the products. The chemistry of the catalyzed hydrogenation of carbon monoxide is important from both scientific and industrial points of view. The Fischer-Tropsch (FT) synthesis supplies an opportunity to obtain hydrocarbon mixtures to be used as an alternative energetic source to petroleum feedstocks. In the last few years, aimed at jnterpretating reaction mechanisms, spectroscopic measurements on the nature of the intermediates have been performed by Kaminski et al. (19861, Lee et al. (1986), and Loggenberg et al. (1987), while insertions of radionuclides for the reagents have been recently studied by Stockwell and Bennet (1988). Theoretical chemists are also engaged on the topic, and very interesting quantomechanical calculations on the bonding and mobility of CH, and CO species over crystalline surfaces have been developed by Zheng et al. (1988). One of the oldest approaches is, however, the probabilistic calculation of product distribution based on mechanistic assumptions. Many reviews on the matter have been published; we mention here the ones written by Shultz et al. (1988), Anderson (1984), Olive and Olive (1984), Herrmann (19821, Biloen and Sachtler (1981), and Bell (1981) in which special emphasis is given to the discussion of the reaction mechanisms. The subject is still under debate. Our contribution is aimed at optimizing reaction mechanisms, following a statistic approach, that gives equations similar to the Anderson-Schultz-Flory (ASF) ones but that describes recently discovered experimental features on the FT product distribution. In the resulting equations, only parameters with clear physical meaning, the growth and termination probabilities, have been introduced. It is known that a lot of factors influence the kind of F T synthesis products and their distribution. However, the common feature of the synthesis is the occurrence of a repeated chain-growth step, a type of surface polymerization. Our approach is modeled here on a catalytic process in which alcohols and saturated and unsaturated hydrocarbons are produced. This is a typical 0888-5885 18912628-0659$01.50/0
situation experimented in the low-temperature synthesis of ruthenium- or rhodium-based catalysts or with the cobalt-copper-chromium oxide system patented by the Institut Francais du Petrole (IFP). Courty et al. (1982) and Sheffer and King (1988) have discussed the effects of preparation parameters on the catalytic properties of these materials. We assume that common intermediates for all three classes of products exist. This hypothesis has also been suggested by Kiennemann (1987), Sachler and Ichicawa (1986), and Takeuchi et al. (1983) based on the experimental results of the promotion effects of basic ions on F T synthesis metals to obtain oxygenates. In our model, branching phenomena and breaks in the ASF plots have also been considered.
Theory Sequences of oligomers of alcohols, alkanes, and alkenes have been considered as FT synthesis products. Herington (1946) first hypothesized a mechanism based on a constant value of chain-growth probability; subsequently Anderson et al. (1951) applied the Shultz and Flory theories for polymerization processes to the FT synthesis, introducing the well-known ASF (Anderson-Shultz-Flory) equations. The most recent developments of this statistical approach are due to Taylor and Wojciechowski (1983, 1984), Wojciechowski (1986), and Rice and Wojciechowski (1987). Our work is aimed a t explaining the following two experimental findings: (1)a break in the ASF plots is frequently observed (we mention here the first observation of Koenig and Gaube (1983) and Huff and Sutterfield (1984)), mainly for the alkane series; (2) branching occurs to a different extent with respect to the length of the chains of the intermediates. In our catalytic tests, short chains show a higher branching probability. When the carbon atom number is increased, a constant lower branching probability value is observed. A detailed discussion on the content of individual monomethyl-branched compounds 0 1989 American Chemical Societv
660 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 In Mn
t
n
I
a
I
I
\
A
!
index ik with k = 1,2,...,(n - k - 2); in this way CH3CH(CH3)CH2CH2is represented with Rk”(3); n/l:2x(il,i2,...,in), M!!L(il,i2,...,in), and 1M(nkUh(il,i2, ...,in) are respectively the molar fractions of oxygenate (ox), saturated hydrocarbon (sh), unsaturated hydrocarbon (uh)products with n carbon atoms of which k are methyl side groups in the positions denoted by the index ik; n/l:)(il,i2, ...,in) is the sum of the molar fractions of the three classes of molecules with n carbon atoms of which k are methyl side groups in the position denoted by the index ik:
M p (i, ,...,in) = MIpd,(il,...,in)
I I I
t
Figure 1. (a) ASF plot obtained considering a sharp break and no overlapping between mechanisms A and Q. (b) Plot obtained with a two-mechanism model, where a break zone instead of a sharp break is considered.
in the product carbon number fractions can be found in the review of Shultz (1985) and in references therein contained. The mathematical description that follows is based on these mechanistic assumptions: (a) Two growth reaction mechanisms are in competition; the first one, which is called A, prevails during the initial polymerization steps, until the carbon atom number, n, of the intermediates is lower than or equal to i (see Figure l),while the second one, which is called 9, prevails for n 3 j . A break zone instead of a sharp break is considered. For both mechanisms, carbon addition to the growing chain occurs at only one end of the intermediates, involving the terminal carbon atom or the neighboring one if the latter does not yeat have a methyl side group attached. (b) For both mechanisms, the monomeric growth unit C1 contains only one carbon atom, and the growth and termination probabilities are constant for all classes of products, independently of the carbon atom number of the intermediates (except for special cases in the first two steps of mechanism A). (c) Three different classes of products are formed through the same intermediates, with different termination acts of the polymerization process. It is well-known that introducing a model with two competitive mechanisms is a way to represent product distributions as a function of growth and termination probabilities. Variations in the slopes of ASF plots are probably the result of differences in the intermediates. Indeed, it is reasonable that steric and electronic effects change with the growth of the adsorbed molecules influencing their mobility and reactivity on the catalyst surface. At this point, it is necessary to introduce a formalism following, as closely as possible, the notation proposed by Anderson and Chan (1979) and used up to now by Wojciechowski and co-workers. In the formalism, 1 is the primary or secondary carbon atom; 2 is the tertiary carbon atom; Rkk)(il,i2,..,,in)is the generic radical group with n carbon atoms and of these k are methyl side groups in the positions denoted by the
+ Mh$k(il,...,in) + Mi’$,(;, ,...,in) (1)
Mechanism A Under kinetic control, growth and termination probabilities can be expressed as ratios between the reaction rates of the alternative paths offered at the intermediates. This means that the probability with which an event E occurs is expressed by the ratio between the rate of event E with the sum of the rates of all the possible events. If mechanism A is represented as in Figure 2, the following are introduced: CAI is the rate of straight addition; is the rate of branched addition; 6 is the rate of addition to a branched chain with branching on the penultimate carbon atom. For the termination reaction rates, y o dis the termination rate to oxygenates, yshA is the termination rate to saturated hydrocarbons, and yuhAis the termination rate to unsaturated hydrocarbons. It is now possible to define ‘YA
a = “A
=
“A
+ P + YoXA + YshA + YuhA
YuhA + P + YoXA + YshA + YuhA
(5%)
where uA is the probability of linear addition, b is the probability of branched addition, d is the probability of addition to a branched intermediate with branching on the penultimate carbon atom, tOd is the termination probability to oxygenates, tshAis the termination probability to saturated hydrocarbons, and tuhA is the termination probability to unsaturated hydrocarbons. Looking at Figure 2, it is now clear that special growth and termination probabilities must be defined for the first two intermediates of the polymerization process. Indeed intermediate 1 cannot terminate to give unsaturated molecules and cannot directly originate a branched intermediate; this last possibility is precluded also for intermediate 11. Therefore, for intermediate 1, the growth probability is aA’
‘YA
= ‘YA
+ Y M ~ O H+ Y C H ~
(34
Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989 661 We now want to write a summation including all the formation probabilities for all the possible products obtainable with mechanism A. To do this, the following terms must be considered: (1)F is introduced in eq 5, which gives the sum of the probabilities of formation of products with a carbon atom number lower than or equal to 3; (2) aAfaA”aAntXA is for linear products with a carbon atoms number lower than or equal to n + 3 (where X is ox, sh, uh), if n = 1 , 2 , etc., such as in CH3(CHz)n+lCHzOH; (3) a A ’ a A ’ ’ a A m b t x A is for products with one methyl side group on the penultimate carbon, if m = 0, 1, etc., such as in CH3CHzCHz(CHz),CH(CH3)CHzOH; (4) aA’aArfaLbdtXA is for products with one methyl side group on an inner carbon atom, if p + q + 1 = 1 and q = 0, 1, etc., and p = 1, 2, etc., such as in CH3CHzCHz(CHz),CH(CH3)(CH2)pCHzOH. Further probabilities of formation of molecules with more than one methyl side group should be considered. In practice, this kind of product is very rate, and it has been decided to neglect it in order to simplify the treatment. The desired summation is given by
A
*OH
A
-
N O ”
m ..
I
k
*B
‘A
1
k
F
+ i
+
[aAfaAf’aAntA] n=l
MSR;,4 Dl t
m
kuhA
koxA
+
[aAfaAf’aAnbtA] n=O
n=O
+
[ a ~ ’ a ~ ’ ’ a ~ ~ b d+t ~1)] (=n1 (7)
which is normalized to one in order to relate the growth and termination probabilities to each other. Equation 7 can be rewritten in a more compact form:
.
Figure 2. Reactions mechanism A. Only apparent constant reaction rates and final products have been indicated. No assumption about the content of oxygen atoms of the intermediates and of the monomeric growth unit is necessary for our treatment.
and the termination probabilities are, with the obvious meanings of the symbols,
F
+ n=O caA’aA’’CZAntA[aA + b + ( n + l)bd] = 1
(8)
Since the ratio between the probability of formation of a peculiar product P and the summation of the formation probabilities for all the possible products is equal to the molar fraction of P, it is possible to state the following relationships for products having three or more carbon atoms: for linear molecules and n 2 3
MAx! = a A ’ a A f ’ a A n - 3 t o d
For intermediate 11, the growth probability is aAfr=
“A “A
+ YoxA + YshA + YuhA
(44
for molecules with one methyl side group on the penultimate carbon atom and n L 4
and the termination probabilities are
kzH8
=
tC~H, =
YahA aA
YuhA “A
for molecules with one methyl side group on an internal carbon atom and n 2 5
+ YoxA + YshA + YuhA
+ YoxA + YshA + YuhA
(4b)
MA’d, = a
~ ~ a ~ ~ ~ U ~ ~ - ~ b d t ~ d
Starting from intermediate 1, the sum of the probabilities of formation of the products with one, two, and three carbon atoms is Equations 9a-c, in logarithmic form, set a linear relationship between logarithms of molar fractions and their carbon atom numbers. Thus, for linear molecules, we have where is the sum of the probabilities of termination for intermediates with more than two carbon atoms.
662 Ind. Eng. Chem. Res., Vol. 28, No. 6, 1989
if only mechanism R is considered, growth and termination probabilities are bonded together by a normalization equation CaRn(toxn+
(13)
=1
t,h,)
n=O
where it is required that the sum of the formation probabilities for all the possible products is equal to 1. It is pointed out that eq 13 is equivalent to In addition, the molar fractions of the products with n carbon atoms of the three classes of compounds are expressed by
Figure 3. Reaction paths of mechanism Q. Only apparent constant reaction rates and final products have been indicated. As for mechanism A, no hypothesis on the content of oxygen atoms in the intermediates is necessary for our treatment.
If eq 9a are inserted in eq 1 and the resulting equation is put in logarithmic form, the following is obtained: In MAo) = n In
UA
+ In [ t A ( a A ’ a A ” / a A 3 ) ]
(11)
Very similar equations are easily obtainable for branched molecules and are shown in the Appendix section. If reaction mechanism A is realistic, the logarithmic plots of the molar fractions of the three classes or products (with the same structure and carbon atom number) versus n must have the same slope but different intercepts on the Cartesian axis. This is true also for the logarithmic plot of molar fractions of eq 11. Evaluation of the growth and termination probabilities can be performed from the slopes and intercepts of the logarithmic plots of the equations that we have derived or from the ratios M[%l)X/~A%= a
M12t4,X/M@t,,X = b M[:’+S,x/Mt24,x =
(12)
n=O
(where X is ox or sh), or expressed in logarithmic form by In MA% = n In an + In ( t x / a n )
Contemporaneous Reaction Mechanisms It is often assumed that a sharp break in the ASF plot exists; if so, mechanisms A and R do not overlap. It seems to us more correct to define a “break zone” (see Figure 11, included between i and j (i < j ) carbon atom numbers, in which both mechanisms are important to define product distributions. It is then hypothesized that for n less than or equal to i only mechanism A is responsible for the growth and termination of the intermediates, while for values of n greater than or equal to j reactions occur following only 0. This situation is represented mathematically with the aid of “smoothing functions”, A ( n ) and B(n), by introducing a new normalization equation in which all the growth and termination probabilities of the two mechanisms influence each other. A(n)and B(n)are analytically defined as A(n)= 1 ndi
(- -)
where X is ox, sh, uh.
Mechanism R In many cases, experimental results show a less-pronounced slope of the logarithmic plots of molar fractions when the carbon atom number increases. This can be interpreted assuming a higher chain growth probability and consequently a lower termination to products probability. It follows that a second mechanism (a)can be assumed to prevail for the longer products (see Figure 1). It has been decided to represent in our model a situation where a decrease occurs in the slopes of the curves of alkanes and alcohols but not in the curves of alkenes, according to some experimental observations discussed by Eigiebor (1985), by Eigiebor et al. (1985), and by Wojciechowski (1986) and performed also in our laboratories. In this way, the mechanism is hypothesized to influence only the production of oxygenates and saturated hydrocarbons. The reaction paths of R are represented in Figure 3, starting from the intermediates with j carbon atoms (see also Figure 1). No branching reactions have been considered. Analogously to the procedure adopted to describe the product distribution of mechanism A, the following growth and termination probabilities are introduced: an is the probability of linear addition, torn is the termination probability to oxygenated products, and tshQ is the termination probability to saturated hydrocarbons. Again,
(16)
n-ix A(n) = cos2 J - i 2
i < n
