Ind. Eng. Chem. Fundam. 1986, 25, 410-413
410
Thermodynamic Product Distributions for the Fischer-Tropsch Synthesis Harvey 0. Stenger, Jr.;
and Charles F. Askonas
Deparfment of Chemical Engineering, Lehigh Unlverslty, Bethlehem, Pennsylvania 180 15
The thermodynamically expected distributions of the products of Fischer-Tropsch synthesis, with regard to molecular weight distribution and olefin formation, are shown to closely resemble distributions which have been observed experimentally. The product distributions include C, to C15 primary olefins, C1 to C15normal paraffins, C, to C, normal alcohols, carbon dioxlde, and water. The thermodynamic calculation predicts values of the Flory parameter a,based on the C, to C15 distribution, between 0.56 and 0.79. a increases with increasing pressure and decreases with increasing temperature.
Introduction It is generally accepted that the product distribution obtained in the Fischer-Tropsch synthesis over various iron catalysts can be described by the condensation polymerization theory of Flory (1953) or with slight variations on his basic hypothesis. Strict interpretation of the Flory model requires only a single parameter, the probability of chain growth, a,defined as a = rp/(rp + rt)
(1)
where r,, is the rate of propagation and rt is the rate of termination of the growing chains. The product distribution that results from the Flory theory can be shown to be represented by
m, = (1- a)an-l
(2)
where n is the number of carbon atoms in the chain and m, is the mole fraction of all the species having n carbon atoms. Satterfield and Huff (1982) reviewed the various models, including the Flory model, that have been used to describe the Fishcher-Tropsch product distribution. Further work by Satterfield et al. (1982) showed that for a potassiumpromoted magnetite catalyst under certain conditions the Flory distribution was followed for C1 to Clo species with a values between 0.67 and 0.71. The data of Hall et al. (1952) showed that a varied between 0.64 and 0.71, with a increasing slightly with increasing pressure. The data of Schlesinger et al. (1954) showed a between 0.55 and 0.68, with a decreasing slightly with increasing temperature. Modifications of the Flory theory have been suggested by investigators to account for deviations in the product distribution from that predicted by the theory. One such deviation is that C2 selectivity is smaller than predicted. Distributions showing these low C2 values have been reported by Stenger and Satterfield (1985a) and by Henrici-Oh6 and Oliv6 (1976). Figure 1 shows data from Stenger (1984), which illustrate the lower C2 selectivity observed for a fused iron catalyst. The effect is shown to increase with increasing conversion. The suggested explanation has been that the C2species have the ability to reincorporate into the polymerization chain. A second deviation from the Flory distribution has been observed for products larger than Cle Huff and Satterfield (1984) report data showing that the selectivity to species greater than Clo is higher than what the Flory model predicts. They also show that such deviations have existed in work by others but went unexplained. Huff and Sat0196-4313/86/1025-0410$01.50/0
terfield account for this variation by postulating that a second polymerization site exists which has a different value of a. Konig and Gaube (1983) also report data supporting the theory that two chain growth probabilities exist when an iron catalyst is promoted with potassium. They postulate that the two iron sites are sites with and without potassium. An alternate explanation is due to Stenger (1985), who postulated that this deviation is a result of a distribution of sites on the catalyst, all of which follow the Flory theory but each with a different a. In all of the previous work, thermodynamic considerations have been omitted. Some thermodynamic calculations have been made by Storch et al. (1951). In their work free energies of the reactions to form selected hydrocarbons from C1 to Czowere calculated for temperatures between 127 and 427 "C. However, they did not extend this work to develop the product distributions that would be the result of thermodynamic equilibrium. It is the goal of the present work to calculate the product distribution that would be the result of thermodynamic equilibrium at typical operating conditions for the Fischer-Tropsch reaction.
Methodology The overall chemical reaction for the Fischer-Tropsch reaction is m
m
CO + UH2 -.+ EaiCiH2i + EbiCiHzi+2 + i=2
i=l
m
i=l
+ dH20 + eC02 (3)
where U is the usage ratio and ai, bi, ci, d, and e are all undetermined stoichiometric coefficients. The products that are assumed to be formed in eq 3 are normal paraffins, primary olefins, normal alcohols, water, and carbon dioxide. Ideal-gas thermodynamic data are available for a large number of these species; thus, it is possible to calculate the product distribution which has a minimum free energy. Calculating this thermodynamic distribution requires minimizing the total free energy of the product mixture, G, with respect to the number of moles of each species i (Ni) (4)
subject to material balance constraints. G iin eq 4 is the free energy of species i in the mixture. For a single-phase 0 1986 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 25, No. 3, 1986 411
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0.1-
z
e
::
-
Q
-
I-
2 0.01, E : 0.031 I
4
2
C&ON
5
6
7
NUMBER
Figure 1. Product distribution showing C2content below that expected from the Flory theory (263 "C, 1.48 MPa, feed ratio = 0.7). Data taken from Stenger (1984).
reaction, the material balance constraints can be written
as
where Mk is the number of moles of element k fed to the reactor, nki is the number of atoms of element k in species i, and N i is the moles of species i leaving the reactor. To minimize eq 4 subject to the constraint of eq 5, the Rand method, developed by White et al. (1958) and reviewed by Gautam and Seider (19791, is employed. Their algorithm uses Newton's method to solve for the product mole fractions and is implemented in the present work using the subroutine RGIBBSavailable in the ASPEN-PLUSsimulation program. To calculate Gi's in eq 4, the ideal-gas values were corrected by using the Redlich-Kwong-Soave equation and the method of residual properties. The product mixture was assumed to behave as an ideal solution.
Rssults In the following results, the compounds included in the product distribution are C1 to CBnormal alcohols, Cz to C15 primary olefins, C1to C16normal paraffins, water, and carbon dioxide. Internal olefins were not included as products since they have been shown by Stenger and Satterfield (1985a) to be secondary products formed by readsorption and isomerization of primary olefis. For all of the calculations, the conversion of H2and CO has been fixed at 100% and all products formed are in the vapor phase. The effects of feed ratio, temperature, pressure, and addition of ethylene or ethanol to the feed are addressed. Feed Ratio. At 100% conversion of Hzand CO, the usage ratio or U in eq 3 will be equal to the feed ratio (FR). Typically for iron-based catalysts, the usage ratio varies between 0.5 and 1.0 with the majority of the results showing it to be approximately 0.7 (Deckwer et al., 1982). Figure 2 shows the product distributions that minimize the free energy of the product mixture for feed ratios of 0.6,0.7, and 0.8 at a temperature of 263 OC and a pressure of 1.48 MPa Figure 2 is a plot of the logarithm of the total organic products (alcohols, olefins, and paraffins) at each carbon number va. carbon number. The data points represent the calculated mole fractions. In Figure 2 the products from C4 to CI5 all fall on straight lines unique for each feed ratio. Corresponding to each feed ratio a value of a has been calculated based on the C4+species. The value of a varies from 0.69 at a usage ratio of 0.8 to 0.75 at a usage ratio of 0.6. At U =
"r =0.001
i
0.00011
5
10
15
CARBON NUMBER
Figure 2. Thermodynamic total product distributions as a function of feed ratio (FR)(temperature = 263 OC, pressure = 1.48 MPa). Points are calculated mole fractions.
I
' i . e EXPERIMENTAL
.CALCULATED
0 05
2
CARBON 5 NUMBER IO
15
Figure 3. Comparison of experimentaland calculated distributions. Calculated points at 263 OC, 1.48 MPa, and FR = 0.7. Experimental points from Stenger (1984) at 263 OC, 1.48 MPa, and FR = 0.7.
0.7, which is the average reported by Deckwer et al. (1982), the value of a is 0.68. This is within the range reported by Satterfield et al. (1982) of 0.67471 for similar operating conditions. The selectivity to C1 in Figure 2 is between 40 and 75 mol % of the total product distribution. This is much larger than what is observed experimentally. Typically, C1 accounts for between 25 and 35 mol 9i of the product distribution (see Figure 1). This result indicates that the reaction to form methane in the Fischer-Tropsch synthesis is not in equilibrium and is significantly restricted. Storch et al. (1951) gave the same conclusion in their free energy calculations. However, this does not preclude that the larger species may not be at equilibrium. Selectivity to methane has been reported by Stenger and Satterfield (1985b) to be influenced by sulfur poisoning of the catalyst, independent of the value of a calculated from the C3+species. This suggests methane is formed by a reaction different than that which forms the larger hydrocarbons. Flory himself stated in his original work (Flory, 1953) that the assumptions used to develop eq 2 may not be valid at small chain lengths. A comparison of the total product distribution on a methane-free basis between those calculated thermodynamically and those obtained experimentally is shown in Figure 3. The experimental data in Figure 3 are taken from Stenger (1984) at conditions identical with those for the calculated points. The only difference is that the
412
Ind. Eng. Chem. Fundam., Vol. 25, No. 3, 1986
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1
t 1
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,
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Figure 4. Influence of temperature on total product distributions (feed ratio = 0.70, pressure = 1.48 MPa). Points are calculated mole fractions.
conversion of H2 was 86% and CO was 97% for the experimental points while they were both 100% for the calculated points. Figure 3 shows a remarkable agreement between the thermodynamic results and the experimental data. Alcohol and Water Formation. The formation of alcohols as predicted by the free energy minimization method is not what is observed experimentally. A t equilibrium, the product distribution contains essentially no alcohols. Thus, the distribution in Figure 2 is entirely that of primary olefins and normal paraffins. Although the model fails to predict the alcohol selectivity, it does indicate that alcohols are not favored as products. This offers an explanation for the decrease in alcohol formation with a decrease in space velocity reported by Stenger and Satterfield (1985a). At low space velocities (high conversions), the reaction has a greater opportunity to approach equilibrium. In their work at 263 " C, 1.48 MPa, and FR = 0.7, the percent oxygenates at C2 decreased from 30% to 4% of the C2 fraction as conversion of CO + H2 was increased from 66% to 93 % Water formation is also predicted by the thermodynamic calculation to be essentially zero. Water is experimentally found to be formed in only small amounts in the Fischer-Tropsch synthesis over iron, since it is strongly limited by the water-gas-shift reaction. At the temperatures considered here, the water-gas-shift reaction favors the formation of H2and C02 rather than H 2 0 and CO. Effect of Temperature and Pressure. The effects of temperature and pressure on the product distribution are shown in Figures 4 and 5, respectively. In Figure 4, the product distribution is shown to favor lighter products as the temperature is increased, with a varying from 0.68 at 263 "C to 0.73 at 232 "C. As in the work of Schlesinger et al. (1954), a decreases with increasing temperature. Stenger (1984) reports that increasing temperature from 232 to 263 "C had the effect of decreasing the a calculated from C3to C, data from 0.66 to 0.61. Figure 4 also shows that increasing the temperature increases the ratio of C3 species to C2species. This ratio was reported by Stenger and Satterfield (1985a) to indicate the extent of reincorporation of C2species. They showed that the C,-C, ratio increased with increasing temperature, as it does in Figure
.
4.
The influence of pressure is shown in Figure 5. In this plot, the temperature has been held fixed a t 263 "C and the feed ratio is 0.70. Here the distribution is shown to favor heavier products with an increase in pressure, with
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,
I
,
I
,
,
.
,
1
7
(feed mole
-
0
2
4
6
8
1
0
CARBON NUMBER
Figure 6. Olefin mole fractions as a function of carbon number (feed ratio = 0.70, pressure = 1.48 MPa). Experimental points are from Stenger and Satterfield (1985a). a increasing from 0.56 at 0.37 MPa to 0.68 at 1.48 MPa.
Olefin Content. Figure 6 shows the calculated mole percent of olefiis at each carbon number vs. carbon number, for the base condition of 263 "C and 1.48 MPa and a feed ratio of 0.70. Also in Figure 6 are the experimental data reported by Stenger and Satterfield (1985a) at the same temperature, pressure, and feed ratio. Although the olefii content predicted by thermodynamics is lower than that observed experimentally, it follows a pattern similar to that observed by Stenger and Satterfield (1985a): where C2 is low, C3 is high and the remainder of the series is essentially constant. The low value of C4 is not observed experimentally; however, internal olefins have not been included in the product spectrum. Since C4 is the first carbon number to have internal olefins, it is likely that omitting them caused the distribution to be low at C4. Also shown in Figure 6 are the thermodynamic results at a lower temperature. This variation with temperature is consistent with that observed experimentally, with the olefin content decreasing with decreasing temperature (Huff, 1982; Stenger, 1984). Effect of Additives to the Feed. It has been proposed that some Fischer-Tropsch products may be readsorbed onto the catalyst and reenter the polymerization chain. Figures 7 and 8 show the effects of the addition of ethylene or ethanol to the feed. Figure 7 relates to ethylene addition. With the addition of 0.1 and 0.2 mol of ethylene per mole of carbon monoxide the distribution is shown to favor heavier products, with a increasing from 0.68 to 0.74 to 0.79. Figure 8 illustrates
Ind. Eng. Chem. Fundam., Vol. 25, No. 3, 1986 413
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Discussion The thermodynamic product distributions presented here are in many ways consistent with those obtained experimentally. It is not postulated by this work that Fischer-Tropsch reaction is at chemical equilibrium. In fact, several features such as C1 selectivity and alcohol formation are clearly not at equilibrium in experimental studies. However, the thermodynamic distributions do predict a value of the chain growth parameter, a,similar to that observed experimentally. They also correctly predict the changes observed in the product distribution with respect to a,olefin formation, and Cz-C3 selectivity when pressure and temperature are changed. They also predict correctly that alcohols and water are thermodynamically unfavored a t high conversions. Although the thermodynamic distributions do not fully match those observed experimentally, it must be stressed that these calculated product distributions are independent of mechanism and catalyst and therefore represent generic distributions. Such generic distributions can be useful to identify trends in selectivity and, more importantly, differences between catalysts. Of major importance in Fischer-Tropsch research is the ability to compare catalysts on a generic basis. Comparison of observed distribution with the thermodynamic distributions is one such method. Registry No. Ethylene, 74-85-1; ethanol, 64-17-5; carbon
8
1
1
5
1
8
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I
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10
8
#
Y X
i
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Figure 8. Effect of ethanol addition to feed (feed ratio = 0.70, temperature = 263 "C,pressure = 1.48 MPa). Points me calculated mole fractions.
that, with the addition of ethanol to the feed, the product distribution favors lighter products, with a decreasing from 0.68 to 0.62 to 0.57 for the addition of 0.1 and 0.2 mol of ethanol per mole of carbon monoxide. For both cases, the formation of alcohols, including ethanol, was still insignificant.
Deckwer, W. D.; Serpemen, Y.; Ralek, M.; Schmidt, 6. Ind. Eng. Chem. Process D e s . Dev. 1882, 21. 231. Flory, P. J. principles of Po!vm chemlsby; Come11 University Press: Ithaca, NY, 1953. Gautam, R.; Selder, W. D. AICh€J. 1878. 25. 991. Hall, C. C.; Gail, D.; Smith, S. L. J . Inst. Pet. 1852, 38, 845. HenricCOilv6. G.; Ollv6, S. Angew. Chem.. Int. Ed. Engl. 1878. 15, 136. Huff, G. A., Jr. Ph.D. Thesis, MIT. CambrMge, MA, 1982. Huff, G. A., Jr.; Satterfield, C. N. J . &tal. 1884, 85, 370. Khig, L.; Gaube, J. Chem.-Ing.-Tech. 1883, 55, 14. Satterfield, C. N.; Huff, 0.A., Jr.; Longweil. J. P. Ind. Eng. Chem. Process Des. D e v . 1882, 2 1 , 465. Satterfield. C. N.; Huff, 0.A., Jr. J . &tal. 1882, 73, 187. Schlesinger, M. D.; Benson, M. E.; Murphy, E. M.; Storch. H. H. Ind. Eng. Chem. 1854, 46. 1322. Stenger, H. G., Jr. Sc.D. Thesis, MIT, CambrMge, MA. 1984. Stenger. H. G., Jr. J . &tal. lB85, 92, 426. Stenger, H. G., Jr.; Satterfield, C. N. Ind. Eng. Chem. Process Des. Dev. 1885a, 24, 411. Stenger, H. G., Jr.; SatterfieM, C. N. Ind. Eng. Chem. Process Des. Dev. 1885b, 24, 415. Storch, H. H.; Golumbic, N.; Anderson, R. 6. The Fischer-Tropsch andRelated Syntheses; Wiley: New York, 1951; pp 11-20. White, W. 8.; Johnson, S. M.; Dantzig, G. 6. J . Chem. Phys. 1858, 28, 751.
Receiued for review October 9, 1984 Revised manuscript receiued August 30, 1985 Accepted September 11, 1985
