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Ind. Eng. Chem. Res. 2007, 46, 5446-5452
Equilibrium Constants for Isomerization of n-Paraffins Laura A. Pellegrini,† Simone Gamba,*,† Susi Bonomi,‡ and Vincenzo Calemma‡ Department of Chemistry, Materials and Chemical Engineering “G. Natta”, Politecnico of Milan, Piazza Leonardo da Vinci 32, 20133 Milan, Italy, and Eni S.p.A. DiVisione Refining & Marketing - Centro Ricerche di San Donato Milanese, Via Maritano 26, 20097 San Donato Milanese, Milan, Italy
A correlation between lumped isomerization equilibrium constants (Keq) and the number of carbon atoms in paraffinic chains has been developed. The aim of the work is to check the meaningfulness from a chemicophysical point of view of previously estimated values of Keq in order to improve the performances of a simulation model for the isomerization/hydrocracking of Fischer-Tropsch (F-T) waxes, a mixture made up of normal paraffins covering a wide range of molecular weights. Owing to the lack of experimental data for paraffins with more than ten carbon atoms, a procedure has been developed to determine equilibrium constants extrapolating the thermodynamical data of low carbon number paraffins. Since in our case the hydrocracking simulation model considers lumped classes of isomers (i.e., monobranched and multibranched), the equilibrium data do not take into account single isomerization reactions but those from a n-paraffin to the lump of its monobranched isomers and from the lump of monobranched isomers to the lump of multibranched ones. The coherence of the estimated constants has been verified by comparison with the little data available in the literature on lumped equilibrium constants. The analysis of equilibrium constants at different temperatures has shown that isomerization becomes endothermic from a number of carbon atoms equal to about 13-14 onward; this result is also supported by enthalpy data. 1. Introduction Cobalt catalyzed F-T waxes are essentially a mixture of normal paraffins covering a wide range of molecular weights (i.e., from C5 up to C80 and more) together with a small percentage of olefins and alcohols. The hydroconversion of F-T waxes over a bifunctional catalyst has two objectives: to maximize the middle distillates yield by cracking of the longer paraffin chains and to improve the cold flow properties of the products by an isomerization reaction. According to the bifunctional mechanism, hydroisomerization and hydrocracking of normal paraffins occur through a series of consecutive reactions, where the cracking products are mainly formed through β-scission of di- and multibranched isoalkanes since they can crack according to more energetically favorable β-scission modes not allowed to the monobranched and linear alkanes.1-4 We are currently developing a kinetic model for the hydrocracking of F-T waxes which considers the following reaction pathway: r r n-C 9 8 MB 9 8 MTB f cracking products
(1)
As a consequence of the reaction pathway considered, the model requires the estimate of each equilibrium constant as a function of the chain length for the following isomerization reactions: n-paraffin to monobranched paraffins lump and monobranched paraffins lump to multibranched paraffins lump. The objective of the work is to estimate a priori the equilibrium constants for the above-mentioned isomerization reactions. The reason is twofold: to choose a suitable relationship between Keq and the chain length and to check the meaningfulness of the model results. In the meantime reliable equilibrium * To whom correspondence should be addressed. Tel.: +39-02 2399 3237. Fax: +39-02 70638173. E-mail:
[email protected]. † Politecnico of Milan. ‡ Centro Ricerche di San Donato Milanese.
data help to better understand the thermal behavior of isomerization reactions and, consequently, to properly operate the reactor. The following points deserve to be mentioned: (1) At first the thermodynamic experimental data necessary for computing Keq, i.e. the ∆Gf°, are available only for a limited number of paraffins; in particular the pertinent literature5 reports data up to decane. (2) Furthermore the number of isomers diverges with the number of carbon atoms; the proposed method for computing the lumped isomerization constants requires the knowledge of the number of monobranched and multibranched isomers for each number of carbon atoms. (3) In the end, and very important for our aims, the equilibrium experimental data of literature on the isomerization of F-T waxes are relevant to equilibrium constants of isomerization between lumps, i.e., between nparaffins and the group of corresponding monobranched isomers as well as between the lump of monobranched and the lump of multibranched isomers. So it is important to well understand the concept of Keq for isomerization between lumps and how to compute it. 2. Computation of ∆Gf° for Paraffins For a generic equilibrium reaction (for example from nparaffins to isoparaffins) Keq
n-C {\} iso-C
(2)
the equilibrium constant Keq is determined from ∆Gf° values according to the well-known equation
∆G° ) -RT ln Keq
(3)
∑i υi∆Gfi°
(4)
where
∆G° )
An average value of ∆Gf° for each lump of paraffins has been evaluated, in the range of the available experimental data,
10.1021/ie0705204 CCC: $37.00 © 2007 American Chemical Society Published on Web 06/30/2007
Ind. Eng. Chem. Res., Vol. 46, No. 16, 2007 5447
as a function of the carbon atoms number and the results extrapolated to heavier paraffins. To overcome the lack of experimental ∆Gf° for paraffins with a high carbon number the first idea was to compute an average ∆Gf° by means of a group contribution method,6 but the attempt was unsuccessful for different reasons: group contribution methods do not allow for distinguishing among the different types of isomers (for instance between a 2- and a 3-methylalkane). The divergent number of isomerization reactions for increasing nC requires a divergent number of ∆Gf° calculations to obtain an average value, and, in addition, criteria are missing to identify a proper isomer whose ∆Gf° could be reasonably assumed as a mean value. According to the factorial experimental plan carried out for the hydrocracking tests1 the analysis has been performed at T ) 632.15 K corresponding to the central point of the plan. For n-paraffins up to C20 experimental data7 for ∆Gf° are given as a function of temperature:
∆Gf°(T) ) a + bT + cT2
Figure 1. ∆Gf° vs nC and TebN for normal paraffins.
(5)
Figure 1 shows a linear trend of ∆Gf° with the carbon atoms number and a quadratic trend with the normal boiling temperature, as trend line equations point out. Literature5,7 reports experimental data for mono- and multibranched paraffins only up to C10. In this work only isomers with methyl and ethyl groups with a maximum of three branches have been considered. This hypothesis is supported by both literature data and theoretical considerations concerning the mechanism of hydroisomerization/ hydrodrocracking operated over a bifunctional catalyst. It is well-known8-10 that hydroconversion of n-paraffins proceeds through consecutive isomerization reactions where the first step is the formation of monobranched isomers which further react to give isomers with higher branching degree. Among the monobranched isomers the methyl group is by far the most abundant followed by the ethyl group, while propyl and butyl groups are negligible. Literature data11 show that the average relative concentration of methyl, ethyl, and propyl groups among the monobranched paraffins is 100/15/1, respectively. According to the isomerization mechanism which provides the formation of protonated cycles as reaction intermediates, when the number of carbons in the protonated cycle increases from three to four and so forth, the probability of their formation rapidly decreases and consequently decreases the formation of branching groups longer than methyl.4,12 For each class (mono- and multibranched) and for a given number of carbon atoms, the average values of ∆Gf° and TebN have been computed. Like normal paraffins monobranched paraffins also show linear and quadratic trends of average ∆Gf° versus carbon atoms number and normal boiling temperature, respectively (Figure 2). Moreover the ratio between the average value of the normal boiling point for monobranched paraffins and the TebN of the corresponding n-paraffin (TebN av MB/TebN n-C) is constant and equal to 0.9814. The same procedure has been applied to obtain an average value of ∆Gf° for multibranched isomers with different nC. Also in this case the trend of ∆Gf° is linear with the carbon atoms number and quadratic with the average normal boiling temperature, as shown in Figure 3. The ratio between the average value of the normal boiling point for multibranched paraffins and the TebN of the corresponding n-paraffin (TebN av MTB/TebN n-C) is constant and equal to 0.9655.
Figure 2. Average ∆Gf° vs nC and average TebN for monobranched paraffins.
Figure 3. Average ∆Gf° vs nC and average TebN for multibranched paraffins.
The average values of ∆Gf° have been extrapolated in order to obtain average values of ∆Gf° for heavier paraffins. Such values have been considered representative of all the isomers not only of methyl and ethyl isomers at most tribranched. The extrapolated behavior of heavier monobranched and multibranched paraffins up to C20 is shown in Figures 4 and 5, respectively. 3. Lumped Equilibrium Constants for Isomerization: Computation Method Literature13 reports lumped equilibrium constants (relevant to the class of mono- and multibranched paraffins) which
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For the isomerization reaction from monobranched to multibranched paraffins a dummy monobranched isomer of composition xlump MB ) ∑xMBi with an average value for ∆Gf° has been considered. The Keq lump is obtained multiplying the average value of Keq by the number of multibranched isomers in the lump:
Keq lump MB-MTB )
∑i Keq MB-MTB = niso MTB‚Keq i
Figure 4. Extrapolated ∆Gf° vs nC and TebN for monobranched isomers.
Figure 5. Extrapolated ∆Gf° vs nC and TebN for multibranched isomers.
increase with the number of carbon atoms. This behavior can be justified because of the increasing number of possible corresponding isomers. As a matter of fact the entropic factor plays a key role and the correct trend of the equilibrium constants cannot be determined considering a single isomer, but it is necessary to take into account the total number of possible isomers. For each single reaction of isomerization to monobranched paraffins the isomerization constant can be evaluated as follows:
Keq n-MBi )
PxMBi
(6)
Pxn-C
The Keq lump is obtained, according to the definition, summing up the Keq of each parallel isomerization reaction:
Keq lump n-MB )
∑i PxMB Pxn-C
i
)
∑i Keq n-MB
i
(7)
This procedure has been applied for paraffins up to C10, for which data are available; for heavier paraffins an average value of Keq has been computed using an average extrapolated value of ∆Gf° (this is the approximation of the method), and the Keq lump is obtained by multiplying the average value of Keq by the number of monobranched isomers in the lump:
Keq lump n-MB )
∑i Keq n-MB = niso MB‚Keq i
av
n-MB
(8)
av
MB-MTB
(9)
It is clear that, according to this method, the determination of the number of mono- and multibranched isomers is a fundamental step. The number of monobranched isomers can be worked out taking into account only monobranched isomers with a single atom of tertiary carbon (isopropyl groups, for instance, are not taken into account since, as a matter of fact, they give rise to multibranched isomers). The number of multibranched isomers has been obtained as a difference between the total number of isomers14 and the number of monobranched ones. The mathematical formulas to compute the number of monobranched isomers are reported in Table 1 where nC is the total number of carbon atoms of the monobranched paraffin. The coherence of the method proposed in eqs 8 and 9, where Keq lump is obtained by multiplying the average value of Keq by the number of monobranched and multibranched isomers, respectively, in the given lump, has been verified by applying the method itself to the isomers for which experimental data are available. Since for a generic reaction Keq can be calculated using eqs 3 and 4, eqs 7 and 8 become, respectively
Keq lump n-MB )
∑i
(
)
- ∆Gn-MBi°
exp
(
RT
)
(10)
- ∆Gav n-MB° ) RT ∆Gf n-C° - ∆Gf MBav° ) K* eq lump n-MB (11) niso MB‚exp RT
Keq lump n-MB = niso MB‚exp
(
)
and similarly for the isomerization from monobranched to multibranched paraffins the equations are the following:
Keq lump MB-MTB )
∑i
( (
/ Keq lump MB-MTB ) niso MTB‚exp
niso MTB‚exp
(
)
- ∆GMB-MTBi°
exp
RT
)
(12)
- ∆GavMB-MTB°
) RT ∆Gf MBav° - ∆Gf MTBav° RT
)
(13)
The values of Keq computed using the corresponding averaged value of ∆G° (i.e. Keq n-MBav ) exp(-∆Gavn-MB°/RT)) and the values of Keq lump calculated according to eq 10 (i.e., from experimental data) and according to eq 11 (i.e., following the average value method) are reported in Table 2. All these values refer to the isomerization reaction from normal to monobranched paraffins. Table 2 shows also the difference between Keq lump calculated according to the two different methods. In the third column the number of monobranched isomers, corresponding to a given
Ind. Eng. Chem. Res., Vol. 46, No. 16, 2007 5449 Table 1. Number of Monobranched Paraffins for a Given Type of Branching type of side chain
nC
-CH3 (MM)
formula
even niso MM ) odd
-C2H5 (ME)
nC - 2 2
niso ME ) niso MM - 2 ) odd
nC - 6 nC - 2 -2) 2 2
niso ME ) niso MM - 1 )
nC - 3 nC - 5 -1) 2 2
niso MNP ) niso ME - 1 )
nC - 8 nC - 6 -1) 2 2
niso MNP ) niso ME - 2 )
nC - 5 nC - 9 -2) 2 2
even odd
-C4H9 (MNB)
even niso MNB ) niso MNP - 2 ) odd niso MNB ) niso MNP - 1 )
-C5H11 (MNPE)
nC - 8 nC - 12 -2) 2 2
{(
niso ME )
{(
niso MNPE ) niso MNB - 1 )
nC - 12 nC - 14 -1) 2 2
niso MNPE ) niso MNB - 2 )
nC - 11 nC - 15 -2) 2 2
niso MNE ) niso MNPE - 2 )
nC - 18 nC - 14 -2) 2 2
niso MNE ) niso MNPE - 1 )
nC - 15 nC - 17 -1) 2 2
odd even odd
Table 2. Average Values of Keq for a Single Isomerization Reaction and Lumped Equilibrium Constants Evaluated from Experimental Data and Average Values (*) from n-Paraffin to Monobranched Paraffins
0
)
nC g 4
nC - 5 2
)
nC g 7
0
int
niso MNP )
{(
niso MNB )
{(
nC e 6
0
nC e9
nC - 8 int 2
)
nC g 10
0
nC e12
nC - 11 2
int
niso MNPE )
niso MNE )
nC e3
nC - 2 2
int
nC - 11 nC - 9 -1) 2 2
even
-C6H13 (MNE)
niso MM )
nC - 3 niso MM ) 2
even
-C3H7 (MNP)
general formula
)
{( 0
nC - 14 int 2
)
{( 0
nC - 17 int 2
)
nC g 13
nC e15 nC g 16
nC e 18 nC g 19
Table 3. Average Values of Keq for a Single Isomerization Reaction and Lumped Equilibrium Constants Evaluated from Experimental Data and Average Values (/) from Monobranched Paraffins to Multibranched Paraffins
nC
Keq n-MBav
niso MB
Keq lump n-MB eq 10
/ Keq lump n-MB eq 11
∆%
nC
Keq MBav-MTBav
niso MTB
Keq lump MB-MTB eq 12
/ Keq lump MB-MTB eq 13
∆%
5 6 7 8 9 10
2.3937 1.1420 0.7654 0.7142 0.8411 0.9179
1 2 3 4 5 6
2.3937 2.4068 3.2016 3.1225 5.0036 6.1004
2.3937 2.2839 2.2961 2.8568 4.2056 5.5074
0.0 5.1 28.3 8.5 15.9 9.7
5 6 7 8 9 10
0.1146 0.5726 0.5722 0.2129 0.2541 0.1799
1 2 5 12 25 48
0.1146 1.2016 4.0331 3.6752 15.1341 15.9417
0.1146 1.1452 2.8611 2.5550 6.3522 8.6362
0.0 4.7 29.1 30.5 58.0 45.8
carbon number, is reported (only the isomers for which experimental data are availablesi.e. methyl and ethyl groups which give rise to isomers with a maximum of three branchess have been considered). Referring to the isomerization reaction from monobranched to multibranched paraffins, the values of Keq computed using the corresponding averaged value of ∆G° (i.e. Keq MBav-MTBav ) exp ( - ∆GavMB-MTB°/RT) and the values of Keq lump calculated according to eq 12 (i.e., from experimental data) and according to eq 13 (i.e., following the average value method) are reported in Table 3. In the third column the number of multibranched isomers, corresponding to a given carbon number, is reported (methyl and ethyl groups to give rise to isomers with a maximum of three branches). Since isomerization reaction takes place in two consecutive steps (from n- paraffin to monobranched paraffin and from monobranched to multibranched ones), the following equation must be verified:
Keq lump n-MB‚Keq lump MB-MTB ) Keq lump n-MTB
(14)
Table 4 reports the way of computing Keq lump n-MTB, resulting from the experimental data, for C8 as an example. Keq lump n-MTB
has been calculated summing up all the equilibrium constant values obtained from the direct isomerization reaction from n-paraffin to multibranched paraffin according to eq 15 and, using average values, to eq 16:
Keq lump n-MTB )
∑i exp
(
)
- ∆Gn-MTBi°
/ Keq lump n-MTB ) niso MTB‚exp
RT
(
(15)
)
- ∆Gavn-MTB°
niso MTB‚exp
(
RT
)
)
∆Gf n-C° - ∆Gf MTBav° RT
(16)
The comparison between the product of the lumped equilibrium constants of the two isomerization steps as from eqs 10 and 12 (see Tables 2 and 3) and the equilibrium constant directly obtained from the experimental ∆Gf° (see Table 4 for C8) for n-paraffins and multiparaffins (eq 15) is made in Table 5. Table 5, which reports results from C5 to C10, shows a remarkable difference between the two different ways of computation. This
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Table 4. Equilibrium Constants for the Isomerization Reaction from n-C8 to Multibranched Paraffins component
∆Gf°‚10-5 [J mol-1]
Keq n-MTB
n-octane 22-Mhexane 23-Mhexane 24-Mhexane 25-Mhexane 33-Mhexane 34-Mhexane 223-Mpentane 224-Mpentane 233-Mpentane 234-Mpentane 2M-3Epentane 3M-3Epentane
2.8491 2.9110 2.9382 2.8738 2.8825 2.9137 2.9200 2.9950 2.9673 2.9918 3.0036 2.9835 2.9973
0.3085 0.1837 0.6258 0.5298 0.2929 0.2597 0.0624 0.1056 0.0663 0.0529 0.0776 0.0597
Keq lump n-MTB
2.6248 Figure 6. Keq (experimental data) by Denayer.13
Table 5. Comparison between “Two Steps” and “Direct” Isomerization Equilibrium Constants nC
Keq lump n-MB‚Keq lump MB-MTB eq 10‚eq 12
Keq lump n-MTB
∆%
5 6 7 8 9 10
0.2742 2.8920 12.9123 11.4755 75.7244 97.2503
0.2742 1.3722 3.0868 2.6248 12.7295 14.6326
0.0 110.8 318.3 337.2 494.9 564.6
is due to the fact that, in the former case, the approximation of fictitious components for monobranched isomers has been added as well. Moreover results obtained using a dummy monobranched isomer show a discrepancy when compared with the experimental data by Denayer et al.13 at the temperature of 506.15 K. It can be seen in Figure 6 that the equilibrium constant from normal to monobranched paraffins is always higher than the equilibrium constant from monobranched to multibranched paraffins. This trend is not in agreement with the way (eqs 11 and 13) used to compute Keq, as reported in Figure 7. In order to always verify eq 14 and avoid such problems, the passage through the dummy monobranched isomer has been deleted, and the isomerization does not take explicitly into account the passage through the monobranched isomers. Only Keq lump n-MB and Keq lump n-MTB are computed by using a direct way, while Keq lump MB-MTB is computed indirectly as
Keq lump MB-MTB )
Keq lump n-MTB Keq lump n-MB
(17)
The new pathway affects only the values of the equilibrium constant for the isomerization step mono-multi which decreases to acceptable levels. For the isomerization step from normal to monobranched paraffins the Keq lump n-MB remains unchanged. The new results are reported in Figure 8 and compared with the experimental data by Denayer.13 Figure 8 shows that the behavior for MB-MTB is now similar to the Denayer one. Figure 9a reports the results obtained following the modified pathway for hydrocarbons up to C20 at 632.15 K: on the left a linear y-axis has been used to represent Keq for an isomerization reaction from normal to monobranched paraffins, while on the right a logarithmic y-axis has been used to represent Keq from monobranched to multibranched paraffins. At 632.15 K and up to C13 the equilibrium constant from normal to monobranched paraffins is higher than the equilibrium constant from monobranched to multibranched paraffins; this behavior is clearly evidenced in Figure 9b.
Figure 7. Keq computed using eqs 11 and 13.
Figure 8. Keq for isomerization from normal to monobranched and monobranched to multibranched paraffins according to the modified pathway (based on eqs 11, 16, and 17) vs Denayer data.13
Analyzing the Keq values at different temperatures a transition from exothermic to endothermic conditions for isomerization reactions can always be detected for nC = 13-14. This behavior is evidenced in Tables 6-8 where the Keq values at three different temperatures are reported for the different isomerization reactions. This change of behavior with the number of carbon atoms, i.e., the isomerization reaction favored by temperature for increasing length of the chain, is not clearly stated in the literature and therefore requires further analysis. So enthalpy data, which are not affected by the simplifying assumptions due to the entropic factor connected to the number of isomers that enters the Keq calculation, have been analyzed to support the previous results. 4. Heat of Isomerization Reactions Like ∆G° average heats of reactions for paraffins up to C10 have been computed from the experimental data5,7sthe two data banks5,7 are compared and are in perfect agreementsand then extrapolated. Data based on heats of reaction agree with equilibrium data obtained for isomerization: isomerization reaction becomes endothermic increasing the chain length independently on the
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Figure 10. ∆Hiso° from normal to monobranched, from monobranched to multibranched, and from normal to multibranched paraffins @ 298 K. Table 7. Keq for Isomerizations from Monobranched to Multibranched Paraffins at Three Levels of Temperaturea / Keq lump MB-MTB (eq 17)
Figure 9. a. Keq for isomerization from normal to monobranched (eq 11), from monobranched to multibranched (eq 17), and from normal to multibranched (eq 16) paraffins up to C20 @ 632.15 K. b. Keq for isomerizations according to the modified pathway for paraffins up to C20 @ 632.15 K. Table 6. Keq for Isomerizations from Normal to Monobranched Paraffins at Three Levels of Temperaturea K*eq lump n-MB (eq 11) nC
T ) 298.15 K
T ) 506.15 K
T ) 632.15 K
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
8.1175 9.0333 9.4505 9.2330 10.1264 9.0507 9.0090 8.5660 7.6307 6.8993 6.6904 5.6519 5.0117 4.4959 3.9154
2.8411 3.6378 4.4272 5.0275 6.3962 6.6134 7.5697 8.2802 8.6568 8.9999 9.9428 9.8157 10.0974 10.4305 10.4644
2.1163 2.8252 3.5895 4.2606 5.6492 6.0998 7.2729 8.2937 9.0675 9.8298 11.2666 11.6566 12.5053 13.4669 14.0817
nC
T ) 298.15 K
T ) 506.15 K
T ) 632.15 K
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2.5818 2.9791 4.0219 4.9692 5.6773 7.6998 9.7801 12.9417 17.9392 25.5319 35.5427 53.5582 78.9177 119.0153 183.2169
0.5325 0.7466 1.2246 1.8383 2.5517 4.2046 6.4887 10.4321 17.5689 30.3801 51.3831 94.0720 168.4117 308.5778 577.1534
0.3439 0.5084 0.8795 1.3925 2.0386 3.5429 5.7665 9.7780 17.3679 31.6750 56.5029 109.1026 206.0017 398.0954 785.3035
a The transition between an exothermic and an endothermic reaction has been evidenced.
Table 8. Keq for Isomerizations from Normal to Multibranched Paraffins at Three Levels of Temperaturea / Keq lump n-MTB (eq 16)
nC
T ) 298.15 K
T ) 506.15 K
T ) 632.15 K
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
20.9579 26.9113 38.0088 45.8802 57.4910 69.6883 88.1088 110.8589 136.8881 176.1528 237.7931 302.7035 395.5136 535.0754 717.3602
1.5130 2.7159 5.4215 9.2420 16.3212 27.8068 49.1177 86.3797 152.0908 273.4193 510.8906 923.3817 1700.5286 3218.6275 6039.5801
0.7277 1.4363 3.1571 5.9328 11.5166 21.6111 41.9393 81.0961 157.4832 311.3601 636.5957 1271.7626 2576.1199 5361.0984 11058.4106
a The transition between exothermic and endothermic reaction has been evidenced. The values for C6-C9 differ from those reported in Table 2 in the value of ∆Gf MBav° used. In Table 2 the exact mean value of the experimental ∆Gf MBi° has been used instead of the value ∆Gf MBav°‚10-5 [J mol-1] ) 0.4290nC - 0.5776 coming from regression (see Figure 2).
a The transition between an exothermic and an endothermic reaction has been evidenced.
temperature level and the change always takes place for a length of chain corresponding to about C13-C14. Figure 10 reports the results obtained at 298 K. This result is also supported by the experimental data on the heat of the single isomerization reactions. Table 9 lists the endothermic reactions from 2-methylheptane to multibranched isomers.5 In general for the isomerization of a 2-methylalkane to multibranched isomers the endothermic behavior increases
with nC not only as absolute values of the heat required but also as a percentage of the total parallel reacting ways (for C8 the 33.3% of the considered paths is endothermic, for C9 the 36%, and for C10 the 43.8%). Up to C8 the heats found in literature for reactions from normal to monobranched isomers are all negative, but their absolute value decreases with an increasing length of the n-paraffin chain.
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Table 9. Endothermic Reactions from 2-Methylheptane to Multibranched Isomers multibranched isomer
∆Hiso° [J mol-1] @ 298 K
multibranched isomer
∆Hiso° [J mol-1] @ 298 K
23-Mhexane 34-Mhexane
1548.82 2469.74
2M-3Epentane 3M-3Epentane
4269.72 502.32
Conclusions The evaluation of equilibrium constants for isomerization of F-T waxes is not an easy task because of the wide spectrum of paraffins involved and of the lack of experimental thermodynamical data for long chain paraffins. The method proposed represents an effective solution of the above-mentioned problems since it fits satisfactorily the few experimental lumped data. Moreover the equilibrium constants computed at different temperatures show that the reaction becomes endothermic beyond C13-C14. This result is confirmed by the presence of numerous endothermic single isomerization reactions whose number and weight increases with the chain length. It has been reported that the hydroconversion of F-T waxes displays a high sensitivity toward the change of temperature. As example an increase of 6 °C led to an increase of conversion of nearly 100%.15 Therefore the knowledge and an accurate control of the thermal profile in the adiabatic reactor are important. It is worth noticing that the absolute value of the heats involved is not very high, but only a deeper analysis, providing experimental data on heavy paraffins, can clarify the matter. Nomenclature a ) constant in ∆Gf°(T) equation (J mol-1) b ) constant in ∆Gf°(T) equation (J mol-1 K-1) c ) constant in ∆Gf°(T) equation (J mol-1 K-2) ∆G° ) variation of Gibbs free energy associated to the isomerization reactions (J mol-1) ∆Gf° ) Gibbs free energy of formation in the gas phase (ideal gas state) (J mol-1) ∆Hiso° ) heat of reaction associated to the isomerization (J mol-1) iso-C ) branched paraffin Keq ) equilibrium constant for isomerization reactions MB ) monobranched paraffin MB-MTB ) relevant to the isomerization reaction from monobranched paraffin to multibranched paraffin MTB ) multibranched paraffin n-C ) normal paraffin nC ) number of carbon atoms niso ) number of isomers n-MB ) relevant to the isomerization reaction from n-paraffin to monobranched paraffin P ) pressure (bar) R ) universal gas constant (J mol-1 K-1) T ) temperature (K) TebN ) normal boiling temperature (K) x ) mole fraction
Greek Symbols υ ) stoichiometric coefficient Subscripts av ) average value i ) relevant to i species lump ) relevant to the lump MB ) relevant to monobranched paraffins MTB ) relevant to multibranched paraffins MB-MTB ) relevant to the isomerization reaction from monobranched to multibranched paraffin n-C ) relevant to n-paraffins n-MB ) relevant to the isomerization reaction from n-paraffin to monobranched paraffin n-MTB ) relevant to the isomerization reaction from n-paraffin to multibranched paraffin Literature Cited (1) Pellegrini, L.; Locatelli, S.; Rasella, S.; Bonomi, S.; Calemma, V. Modeling of Fischer-Tropsch Products Hydrocracking. Chem. Eng. Sci. 2004, 59, 4781. (2) Pellegrini, L.; Bonomi, S.; Gamba, S.; Calemma, V.; Molinari, D. The “All Components Hydrocracking Model”. Chem. Eng. Sci. 2007, doi: 10.1016/j.ces.2007.01.076. (3) Sie, S. T.; Senden, M. M. G.; Van Wechem, H. M. H. Conversion of Natural Gas to transportation Fuel via the Shell Middle Distillate Synthesis Process. Catal. Today 1991, 8, 371. (4) Marcilly, C. Catalyse acido-basique: Application au raffinage et a` la pe´ trochimie; Technip Eds.: Paris, 2003; Vol. 1. (5) Stull, D. R.; Westrum, E. F., Jr.; Sinke, G. C. The Chemical Thermodynamics of Organic Compounds; Wiley: New York, 1969. (6) Benson, S. W. Thermochemical Kinetics: Methods for the Estimation of Thermochemical Data and Rate Parameters; Wiley: New York, 1976. (7) Aspen HYSYS, Release 2004, Simulation Basis; Aspen Technology: Cambridge, MA, 2004. (8) Weitkamp, J. The Influence of Chain Length in Hydrocracking and Hydroisomerization of n-alkanes. In Hydrocracking and Hydrotreating; Ward, J. W., Qader, S. A., Eds.; ACS Symposium Series 20, 1975; p 1. (9) Martens, J. A.; Tielen, M.; Jacobs, P. A. Attempts to rationalize the distribution of hydrocracked products. III. Mechanistic aspects of isomerization and hydrocracking of branched alkanes on ideal bifunctional largepore zeolite catalysts. Catal. Today 1987, 1(4), 435. (10) Froment, G. F. Kinetics of the hydroisomerization and hydrocracking of paraffins on a platinum containing bifunctional Y-zeolite. Catal. Today 1987, 1(4), 455. (11) Weitkamp, J. Isomerization of Long-Chain n-Alkanes on a Pt/CaY Zeolite Catalyst. Ind. Eng. Chem. Prod. Res. DeV. 1982, 21, 550. (12) Martens, J. A.; Jacobs, P. A. Elementary Steps and Mechanism. In Handbook of Heterogeneous Catalysis; Ertl, G., Knozinger, H., Weitkamp, J., Eds.; VCH Wiley Company: 1997; Vol. 3, p 1137. (13) Denayer, J. F.; Baron, G. V.; Souverijns, W.; Martens, J. A.; Jacobs, P. A. Hydrocracking of n-Alkane Mixtures on Pt/H-Y Zeolite: Chain Length Dependence of the Adsorption and the Kinetic Constants. Ind. Eng. Chem. Res. 1997, 36, 3242. (14) On Line Encyclopedia of Integer Sequences; http://www.research.att.com/∼njas/sequences/Seis.html (accessed Dec 2005). (15) Leckel, D. Hydrocracking of Iron-Catalyzed Fischer-Tropsch Waxes. Energy Fuels 2005, 19, 1795.
ReceiVed for reView April 12, 2007 ReVised manuscript receiVed May 17, 2007 Accepted May 23, 2007 IE0705204
