Methane Generation from Methylated Aromatics: Kinetic Study and

Energy & Fuels 2000, 14, 1143-1155

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Methane Generation from Methylated Aromatics: Kinetic Study and Carbon Isotope Modeling Franc¸ ois Lorant,* Franc¸ oise Behar, and Mireille Vandenbroucke Geology and Geochemistry Research Division, IFP, 1-4 Avenue de Bois Pre´ au, BP 311, 92506 Rueil-Malmaison Cedex, France

Daniel E. McKinney Shell International Expl. & Prod., 3737 Bellaire Blvd., Houston, Texas 77025

Yongchun Tang Chevron Research and Technology Co., Richmond, California 94802 Received December 17, 1999. Revised Manuscript Received July 19, 2000

The aim of this work was to elaborate a mathematical model that accounts for the carbon isotopic composition of methane generated during the thermal cracking of two model compounds: 9-methylphenanthrene (9-MPh) and 1-methylpyrene (1-MPyr). Pyrolysis experiments were carried out in an anhydrous closed system (gold vessels) during times ranging from 1 to 120 h under isothermal conditions (400-475 °C) at a constant pressure of 150 bar. Global rate constants were determined for methane generation from 1-methylpyrene decomposition, similar to those determined by Behar et al. (see ref 36 in the text) for 9-MPh thermal cracking. Two main processes of methane formation were recognized: one related to the loss of the methyl group and the second corresponding to the opening of the aromatic rings, the second of which is hydrogen pressure dependent. The derived apparent first-order kinetic parameters were determined only for the first process: E ) 55.6 kcal/mol and A ) 4.2 × 1012 s-1. These parameters are in the same range as those found for methane generated from 9-MPh (ref 36). When these results are extrapolated to geological conditions, methane generation occurs at temperatures lower than 200 °C and, thus, constitutes a significant source for natural gas accumulations. This source of natural gas can compete with late methane generation from kerogen. Based on the global kinetic scheme proposed for methane generation, a model of carbon isotopic fractionation was elaborated for predicting the isotopic composition of methane. Results show that very high isotopic fractionation can take place when the methylated aromatics are thermally degraded: the demethylation reaction leads to an isotopic fractionation between the generated methane and its source which is significantly dependent upon the isotopic heterogeneity of the aromatic compound. This study shows that specific isotopic signatures in natural gas might fingerprint the secondary cracking of aromatics in deep reservoirs.

Introduction The geochemical study of thermogenic hydrocarbon gases is of interest due to the fact that their isotopic and molecular signatures give important information on their genetic and postgenetic histories. The carbon isotopic ratios of the various light hydrocarbon gases are related to the isotopic composition of the different kerogen types or oil from which they originate.1-3 In addition, the 13C/12C ratio exhibits an increase with maturity.2,4-10 Complicating the picture even more are secondary processes which affect the 13C/12C ratio such * To whom correspondence should be adressed. E-mail: [email protected]. (1) Schoell, M. AAPG Bull. 1983, 67 (12), 2225-2238. (2) Clayton, C. Marine Pet. Geol. 1991, 8, 232-240. (3) Scott, A. R.; Kayser, W. R.; Ayers, W. B., Jr. AAPG Bull. 1984, 78 (8), 1186-1209. (4) Smith, J. E.; Erdman, J. G.; Morris, D. A. Eighth World Pet. Congr. Proc. 1971, 2, 13-26.

as migration,4,11-13 adsorption-desorption processes,14 and bacterial alteration15 which all can induce isotopic fractionation. It is widely accepted16 that the thermal evolution of oils is controlled by the kinetics of cracking reactions. (5) Galimov, E. M.; Posyagin, V. I.; Prokhov, V. S. Geokhimiya 1972, 8, 977-987. (6) Stahl, W.; Carey, B. D. Chem. Geol. 1975, 16, 257-267. (7) Schoell, M. Geochim. Cosmochim. Acta 1980, 44, 649-671. (8) James, A. T. AAPG Bull. 1983, 67 (7), 1176-1191. (9) Faber, E. Erdo¨ l Erdgas Kohle 1987, 103, 210-218. (10) Lorant, F.; Prinzhofer, A.; Behar, F.; Huc, A. Y. Chem. Geol. 1998, 147, 249-264. (11) Galimov, E. M. NASA Technical Translation; NASA TT F-682, Washington, DC, 1975; 395 pp. (12) Prinzhofer, A.; Huc, A. Y. Chem. Geol. 1995, 126, 281-290. (13) Pernaton, E.; Prinzhofer, A.; Schneider, F. Rev. Inst. Fr. Pet. 1996, 51 (5), 635-651. (14) Friedrich, H. U.; Ju¨ntgen, H. Adv. Org. Geochem. 1972, 639646. (15) James, A. T.; Burns, B. J. AAPG Bull. 1984, 68 (8), 957-960.

10.1021/ef990258e CCC: $19.00 © 2000 American Chemical Society Published on Web 09/28/2000

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Under this hypothesis, petroleum geochemists can simulate, experimentally, the low-temperature, long residence times of natural thermal processes by operating at higher temperatures, usually between 250 and 550 °C.17-31 Under laboratory conditions, reactions are rapid enough to monitor cracking with acceptable time (i.e., a few minutes to a couple of months). These experimental simulations are presently the best way to elaborate mathematical models that describe oil cracking and contribute to petroleum evaluation in natural reservoirs. Nevertheless, due to the diversity and the complexity of the chemical composition of oils, the development of a mathematical model can only be made on an empirical basis by grouping hydrocarbon molecules of similar structure and similar thermal stability into chemical classes. It is important to emphasize that theoretically the use of such global models of laboratory reactions to extrapolate pyrolysis data to geologic conditions is not satisfactory. Indeed, stoichiometric and apparent kinetic parameters (activation energy, frequency factor, reaction order) of lumped reactions may vary significantly with the temperature. A recent study performed by Domine´ et al.32 on the decomposition of a n-alkane illustrates potential uncertainties inherent to the geochemical use of global kinetic models. In the present paper, we will however assume that global laboratory reactions are representative of chemical processes that may occur in natural oil reservoirs. The reliability of our work can be contested, until the kinetic model we will propose is validated by comparing natural and predicted data. The determination of kinetic parameters for cracking of each chemical class (apparent activation energy Ei, preexponential factor Ai, and stoichiometric coefficients xi) in a global model is usually made on the basis of a set of reference pyrolysis experiments. It consists of determining a minimum error function defined as the mean square residual of the model versus the experiments. To minimize the number of free parameters, normally, the same preexponential factor is utilized for all competing thermal cracking reactions. This assump(16) Tissot, B. P.; Welte, D. H. Petroleum formation and occurrence, 2nd ed.; Springer-Verlag: Berlin, 1984. (17) Tissot, B. P.; Espitalie´, J. Rev. Inst. Fr. Pet. 1975, 30, 743777. (18) Monthioux, M.; Landais, P.; Monin, J. C. Org. Geochem. 1985, 8 (4), 275-292. (19) Ungerer, P., Pelet, R. Nature 1987, 327 (6117), 52-54. (20) Espitalie´, J.; Ungerer, P.; Irwin, I.; Marquis, F. Org. Geochem. 1988, 13 (4-6), 893-899. (21) Horsfield, B.; Disko, U.; Leibtner, F. Geol. Rund. 1989, 78 (1), 361-374. (22) Horsfield, B.; Schenk, H. J.; Mills N.; Welte D. H. Adv. Org. Geochem. 1991, 191-204. (23) Ungerer, P. Org. Geochem. 1990, 16 (1-3), 1-25. (24) Burnham, A.; Braun, R. Org. Geochem. 1990, 16 (1-3), 2739. (25) Behar, F.; Kressmann, S.; Rudkiewicz, J. L.; Vandenbroucke, M. Org. Geochem. 1991, 19 (1-3), 173-189. (26) Behar, F.; Ungerer, P.; Kressmann, S.; Rudkiewicz, J. L. Rev. Inst. Fr. Pe´ t. 1991, 46, 151-181. (27) Lewan, M. In Organic Geochemistry; Engel, M. H., Macko, S. A., Eds.; Plenum Publishing Corporation: New York, 1994; Chapter 18, pp 419-440. (28) Pepper, A. S.; Corvi, P. J. Mar. Pet. Geol. 1995, 12 (3), 291319. (29) Pepper, A. S.; Dodd, T. A. Mar. Pet. Geol. 1995, 12 (3), 321340. (30) Behar, F.; Vandenbroucke, M.; Tang, Y.; Marquis, F.; Espitalie´, J. Org. Geochem. 1997, 26 (5-6), 321-339. (31) Lewan, M. Geochim. Cosmochim. Acta 1997, 61, 3691-3722. (32) Domine´, F.; Dessort, D.; Brevart, O. Org. Geochem. 1998, 28 (9-10), 597-613.

Lorant et al.

tion is commonly used in kinetic models dealing with coal evolution33 or with other types of organic matter.19,22,29,34,35 It must be noticed however that such an assumption is arbitrary and not supported by any theoretical consideration. For a type II kerogen, this factor is around 1014 s-1. A recent kinetic study on 9-MPh36 has clearly shown that the global frequency factor, A, calculated for 9-MPh thermal decomposition is very different from that of n-C25: 4.5 × 1010 s-1 and 6.1 × 1017 s-1, respectively.37 When these parameters are used for extrapolation to geological conditions, the two corresponding Arrhenius diagrams cross each other at a temperature of 315 °C. This result indicates that methylated aromatics are less stable than their n-alkane counterparts at temperatures below 200 °C. This conclusion was recently confirmed in a study38 of a high-temperature/high-pressure reservoir in the Elgin Field (North Sea, reservoir temperature ) 190 °C), where oils exhibit very high saturate/ aromatic ratios. Consequently, as these methylated aromatics decompose in natural systems, they can be a new source for natural gas accumulations and, therefore, can be a significant contributor to methane generation during early and late cracking of source rocks and reservoired petroleum.20,30,39-43 This kinetic behavior from methylated aromatics explains why pyrolysis experiments at laboratory conditions, where aromatics are more stable than saturates, fail to reproduce the observed methane proportion calculated by global kinetic models using an unique frequency factor.38 This paper focuses specifically on methane generation from methylated aromatics, which are present in significant amounts in both source rock extracts and reservoir oils. Our aim is to confirm this new source contribution to methane by studying another alkyl aromatic compound, 1-MPyr, and to derive, from a global kinetic scheme, an isotope fractionation model to predict the generation rate and isotopic signature of methane in both laboratory and geological conditions. 1-MPyr was chosen because it has already been extensively studied by Smith and Savage.44-47 Because these authors have clearly shown that methane is derived mainly from secondary reactions, our pyrolysis condi(33) Ju¨ntgen, H.; Klein, J. Erdo¨ l Kohle-Erdgas-Petrochem. vereinigt Brennstoff-Chem. 1975, 287 (2), 65-73. (34) Campbell, J. H.; Gallegos, G.; Cregg, M. Fuel 1980, 59, 727732. (35) Sweeney, J. J.; Burnham, A. K.; Braun, R. L. AAPG Bull. 1987, 71 (8), 967-985. (36) Behar, F.; Budzinski, H.; Vandenbroucke, M.; Tang, Y. Energy Fuels 1999, 13, 3 (2), 471-481. (37) Behar, F.; Vandenbroucke, M. Energy Fuels 1996, 10, 932940. (38) Vandenbroucke, M.; Behar, F.; Rudkiewicz, J. L. Org. Geochem. 1999, 30 (9), 1105-1125. (39) Serio, M. A.; Hamblein, D. G.; Markham, J. R.; Solomon, P. R. Energy Fuels 1987, 1, 138-152. (40) Behar, F.; Vandenbroucke, M.; Teermann, S. C.; Hatcher, P. G.; Leblond, C.; Lerat, O. Chem. Geol. 1995, 126, 247-260. (41) Tang, Y.; Jenden, P. D.; Nigrini, A.; Teerman, S. C. Energy Fuels 1996, 10 (3), 659-671. (42) Lorant, F.; Behar, F.; Tang Y. Eighteenth International Meeting on Organic Geochemistry, Maastricht, The Netherlands, Sept 6-10, 1997. (43) Lorant, F. Ph.D. Thesis, Universite´ Louis Pasteur, Strasbourg, France, 1999. (44) Smith, C. M.; Savage, P. E. AIChE J. 1991, 37 (11), 1613-1624. (45) Smith, C. M.; Savage, P. E. Energy Fuels 1992, 6, 195-202. (46) Smith, C. M.; Savage, P. E. AIChE J. 1993, 39 (8), 1355-1362. (47) Smith, C. M.; Savage, P. E. Chem. Eng. Sci. 1994, 49 (2), 259270.

Methane Generation from Methylated Aromatics

tions were adjusted in such a way that high conversions were reached. A global kinetic scheme for methane production was proposed and compared to results obtained in our previous study on 9-MPh. For this latter compound, additional experiments were carried out in order to better constrain the methane generation and measure its isotopic fractionation. Subsequently, the δ13C of methane for both model compounds was measured at various conversion rates by GC-C-IRMS (i.e., a gas chromatograph coupled with a combustion interface and a mass spectrometer) in order to elaborate a common isotope fractionation model similar to work published previously by Sackett and coauthors.48-50 Their studies demonstrated the large influence of kinetic effects, compared to equilibrium processes, on the carbon isotopic signature of generated hydrocarbon gases. However, their work was restricted to n-alkane decomposition, and to our knowledge, there is no similar work available in the literature describing the same approach on gas generated from alkyl aromatics. Experimental Section Samples. 1-MPyr was purchased from Aldrich (99 wt % purity). Reagent grade chemicals used in the synthesis of 9-MPh were purchased from Aldrich. Synthesis of the target hydrocarbon was accomplished using standard synthetic.51 It was purified by liquid chromatography on silica gel and its purity checked by gas chromatography. Pyrolysis Experiments. Pyrolysis experiments were carried out in gold tubes (40 mm length, 5 mm i.d., and 0.5 mm thick) sealed by welding under an argon atmosphere and containing between 30 and 200 mg of initial sample.52 The gold tubes were placed in pressurized autoclaves in a furnace preheated at the chosen isothermal temperature (the heat-up time for a sample being ∼15 min) and kept at a pressure of 14 MPa during the entire course of the experiment. We assume that the pressure within the autoclaves is entirely transmitted inside the gold tubes by crushing. Temperature was measured (accuracy (1 °C) by a thermocouple placed within an empty tube in the cell. Pyrolysis time was measured from the point when the desired isothermal temperature was reached. At the end of the desired reaction time, the cells were removed from the oven, quenched in a cold water bath, and slowly depressurized as to not rupture the gold tube. Subsequently, the gold tube was removed from the autoclave and weighed. Gas Analysis. The gold tube was placed in a vacuum line (pressure equal to 10-5 MPa) and connected to a cold trap filled first with liquid nitrogen.52 After isolating the extraction line from the vacuum pump, the tube was pierced with a needle, allowing the permanent gases (H2, C1, and Ar) to be volatilized into the line and condensable compounds to be trapped by liquid nitrogen. Permanent gases were concentrated by a Toepler pump into a calibrated volume in order to quantify their total yield and to recover them for molecular analysis as described below. Then, the liquid nitrogen trap was heated to -100 °C, allowing condensable gases (C2-C4 alkanes) to be recovered and quantified by the same procedure as that used for permanent gases. Molecular characterization and quanti(48) Sackett, W. M.; Nakaparksin, S.; Dalrymplen, D. International Meeting on Organic Geochemistry, Oklahoma, USA, 1966. (49) Sackett, W. M. AAPG Bull. 1968, 52, 953-957. (50) Franck, D. J.; Sackett, W. M. Geochim. Cosmochim. Acta 1969, 33, 811-820. (51) Richman, J.; Bortiatynski, J. M.; Hatcher, P. G. 1998. Synthesis of 13C-labeled polycyclic aromatic hydrocarbons (PAHs). Unpublished results. (52) Behar, F.; Saint-Paul, C.; Leblond, C. Rev. Inst. Fr. Pet. 1989, 44, 387-397.

Energy & Fuels, Vol. 14, No. 6, 2000 1145 fication of the total gas fraction were performed by gas chromatography. After molecular characterization and quantification, the gaseous fraction was submitted to GC-C-IRMS analysis (Micromass Optima) for measurement of the 13C/12C ratio of methane. The GC conditions were the following: split injector (ratio 15/1) at 150 °C, a GCQ (J&W Scientific) column (30 m, 0.32 mm i.d.), and initial temperature of 40 °C during 10 min. The standards were (i) CO2 that was injected at the beginning and at the end of each analysis and (ii) calibrated CH4 used as an external standard. Results were directly given in delta units (i.e. δ13C) according to

δ13C )

[

]

(13C/12C)sample (13C/12C)std

× 1000

(1)

where (13C/12C)std refers to PDB (i.e., 13C/12C ) 11 237 ppm). With this notation, negative δ13C values, as usually observed on organic compounds, indicate a relative depletion of 13C in the analyzed sample, compared to the reference. Analysis of the C7+ Fraction. After the gas was collected and analyzed, the pierced gold tube was cut open and submersed in pentane. After extraction for 1 h, by stirring under reflux, the solution was filtered and accurately divided into two fractions, by weight. After addition of an internal standard (n-C25), the first solution was injected as is (i.e., without solvent evaporation) into a gas chromatograph for identification and quantification of individual compounds. Both the internal standard and an external calibration of the FID with 1-MPyr were used for quantification, allowing for calculation of respective response factors followed by calculation of 1-MPyr in each extract. The chromatograph was equipped with an on-column injector. The column utilized was a fused silica capillary column (J&W Scientific, Inc. DB-1) (60 m length, 0.32 mm i.d., and 0.25 µm film thickness). The temperature program was initial temperature of 20 °C, final temperature of 320 °C with a final hold of 40 min, and heating rate from 20 to 200 °C at 5 °C/min, from 200 to 250 °C at 1 °C/min and from 250 to 320 °C at 5 °C/min. The second solution was evaporated and weighed. The amount of insoluble residue, if any, was determined by difference as follows:

residue ) 100% - % gas - % C7+ extract

(2)

A subset of C7+ fractions was analyzed by GC-C-IRMS (Micromass Isoprime). Similar to the determination of the δ13C for the generated methane, CO2 was injected at the beginning and at the end of each analysis. Since the internal standard was still present in the mixture to be analyzed, its 13C/12C ratio was used as a corrective measure. The 13C/12C ratio was determined by direct combustion: (δ13C n-C25)comb ) -27.9‰. Knowing this isotopic composition, it was possible to correct ((δ13C X)cor) all the measured data ((δ13C X)meas). For example, for a given compound, the (δ13C X)cor can be determined as follows:

(δ13C X)cor ) (δ13C X)meas + ((δ13C n-C25)comb - (δ13C n-C25)meas) For these set of experiments, the GC conditions were as follows: a split injector (ratio 5/1) was utilized at 270 °C. The column utilized was a 30 m, 0.25 mm i.d., 0.25 µm film thickness, fused silica capillary column (J&W Scientific, Inc. DB-1). Approximately, 1 µL of the diluted sample was injected onto a split/splitless injector (injector temperature ) 270 °C) operating in the split mode (ratio 5:1). The column temperature was programmed from 35 to 150 °C at a heating rate of 5 °C/ min and from 150 to 300 °C at a heating rate of 2 °C/min with a final isothermal time of 4 min.

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Table 1. Mass Balances (in wt %) Obtained during Thermal Cracking of 9-MPha CH4, Ph, M-Ph, D-MPh, C20+ Aro, char, wt % wt % wt % conv, wt % wt % wt % ( 0.1 ( 0.2 ( 0.2 ( 0.2 (3 (3 T, °C t, h % 400 400 425 425 400 425 450 475

4 7.0 6 9.9 4 21.4 9 47.5 48 59.4 24 84.0 24 >99 24 >99

1.5 2.2 5.7 16.2 21.0 35.5 59.0 87.0

nd 1.8 6.1 19.5 23.0 38.0 nd nd

nd 0.0 0.0 1.8 2.8 9.9 nd nd

nd 0.8 1.5 4.7 5.1 3.5 nd nd

nd 7 13 13 21 12 nd nd

nd 0 0 7 6 17 nd nd

a Ph is phenanthrene, M-Ph’s are 9-MPh isomers, and D-MPh’s are dimethylphenanthrene isomers.

Uncertainty in the Experimental Data. The accuracy of quantitative data may strongly vary with both the thermal severity and the absolute amount of reactant loaded in the gold vessels. Nevertheless, considering the procedures previously described, we estimate that the amount of C20+ aromatic fraction and insoluble residue can be given with an average accuracy of (3 wt %. Compounds detected by GC were quantified more precisely, and data are replicable by (2 mg/ g. For gas analysis, the blank was usually below 0.5 µmol of nitrogen coming from air contamination, and the calibrated volume of the Toepler pump enabled accurate measurement of total gas to as low as 1 µmol. Hence, each individual gas was quantified with an average precision of (0.2 mg/g. For 9-MPh pyrolysis experiments, the uncertainty in gas data is higher, i.e., (1.0 mg/g, because the amount of reactant introduced in the gold tubes was much lower than that used in the 1-MPyr experiments. Carbon isotope analyses were generally replicable by (0.5 delta unit for methane generated during the pyrolysis of 1-MPyr, and (1.0 delta unit for methane generated during the pyrolysis 9-MPh. Measurements performed on the C7+ fraction are given with a precision of ( 0.1 delta unit.

Results and Discussion: Kinetic Study Mass Balances. We define the conversion of a reactant as follows:

conv ) 1 - residual reactant/initial reactant (in weight %) (3) High conversions of 9-MPh and 1-MPyr were observed at 150 bar when pyrolysis experiments were carried at 400, 425, 450, and 471 or 475 °C, for residence times ranging from 1 to 120 h. Note that under such pressure and temperature conditions, these substances are liquid. Mass balances obtained for these experiments are reported in Table 1 for the 9-MPh and in Table 2 for 1-MPyr. Results are sorted by increasing conversion. It is worth noting that, as expected, the lowest data accuracy is observed for fractions evaluated by difference (e.g., both the C20+ Aro and the insoluble residue). Moreover, because a clear distinction is not evident between these two chemical classes by solvent solubility in n-pentane, an underestimation of the C20+ Aro is often compensated by an overestimation of the insoluble residue. The results clearly indicate that 9-MPh is more stable than 1-MPyr. This is in good agreement with the previous studies of Smith and Savage45 and with the Dewar reactivity numbers53,54 for these two model (53) Dewar, M. J. S. J. Am. Chem. Soc. 1952, 74, 3357-3363.

compounds (respectively, 1.86 and 1.51). However, our conversion estimation for 1-MPyr seems to be higher than that published by Smith and Savage.45 This discrepancy is due to a difference in the conversion definition. Smith and Savage have indeed added the remaining 1-MPyr (reactant) to the amounts of generated methylpyrene isomers (products). Thus, the global conversion is underestimated in comparison to that based on the remaining 1-MPyr only. In a previous work,36 we have proposed a global reaction for methane generation according to the following normalized stoichiometry (in wt %):

9-MPh f 6.4% CH4 + 34.0% Ph + 11.0% C20+ Aro + 47.1% char (4) This reaction accounted for methane generation up to 99.4 wt % 9-MPh conversion (i.e., 425 °C/72 h).36 In the present study, some experiments were carried out at higher severity, and thus, the maximum yield of methane (8.7% at 475 °C/24 h in Table 1) is higher than 6.4%. These observations suggest that above 99.5 wt % conversion of 9-MPh, a second reaction takes place for methane generation, which is mainly related to secondary or tertiary cracking processes. Phenanthrene generation is observed as soon as 9-MPh starts to be degraded. It was shown in the previous study36 that above 80% conversion its yield remains fairly constant and decreases very slowly above 98%. For 1-MPyr (Table 2), because conversions are much higher than those of 9-MPh and the experiments are more numerous and precise, secondary product formation is easier to describe. One observes that a large amount of demethylated aromatic is formed during 1-MPyr degradation, and the maximum pyrene yield is 43 wt %. Above 97 wt % conversion, this compound starts to decay. The methylpyrene isomers, which are more stable than the reactant, are also generated, and their amount continuously decreases above 75 wt % conversion. The same is true for the dimethyl isomers and the C20+ aromatics. Consequently, a large part of methylated structures are degraded before the maximum yield of pyrene is reached. This means that, up to the maximum production of pyrene, methane mainly originates from the methylated aromatics. During this step, small amounts of molecular hydrogen and ethane appear. Phenanthrene is also generated and its yield rises continuously (Table 2). Subsequently, when pyrene begins to decrease, the remaining methylated structures continue to be cracked, and less than 1 wt % is present at 471 °C/24 h. At this level of thermal stress, generation of propane is observed, and the maximum yield reached in the most severe conditions is 0.1 wt %. Phenanthrene generation, which has already started, continues to increase and reaches a maximum of 1.4 wt % at 99.2 wt % conversion of 1-MPyr. At this time, phenanthrene undergoes thermal decomposition. During this stage, pyrene is the major product in the mass balance and may be considered as the major source for a late generation of methane. When the absolute amount of pyrene falls from 430 to 191 mg/g, around 6 mg/g phenanthrene, 16 mg/g methane, and 4 mg/g (54) Dewar, M. J. S.; Thiel, W. J. Am. Chem. Soc. 1977, 99, 48994907.


Energy & Fuels, Vol. 14, No. 6, 2000 1147

Table 2. Mass Balances Obtained during Thermal Cracking of 1-MPyra

T, °C

t, h

conv, %

424 450 471 424 450 450 471 471 450 424 471 450 424 450 424 471 471

6.25 2.25 1 15.17 4 6 2 3.33 9 48 6 15 72 25.7 120 15 24

75.3 78.6 86.1 87.4 88.5 91.7 91.9 94.2 94.8 96.0 96.3 96.7 98.0 99.1 99.2 99.3 99.8

H2, mg/g ( 0.2

CH4, mg/g ( 0.2

C2H6, mg/g ( 0.2

C3H8, mg/g ( 0.2

Ph, mg/g ( 2.0

Pyr, mg/g ( 2.0

M-Pyr, mg/g ( 2.0

D-MPyr, mg/g ( 2.0

C20+ Aro, wt % (3

char, wt % (3

0.1 0.1 0.3 0.2 0.3 0.4 0.5 0.6 0.5 0.7 0.8 0.7 1.1 1.3 1.7 2.0 3.5

12.3 16.7 23.9 24.9 27.6 34.1 34.2 39.3 39.2 44.1 44.2 46.6 48.4 52.0 53.2 55.0 60.1

0.4 0.5 0.8 0.9 1.0 1.1 1.1 1.2 1.2 1.4 1.4 1.5 1.7 2.1 2.5 3.1 5.3

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.4 0.6 0.8 1.2

1.5 1.9 2.6 3.4 3.3 4.0 4.1 5.5 6.3 8.9 7.1 6.8 11.4 11.6 14.2 10.2 7.5

312.3 346.6 374.7 373.8 388.1 411.0 408.0 414.3 429.6 433.7 428.8 430.2 415.4 370.0 358.9 369.1 191.4

336.5 323.7 264.7 268.0 248.6 199.2 191.4 143.6 133.8 108.1 98.0 89.8 61.7 31.5 28.9 29.9 8.3

123.1 110.7 71.2 65.1 56.6 35.6 37.7 20.1 16.8 12.8 11.5 10.0 7.5 6.2 6.0 4.9 3.5

18 18 20 17 20 18 18 16 17 10 11 13 8 11 6 9 5

4 3 6 10 8 13 15 23 21 30 31 30 38 43 49 45 68

a Ph is phenanthrene, M-Pyr’s are 1-MPyr isomers, and D-MPyr’s are dimethylpyrene isomers. Note that C 20+ Aro and char amounts are given in wt %, whereas other fractions are given in mg/g.

ethane are generated. If these additional amounts were only related to the transformation of pyrene, they would represent approximately 10 wt % for a complete pyrene conversion, and the remaining 90 wt % necessary to close the mass balance would come from char. Thus, besides methane formation, pyrene is mainly converted to char. This confirms that, as suggested by previous studies,36,45 char is not a primary product. Associated with this coking process, a sharp increase of molecular hydrogen is observed above 96 wt % 1-MPyr conversion, which might likely correspond to the loss of hydrogen from aromatic rings. Besides pyrene and phenanthrene, char may also have other precursors such as the C20+ aromatics.55 In the most severe conditions, this fraction largely predominates and reaches a maximum yield of 68 wt %. A second mechanism involving hydrogenation reactions takes place at high severity, according to reaction 2 in Figure 1. To summarize, two global steps can describe the overall generation of methane (Figure 1): Step 1: Up to the maximum production of pyrene (i.e., 43 wt % occurring for 96-97% conversion of 1-MPyr), methane is generated from the decomposition of the methyl and dimethyl isomers, and most of the C20+ Aro. This demethylation process is illustrated in Figure 1. Detailed mechanisms are given in ref 45. At this stage the formation of molecular hydrogen is very small, so this step is correctly modeled by the reaction k1

MPY 98 xCh4 + (1 - x)PYR

(5a)

where MPY is a lumped reactant that refers to the sum of all methylated aromatics plus the C20+ Aro, PYR is the pyrene, x is the mass stoichiometric coefficient, and k1 is the rate constant. Step 2: Above 97 wt % conversion, the pyrene is transformed, on one hand, into molecular hydrogen and char by condensation (5b), and, on the other hand, into hydrocarbon gases (CH4, C2H6) and phenanthrene by hydrogenation and decomposition (5c), following a mechanism schematized in Figure 1: (55) Poutsma, M. L. Energy Fuels 1990, 4 (2), 113-131.

k2

PYR 98 yH2 + (1 - y)CHAR

(5b)

k3

] ARO 98 z1CH4 + z2C2H6 + z3PH (5c) PYR [\ p(H ) 2

PH is phenanthrene, ARO refers to the sum of alkylphenanthrenes depicted in Figure 1 (the term ARO used here should not be confounded with the fraction C20+ Aro described previously), k2 and k3 are rate constants, and y, z1, z2, and z3 are mass stoichiometric coefficients. A consequence of the hydrogenation of pyrene is that the gas dryness (i.e., the ratio of C1 over C1-C3) is a decreasing function of the severity, due to the late generation of ethane and propane. However, even at very high thermal stress, the gas dryness is still higher than 90% in mass units (95% in volume units). Also, note that, since very small amounts of ethane and phenanthrene were recovered for lower conversions in our experiments, a small overlap between this second step and the previous one may not be excluded. Kinetic Parameters for Methane Generation during 1-MPyr Pyrolysis. The key problem for determining the apparent rate constants for the specific generation of methane is the calculation of the conversion. A conversion curve based on the decay of a given reactant (1-MPyr in the present study) cannot be established since (i) the formation of methane is not related to a single reactant only, but at least two lumped reactants, and (ii) the rate of decomposition of these lumped reactants is not necessarily similar to the rate of formation of methane. Therefore, kinetic parameters can be derived only from the methane generation curves. It has been shown in the previous work on 9-MPh36 that methane generation through demethylation (reaction 5a) follows a global first-order reaction with respect to the methylated compounds (here noted MPY). It is thus reasonable to assume also a first-order mechanism in the present kinetic scheme:

(

)

d[CH4] dt

step

1

) xk1[MPY] ) xk1[MPY]0e-k1t (6)

with k1 ) A1e-E1/RT. In the second step, methane is formed from the demethylation of compounds referred

1148


Lorant et al.

Figure 1. Main stages of methane formation during 1-MPyr pyrolysis.

to as ARO. Hence, to be consistent with reaction 5a, the rate of methane formation through reaction 5c should also be first order with respect to ARO:

(

)

d[CH4] dt

step

2

) z1k3[ARO]

Thus, assuming that the formation of ARO by reaction 5b is pseudo first order with respect to PYR and first order with respect to the partial pressure of H2, the concentration of ARO might be proportional to the product [PYR][H2]:

(7)

with k3 ) A3e-E3/RT. Now, according to mechanism 5a, the amount of ARO is controlled by the availability of hydrogen radicals, and is consequently linked to the partial pressure of H2 in the system. Since the elimination of an H-atom from the hydropyrenyl radical has a relatively low activation energy (about 35 kcal/mol according to Smith and Savage45), the hydrogenation of pyrene at high temperature is a reversible process.

[ARO] # K[PYR][H2]

(8)

where K is an equilibrium constant (the character “#” signifies that the terms in eq 8 are not strictly equal, but proportional). Equation 7 may thus be rewritten as

(

)

d[CH4] dt

step

2

) z1k3[ARO] # z1k3K[PYR][H2] ) z1k′3[PYR][H2] (9)



with k′3 ) A′3e-E′3/RT. The overall methane generation rate is obtained after summing eqs 6 and 9:

(

Table 3. Fitting ai and bi Coefficients Used in Eq 13, for Three Temperaturesa T ) 424 °C

)

d[CH4] ) xk1[MPY]0e-k1t + z1k′3[PYR][H2] (10) dt

In our experiments, all the generated hydrogen is kept in the system, so the hydrogenation reaction is likely to occur. However, the occurrence of such a process of methane formation under geological conditions is questionable, since H2 does not usually remain within natural systems (e.g., reservoirs, source rocks, etc.) due to its high diffusion capacity. For that reason the present study has been mainly focused on the first step of methane formation: the demethylation process. To determine reliable apparent kinetic parameters for this reaction from our experimental data, we cannot completely neglect the overlap that may occur between the two steps of methane formation. Indeed, even a slight contribution of the second reaction to the first one might significantly shift final E and A values. Therefore, kinetic parameters for step 1 (reaction 5a) should only be obtained by solving the set of differential equations that describes reactions 5a-5c, and by optimizing both rate constants and stoichiometric coefficients. However this solution would remain uncertain, because the number of experimental data that could be used to calibrate the model would be fairly insufficient considering the number of unknowns to be determined. To overcome this problem, eq 10 only was evaluated by the following approach. Integrating eq 10 with respect to the time leads to

∫

[CH4] ) x[MPY]0(1 - e-k1t) + z1k′3 t[PYR][H2] dt (11) The variation of the product [PYR][H2] as a function of the time for a given temperature may be numerically modeled by a known function, calibrated on the experimental data, so that the term on the right in eq 11 can be integrated. We use the notation ψ(t) as this fitting function: ψ(t) ) [PYR][H2]. The choice of ψ(t) to interpolate the product [PYR][H2] is restricted to certain conditions: ψ(t) must be a continuous function of time, still positive, and easy to integrate. However, dψ(t)/dt might be positive or negative. The function must also verify ψ(t)0) ) 0, and finally it should be monotonic between two experimental values. The type of mathematical function we suggest to complete these conditions is the following:

a1 b1 a2 b2 a3 b3 a4 b4

1958.1223 -0.011930 -776.3858 -0.026018 1.9830 0.035252

T ) 450 °C

T ) 471 °C

6994.4895 -0.002235 -1083.3189 -0.609576 1172.5467 -0.538549

0.7539 -0.397945 3102.0186 -0.018702 72.0414 -1.349601 1.4282 0.373351

a These parameters were adjusted on experimental data given in Table 2, using eq 12.

Table 4. Kinetic Parameters Obtained for Methane Generation during the Pyrolysis of 1-MPyra step 1: demethylation E1 A1 x a

55.6 kcal/mol 4.2 × 1012 s-1 4.6 wt %

step 2: hydrogenation E′3 z1A′3

39.1 kcal/mol 9.8 × 106 wt % s-1

Step 1 refers to reaction 5a and step 2 to reactions 5b and 5c.

The values of ai and bi coefficients given in Table 3 were obtained by fitting with eq 12, the product [PYR][H2] experimentally observed. A comparison between ψ(t) and the experimental data at 424, 450, and 471 °C is shown later in Table 5(the uncertainty given for the product [PYR][H2] was calculated according to average errors indicated in Table 2). For a given set of fitting coefficients, modeling the generation of methane through eq 13 necessitates the determination of six parameters: x, E1, A1, z1, E′3, and A′3. This number may be reduced to five because z1 and A′3 equally compensate in eq 13. Indeed, since z1 and A′3 are both constants, their product is also a constant. There is a compensation between these two parameters because the problem z1A′3 ) constant has an infinity of solutions. Hence, only the product z1A′3 needs to be calibrated, not z1 and A′3 separately. In other respects, we must emphasize the fact that, because ψ(t) is only a fitting function, it has no physical meaning and its use is restricted to the range of time in which the corresponding ai and bi coefficients have been determined. Consequently eq 13 is not valid outside this experimental range of time. Since the end of step 2 is never reached in our experiments, eq 13 cannot properly extrapolate the total amount of gas due to reaction 5c. Therefore the values of z1A′3 and E′3 are not expected to have any physical significance. All kinetic and stoichiometric parameters of the model have been numerically determined by minimizing a quadratic error function F defined as

4

b1t

ψ(t) ) a1e

+

ai(1 - eb t) ∑ i)2

(12)

i

where ai and bi are fitting coefficients, appropriate for one temperature only. Replacing [PYR][H2] by eq 12 in eq 11 leads, after integration with respect to time, to the expression of [CH4] as a function of t, at a constant temperature:

[CH4] ) x[MPY]0(1 - e-k1t) + 4 a a1 i b1t (e - 1) + (bit + 1 - ebit) z1k′3 b1 i)2bi

{

∑

}

(13)

F)

1N

∑([CH4]measured - [CH4]calculated)2

2i)1

(14)

The optimized values are reported in Table 4. Based on these parameters, total predicted methane amounts were compared to experimental data, and the contribution of step 2 in each experiment was calculated as indicated in Table 5. Data in this table show that the contribution of the pyrene hydrogenation process on overall methane generation, as calculated by the model, is less than 1213% for 1-MPyr conversion below 96-97%, which is in

1150


Lorant et al.

Table 5. Calculated versus Measured Methane Concentrations for the Pyrolysis of 1-MPyr

T, °C

calcd CH4 [PYR][H2] expt contribution 1-MPyr CH4, expt, calcd, of step 2 conv, mg/g total, (mg/g)2 (mg/g)2 % ( 0.2 mg/g mg/g % ( 8.6 ( 8.6

t, h

424 6.25 424 15.17 424 48 424 72 424 120 450 2.25 450 4 450 6 450 9 450 15 450 25.7 471 1 471 2 471 3.33 471 6 471 15 471 24

75.3 87.4 96.0 98.0 99.2 78.6 88.5 91.7 94.8 96.7 99.1 86.1 91.9 94.2 96.3 99.3 99.8

12.3 24.9 44.1 48.4 53.2 16.7 27.6 34.1 39.2 46.6 52.0 23.9 34.2 39.3 44.2 55.0 60.1

12.7 25.0 43.4 47.9 54.0 17.8 26.9 33.9 40.2 45.8 49.7 22.0 33.7 41.4 46.8 53.7 60.8

0.0 0.1 1.2 2.9 7.9 0.0 0.1 0.2 0.5 1.4 3.6 0.1 0.2 0.6 1.5 7.5 14.6

0.1 0.4 2.7 6.0 14.6 0.1 0.3 0.7 1.3 3.0 7.3 0.3 0.7 1.4 3.3 14.0 24.0

21.9 71.0 290.6 448.7 613.8 38.1 112.6 176.7 214.8 318.4 481.0 108.6 191.7 261.0 390.2 745.6 668.0

23.7 69.6 291.2 448.4 613.8 50.1 110.0 164.0 223.8 319.6 479.6 111.3 181.2 257.8 397.5 740.9 666.9

good agreement with our previous observations. An interesting consequence of this result is that we can confirm the first stage of methane generation indeed follows a first-order reaction kinetics, by using a Guggenheim diagram. This method is fully described in the Appendix. It allows both verifying the order of a reaction and determining a rate constant and a stoichiometric coefficient (i.e., the x value) when measurements have been performed on one product of the reaction only, and when the conversion is unknown. A Guggenheim diagram is a plot, versus time, of the logarithm of the difference between the successive values in a set of experimental data, when these data are all separated by the same time interval. If the reaction is first order, we show in the Appendix that two successive values are related to the time of the smallest value by

ln(∆Q) ) -kt + ln(Qmax(1 - e-k∆)

(15)

where ∆Q is the difference between the two values, ∆ is the constant time interval (i.e., if the first value has been obtained at a time t, then the other one corresponds to the time t + ∆), Qmax is the infinitive amount (i.e., stoichiometric coefficient), and k is the rate constant. Thus, in a Guggenheim plot any linear correlation should indicate a first-order reaction with the slope of the line giving k and the origin value being a function of Qmax. This methodology was applied for two temperatures, 450 and 471 °C, with respective ∆ values at 2 and 1 h. The resulting Guggenheim plots are displayed in Figure 2. Although only three points for each ∆ value can be plotted, two straight lines appear in this diagram (note that the absolute uncertainty on these points can be estimated at (0.06, in ln(mg/g), according to error ranges given in Table 2). The correlation coefficients are 0.9839 for 450 °C and 0.9973 for 471 °C, and the stoichiometric coefficients are 4.6 and 4.3 wt %, respectively. Theoretically, these two values should be identical because they represent the infinitive amount for a single reaction that must be equivalent whatever the pyrolysis temperature. Their difference (i.e., 0.3 wt %)

Figure 2. Guggenheim plots at 450 and 471 °C based on methane data in Table 2.

is actually higher than the uncertainty in gas data given in Table 2 (i.e., (0.02 wt %); however they are both very similar to the value of 4.6 wt % obtained by optimization (see Table 4). We are aware that the use of the Guggenheim method with three points only is not really accurate. The plot in Figure 2 allows us to verify only that the hypothesis of a pseudo-first-order demethylation step is likely operative in laboratory conditions. Extrapolation to Sedimentary Basin Temperatures. The kinetic parameters corresponding to step 1 in Table 4 are fully consistent with those already obtained for methane generation during 9-MPh pyrolysis36 for which E was 54.5 kcal/mol and A was 1.1 × 1012 s-1. This similarity allows us to propose a set of kinetic parameters, taken as an average value of E at 55 kcal/mol and of A at 3 × 1012 s-1, for modeling the generation of methane by demethylation of methylated aromatics. It is worth clarifying that the entire model of methane generation proposed in this paper (i.e., eq 13, which includes both step 1 and step 2) cannot be used outside our experimental conditions. Nevertheless, we consider that apparent kinetic parameters for the demethylation step only (E1 and A1 in Table 4), derived by deconvolution of the pyrolysis data, can be significantly compared to other global rate parameters obtained in equivalent pyrolysis conditions. As briefly discussed in the Introduction, the laboratory validity of kinetic parameters does not mean that it is correct to extrapolate our data to geologic environments using this kind of demethylation model. However, assuming the same rate law with constant kinetic parameters whatever the temperature is so far the most practical way to predict cracking reactions in reservoir oils. When it is possible, this operation should be validated by comparing the extrapolated data to direct observations (i.e., chemical composition of fluids in geological reservoirs). The recent study38 performed on the Elgin Field (North Sea), already cited in the Introduction, offered such a possibility. It allowed us to validate the use of a single first-order model established from laboratory experiments,36 to account for the global decomposition of methylated aromatics in geological conditions. Therefore, we can hope that the corresponding methane generation model presented here yields gas amounts and formation rates consistent with natural processes.

Methane Generation from Methylated Aromatics Table 6. Isotopic Signature of Methane Generated during Thermal Cracking of 1-MPyr (δ13C1-MPyr ) -26.8‰ vs PDB)

T, °C

t, h

1-MPyr, conv, %

424 424 424 424 424 450 450 450 450 450 450 471 471 471 471 471

6.25 15.17 48 72 120 2.25 4 6 9 15 25.7 2 3.33 6 15 24

75.3 87.4 96.0 98.0 99.2 78.6 88.5 91.7 94.8 96.7 99.1 91.9 94.2 96.3 99.3 99.8

CH4, mg/g ( 0.2

δ13CCH4, ‰ vs PDB ( 0.5

12.3 24.9 44.1 48.4 53.2 16.7 27.6 34.1 39.2 46.6 52.0 34.2 39.3 44.2 55.0 60.1

-63.3 -60.9 -55.5 -54.8 -50.6 -62.1 -59.9 -58.7 -57.3 -55.3 -52.7 -58.0 -57.4 -53.8 -50.3 -47.1

With kinetic parameters given above, the window of methane generation from the methylated aromatics in sedimentary basins is approximately 160-200 °C, assuming a geothermal gradient at 25 °C/km and a sediment burial of 50 m/My. At this level of organic maturation, the amount of gas that can be generated by cracking of the methylated aromatics is typically in the range of that expected from kerogen cracking during metagenesis.16,30,43 Such aromatic compounds therefore constitute an important source of gas in sedimentary basins, much more than n-alkanes, which (i) remain thermally stable below 180 °C,37 and (ii) do not reveal a large methane potential until the degradation of light oil occurs. Other direct implications for gas exploration would be the following: (i) In terms of chemical composition, the gas generated from these methylated aromatics is almost pure methane (dryness higher than 90% in mass units). Its contribution to natural gas could partly explain for reservoirs at temperatures higher than 150 °C the common richness of natural gas in methane in comparison to the proportion of the other hydrocarbon gases such as C2H6, C3H8, and C4H10. (ii) The contribution of the methylated aromatic secondary cracking on the carbon isotopic signature of methane in reservoirs should be significant. For this reason our task in the next part of this paper is to characterize, isotopically, this important source of methane.

Energy & Fuels, Vol. 14, No. 6, 2000 1151 Table 7. Isotopic Signature of Methane Generated during Thermal Cracking of 9-MPh (δ13C9-MPh ) -29.9‰ vs PDB)

T, °C

t, h

9-MPh, conv, %

400 400 400 425 425 425 450 475

4 6 48 4 9 24 24 24

7.0 9.9 59.4 21.4 47.5 84.0 > 99 > 99

Experimental Observations. Isotopic compositions of methane generated during the pyrolysis of 1-MPyr and 9-MPh are reported in Tables 6 and 7. The initial 13C/12C ratios of 1-MPyr and 9-MPh, determined by both combustion (Dumas technique) and GC-C-IRMS, were measured at -26.6‰ and -29.9‰ vs PDB, respectively. Since products such as pyrene and phenanthrene are, according to the kinetic scheme previously proposed, important sources for methane in our experiments at high severity, a subset of GC-C-IRMS analyses was also performed on pyrene. The results, given in Table 8, indicate that this compound is slightly fractionated compared to 1-MPyr, by +2‰ approximately. Consider-

δ13CCH4, ‰ vs PDB ( 1.0

1.5 2.2 21.0 5.7 16.2 35.5 59.0 87.0

-110.4 -112.6 -110.6 -110.2 -110.1 -106.7 -98.4 -80.2

Table 8. Isotopic Composition of Pyrene for a Subset of Experiments on 1-MPyr Pyrolysis

T, °C

t, h

CH4, mg/g

450 424 424 471

2.25 48 120 24

16.7 44.1 53.2 60.1

δ13C pyrene, ‰ vs PDB ( 0.1 -24.5 -24.3 -23.7 -23.1

ing the molecular weight of pyrene, a small but significant isotopic fractionation is observed with increasing thermal stress, in the magnitude of 1.4‰. Data in Tables 6 and 7 show that, in both cases, the δ13C of methane in the investigated time and temperature intervals is a positive and monotonic function of the thermal severity. The large isotopic fractionation between the generated methane and its initial reactant is noteworthy. This phenomenon is clearly evident on the 9-MPh data in that the isotopic separation ranges from -80‰ to -50‰. The isotopic fractionation between the methane and the 1-MPyr is smaller: between -37‰ and -20‰ (i.e., in the same range as observed in refs 47-49 during the pyrolysis of n-alkanes under similar experimental conditions). In a decomposition reaction, the isotopic signature of a product (i.e., methane in the present study) depends on three parameters (assuming the isotopic equilibrium is never reached): the degree of conversion of the reactant, its initial isotopic signature (δ13C0) and the isotopic fractionation factor (R). This latter is defined as the ratio between the rate constants of the13Csubstituted and nonsubstituted reactant decomposition reactions, and consequently depends on temperature according to an Arrhenius-like law as follows:

R) Isotopic Characterization of Methane

CH4, wt % ( 0.1

13

k 13k ≈ ) Ωe-∆E/RT 12 k k

(16)

where ∆E is the variation of the activation energy due to the isotopic substitution; Ω is the ratio between the frequency factors for the decomposition of the 13Csubstituted and nonsubstituted reactants. Since the conversion depends only on the reaction rate, complete isotopic characterization of this product is determined by assigning values to δ13C0, ∆E, and Ω. The δ13C0 controls the 13C/12C ratio of the integrated product at the end of reaction, which might differ from the initial 13C/12C ratio of the reactant. Such a difference, when it exists, is referred to as the precursor effect. Usually molecules such as methylated aromatics are not isotopically homogeneous because the carbon-13 is

1152


preferentially concentrated in the aromatic rings rather than in the methyl group.11 Unfortunately, the 13C/12C ratio of the methyl group in the 1-MPyr used for our experiments was undetermined, because chemicals from which it was synthesized were not available (i.e., the molecule was synthesized in an outside industrial laboratory). Consequently the magnitude of the precursor effect was not directly assessable on this compound. This was, however, possible on 9-MPh. Indeed, we were able to recover an aliquot of the 9-bromophenanthrene used to synthesize this molecule and measure its carbon isotopic composition: δ13CC14H9Br ) -25.5 ( 0.1‰. Knowing the δ13C of the 9-MPh (-29.9‰), the specific 13C/12C ratio was calculated by difference: δ13C CH3 ) -91.5‰. This δ13C value is actually very consistent with that measured near the end of the demethylation step: at 450 °C/24 h, 59 mg/g methane was generated with δ13C ) -98.4‰, and at 475 °C/24 h, 87 mg/g methane was formed with δ13C ) -80.2‰ (Table 7). Hence, by interpolation, 64 mg/g methane (cf. reaction 4) should correspond to a δ13C value of approximately -95‰. This value is very close to -91.5‰, and this is also in agreement with the fact that the demethylation and hydrogenation steps are slightly overlapping. Following the same logic, it is possible to estimate the isotopic ratio of the methyl group in 1-MPyr. As shown in Table 6, at the end of the demethylation step (i.e., 44-48 mg/g methane generated) a δ13C between -54‰ and -56‰ was measured on methane. Thus, we can reasonably expect δ13C0 ) δ13CCH3 ) -54‰ to -56‰ in the case of 1-MPyr. The variation of the 13C/12C ratio as a function of time and temperature is the result of a kinetic effect, the magnitude of which is determined by the values of ∆E and Ω in eq 16. Because, in a closed system only, the isotopic fractionation between a product of a reaction and the reactant does not remain constant when the severity increases, the kinetic effect should be observed at very low conversion. For instance, for conversions below 10%, the δ13C of methane generated during the pyrolysis of 9-MPh is around -111‰ (Table 7). This average value corresponds to the sum of both precursor and kinetic isotope effects. The contribution of the precursor effect is known: (29.9 - 91.5) ) -61.6‰. Thus the contribution of the kinetic effect should be at least (61.6 + 29.9 - 111) ) -19.5‰, which corresponds to an isotopic fractionation factor (R) of approximately 0.98 at 400 °C. For 1-MPyr, a similar calculation cannot be performed because the experiments start at 75% conversion (Table 6). At constant temperature, both precursor and kinetic effects might compensate each other, especially when the conversion is low. The best way to overcome this problem is to treat the evaluation of δ13C0, ∆E, and Ω like the acquisition of stoichiometric and kinetic parameters (i.e., from the analysis of data obtained at various temperatures and residence times). Considering the number of isotopic data available for each compound, it was not possible to determine specific isotopic parameters for the generation of methane from 9-MPh pyrolysis. Consequently, the model of isotopic fractionation described below was developed and calibrated on the 1-MPyr data only.

Lorant et al.

Isotopic Fractionation Modeling. Although we have assumed in reaction 5a that methane and pyrene are generated at the same rate, these molecules do not exhibit similar isotopic evolutions (Tables 6 and 7). This discrepancy is due to the fact that, regarding elementary processes, methane and pyrene are not formed through the same reaction pathway.45 Actually, each pathway can be related to the evolution of a specific precursor within the reactant (the methyl group for methane, the aromatic rings for pyrene) and is characterized by specific values of the isotopic fractionation factor and δ13C0. Hence, to account for the generation of the 13Clabeled methane, it is necessary to modify the global kinetic scheme by introducing parallel reactions with individual rate constants. Reaction 5a then becomes

where δ13C10 and δ13C20 correspond, respectively, to the isotopic ratios of the methyl group and the aromatic rings within the initial 1-MPyr, and R1 is the apparent isotope fractionation factor between the methane and MPY: R1 ) Ω1 exp(-∆E1/RT) according to eq 16. Note that we neglect the small isotopic fractionation that might occur between MPY and PYR. For reactions 5b and 5c, the initial isotopic composition of all the generated products (i.e., the aromatic ring carbons) should be the same. Hence

One may easily demonstrate the expression of d[13CH4]/ dt compares to that proposed in eq 10:

(

)

d[13CH4] 13 ) x13k1[MPY]0e- k1t + z113k′3[13PYR][H2] dt (18)

with 13k′3 ) R′3k′3 and R′3 ) Ω′3 exp(-∆E′3/RT) (k′3 refers to eq 9). By definition, the isotopic ratio of methane is

[13CH4] [13CH4] ≈ RCH4 ) 12 [CH4] [ CH4]

(19)

Thus, modeling the methane δ13C necessitates solving, simultaneously, eqs 10 and 19. Following the solution proposed in eq 11 for [CH4], the solution of eq 18 at constant temperature can be written:

[13CH4] ) x[13MPY]0(1 - e-

13k t 1

)+

∫

z1 k′3 t[13PYR][H2] dt (20) 13

Then, introducing the interpolation function ψ′(t) for the product [13PYR][H2] such as



4

ψ′(t) ) a′1eb′1t +

a′j(1 - eb′ t) ∑ i)2

(21)

i

T ) 424 °C

where a′i and b′i are fitting coefficients, and replacing [13PYR][H2] by ψ′(t) in eq 20 allows, after integration with respect to t, derivation of an expression of [13CH4] at constant temperature:

[13CH4] ) x[13MPY]0(1 - e- k1t) + 4 a′ a′1 i z113k′3 (eb′1t - 1) + (b′it + 1 - eb′it) b′1 i)2b′i 13

{

}

∑

Table 9. Fitting a′i and b′i Coefficients Used in Eq 23, for Three Temperaturesa

(22)

a′1 b′1 a′2 b′2 a′3 b′3 a′4 b′4

1910.1483 -0.011931 -757.3643 -0.026022 1.9344 0.035223

T ) 450 °C

T ) 471 °C

6823.1245 -0.002235 -1056.7776 -0.609579 1143.8193 -0. 538545

0.7353 -0. 397849 3025.7089 -0.018712 70.2692 -1.348656 1.3930 0. 373258

a These parameters were adjusted on experimental data given in Table 8, using eqs 12 and 21.

In this equation, [13MPY]0 should refer to the initial isotopic composition of the methyl group. Thus, one can write δ13C10 ) {([13MPY]0/[12MPY]0)/Rstd} × 1000, with [12MPY]0 ≈ [MPY]0, and where Rstd is the standard PDB isotopic ratio: Rstd ) 11 237 ppm. The expression giving the δ13C of methane at constant temperature, obtained after dividing eq 22 by eq 11, is then

δ13Cmethane 1000

[ (

+ 1 ) xRstd

{

δ13C10 1000

)

+ 1 (1 - e-R1k1t) +

}]/

4 a′ z1R′3k′3 a′1 i (eb′1t - 1) + (b′it + 1 - eb′it) b′ b′ [MPY]0 1 i)2 i

[

∑

-k1t

x(1 - e

z1k′3

{

a1 )+ (eb1t - 1) + [MPY]0 b1 4 a i (bit + 1 - ebit) b i)2 i

∑

}]

Figure 3. Fitting of the δ13C of pyrene based on the ratio of the two fitting functions ψ′(t) and ψ(t).

F)

(23)

The fitting parameters a′i and b′i in eq 23 are given in Table 9. They were adjusted in order to account for the experimental δ13C values of pyrene reported in Table 8. Due to the low number of data, a precise fitting of the product [13PYR][H2] at each temperature was not possible. The isotopic ratio of pyrene was plotted against the amount of methane, as displayed in Figure 3, and values of a′i and b′i were manually attuned, until the function (ψ′/ψ - 1) × 1000 approximately fits the data. With this set of fitting coefficients, the isotopic composition of methane explicitly depends on five parameters: δ13C10, Ω1, ∆E1 (i.e., R1), Ω′3, and ∆E′3 (i.e., R′3). The value of δ13C20 is implicit: it should actually be accounted for by the relative shift between the coefficients a′i and ai. We also emphasize that eq 20 is restricted to the range of time within which the coefficients ai, bi, a′i, and b′i have been defined, and consequently the values of Ω′3 and ∆E′3 might not have any physical significance. Our aim here was to determine values of Ω1 and ∆E1, which are significant at laboratory temperatures. This operation necessitates correcting the δ13C of methane for the contribution of the hydrogenation reaction on the demethylation step. The five isotopic parameters were calibrated together by numerical optimization. Equation 23 was used to calculate the δ13C of methane at each experimental condition. The obtained values were compared to the measured δ13C by introducing an error function F, defined as

1

N

(δ13Cexpt - δ13Ccalcd )2 ∑ i i 2 i)1

(24)

where N is the total number of measurements. To reduce the number of free parameters, we imposed that Ω1 ) Ω′3 ) Ω. Acceptable final values were defined between 0 and 100 cal/mol for ∆E1 and ∆E′3, and between 0.990 and 1.050 for Ω, following recent calculations of Tang et al. (in press). Moreover, to overcome local minima problems, optimization procedures were run many times with different sets of initial values, except that of δ13C10 which was estimated at -55‰, according to the estimations already performed. The final isotopic parameters obtained after optimization are summarized in Table 10. A comparison between the modeled and the experimental δ13C is depicted in Figure 4. The accuracy of optimized parameters is discussed below. The value of δ13C10 obtained after optimization is consistent with that initially estimated (see previously). This consistency was somewhat expected, since we have already demonstrated that the overlap between the two steps of methane generation is slight. The value of Ω at 1.0241 is in very good agreement with those already suggested for n-alkanes by Tang and Jenden,56 1.021; and by Poliakov,57 1.017. However, it should be emphasized that such values (i.e., higher than 1) have not been yet clearly explained on a theoretical basis. ∆E1 is 43.3 cal/mol, which is close to the 50 cal/mol calculated by Tang and Jenden (1995) for the direct demethylation (56) Tang, Y.; Jenden, P. D. Seventeenth International Meeting on Organic Geochemistry, Donastia-San Sebastian, The Basque Country, Spain, 1995. (57) Poljiakov, V. B. Ph.D. Thesis, Geochemistry and Analytical Chemisty Institute, Russian Academy of Sciences, Moscow, 1996.

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Lorant et al.

Figure 5. Predicted δ13C of methane generated during 1-MPyr thermal cracking in geological conditions, assuming a geothermal gradient at 25 °C/km and a sediment burial at 50 m/My. The different curves correspond to various initial δ13C for the methyl group.

Figure 4. Comparison between experimental and calculated δ13C of methane generated during 1-MPyr thermal cracking. Table 10. Isotopic Parameters Obtained for Methane Generation from 1-MPyr step 1: demethylation ∆E1 δ13C10

step 2: hydrogenation

43.3 cal/mol ∆E′3 -57.5 ‰ Ω ) 1.0241

33.6 cal/mol

of toluene. It is worth noting that these values of ∆E and Ω are also very similar to those characterizing the isotopic composition of methane generated during the pyrolysis of a n-alkane.58 These results would therefore indicate that, regarding the formation of methane by thermal cracking, saturates and aromatics exhibit similar isotope kinetic effects. Differences of methane isotopic signatures during the pyrolysis of these two compounds should mostly be attributed to the precursor effect. Extrapolation to Geologic Conditions. At a temperature above 160 °C (typically in HP/HT reservoirs), methane, originating from secondary cracking, likely comes from aromatics and not from n-alkanes. Assuming that the rate of methane formation during the demethylation process can be modeled by extrapolating reaction 5a to natural conditions, it is possible to predict the isotopic signature for this gas using isotopic parameters reported in Table 10. We also assume that lowtemperature processes are correctly represented by laboratory experiments. (58) Tang, Y.; Perry, J. K.; Jenden, P. D. Geochim. Cosmochim. Acta, in press.

The only unknown that remains to extrapolate our data is the magnitude of the isotopic heterogeneity in natural methylated aromatics. To overcome the problem, we assumed an average initial δ13C for such aromatcics, e.g., δ13CAro ) -28‰, and we calculated the isotopic composition of methane for various values of δ13CCH3 (i.e., δ13C10 in our model). The results are displayed in Figure 5. When δ13CCH3 ≈ δ13CAro, the isotopic composition of the generated methane is not controlled by the precursor effect. Because ∆E1 determined for 1-MPyr is relatively high, the kinetic isotope effect induces a large isotopic shift (approximately -30‰ at 150 °C). Since it is unlikely, for theoretical reasons, that the δ13C of the methyl group is higher than that of the carbon in the aromatic group, the δ13C shift is expected to be larger than when assuming δ13CCH3 ≈ δ13Caro, as seen in Figure 5. At the same maturity level, late methane that originates from mature kerogen is characterized by much lower δ13C values.43,59 Regardless of postgenetic isotopic processes, δ13C of methane below -35‰ in deep reservoirs should, thus, indicate that gas mainly originates from secondary cracking of the aromatics. For example, this process may explain the low value of δ13C measured on methane (around -40‰) in the Elgin Field (North Sea), where secondary cracking of the aromatics actually occurred.38 Conclusions Specific methane formation from methylated aromatics was studied by pyrolyzing, separately, in a closed system, two model compounds: 9-methylphenanthrene and 1-methylpyrene. Since gas generation occurs mainly during secondary cracking of these starting materials,45 the pyrolysis conditions were adjusted in a such a way that conversion was above 75 wt % for the two reactants. Based on experimental data, two global reactions were proposed for gas formation. The first one is a demethylation of the reactants, formation of methylated products such as methyl and dimethyl isomers, and formation of C20+ aromatics. During this step, the main (59) Chung, H. M.; Sackett, W. M. Geochim. Cosmochim. Acta 1979, 43, 1979-1988.


products generated are phenanthrene for the 9-MPh experiments36 and pyrene for the 1-MPyr experiments (this study). Among the gases, methane largely predominates, whereas only a very low yield of ethane is observed and heavier hydrocarbon gases are not generated at all. The second stage of methane generation is related to the opening of a ring in the aromatic structures such as pyrene or phenanthrene. This reaction leads to aromatics with a smaller number of rings than that of the reactant, and formation of methane, ethane, and propane. Rate of Methane Generation. Apparent kinetic parameters for the demethylation process were obtained by a numerical optimization method. The obtained values, E ) 55.6 kcal/mol and A ) 4.2 × 1012 s-1, are in the same range as those found for methane generated from 9-methylphenanthrene in ref 36. Hence, it is likely that such aromatic structures largely contribute to the volumes of methane found in reservoirs with temperature lower than 200 °C, where the gas wetness is generally low. Note that the amounts of methane originating from cracking of the methylated aromatics are actually in the same range as that expected from kerogen cracking during metagenesis.30,43 Also, our study shows that, below 200 °C, light aromatics (C15-) may be generated. Consequently, the ratio C15+ saturates/ aromatics is expected to increase with maturity as well as the ratio C15-/C15+ aromatics. To model the cracking of methylated aromatics, we have made assumptions, which are not supported by theoretical aspects of thermal cracking kinetics. Nevertheless, the conclusions of this study are in good agreement with observations done on natural systems,38 and tend to validate the global approach developed in this paper. Methane Isotopic Composition. Apparent isotopic parameters specific to the demethylation process were also determined by a numerical optimization. The kinetic isotope effect is characterized by ∆E and Ω values (i.e., 43.3 cal/mol and 1.0241) similar to those observed for the formation of methane by pyrolyzing n-alkanes. Our study shows that an important parameter, specific to aromatic structures, that controls the isotopic composition of methane is the isotopic heterogeneity of the reactant (i.e., the precursor effect). Calculations indicate that methane generated within the oil window by secondary cracking of the aromatics might exhibit very low δ13C values, below -60‰ at 150-160 °C. These values differ significantly from methane generated from mature kerogens, which constitutes another important source of gas in this range of maturity. Thus, an important result of this work is to show that specific methane isotopic signatures lighter


than -35‰ might fingerprint the secondary cracking of aromatics in HP/HT reservoirs. Acknowledgment. Caroline Sulzer is gratefully acknowledged for the quantification and the isotopic characterization of methane and aromatic compounds by GC and GC-C-IRMS. We thank also T. Lesage for the preparation of gold vessels and drawing of some figures. Appendix: Guggenheim Plot Guggenheim60 proposed a method that allows the rate constant k of a first-order reaction to be determined, when only the generation curve of a product is partly known. Suppose a series of experiments has been performed at constant temperature, and quantities, Q, of a product have been measured at various times separated by a constant interval ∆:

amount ) Q0 Q1 Q2 ... Qn time ) t0 t0 + ∆ t0 + 2∆ ... t0 + n∆ Since the reaction is first-order with respect to the reactant, the amounts Q and Q′ generated at times t and t + ∆, respectively, are given by

Q ) Qmax(1 - e-kt) Q′ ) Qmax(1 - e-k(t+∆)) ) Q′ ) Q∞(1 - e-kte-k∆) where Qmax is the infinitive value (i.e., the maximum amount of product that can be generated through this reaction). Subtracting Q from Q′ leads

Q′ - Q ) Qmax(e-kte-k∆-e-kt) ) Qmaxe-kt(e-k∆ - 1) Hence

ln(Q′ - Q) ) ln(Qmax(e-k∆ - 1)) - kt Since Qmax and ∆ are constants, a plot of ln(Q′ - Q) versus time should display a straight line, the slope of which gives k. Moreover, the intercept on the y-axis allows determination of Qmax. An additional and very useful feature of this method is that any linear correlation in such a plot indicates the reaction is first-order. EF990258E (60) Guggenheim, E. A. Philos. Mag. 1926, 2, 538.

Methane Generation from Methylated Aromatics: Kinetic Study and

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