Reaction Kinetics of Stable Carbon Isotopes in Natural Gas

Energy & Fuels 2001, 15, 517-532

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Reaction Kinetics of Stable Carbon Isotopes in Natural GassInsights from Dry, Open System Pyrolysis Experiments Bernhard Cramer,*,† Eckhard Faber,† Peter Gerling,† and Bernhard M. Krooss‡,§ Federal Institute for Geosciences and Natural Resources (BGR), Stilleweg 2, 30655 Hannover, Germany, and Institute of Petroleum and Organic Geochemistry, Forschungszentrum Juelich GmbH, D-52425 Juelich, Germany Received April 25, 2000. Revised Manuscript Received February 1, 2001

Open system nonisothermal pyrolysis with on-line compound-specific 13C/12C stable-isotope analysis (Py-GC/IRMS) has been performed on three carbonaceous sediments from NW Germany (Carboniferous, Westphalian coal, HI ) 286 mgHC/gTOC, Ro ) 0.72%), West Siberia (Cretaceous, Cenomanian shale, HI ) 192 mgHC/gTOC, Ro ) 0.43%), and Malaysia (Tertiary, Miocene coal, HI ) 190 mgHC/gTOC, Ro ) 0.36%). The study was focused on the generation of methane, ethane, and propane + propene. Measured δ13C-values of pyrolytically generated light hydrocarbons were in the range of δ13C-values commonly observed in thermogenic natural gas (-20 to - 40‰, PDB). While the isotopic composition of the pyrolysis products showed a general enrichment in 13Cspecies with increasing temperature, the isotopic trends of methane displayed characteristic structures involving reversals in certain temperature intervals. On the basis of the experimental data, reaction kinetic parameters have been derived for each isotopic species of the hydrocarbon gases assuming parallel first-order reactions and an Arrhenius-type temperature dependence. The resulting kinetic parameter sets for the Westphalian coal were then tentatively applied to geologic temperature histories to model the chemical and isotopic composition of natural gas generated and accumulated in reservoirs of the NW German Basin. The isotopic compositions (δ13C-values) of methane computed in this simulation show a good agreement with actual isotopic compositions of the natural gases in NW German gas fields. It is demonstrated that the combination of isotope-specific reaction kinetics with the regional thermal history provides a useful tool to account for variations in the isotopic composition of reservoir gases in the course of the accumulation history. These results indicate that, despite the undisputed differences between laboratory and natural conditions for gas generation, open system nonisothermal pyrolysis provides isotope-specific reaction kinetic parameters that satisfactorily describe the isotope effects associated with thermogenic natural gas generation in geologic systems. Application of these parameters in basin modeling studies permits prediction/reconstruction of isotopic compositions of natural gases with the same level of confidence as commonly applied bulk and compound-specific kinetic parameters.

1. Introduction It is widely accepted, that most of the natural gas is generated by thermal degradation of sedimentary organic matter. Nevertheless, because of the complex structure of kerogen, it is not well understood which reactions proceed during thermal gas generation. Gas generating reactions during dry rock-pyrolysis experiments in an open system are irreversible.1 In consequence, a chemical reaction kinetic approach was used to describe the generation dynamics of natural gas * Author to whom correspondence should be addressed. E-mail: [email protected]. † Federal Institute for Geosciences and Natural Resources (BGR). ‡ Institute of Petroleum and Organic Geochemistry, Forschungszentrum Juelich GmbH. § Present address: Institute of Geology and Geochemistry of Petroleum and Coal, Aachen University of Technology, Lochnerstr. 4-20, 52056 Aachen, Germany. (1) Hanbaba, P.; Ju¨ntgen, H. Adv. Org. Geochem. 1969, 1968, 459471.

components during artificial heating.2-4 This early work was mostly focused on gas generation from coal. According to this approach more recent studies developed kinetic models of petroleum generation.5-7 Here it was assumed that petroleum generates from kerogen as a result of a series of reactions, breaking bonds within the kerogen structure. To model these generation reactions of individual gas components, first-order reaction kinetics was proved useful.8 Whereas higher and noninteger reaction orders in many cases are believed to (2) Kro¨ger, C.; Bru¨cker, R. Brennstoff-Chemie 1961, 42 (10), 305311. (3) van Heek, K. H.; Ju¨ntgen, H.; Peters, W. Brennstoff-Chemie 1967, 48, 163-194. (4) van Heek, K. H.; Ju¨ntgen, H. Ber. Bunsen-Ges. Phys. Chem. 1968, 72, 1223-1231. (5) Tissot, B.; Espitalie, J. Rev. de l’Inst. Francais du Petrole 1975, 30 (5), 743-777. (6) Braun, R. L.; Burnham, A. K. Energy Fuels 1987, 1, 153-161. (7) Ungerer, P.; Pelet, R. Nature 1987, 327, 52-54. (8) Hanbaba, P.; Ju¨ntgen, H.; Peters, H. Brennstoff-Chemie 1968, 49 (12), 368-376.

10.1021/ef000086h CCC: $20.00 © 2001 American Chemical Society Published on Web 03/20/2001

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be more plausible and were also successfully used to describe petroleum generation,6,9 there is no serious way to derive the real reaction order from petroleum generation studies. Particularly, it is difficult to distinguish between nth-order models and distributed activation energy models.10 For a first-order reaction the temperature dependence of the rate coefficient (k(T)) is commonly expressed by the semiempirical Arrhenius equation:

( )

k(T) ) A exp -

Ea RT

(1)

Here Ea is the activation energy (in J/mol), T the temperature (in K), and R the gas constant (J/mol/K). The preexponential factor A (1/s) is also denoted as “frequency factor”. It should be recognized that eq 1 is empirical with only qualitative justification. According to the transition state theory the preexponential factor depends on temperature which is in contrast to eq 1. However, for practical use it was shown that the Arrhenius equation can be considered an adequate approximation over the entire temperature range of petroleum formation in nature and in laboratory studies.11 The stable carbon isotope ratios of individual light hydrocarbon components such as methane, ethane, propane, and carbon dioxide are the most important parameters to classify natural gas with respect to its generation process and its post-genetic history.12,13 The knowledge that thermally generated gas components such as methane, ethane, and propane are getting isotopically heavier with increasing maturity of the source rock led to the development of empirical relationships between the δ13C of the gas and the maturity of the source rock, expressed as vitrinite reflectance equivalent.14-16 Although they were not based on a fundamental understanding of the processes effecting isotope fractionation during gas generation, these empirical maturity indications of natural gas found wide application in gas exploration. In the past, attempts to mathematically describe isotope fractionation during thermal gas generation were mainly based on two approaches. Assuming thermodynamic equilibrium, isotope distribution functions (β-factors) were used.17,18 Because most researchers nowadays feel that gas generation and associated isotope fractionation depend on both time and temperature, this thermodynamic model is not widely accepted. The second approach used Rayleigh distillation equations19 to model isotope distribution between gas and precursor material as function of the progress of the gas (9) Ju¨ntgen, H. Erdo¨ l und Kohle, Erdgas, Petrochemie 1964, 17 (3), 180-186. (10) Burnham, A. K.; Braun, R. L. Energy Fuels 1999, 13 (1), 1-22. (11) Waples, D. W. Org. Geochem. 2000, 31, 553-575. (12) Schoell, M. Chem. Geol. 1988, 71, 1-10. (13) Whiticar, M. J. AAPG Mem. 1994, 60, pp 261-283. (14) Stahl, W. J.; Carey, B. D. J. Chem. Geol. 1975, 16, 257-267. (15) Ping, S.; Qixiang, S.; Xianbin, W.; Yongchang, X. Sci. Sin. 1988, 31, 734-747. (16) Faber, E. Erdo¨ l Erdgas Kohle Z. 1987, 103 (5), 210-218. (17) Galimov, E. M.; Ivlev, A. A. Russ. J. Phys. Chem. 1973, 47, 1564-1566. (18) James, A. T. AAPG Bull. 1983, 67 (7), 1176-1191. (19) Rayleigh, R. S. The London, Edinburgh, and Dublin Philos. Mag. 1896, 42, 493-498.

generating reaction.20-23 In general, these models apply one single first-order reaction to calculate gas generation from kerogen with a temperature-independent isotope fractionation factor. Early it was shown that gas generation from coal can be described more appropriately by a distribution of activation energies rather than by one single reaction.9 In accordance, Galimov24 pointed out that modeling of isotope fractionation with one single gas generating reaction results in unrealistic isotope ratios of the gas component. Consequently, he applied individual Rayleigh equations to a set of gas generating reactions.25 Smith et al.26 proposed that the chemical kinetic effect of slightly different rates in a given reaction would lead to the observed isotope ratios in hydrocarbons. They introduced a mathematical model explaining the range in stable carbon isotope ratios of methane through pentane depending on the isotope signature of hydrocarbon precursors and the ratio of rate constants of the individual isotope species. The ratio of rate constants was assumed to be insensitive to temperature. Stable carbon isotope ratios of pyrolytically derived gas components from kerogen have been measured in many laboratory studies.27-34 Whereas Andresen et al.32 highlighted the differences between isotope ratios of gas from laboratory experiments and naturally occurring gas, Berner et al.21 successfully modeled measured δ13Cvalues of pyrolytically derived methane, ethane, and propane with Rayleigh equations. For the geological application, polynomial functions were fitted through the data and an applicable gas genetic interpretation tool was developed.35 Recently researchers have started to combine the widely accepted reaction kinetic concept to describe gas generation with the experience of genetic classification of natural gas using stable isotope ratios. Tang and Jenden36 conducted quantum mechanical calculations to quantify isotope fractionation during natural gas generation for a large number of possible reactions. They presented a general prediction scheme of δ13C(20) Clayton, C. Mar. Petrol. Geol. 1991, 8, 232-240. (21) Berner, U.; Faber, E.; Scheeder, G.; Panten, D. Chem. Geol. 1995, 126, 233-245. (22) Berner, U.; Faber, E.; Stahl, W. Chem. Geol. 1992, 94, 315319. (23) Rooney, M. A.; Claypool, G. E.; Chung, H. M. Chem. Geol. 1995, 126, 219-232. (24) Galimov, E. M. Zh. Fizich. Khim. 1974, 48 (6), 811-814. (25) Galimov, E. M. Chem. Geol. 1988, 71, 77-95. (26) Smith, J. E.; Erdman, J. G.; Morris, D. A. 8th World Petrol. Congr. 1971, 13-26. (27) Friedrich, H.-U.; Ju¨ntgen, H. Erdo¨ l und Kohle - Erdgas Petrochemie vereinigt mit Brennstoff-Chemie 1973, 26 (11), 636-639. (28) Rohrback, B. G.; Peters, K. E.; Kaplan, I. R. AAPG Bull. 1984, 68 (8), 961-970. (29) Gaveau, B.; Letolle, R.; Monthioux, M. Fuel 1987, 66, 228231. (30) Mycke, B.; Hall, K.; Leplat, P. Org. Geochem. 1994, 21 (6-7), 787-800. (31) Andresen, B.; Barth, T.; Irwin, H. Chem. Geol. 1993, 106, 103119. (32) Andresen, B.; Throndsen, T.; Roeheim, A.; Bolstad, J. Chem. Geol. 1995, 126, 261-280. (33) Lorant, F.; Prinzhofer, A.; Behar, F.; Huc, A.-Y. Chem. Geol. 1998, 147, 249-264. (34) Cramer, B.; Krooss, B. M.; Littke, R. Chem. Geol. 1998, 149, 235-250. (35) Berner, U.; Faber, E. Org. Geochem. 1996, 24 (10-11), 947955. (36) Tang, Y.; Jenden, P. D. Organic geochemistry: developments and applications to energy, climate, environment and human history; Grimalt J. O., Dorronso, C., Eds.; Donosta: San Sebastian, 1995; pp 1067-1069.

Reaction Kinetics of Carbon Isotopes in Natural Gas

Energy & Fuels, Vol. 15, No. 3, 2001 519

values of methane in thermally generated natural gas. Lorant et al.33 used a kinetic isotope effect (KIE) to model isotope fractionation in a complex reaction scheme for hydrocarbon generation from kerogen. Doing so they were able to describe the δ13C-values of gas components which were derived from closed-system pyrolysis. However, due to the fact that the KIE they applied was independent of temperature they were not able to predict δ13C-values under geological conditions. Cramer et al.34 modeled methane generation from coal with a gross kinetic approach by assuming a set of parallel first-order pseudo-reactions with a common preexponential factor.37 Associated isotope fractionation was described by applying a kinetic isotope effect for the entire set of reactions. The KIE can be defined as the ratio of the rate coefficients (eq 1) of the light to the heavy isotope species:

KIE(T) )

k12C (T) k13C (T)

)

(

)

(Ea12C - Ea13C) A12C ‚ exp A13C RT

(2)

Assuming equal preexponential factors (A12C/A13C ) 1), ∆Ea-values (Ea12C - Ea13C) of -102 and -103 J/mol were calculated for stable carbon isotope fractionation during primary methane generation from two Siberian coals.34 As with gas generation, this reaction kinetic approach allows the extrapolation of δ13C-values measured during laboratory pyrolysis experiments to geological heating rates. So, isotope ratios of thermally generated gas components can be predicted. In a collaborative effort between BGR and Forschungszentrum Juelich an open system, nonisothermal pyrolysis unit was designed on the basis of an existing experimental setup.38 This unit was coupled on-line with a gas chromatograph and an isotope ratio mass spectrometer (PY-GC-IRMS), thus permitting to measure the generation and the isotope ratios of pyrolytically generated methane, ethane, and propane + propene at different heating rates with high time resolution. In this study PY-GC-IRMS experiments were performed on three different early-mature coals. On the basis of these measurements an improved reaction kinetic model of isotope fractionation during gas generation was developed. By applying this isotope model to real gas field data, the value of the new approach in reconstructing individual accumulation histories will be demonstrated. 2. Experimental Section The PY-GC-IRMS equipment consists of an open system pyrolysis furnace, a gas chromatographic unit, an isotope ratio mass spectrometer, as well as of a computerized remote control and data sampling unit. For rock pyrolysis, an open system pyrolysis unit designed for dry, nonisothermal experiments at variable heating rates was used. Powdered aliquots of 100-300 mg rock were placed in a quartz glass reactor which was permanently flushed with 20 mL/min helium as carrier gas. The reactor was heated in a horizontal single zone furnace. It was equipped with an internal metal coat to homogenize the temperature field around the rock material. Based on NiCr-Ni thermocouples within the metal coat and directly dipping into the sample, (37) Schaefer, R. G.; Schenk, H. J.; Hardelauf, H.; Harms, R. Org. Geochem. 1990, 16 (1-3), 115-120. (38) Schaefer, R. G.; Galushkin, Y.; Kolloff, A.; Littke, R. Chem. Geol. 1999, 156, 41-65.

the accuracy of the temperature measurement resulted in an error of about (2 °C.38 Gas from the pyrolysis reactor was sampled by switching the continuously flushed sampling loop of 2 mL volume into the GC. Three packed columns enabled the chromatographic separation of methane, ethane, ethene, propane + propene, carbon monoxide, and carbon dioxide. First, CO2 was isolated on a Porapack Q column and hydrocarbons heavier than propane were retarded. On a second column filled with HayeSep D, C2 and C3 hydrocarbons were separated. Highermolecular-weight hydrocarbons were eliminated from the separation process via back-flush on the Porapack Q column. Methane and CO left the HayeSep D column together and were passed onto a molecular sieve 13 Å column with a separate carrier gas supply for further separation. After leaving the HayeSep D column, ethene and ethane were flushed directly into the mass spectrometer unit. Meantime methane and CO were separated on the molecular sieve column and were transferred to the IRMS after ethane had passed through. All GC separations were conducted isothermally at 40 °C. In the last step of the procedure the GC was rapidly heated to 150 °C. Doing so, the elution of propane + propene was accelerated and contaminants on the first column were flushed back efficiently. Propane and propene were not separated well enough for integration and isotope ratio calculations. Therefore, both peaks were combined to one component which is referred to as propane + propene or C3H6/8. The duration of a chromatographic run was 20 min. According to the GC method described above the gas components entered the mass spectrometer system in the order carbon dioxide, ethene, ethane, methane, carbon monoxide, and propane + propene. Except for CO2, all gas species were oxidized at a temperature of about 1050 °C in a CuO combustion interface. After removal of the combustion water in a phase separator, all peaks entered the mass spectrometer (Finnigan MAT 252®) instrument for stable carbon isotope analysis. The measured data were referred to an in-house δ13C standard (500 vpm methane, 500 vpm ethane, and 500 vpm propane in helium) which usually was injected every four measurements. Then the data were corrected for 18O and normalized to PDB standard applying the usual notation:

δ13C )

(

)

R - 1 1000 Rstd

(3)

Here, R is the isotope ratio of the sample and Rstd the isotope ratio of the standard. Quantification of the gas components was achieved by summing up the integrated areas of the 12Cand the 13C-peak. Components of gas samples were calibrated to the three standard peaks with corresponding carbon numbers (methane, CO, and CO2 calibrated with methane, ethane, and ethene with ethane, and propane + propene with propane). Because ethene, CO, and CO2 were not related to a component specific standard they were not taken into account for further interpretation. An example of the generation and the δ13C-values of the detected gas components during one experiment is shown in Figure 1. Aliquots of each coal were pyrolyzed at three different heating rates 0.2, 0.7 or 1.0, and 2.0 K/min. A repeat run at 2.0 K/min was performed for each coal without measuring C3H6/8 to check the reproducibility of the analytical technique and to increase the number of data points for the highest heating rate. Figure 2 comprises the δ13C-values of methane from all duplicate experiments. Whereas for coal A both measurements result in almost identical trends, coals B and C show at low and at very high temperatures some small deviations of up to 1‰. These deviations might be contributed to the larger error in δ13C-measurement of small volumes of gas at the beginning and at the end of gas generation.

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Coal C. The youngest and most immature coal (Ro ) 0.36%) was taken from a brown coal mining area in the Sarawak district, Malaysia, from the Merit coal formation (or Nyalau formation) of Lower to Middle Miocene age. It was deposited in a freshwater environment,41 explaining its low sulfur content (Table 1). 4. Results

Figure 1. Concentrations in parts per million of volume of the pyrolysis gas (vpm) and δ13C-values of individual gas components during an open system pyrolysis of coal A with a linear heating rate of 0.2 K/min as function of temperature T in degrees centigrade (°C). Please note, CO and CO2 are not calibrated specifically (see text).

Figure 2. Reproducibility of the PY-GC-IRMS measurements. Experiments with heating rates of 2 K/min were repeated for each coal.

3. Coal Samples Three coal samples were selected for this study, representing different geographic as well as stratigraphic settings. The geochemical characteristics of these coal samples are summarized in Table 1. Coal A. The oldest coal (Paleozoic) originated from the Ruhr basin, NW Germany, from the Westphalian C. With a vitrinite reflectance of 0.72%, coal A has the highest maturity level in this sample set and the highest carbon content (76.9%). Detailed organic geochemistry exists for this coal.39 Coal B. This Mesozoic coal (Ro ) 0.43%) was cored at 1450 m depth, about 200 km east of the largest gas field on Earth, the Urengoy field in West Siberia, and is the youngest unit of Cenomanian age of the terrestrial Pokur formation.40 (39) Gerling, P.; Mittag-Brendel, E.; Sohns, E.; Faber, E.; Wehner, H. BGR-Report 1995, No. 112440. (40) Cramer, B.; Poelchau, H. S.; Gerling, P.; Lopatin, N. V.; Littke, R. Mar. Petrol. Geol. 1999, 16, 225-244.

4.1. Changes in Chemical Composition of Coal. The measured vitrinite reflectance of the coals during all experiments increased by about 5 to 6% Ro (Table 1). Because of the thermal cleavage of the volatile components, H, O, and S contents of the organic matter decreased. The apparent increase in C content reflects the loss of volatile components containing other elements, with the remaining kerogen beeing relatively enriched in C. The δ13C of the organic matter increased slightly during the experiments (Table 1). 4.2. Gas Generation and δ13C-Values. The overall appearance of the gas generation curves was very similar for the three coal samples in all experiments (Figure 3). Methane was the dominate hydrocarbon species and was generated over a wide temperature range. The generation of hydrocarbons other than methane was limited to temperatures up to 600 °C. Methane. The highest peak generation rate was observed for methane from coal A (242 µg/gTOC/K) followed by methane from coal B and coal C (Figure 3). Apart from differences in the absolute generation rates, the methane generation patterns for the three coals are very similar. The temperatures of maximum methane generation (Tmax-values) for heating of 0.2 K/min range between 426 °C for coal C and 447 °C for coal A (Figure 3). At first glance, δ13C-trends of methane do not appear to be closely related to the methane generation curves (Figure 3). While methane from coal C displays a local δ13C-maximum at temperatures just above 300 °C with about -29‰, the δ13C-values of methane from the other coal samples start with values of about -30 to -32‰, and decrease with increasing temperature to a minimum value around -34 to -35‰ at 395 °C. Above 395 °C, δ13C-values of methane from all coal samples continuously increase during the largest part of the generation interval (Figure 3). Whereas methane from coals A and B shows an almost identical increase, the δ13C-trend of methane from coal C is less steep. The maximum in δ13C of methane from all samples at about 550 °C has the lowest δ13C-value for coal C (-25‰). With rising temperature the δ13C again decreases by up to 10‰. Between 600 and 700 °C the δ13C of methane from all three samples reflects a second minimum (Figure 3). Ethane. Ethane generation mainly proceeds within the temperature interval from 300 to 500 °C (0.2 K/min). The differential generation curve (Figure 3) is almost symmetrical with Tmax-values ranging between 394 °C (coal C) and 407 °C (coal A) and maximum generation rates of 33 (coal C) to 88 µg/gTOC/K (coal A). With increasing temperature, δ13C increases from about -30‰ for coal A and about -35‰ for coals B and C up (41) Liaw, K. K. Ph.D. Thesis, Technische Hochschule, Karlsruhe, Germany, 1994.



Table 1. Geochemical Characteristics of the Three Pyrolyzed Coals before and after the Pyrolysis Experimentsa coal A

coal B

coal C

original 0.2 K/min 0.7 K/min 2 K/min 1 2 K/min 2 original 0.2 K/min 1.0 K/min 2 K/min I 2 K/min II original 0.2 K/min 0.7 K/min 2 K/min I 2 K/min II

Ro (%)

TOC (%)

δ13C (‰)

Tmax (°C)

HI (mgHC/gTOC)

H/C

O/C

N/C

S/C

0.72 6.68 6.27 6.33 6.72 0.43 6.22 5.88 6.00 5.72 0.36 4.99 5.18 5.34 5.18

76.9

-24.6 -24 -24

431

286

0.84

0.15

0.016

0.012

0.16

0.05

0.015

0.008

1.00

0.21

0.014

0.005

0.17

0.04

0.016

0.003

1.31

0.50

0.013

0.004

0.16

0.05

0.010

0.000

83 69.3 84.2 47.8 58.9

-24 -25.5 -24 -23.9 -24.1 -28.5 -28.4 -28.3 -28.3

424

401

192

190

a R is the measured vitrinite reflectance. TOC is the total content of organic carbon and δ13C reflects the standardized stable carbon o isotope ratio of bulk organic carbon. The hydrogen index HI and the temperature of maximum hydrocarbon generation Tmax were determined with the Rock-Eval Pyrolysis Method. H/C, O/C, N/C, and S/C are the molecular ratios of hydrogen, oxygen, nitrogen, sulfur, and carbon.

Figure 3. δ13C and generation rate of methane, ethane, and propane + propene from the three coals for the experiments with 0.2 K/min heating. Please note, methane has another temperature scale than the other components. The scale for the generation rate is different for each gas.

to values of -18‰ for coals A and B and about -25‰ for coal C (Figure 3). At temperatures above 450 °C where ethane generation is already in its final stage, δ13C-trends of ethane from coals A and B show inflections. Propane + Propene. Generation of propane + propene is restricted to a narrower temperature range than ethane (300 to 475 °C at 0.2 K/min). With maximum generation rates of 41 (coal C) to 110 µg/gTOC/K (coal B), Tmax-values for 0.2 K/min range between 377 and 405 °C. δ13C-values of propane + propene from all samples increase with increasing temperature during the entire experiment over a range of about 12‰ (Figure 3). In comparison with ethane, propane + propene are isotopically about 2 to 4‰ heavier. 4.3. δ13C of Methane from the Pokur Formation. The rock sample from the West Siberian Pokur formation coal B is identical to sample “Pk2” of Cramer et al.34 and to “E41903” of Schaefer et al.38 Both cited investigations conducted nonisothermal dry open system laboratory pyrolysis studies with this coal. Whereas methane generation is almost identical in all studies, stable carbon isotope ratios of methane measured off(42) Littke, R.; Cramer, B.; Gerling, P.; Lopatin, N. V.; Poelchau, H. S.; Schaefer, R. G.; Welte, D. H. AAPG Bull. 1999, 83 (10), 16421665.

line34 and the on-line measured data presented here differ significantly. The data sets display almost parallel trends with an offset in δ13C of about 3 to 4‰ with isotopically lighter methane in the off-line data. During on-line pyrolysis presented here calibration with a standard gas was performed every four measurements and duplicates of experiments show good reproducibility (Figure 2). In contrast, mass spectrometric measurements for the off-line study34 were performed by a commercial laboratory and a quality control was not possible after recognizing the difference in isotope data. One major advantage of on-line pyrolysis measurements is that the standard gas takes the same way through the analytical device as the sample gas. In contrast, different analytical treatment of samples and standards during off-line experiments as well as complex handling of the gas samples from pyrolysis until combustion involve many possible error sources. In conclusion, we are confident of the quality of our online isotope data presented here. Methane in gas fields of West Siberia is characterized by δ13C-values of -51‰ in average.42 Based on the isotopic data available at that time Cramer et al.34 supposed that at least certain amounts of the isotopically light methane within the reservoirs might have been generated from the early-mature coal of the Pokur formation. In light of our new results, with early generated methane being isotopically much heavier (Figure 3), methane from the gas fields can no longer be attributed to an early in-situ generation from the coal of the Pokur formation. It was proposed that the gas migrated laterally over long distances dissolved in groundwater until it was released and accumulated in the recent fields.40 In consequence, the source of the gas must be located several hundred kilometers apart of the recent fields. Potential geochemical and isotopic fractionation processes associated with this migrational transport make it difficult to decipher the real, primary generation process of the accumulated methane in West Siberia. 4.4. The Effect of Heating Rate on the δ13C of the Gas. By conducting different pyrolysis experiments with one coal it was possible to investigate the effect of heating rate on the δ13C of individual hydrocarbon components. As an example Figure 4 shows the δ13C of

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Figure 4. δ13C-values of methane from coal A for three heating rates. Data from both experiments with 2.0 K/min heating are combined for better resolution. For comparison, dashed lines display the differential generation curves of methane.

methane from coal A at heating rates between 0.2 and 2.0 K/min compared to the associated differential generation curves. As expected, with increasing heating rate methane generation shifts to higher temperature. Tmax-values increase from 447 °C (0.2 K/min) to about 515 °C (2 K/min). In addition, the maximum generation rate decreases and the generation peak extends over a wider temperature range. Interestingly, the δ13C-trends of methane from the different experiments are very similar. Together with methane generation they are just shifted with increasing heating rate toward higher temperatures. Comparing the local maximum of the δ13C-trends, around 550 to 600 °C a stochastic scatter in the highest δ13C of 0.6‰ is observed. The scatter in the local δ13C-minimum around 380 °C is even smaller (0.2‰). Except for experiments where δ13C-values at the real isotope extrema were not measured, the scatter in δ13C of methane with heating rate is within the range of 1‰. So, a relevant heating-rate dependence of the isotope trends was not detected. Also isotope trends of ethane and propane + propene do not change significantly with heating rate. 4.5. Mass and Isotope Balance. In the case of exhausted hydrocarbon generating reactions at the end of a pyrolysis experiment, the realized generation potential of the generated gas components f0 (mgHC/gTOC) (the cumulative yield) can be approximated from the s measured data by adding up all generation rates r (mgHC/gTOC/K):

and between 3.6 and 8.3 mg/gTOC for propane + propene these are in good agreement with published generation potentials of these hydrocarbons derived from similar pyrolysis experiments on coal.38,43,44 On a mass basis the generation potential of CH4 from all three coal samples amounts to about 2.5 times the sum of the generation potentials of C2H6 and C3H6/8. Coal A exhibits the highest generation potentials for the detected hydrocarbons (e.g., 37 mg/gTOC of CH4). Whereas the potentials of coal B are slightly smaller, coal C shows much less potential for light hydrocarbon generation (Table 2). For example, methane generation of coal C reaches only about 50% of the potential of coal A (Table 2). The reproducibility of the realized generation potentials relies on analytical precision and on the uncertainties in the discrete way of its calculation (eqs 4,5). It can be checked by comparing different experiments of one sample. In Table 2 the standard deviations of generation potentials are given in percent related to the average value. The largest scatter is observed for ethane from coal A where the standard deviation of four experiments reaches 7.1%. With an average standard deviation of 4.5% the generation potentials are rated as reproducible. Coal samples A and B show no trend in the cumulative yield of C1 to C3 hydrocarbons with heating rate. The slight increases of the generation potentials of the detected hydrocarbon components from coal C with increasing heating rate (Table 2) are within the range of scatter of generation potentials from the other coal samples. The isotope trends in Figure 3 show that the δ13Cvalues increase at a given temperature with increasing C-number of the hydrocarbon component (δ13CH4 < δ13C2H6 < δ13C3H6/8). According to the calculation of the realized generation potential (eqs 4,5), and considering the restrictions given there, it is also possible to compute the stable carbon isotope ratios of the hydrocarbon precursors within the kerogen at the beginning of the pyrolysis experiment.34 This initial isotope ratio of the precursor R0prec can be expressed as ratio of the finally realized generation potentials of the generated 13C-gas species 13f0 to the generated 12C-gas species 12f0. Because isotope ratios are not based on mass but on the number of molecules these generation potentials have to be multiplied by the molar mass of the respective isotopic hydrocarbon species (MH13C,MH12C):

s

f0 =

∑ rq ∆Tq q)1

(4)

Here the representative temperature range ∆T in Kelvin can be taken from

∆Tq )

Tq+1 - Tq-1 2

(q ) 1...s)

(5)

With increasing number of measurements during one experiment, also the reliability of this approximation increases. So, it is crucial to realize a high T-tresolution during the pyrolysis experiments. In Table 2 the realized generation potentials of the three hydrocarbon components investigated are summarized. With values between 18.8 and 38.6 mg/gTOC for methane, between 2.7 and 8.4 mg/gTOC for ethane,

13

R0prec = 12

f0‚MH13C

f0‚MH12C

(6)

Table 2 lists the δ13C0prec-values (standardized according to eq 3) of the initial precursors from all experiments calculated with eq 6. These values show no obvious variation with heating rate. Standard deviations of δ13C0prec-values of methane and ethane vary between 0.2 and 0.5‰ which is within the range of analytical error. With up to 2.3‰ deviations for propane + propene are higher. This is due to the smaller number of δ13Cmeasurements in the narrower temperature interval of (43) Littke, R.; Krooss, B.; Idiz, E.; Frielingsdorf, J. AAPG Bull. 1995, 79 (3), 410-430. (44) Krooss, B.; Littke, R.; Mu¨ller, B.; Frielingsdorf, J.; Schwochau, K.; Idiz, E. F.; Chem. Geol. 1995, 126, 291-318.



Table 2. Total Realized Generation Potential f0 (cumulative yield) and Cumulative δ13C-values of Hydrocarbons δ13c0prec from All Pyrolysis Experiments (eqs 3 and 6)a CH4 coal A

coal B

coal C

a

0.2 K/min 0.7 K/min 2.0 K/min I 2.0 K/min II average std. deviation 0.2 K/min 0.7 K/min 2.0 K/min I 2.0 K/min II average std. deviation 0.2 K/min 0.7 K/min 2.0 K/min I 2.0 K/min II average std. deviation

C2H6

C3H6/8

f0 (mg/gTOC)

δ13C0prec (‰)

f0 (mg/gTOC)

δ13C0prec (‰)

37.0 38.6 38.4 33.8 37.0 6.0% 33.9 36.3 35.7 34.9 35.2 3.0% 18.8 19.7 20.2 21.0 19.9 4.6%

-27.0 -26.8 -26.8 -26.5 -26.8 0.2 -28.0 -27.5 -27.6 -26.9 -27.5 0.4 -30.8 -30.5 -30.6 -29.8 -30.4 0.4

7.9 8.4 8.4 7.2 8.0 7.1% 6.6 7.3 6.9 6.9 6.9 4.1% 2.7 2.9 3.0 3.1 2.9 5.8%

-23.3 -22.8 -23.0 -23.8 -23.2 0.5 -24.3 -23.5 -23.7 -23.2 -23.7 0.4 -28.8 -28.4 -29.0 -28.1 -28.6 0.4

f0 (mg/gTOC)

δ13C0prec (‰)

7.1 7.4 7.2

-22.4 -22.1 -23.3

7.3 1.9% 7.6 8.3 7.7

-22.6 0.6 -23.3 -23.0 -22.0

7.9 4.8% 3.6 3.7 3.9

-22.8 0.7 -28.2 -26.0 -23.6

3.7 3.2%

-25.9 2.3

Standard deviations of the generation potential are given in percent related to the absolute average value.

C3H6/8 generation as well as lower concentrations of these components. In Figure 5 the average δ13C0prec-values of the three hydrocarbon components are compared with the δ13C of bulk organic matter. As indicated by the δ13C trends (Figure 3) the initial hydrocarbon precursors get depleted in 12C with increasing carbon number of the generated hydrocarbon. Whereas differences in average δ13C0prec-values between methane and propane + propene for all coal samples are very similar (∆δ13C0prec 4.5‰) the difference between methane and ethane for coal C is about 1.5‰ smaller compared to coals A and B. In comparison with the δ13C of bulk organic matter initial methane precursors in all coal samples are enriched in 12C by about 2‰ (Figure 5). Except for ethane from coal C precursors from all other detected hydrocarbon components are isotopically heavier than the bulk material. As proposed by Cramer45 these trends in δ13C of hydrocarbon precursors might provide insight into the intramolecular isotope distribution within the kerogen.

volves the major advantage that reaction kinetics are exclusively calculated with established standard procedures. 5.1. Reaction Kinetic Concept. For bulk petroleum generation Schaefer et al.37 applied a reaction kinetic model with a set of parallel first-order reactions each of them defined by a discrete activation energy and an individual generation potential and all with one common preexponential factor. Recently, this approach was extended to describe the generation of individual gas components such as light hydrocarbons38 or nitrogen.44 The kinetic equations for this model of parallel reactions have been summarized elsewhere.34 Accordingly, for nonisothermal systems the residual generation potential f, the cumulative amount of reaction product c, and the reaction rate r of each first-order reaction i at time t can be expressed as

ci(T(t)) ) f0i - fi(T(t))

(8)

5. Reaction Kinetic Modeling of Gas Generation and Isotope Fractionation

ri(T(t)) ) ki(T(t)) ‚ fi(T(t))

(9)

On the basis of the improved data resolution in comparison to previous work,34 a more sophisticated reaction kinetic concept was developed to describe stable carbon isotope ratios of pyrolytically generated gas components. The basic idea was to treat both isotope species of each hydrocarbon gas as separate gas components. After measuring the bulk generation curves and δ13C-values of the gas, the generation curves were divided into two, one for each isotope species. Then individual sets of reaction kinetic parameters were derived for each isotope species. On the basis of these kinetic parameters, generation of 12C- and 13C-hydrocarbons was modeled individually and both generation curves were recombined to δ13C-values. Except for the procedures of dividing the generation curve and recombining the individual isotope curves, this method in(45) Cramer, B. Ber. FZ Ju¨ lich 1997, 3412, 187.

fi(T(t)) ) f0i exp(-

∫0t ki(T(t))dt)

(i ) 1...n) (7)

Here f0i denotes the initial generation potential of reaction i. The rate constant ki is defined by the Arrhenius equation (eq 1). By summing up the corresponding numbers for all parallel reactions the total amounts of generated product, residual generation potentials, and generation rates at time t can be calculated: n

a(T(t)) )

∑ ai(T(t)) i)1

(a ) f, c, r)

(10)

To derive isotope-specific kinetic parameters, the differential generation curves of the hydrocarbon components were divided into the differential generation curves of both contributing isotope species. The mea(46) Patijn, R. J. H. Erdo¨ l Kohle Erdgas Petrochem. 1964, 17, 2-9. (47) Stahl, W. Ph.D. Thesis, TH Clausthal, Clausthal-Zellerfeld, Germany, 1968.

524


Cramer et al.

Table 3. Reaction Kinetic Parameters for Light Hydrocarbon Generation from Coals Coal A CH4 A ) 1.04E+11 s-1 Ea (kJ/mol) 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 305 310 315

C2H6 A ) 1.15E+12 s-1

12C-potential

13C-potential

(µg/gTOC)

(µg/gTOC)

δ13Ci0 (‰)

74

0.9

-20.9

589 1424 1668 3157 4479 4205 3629 3726 3477 2754 2162 1694 1196 698 510 576 530 321 133 115 164 109 61 73 36

6.8 16.4 19.1 36.4 51.9 48.8 42.2 43.4 40.5 32.2 25.3 19.8 14.0 8.2 5.9 6.7 6.1 3.7 1.6 1.3 1.9 1.3 0.7 0.8 0.4

-29.4 -34.7 -40.6 -34.3 -30.2 -27.8 -26.2 -25.4 -23.7 -21.1 -19.2 -19.5 -20.5 -21.4 -25.2 -28.6 -29.0 -28.1 -26.8 -29.0 -30.2 -29.6 -30.8 -30.4 -28.9

12C-potential

13C-potential

(µg/gTOC)

(µg/gTOC)

C3H6/8 A ) 4.79E+11 s-1 δ13Ci0 (‰)

651 1415 1644 1610 1353 814 409 266 137

7.3 16.0 18.6 18.3 15.4 9.3 4.7 3.0 1.6

-28.7 -27.6 -25.9 -22.3 -19.1 -17.8 -18.0 -18.7 -17.9

39

0.4

-22.0

12C-potential

13C-potential

(µg/gTOC)

(µg/gTOC)

δ13Ci0a (‰)

13

0.15

-43.7

13 12

0.14 0.14

-86.4 -15.0

696 1916 2185 1618 688

7.8 21.4 24.5 18.3 7.8

-29.6 -26.9 -23.0 -18.5 -13.5

98 141 99 55 28 13

1.1 1.6 1.1 0.6 0.3 0.2

-19.5 -16.9 -16.4 -16.2 -16.2 -16.2

Coal B CH4 A ) 4.18E+11 s-1

C2H6 A ) 6.52E+13 s-1

Ea (kJ/mol)

12C-potential

13C-potential

(µg/gTOC)

(µg/gTOC)

δ13Ci0 (‰)

170 175 180 185 190 195 200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295 300 305 310 315

110 94 285 661 1009 1761 2629 3227 3388 3106 3025 2890 2558 2075 1637 1283 993 783 694 685 622 485 326 198 133 108 79 43 16 3

1.3 1.1 3.3 7.7 11.6 20.3 30.3 37.3 39.3 36.1 35.1 33.6 29.8 24.2 19.1 15.0 11.6 9.1 8.1 8.0 7.2 5.6 3.8 2.3 1.5 1.3 0.9 0.5 0.2 0.03

-27.2 -38.0 -31.8 -29.8 -33.5 -36.0 -34.8 -31.4 -28.7 -27.7 -26.9 -25.3 -23.4 -21.9 -21.0 -20.5 -21.3 -23.7 -26.5 -27.3 -26.7 -26.2 -26.6 -28.1 -27.4 -23.5 -21.4 -23.1 -31.9 -82.0

12C-potential

13C-potential

(µg/gTOC)

(µg/gTOC)

C3H6/8 A ) 5.41E+12 s-1 δ13Ci0 (‰)

12C-potential

13C-potential

(µg/gTOC)

(µg/gTOC)

δ13Ci0 (‰)a

54

0.6

-27.6

10

0.1

-22.7

223 268

2.5 3.0

-29.7 -27.5

68 35

0.8 0.4

-24.8 -21.2

2.8 10.4 16.6 16.2 11.7 7.9 4.9 2.9 1.5 0.6 0.3 0.2

-33.8 -28.6 -26.0 -23.2 -20.7 -19.0 -18.5 -19.2 -19.1 -16.2 -15.8 -21.6

3.8 14.1 25.3 24.4 12.1 2.2

-29.9 -28.3 -24.3

248 923 1472 1427 1030 690 431 252 130 55 26 17

338 1264 2257 2168 1073 193 38 110 58

0.4 1.2 0.7

-37.2 -28.5 -23.4

-7.7



Table 3. (Continued) Coal C CH4 A ) 7.45E+12 s-1

C2H6 A ) 2.25E+12 s-1

Ea (kJ/mol)

12C-potential

13C-potential

(µg/gTOC)

(µg/gTOC)

δ13Ci0 (‰)

180 185 190 195 200 205 210 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295 300 305 310 315 320

179 110 370 511 611 774 1148 1468 1554 1695 1711 1565 1408 1256 1127 915 728 632 505 352 268 279 299 255 159 83 61 65 69

2.1 1.3 4.3 5.9 7.1 8.9 13.2 16.9 17.9 19.6 19.8 18.1 16.3 14.6 13.1 10.7 8.5 7.4 5.9 4.1 3.1 3.2 3.5 3.0 1.8 1.0 0.7 0.8 0.8

-31.0 -31.6 -27.2 -26.9 -30.0 -33.8 -36.2 -36.0 -34.6 -33.1 -32.0 -30.7 -29.2 -28.1 -26.6 -24.8 -24.1 -25.0 -25.8 -26.2 -28.4 -30.7 -30.0 -28.4 -27.7 -29.2 -32.4 -29.8 -21.8

a

13C-potential

107 49 312 591 697 524 311 194 112 40 13 14 8

1.2 2.2 1.8 1.2

C3H6/8 A ) 6.67E+13 s-1

(µg/gTOC)

δ13Ci0 (‰)

1.20 0.55 3.50 6.64 7.86 5.93 3.52 2.20 1.27 0.46 0.14 0.16 0.09

-32.9 -23.7 -33.7 -31.9 -28.6 -26.2 -25.1 -24.5 -23.8 -25.8 -31.7 -23.3 -17.6

-35.0 -25.3 -23.6 -23.0

0.014 0.025 0.021 0.013

δ13Ci0 values of C3H6/8 calculated assuming an average mole mass 43 for the

12C-

12C-potential

13C-potential

(µg/gTOC)

(µg/gTOC)

δ13Ci0 (‰)a

25 77 118 102 194 268 383 728 700 513 340 175 51

0.28 0.86 1.33 1.14 2.18 3.00 4.40 8.15 7.83 5.76 3.82 1.98 0.58

-29.0 -27.0 -26.4 -25.8 -25.8 -26.1 -26.6 -26.8 -26.4 -23.9 -20.4 -17.4 -9.4

7 21 19 11

0.08 0.23 0.21 0.12

-42.4 -44.0 -39.8 -15.7

and of 44 for the

13C-species.

Combination of eqs 11 and 12 yields the expressions for the isotope-specific generation rates:

MH13C r(T(t)) ) r(T(t))‚ R(T(t))‚MH12C + MH13C

12

13

Figure 5. δ13C-values of light hydrocarbon precursors for the three coal samples A, B, and C in comparison with measured δ13C-values of bulk organic matter (OM). Precursor isotope ratios were calculated applying eq 6.

sured overall generation rate r(T(t)) is the sum of the generation rates of both stable carbon isotope species:

r(T(t)) ) 12r(T(t)) + 13r(T(t))

(11)

Furthermore, the isotope ratio R of the gas generated at time t is the ratio of the instantaneous reaction rates at time t multiplied by the molar mass of the isotopic hydrocarbon species MHC: 13

R(T(t)) )

12

r(T(t))‚MH13C

r(T(t))‚MH12C

(12)

r(T(t)) ) R(T(t))‚r(T(t))

MH12C R(T(t))‚MH12C + MH13C

(13)

(14)

Here R(T(t)) can be calculated from the measured δ13Cvalues after rearranging eq 3. In Figure 6 generation rates of both stable carbon isotope species of methane derived from eqs 13 and 14 are shown for one pyrolysis experiment with coal C. Interestingly, the maximum generation rates of both isotope species of methane were detected at the same temperature of about 425 °C (Figure 6). In this plot both generation curves are almost parallel. The tiny differences between both curves are “magnified” by the δ-standardization according to eq 3 (Figure 6). Based on these isotopically individual generation curves, reaction kinetic sets were modeled for both isotope species of each hydrocarbon component. Although each isotope species was treated as a single component, all three gas components (CH4, C2H6, C3H6/8) revealed for both isotopic molecules identical preexponential factors (Table 3). For the example of methane from coal C (Figure 6) Figure 7 displays the individual activation energy distributions of the 12C- and the 13C-

526


Cramer et al.

species. With the common preexponential factor of 7.45 × 1012 s-1 discrete activation energies lie within the range between 180 and 320 kJ/mol with the largest generation potential at an activation energy of 230 kJ/ mol. Besides the fact that about 100 times as much 12Cmethane is generated in comparison to 13C-methane (Figure 6), differences in activation energy distributions of both isotopic species are not obvious from Figure 7. According to eq 6, a hypothetical initial isotope ratio of each parallel reaction can be calculated by relating both individual generation potentials 13f0i and 12f0i. By expressing this isotope ratio in terms of δ13C-values (eq 3), the differences in activation energy distributions are “magnified” and a much clearer insight into the modeled isotope signatures of the hypothetical hydrocarbon gas precursors is given (Figure 7). Within the range of activation energies δ13C0i-values vary within the same range as the δ13C-values of the product methane (Figure 6) and the trend with increasing Ea is very similar to the δ13C trend of methane with increasing temperature. By applying equations similar to eq 12 the differential isotope ratio R of the product, the isotope ratio of the cumulative product Rcum as well as the isotope ratio of the remaining precursor Rprec at time t can be expressed:

Figure 6. Generation rates of 12C- and 13C-methane from coal C for laboratory pyrolysis with 0.2 K/min heating calculated from bulk methane generation and measured stable carbon isotope ratios according to eqs 13 and 14. For better comparison the generation rates in µg/gTOC/K are shown in log-scale. The δ13C of methane is plotted for comparison. Solid lines fitting both generation curves as well as the δ13C-trend are modeled according to the procedure described in the text.

n

R(T(t)) )

13 ri(T(t))‚MH ∑ i)1

13C

(15)

n

12 ri(T(t))‚MH ∑ i)1

12C

n

Rcum(T(t)) )

13 ci(T(t))‚MH ∑ i)1

13C

n

12 ci(T(t))‚MH ∑ i)1

(16)

12C

n

Rprec(T(t)) )

13 fi(T(t))‚MH ∑ i)1

13C

n

∑ i)1

12

Figure 7. Individual activation energy distributions of 12Cmethane and 13C-methane from coal C. For better comparison generation potentials are plotted in log-scale. The spacing between discrete activation energies is 5 kJ/mol. δ13Ci0-values are calculated from the ratios of the individual generation potentials according to eqs 3 and 6.

(17)

fi(T(t))‚MH12C

The resulting δ13C trend of the differential methane is plotted as a solid line in Figure 6. All trends in measured δ13C of methane are represented almost perfectly by the model. During the main phase of gas generation there is just a small offset of the synthetic trend of less than 0.5‰ toward heavier methane. At this point it should be emphasized again, that the calculated δ13C0i-values (Figure 7) are model parameters rather than representing real isotope ratios of existing methane precursors. Because these values were derived from the measured isotope ratios and due to the fact that, with increasing temperature, the parallel reactions will generate the product with subsequently increasing activation energy, the δ13C0i-values as function of the activation energy display a shape very similar to the δ13C-trend of the product as a function of reaction temperature (Figures 6 and 7). So, while increasing the temperature the parallel reactions of our model with

subsequently increasing activation energies will start to produce gas, each contributing a constant stable carbon isotope ratio of the product. In consequence, the δ13C of the overall product is a result of a continuous mixture of the participating reactions andsmost importantsno real isotope fractionating effect is active in terms of differences in activation energies and/or preexponential factors between both isotope species (eq 2). This approach is in strong contrast to previous work34 where a constant isotope ratio of the hypothetical precursors was assumed and the isotope trends of the product were fitted by applying real isotope effects. Obviously, both approaches are applicable for describing isotope trends of pyrolytically generated gas components from laboratory experiments. The question remains, how the differences in both models affect isotope trends while extrapolating to geological heating rates. This will be tested in the following section. 5.2. ∆Ea versus Differences in Precursor Isotope Signature. The method of isotope modeling described above (model III) was compared with the method of Cramer et al.34 applying one constant ∆Ea (model I) and a modified version which fits the measured isotope trend by adapting individual ∆Ea-values for each hypothetical reaction (model II). Figure 8 displays the δ13C-values of methane from coal B measured during pyrolysis with


Figure 8. Comparison of three different reaction kinetic approaches to model the stable carbon isotope trend of methane from coal B generated during pyrolysis at 2 K/min heating and for an extrapolated heating rate of 10 K/Myr. Model I presumes one constant ∆Ea which for methane from coal B has a value of -112 J/mol and constant δ13C0prec of -27.5‰ for all reactions. While keeping the constant δ13C0prec, model II was calibrated by fitting individual ∆Ea-values for each hypothetical, parallel reaction (Figure 9). As described in detail in the text model III requires no ∆Ea. The isotope trend is fitted by applying individual δ13C0prec-values. The δ13C0prec-values applied are shown in Figure 9.

Figure 9. Comparison of the parameters ∆Ea and δ13Ci0 (Table 3) as a function of the activation energy for models I through III to describe the δ13C-trend of methane from coal B as shown in Figure 8. Not displayed are the δ13Ci0-values (model III) for the highest activation energy (-82‰) and the ∆Ea-values (model II) for reactions above 290 kJ/mol (question mark, further explanation in the text).

2 K/min heating in comparison with the three modeled trends. The main trend of increasing δ13C of methane with increasing temperature between about 400 and 560 °C is represented adequately by all methods (Figure 8). Models II and III fit the measured δ13C-values of methane almost perfectly, with model II deviating from the measured trend at temperatures above 650 °C. Model I overestimates isotope fractionation in laboratory pyrolysis at low temperatures (up to about 380 °C) and underestimates isotope fractionation at temperatures above 600 °C. For model I, a ∆Ea-value of -112 J/mol was fitted. The reaction-specific ∆Ea-values of model II are summarized in Figure 9. Starting with ∆Ea-values of -5 J/mol at low activation energies the ∆Ea increases up to -112 J/mol (the value of model I). Between 225 and 260 kJ/mol the ∆Ea remains constant. With further increase of the activation energy, ∆Ea increases to compensate the mismatch of model I. ∆Ea-values in the order of more than 1 kJ/mol as shown in Figure 8 are


questionable from the theoretical point of view.36 Above about 620 °C (Figure 8) the ∆Ea-concept fails absolutely, because even very large “mathematical” differences in activation energy of more than 10 kJ/mol (question mark in Figure 9) are not sufficient to explain the observed δ13C of methane (if a homogeneous isotopic composition of the precursor structures is assumed). The isotope trends of models II and III extrapolated to 10 K/Myr predict δ13C-values of methane in the same range as those measured in the laboratory experiments. Like hydrocarbon generation also the isotope trend at low heating rates is restricted to narrower temperature ranges. This results in steeper isotope trends (plotted vs temperature) compared to laboratory measurements (Figure 8). Whereas the extrapolated trend of model III is as smoothed as for laboratory heating, both models based on ∆Ea-values show some oscillation. The reason for this observation lies in the different mathematical procedures. As described above, δ13C-values of model III are continuous mixtures of isotopically constant products from all hypothetical reaction sites contributing to the overall generation at a given temperature. So, the onset and offset of individual discrete reactions do not disturb a continuous isotope trend but rather cause the trend. In contrast, in models II and III each hypothetical reaction site produces gas with a wide range of isotope ratios starting with isotopically light gas and ending with a heavy rest. At low heating rates these reactions proceed in narrower temperature ranges. If the spacing in Ea-values is not narrow enough, the offset of one discrete reaction and the onset of another reaction may result in an overlap of isotopically heavy gas with isotopically light gas. This causes the observed oscillations in the isotope trend. Obviously, the spacing in activation energy of 5 kJ/mol (Table 3) is not sufficient to produce smoothed isotope trends at low heating rates with these methods. In conclusion, for the concept of parallel first-order reactions and constant preexponential factors of the isotope species both approaches, differences in activation energy as well as differences in generation potentials, can be used to describe δ13C-values of gas generated from laboratory pyrolysis. In addition, both methods result in very similar isotope trends when extrapolated to geologically relevant time-temperature histories. So, both variables, ∆Ea and δ13C0i, can have the same effect on the δ13C of the product. A ∆Ea too low to explain isotope ratios of the product can be compensated by isotopically lighter hypothetical precursor sites and vice versa. Comparing models II and III (Figure 9) in the light of these findings makes clear that both distributions of ∆Ea and δ13Ci0 are endmembers where the other possible parameter was not taken into account. A reaction kinetic picture of isotope fractionation claiming any reference to reality has to include both parameters and probably both parameters will be unevenly distributed over the activation energy range. As long as there is no good approximation of one of these distributions we can use the endmembers described above simply as mathematical model parameters. For practical use, the more pragmatic method based on differences in the isotope signature of the hypothetical precursor sites (model III) appears most appropriate. On one hand, it avoids problems while applying common spacing of the

528


Cramer et al.

δ13C-values of propane + propene. While in all cases the generation of C3H6/8 was represented satisfactorily, calculated isotope trends differed from the measured values in a nonsystematic way by up to 2‰ for coal B and up to 3.5‰ for coal C. The reason for these deviations might be the overlap of the two distinct hydrocarbons propane and propene. Probably our model, assuming a mixture of two components, is not adequate to handle mixtures of 4 components (12C3H6, 13C3H6, 12C H , 13C H ). For example, even small differences in 3 8 3 8 the preexponential factors of propane and propene, which are not taken into account in our calculations, might lead to these problems. The best fit to measured δ13C-values of C3H6/8 was achieved for coal A (Figure 10). 5.4. Extrapolation to Geologically Relevant Heating Rates. The extrapolation of hydrocarbon generation to a heating rate of 10 K/Myr as shown in Figure 10 results in a predicted peak generation phase of methane at 170 °C and of ethane and propane + propene at 140 °C. With respect to the measured values, extrapolated isotope trends are just compressed to smaller temperature ranges and, in consequence, appear with steeper slopes. Interestingly, all trends are prolonged in the δ13C-direction. This effect results in higher maximum and lower minimum values of the δ13C-trends. At the extreme δ13C-values, these deviations do not exceed 1‰. For now the question remains open, whether this is a real effect or just a mathematical artifact. 6. Application to Natural Gas Studies

Figure 10. Results of reaction kinetic modeling of hydrocarbon generation and δ13C-values shown for specific examples. In addition to the measured and modeled data for laboratory experiments, one modeled generation and stable isotope trend is also shown for an extrapolated heating rate of 10 K/Myr. Please note the different scaling of the axes. For measured δ13C-values, open circles represent the pyrolysis experiment with 0.2 K/min, triangles with 0.7 K/min, and rectangles with 2.0 K/min heating.

discrete activation energies as shown above. On the other hand this method can be used with standard reaction kinetic procedures. 5.3. Results of Reaction Kinetic Modeling. The concept of generation and isotope modeling presented above was successfully applied to all experiments and to all hydrocarbon components. The isotope-specific reaction kinetic sets of hydrocarbon generation as well as the resulting δ13Ci0-values are summarized in Table 3. Measured generation curves and isotopic trends for methane from coal B, ethane from coal C, and propane + propene from coal A and the corresponding modeled trends of gas generation and δ13C-values are shown in Figure 10. In general, in all cases hydrocarbon generation was fitted almost perfectly. Modeled isotope trends of methane and ethane for all coal samples match the measured δ13C-values satisfactorily. Some deviations are observed at the beginning and at the end of generation, due to smaller analytical precision at low hydrocarbon concentrations (Figure 10). Problems arose when attempting to fit the measured

6.1. Natural Gas from Carboniferous Coals, NW Germany. With 0.72% Ro (Table 1) coal A represents the lowest mature accessible Westphalian coal from NW Germany. The Westphalian coals are the predominant source rocks of commercial gas fields in NW Germany.46,47 We reconsidered our database to select the gas fields in NW Germany exclusively sourced from Westphalian coals. The ranges of δ13CH4-values within the reservoir as function of the known maturity range of the underlying Westphalian coal are plotted in Figure 11 together with modeled isotope trends of Westphalian coal A. The initial maturity of gas accumulation was set to be the pre-maturation stage of coal A (0.72% vr) because modeling of δ13C-values of methane from earlier maturation stages is believed to be erroneous. The most important observation is that the modeled trend of instantaneously generated methane plots along the data scatter of the reservoir gas. δ13C-values of methane from the four gas fields with maturities of the underlying coal below 1% Ro, are on average about 2‰ higher (less negative) than expected from the calculations (Figure 11). An explanation for this phenomenon could be that the mean maturity value of the underlying coal formation (dot in Figure 11) does not represent the rank of the main gas producing seam. Probably, at these low maturities the stratigraphically oldest coal at the lower end of the displayed maturity range with ranks above 1% Ro contributed most of the gas. In this case, natural gas data from these four gas fields have to be shifted to higher maturities and would be also covered by the isotope model. Beside these exceptions, the majority of the gas field data lie between the modeled trends of instantaneously generated and totally accumulated gas


Figure 11. Modeled stable carbon isotope ratios of methane from Westphalian coal A (10 K/Myr) in comparison with natural gas data from NW German reservoirs which are known to have its source within the Westphalian coal (gas data taken from Gerling et al.,39 maturity of Westphalian coals beneath the reservoirs by courtesy of Dr. H. J. Koch, BGR). δ13C-values are shown as a function of source rock maturity in vitrinite reflectance equivalent (vr). Maturity was assigned to modeled values by applying the EASY%Ro.48 In addition to the isotope trend of instantaneously generated methane (inst. δ13CH4), also the trend of cumulative methane was calculated (cumul. δ13CH4) starting to accumulate from 0.72% vitrinite reflectance equivalent (pre-maturation of coal A). For the reservoir gas data, mean values together with the known range of δ13C-values of methane within the reservoir as well as the known range of the maturity of the Westphalian coal beneath the reservoir are displayed.

(Figure 11). So, they can be explained by the model as partly accumulated gas within the respective reservoirs. Based on the burial history of the source rock beneath individual gas fields, the proportion of realized generation potential and the proportion of accumulated gas within a reservoir can be derived from isotope modeling. 6.2. Reconstructing the Accumulation History of a Gas Field in NW Germany. The maturation of sedimentary organic matter in the NW German basin was influenced by various events.49 Late Palaeozoic sediments were first matured by pre-Permian subsidence (Namurian to Stephanian). A Late Carboniferous tectonic inversion (uplift) was followed by a second phase of subsidence during Permian to Tertiary times. This subsidence was interrupted by an Upper Jurassic or an Upper Cretaceous inversion which in some areas caused uplift, in other areas extensive faulting. On the basis of this history, it was suggested that many oil and gas fields existing prior to the inversion were destroyed due to excessive pressure or dysmigration due to structural reorientation, breaching of traps, or fracturing of cap rocks.50-53 In Figure 12, the upper diagram shows the individual temperature history of the Westphalian coal beneath a (48) Sweeney, J. J.; Burnham, A. K. AAPG Bull. 1990, 74 (10), 1559-1570. (49) Gerling, P.; Kockel, F.; Krull, P.; Stahl, W. Geolog. Jhb. 2000, D 107, 201-215. (50) Binot, F.; Gerling, P.; Hiltmann, W.; Kockel, F.; Wehner, H. Generation, accumulation and production of Europe’s hydrocarbons; Spencer, A. M., Ed.; Springer: Berlin, 1993; pp 121-139. (51) Baldschuhn, R.; Best, G.; Kockel, F. Generation, accumulation and production of Europe’s hydrocarbons III; Spencer, A. M., Ed.; Springer: Berlin, 1993; pp 149-159. (52) Kockel, F.; Wehner, H.; Gerling, P. The petroleum systemsfrom source to trap; Magoon, L. B., Dow, W. G., Eds.; AAPG: Tulsa, 1994; pp 573-586. (53) Gerling, P.; Kockel, F.; Krull, P. DGMK-Forschungsber. 1999, 433, 100 pp.


Figure 12. Case study on reaction kinetic isotope modeling of methane from a NW German gas field. The upper plot shows the temperature history of the source rock (Westphalian coal) beneath the reservoir and the calculated cumulative methane generation (reaction kinetic model of coal A, Table 3). Measured δ13C of methane within the gas reservoir (-24‰) is shown in the lower plot at 0 Myr. Stable carbon isotope trends were modeled for instantaneously generated methane and for total cumulative methane. The accumulation of methane since the reburial almost perfectly explains the δ13C of methane found within the gas field. The shaded area beneath the cumulative generation curve points out the relative amount of methane generated since the uplift.

particular gas field as well as the cumulative methane generation which was calculated applying the reaction kinetic data set of coal A. With about 50% realized generation potential the main proportion of methane was generated until the Jurassic uplift (160 Myr). Methane generation from Westphalian coals restarted during the subsequent deeper burial of the second phase of subsidence (since 100 Myr). The lower part of Figure 12 compiles measured as well as modeled stable carbon isotope ratios of methane for this field as a function of geological time. The modeled δ13C-values of methane were calculated by applying the burial history of the field to the reaction kinetic isotope model. Today (0 Myr) the gas is characterized by a δ13CH4 of -24.0‰ (Figure 12). This value plots between the isotope values of currently generated and cumulative methane. Assuming that the gas generated prior to the uplift dysmigrated, the double line in the lower part of Figure 12 displays the evolution of the δ13C of methane which accumulated in the reservoir since the beginning of re-burial. This modeled trend predicts a δ13C of methane in the recent gas field of -23.5‰. With only 0.5‰ difference, this predicted value matches the measured value satisfactorily. On the basis of this model it can be also estimated from methane generation calculations that about 20% of the total methane generation potential of the Westphalian coal has accumulated in the reservoir (Figure 12). 6.3. Stacked Reservoir. The second case is also taken from NW Germany. A lower gas reservoir sealed by a thick sequence of Zechstein salt (Permian) contains methane with a lighter stable carbon isotope signature (-23‰) than a Triassic reservoir (-21‰) above the salt (Figure 13). Both reservoirs were sourced by the Westphalian coal. In this area the Upper Mesozoic basin inversion caused no significant uplift but led to extensive compressive faulting.54 A deep reaching fault crosses the entire salt sequence (Figure 13). Higher

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that the entrapment of gas within the upper reservoir was caused by migration of gas along the fault. 7. Discussion

Figure 13. Stacked gas reservoirs in NW Germany with distinct δ13C-values of methane. The geological sketch is taken from Baldschuhn and Kockel.54 The lower gas accumulation is sealed by a thick layer of Zechstein (Permian) salt, the upper accumulation is above the salt. Both fields are sourced from the Westphalian coal beneath the salt. Based on the burial history of the coal and the timing of faulting the salt, the reaction kinetic model explains the lower reservoir as accumulated over a period of about 170 Myrs. Here about 30% of the entire methane generation potential of the coal is trapped (horizontally shaded area). The δ13C of methane in the upper reservoir is explained by the model accumulated gas since faulting of the salt (since 85 Myrs). The black arrows in the geological sketch point out the inferred migration path along the fault.

nitrogen and enhanced helium contents in the upper reservoir (He: 0.07%, N2: 12.6%) argue for migration of the entrapped gas along this deep reaching fault.55 Results of calculating methane generation and stable isotope distribution with the reaction kinetic set of coal A for the particular burial history of the Westphalian coal beneath the gas field are displayed in Figure 13. The δ13C of methane within the lower reservoir corresponds to an accumulation since about 170 Myrs (Figure 13). This implies that about 30% of the methane potential of the coal is trapped within this reservoir. In contrast, accumulation of the gas generated since the opening of the fault (about 85 Myrs ago) can account for the δ13C of methane within the upper reservoir (Figure 13). Here only 10% of the methane potential of the coal is trapped. In conclusion, the results of reaction kinetic isotope modeling support the earlier findings (54) Baldschuhn, R.; Kockel, F. Ber. Naturwiss. Ges. Hannover 1998, 140, 5-98. (55) Stahl, W. J.; Gerling, P.; Bandlowa, T.; Bru¨ckner-Ro¨hling, S.; Everlien, G.; Hoffmann, N.; Kessel, G.; Koch, J.; Kockel, F.; Krull, P.; Mittag-Brendel, E.; Sohns, E.; Wehner, H. World Energy, a Changing Scene; Ku¨rsten, M., Ed.; Schweizerbart: Stuttgart, 1996; pp 169-191. (56) Schenk, H. J.; Horsfield, B.; Krooss, B. M.; Schaefer, R. G.; Schwochau, K.; Petroleum and basin evolution; Welte D. H., Horsfield B., Baker D. R., Eds.; Springer: Berlin, 1997; pp 231-269. (57) Burnham, A. K. Geochim. Cosmochim. Acta 1998, 62, 22072210. (58) Lewan, M. D. Geochim. Cosmochim. Acta 1998, 62, 2211-2216.

The application of pyrolytic methods in the study of petroleum and natural gas generation involves compromises and simplifications and has always been a source of controversial discussion and disputes concerning technical aspects and interpretation models. An overview of the use of chemical reaction kinetics in petroleum exploration has been given by Schenk et al.56 These authors also address the shortcomings and limitations of this approach which has been driven by the pragmatic need to predict the rate of conversion of organic matter on time scales not accessible to experimental verification. Laboratory pyrolysis experiments represent the only way to investigate thermogenic gas generation from sedimentary organic matter under controlled conditions. Common points of dispute relate to the experimental conditions (closed or open, hydrous or dry, isothermal or nonisothermal) of the pyrolysis methods, and to the evaluation and interpretation of the experimental data (parallel reactions or reaction networks, discrete or continuous activation energy distributions, etc.). The main lines of controversy are reflected in the discussion and reply by Burnham57 and Lewan.58 We do not wish to reiterate these argumentations here but state our point of view regarding the experimental method and the interpretation of the results. 7.1. Experimental Method. Open system nonisothermal pyrolysis indisputably provides useful information on the thermal stability of sedimentary organic matter. The most prominent example is the Rock-Eval pyrolysis method, which has become the most widely used screening technique for petroleum source rock appraisal. The systematic application of nonisothermal pyrolysis for the assessment of the kinetics of gas generation from coals dates back to the 1960’s. The principles of the experimental techniques and the reaction kinetic interpretation methods have been summarized and discussed in some detail by Ju¨ntgen and van Heek.59 Dry open system nonisothermal pyrolysis is presently the technique yielding the highest density and quality of data for kinetic evaluation. Basically, one single nonisothermal experiment can provide a complete kinetic data set which is usually further constrained by running several experiments at different heating rates. In open system pyrolysis experiments the generated gas is removed instantaneously from the reactor by an inert carrier gas flow. This method allows the continuous detection of hydrocarbon formation rates as a function of temperature. These rates constitute the most common database for kinetic modeling of nonisothermal simulation experiments.56 Because the progress of the reaction is monitored continuously, uncertainties and reproducibility problems are thus strongly reduced as compared to multiple isothermal experiments in closed or open systems. Only this high data density and quality warrants the application of detailed and sophisticated kinetic analysis.57 While it must be conceded that the (59) Ju¨ntgen, H.; van Heek, K. H. Fortschritte der Chemischen Forschung/Topics in Current Chemistry 1969/70, 13, 601-699.


experimental conditions of open system nonisothermal pyrolysis are far off those prevailing in the subsurface during the thermal generation of petroleum and natural gas, it can be argued that this methods provides basic kinetic data that can be applied, with due caution, for the prediction of gas and petroleum generation processes in sedimentary systems at geological time/temperature conditions. There is a wide consensus that the thermal decomposition of sedimentary organic matter involves a free radical mechanism and homolytical cleavage of covalent bonds. Evidence from hydrous pyrolysis experiments60 also indicates that an ionic mechanism involving water is not likely. The open system nonisothermal pyrolysis technique provides information on the thermal stability spectrum of covalent bonds cleaved during primary cracking of organic matter. In the context of a kinetic reaction scheme this thermal stability information represents a good proxy for primary petroleum and gas generation as evidenced for instance by the comparison of dry, open system pyrolysis and hydrous pyrolysis results.57 The application of kinetic parameters from laboratory pyrolysis experiments to geologic petroleum systems cannot be taken for granted, but must be demonstrated for well constrained case studies. The agreement of predictions based on laboratory kinetics with observations in natural systems, as documented in this paper, does not furnish an ultimate proof of correctness, but should be considered as a necessary step to build up confidence in this concept, specifically with respect to the new dimension of the prediction of stable isotope ratios. It needs to be pointed out here that the open system nonisothermal technique is associated with two main problems, namely, the quantity and the composition of gaseous products. Experimental methane yields in open system nonisothermal pyrolysis barely ever exceed 50 mg/g of organic matter while yields from closed system pyrolysis amount up to 250 mg/g (25 wt %) of initial (type II) kerogen.33 This discrepancy can be largely explained by substantial amounts of methane being formed from secondary cracking reactions in closed systems, while open system pyrolysis samples only primary gas. Although secondary cracking processes may be less important for type III kerogen and coals, this fact should be kept in mind when using open system pyrolysis data. The second disturbing aspect concerning the open system pyrolysis method is the composition of the product gases. Apart from the hydrocarbon gases ethane and propane also their alkene homologues (ethene and propene) are generated in the experiments. Furthermore, large quantities of carbon monoxide, which does not occur in natural systems, are formed during dry open system pyrolysis. The products generated in other pyrolysis methods (closed system, dry or hydrous) usually show a better resemblance to naturally occurring petroleum and the corresponding methods are therefore claimed to reproduce (“mimic”) the processes of petroleum generation in geological systems in a better way. Gas generation during hydrous pyrolysis is not proceeding to a high degree of completion and this limits (60) Lewan, M. D. Geochim. Cosmochim. Acta 1997, 61 (17), 36913723.


the kinetic interpretation. Another severe limitation of closed system pyrolysis is the accumulation of products over the entire reaction period. The (differential) reaction rate has to be extracted from an integrated trend determined from a number of individual experiments with an inherent scatter of analytical data. The overlap of primary and secondary cracking in closed system pyrolysis requires an additional deconvolution step importing further uncertainties. Although even under open system conditions a certain overlap of primary gas generation with secondary cracking of high-molecularweight primary petroleum components cannot be avoided, this method probably provides the closest approach to primary cracking reactions. 7.2. Interpretation of Experimental Data. Generally, the experimental results of the pyrolysis experiments in this study have been interpreted in terms of first-order kinetics. Although the theory of chemical reaction kinetics provides techniques to explicitly determine the order of reactions, this treatment makes sense only for well-defined reactions under precisely controlled experimental conditions. As discussed by Schenk et al.56 the assumption of first-order kinetics is appropriate and widely accepted for the thermal decomposition reactions of sedimentary organic matter. Although effective reaction orders other than one, and even fractional orders can be used to fit experimental generation curves, it is difficult to justify their use in terms of reaction mechanisms and it is certainly desirable to keep the reaction kinetic model as simple as possible. The assumption of a set of parallel reactions56 for the thermal generation of petroleum and natural gas is dictated by the complex chemical composition of sedimentary organic matter. It has been shown repeatedly57,59 that this model is a prerequisite for realistic extrapolations of laboratory data to geologic heating rates. Approaches using either discrete or continuous distributions of activation energies have been described in the literature.10 The discrete activation energy distribution used in this work ensures compatibility of the kinetic parameters determined here with those commonly used in numerical basin modeling. It allows for straightforward integration of the prediction of isotopic composition of natural gas into established basin modeling schemes. 7.3. Using Laboratory Data to Describe Natural Gas Generation. Open system laboratory pyrolysis experiments take into account primary cracking reactions only. Considering methane in natural gas, stable carbon isotope ratios do not depend exclusively on fractionation processes associated with this kind of primary reactions. From the moment of its generation the gas is subjected to isotopic alterations with different intensities by physical, chemical, and biological processes. While some authors claim that isotopic fractionation due to diffusional migration is crucial61 others believe that these processes in general do not significantly alter the gas.62,63 In this context, a much more important parameter is the time-temperature interval in the maturation history of the source rock during (61) Prinzhofer, A.; Pernaton, E. Chem. Geol. 1997, 142, 193-200. (62) Fuex, A. N. Adv. Org. Geochem. 1980, 12, 725-732. (63) Faber, E.; Berner, U.; Hollerbach, A.; Gerling, P. Geol. Jhb. 1997, D 103, 103-127.

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which the accumulated gas was generated. Due to diffusional losses through the cap rock gas reservoirs are believed to be dynamic systems. In consequence, it seems unlikely that gas may be kept totally in a reservoir over long geological time. While active, these losses will subsequently alter the composition of the remaining gas. Krooss and Leythaeuser64 stated that these diffusional losses may affect commercial-size reservoirs in the range of at least tens of million years. Disregarding these potential losses the reaction kinetic model permits us to calculate the entire range of possible δ13C-values of methane depending on the accumulation history. 8. Concluding Remarks and Outlook A new technique was presented which provides possibilities to deduce the generation and accumulation history of natural gas from δ13C-values of gaseous hydrocarbons. This new approach consists of two parts, a new analytical technique and a numerical model. Both components have scientific potential exceeding the work presented in this paper. Here we have focused our attention on the analytical and mathematical description of the generation and isotope dynamics of light hydrocarbons from coal and examples of its geological applicability. Besides, the component- and isotopespecific analytical tool of on-line coupled pyrolysis GCIRMS measurements can provide valuable insights into the molecular structure of kerogen, into reaction mechanisms during thermal decomposition of kerogen, and into intramolecular isotope distributions. To achieve this, also non-hydrocarbon components such as CO, CO2, and N2 as well as hydrocarbons heavier than propane from a variety of source rocks should be considered and used for more detailed isotope balances. (64) Krooss, B. M.; Leythaeuser, D. AAPG Bull. 1997, 81 (1), 155161.

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Applying so far published empirical approaches to relate natural gas to type and maturity of the source rock it should be kept in mind that some of the factors influencing the δ13C-values of natural gas in reservoirs are not taken into account. In addition to the kerogen type and the maturity of the source rock, factors such as stable carbon isotope signature of the hydrocarbon precursors within the kerogen as well as the burial and accumulation history should be considered. Although empirical relationships are valid at least for the geological setting they were designed for, stable isotope methods in complex case studies will require more flexible models, such as the reaction kinetic approach presented here. Because of the direct coupling of stable isotope ratios with the hydrocarbon generating process, questions regarding the timing of entrapment, the amount of accumulated gas, the size of the recharge area, or the amount of actively producing source rock as well as questions regarding reservoir compartments can be solved on the basis of stable isotope data. In this way reaction kinetic models of stable isotopes in natural gas have the potential to become a powerful tool in basin simulation studies. Acknowledgment. The authors thank R. Gaschnitz for his pioneering work in setting up the technique of on-line coupled pyrolysis-GC-IRMS performed under the framework of BGR/FZ-Juelich cooperation. Valuable discussion and continuous interest in the study as well as assistance with the experimental work by Dr. R. G. Schaefer (Forschungszentrum Juelich) is appreciated. Vitrinite reflectance data were supplied by Dr. H. J. Koch (BGR). EF000086H

Reaction Kinetics of Stable Carbon Isotopes in Natural Gas

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