Modeling Isotope Fraction During Primary Cracking of Natural Gas

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Ž .Chemical Geology 149 1998 235–250

Modelling isotope fractionation during primary cracking of natural gas: a reaction kinetic approach

Bernhard Cramer ),1, Bernhard M. Krooss, Ralf Littke 2

( ) Institute of Petroleum and Organic Geochemistry ICG-4 ; Research Centre Julich, 52425 Julich, Germany¨ ¨

Received 15 April 1997; accepted 3 April 1998

Abstract

Ž .A numerical model has been developed to compute stable carbon isotope variations in natural gas methane by

calculating13

CH and12

CH generation as a set of parallel first-order reactions of primary cracking. The goal of this work 4 4

was to combine the description of isotope fractionation with established kinetic models for gas generation. Stable carbon

isotope ratios of methane from sedimentary organic matter are characterized by the initial carbon isotope ratio of methane

precursors within the organic matter and by a constant difference in activation energy between12

C- and13

C-methane

generation from corresponding precursor sites. Methane generation is calculated separately for12

C- and13

C-methane. A

difference in activation energy automatically implies a temperature dependence of fractionation processes which has not

been taken into consideration in previous works. This new model offers a theoretical explanation and mathematical

description of the observed variability of d 13

C-values of methane during open-system pyrolysis experiments. Carbon

isotopes of methane within natural gas of thermogenic origin can be simulated for any geological temperature history. The

application of the method to two coaly rock samples of the Pokur formation from northern West Siberia results in simulatedcarbon isotope values of methane which are very similar to those in the natural gas within the reservoirs of the Pokur

Ž 13 .formation d C sy42‰ to y54‰ . This finding supports a thermogenic origin of the gas at an early stage of 1

maturation. q 1998 Elsevier Science B.V. All rights reserved.

Keywords: Methane; Natural gas; Isotope fractionation; Reaction kinetics; West Siberia; Pokur formation

1. Introduction

Stable isotopes of natural gas components have

been used to identify source rocks and to recognize

)

Corresponding author.1

Current address: Federal Institute for Geosciences and NaturalŽ .Resources BGR , Stilleweg 2, 30655 Hannover, Germany. E-mail:

[email protected]

Current address: Institute of Geology and Geochemistry of

Petroleum and Coal, Aachen University of Technology, Lochner-

str. 4-20, 52056 Aachen, Germany.

Ž .possible secondary alterations of the gas. Stahl 1968Ž .and Stahl and Carey 1975 established first empiri-

cal relationships between the maturity of source rocks

and the stable carbon isotope composition of relatedgaseous hydrocarbons. Since these early milestones a

variety of such empirical relationships has been de-

veloped serving as important tools to solve appliedŽgeological problems Faber, 1987; Berner and Faber,

.1988; Shen et al., 1988; Berner, 1989 . However,

these models have severe limitations, because they

are not based on a fundamental understanding of

0009-2541r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.Ž .PII S 0 0 0 9 - 2 5 4 1 9 8 0 0 0 4 2 - 4



( ) B. Cramer et al.r Chemical Geology 149 1998 235–250236

what controls isotopic fractionation and are therefore

not generally applicable to all types of sedimentary

basins, source rocks, and thermal histories.

Recent developments both with respect to the

kinetics of hydrocarbon gas generation and the de-

scription of isotopic fractionation processes provide

the basis for a gradual replacement of the empirical

approach by a more mechanistic one.

The application of chemical reaction kinetics toŽ .oil and gas formation Tissot and Espitalie, 1975´

has resulted in new prediction tools which are now

widely applied in basin modelling. Extensive experi-

mental studies on hydrocarbon generation by Juntgen¨Žand co-workers e.g., van Heek and Juntgen, 1968;¨

.Hanbaba and Juntgen, 1969 and other groups have¨provided the initial database which has since then

been extended continuously. One of the main results

of these studies was that, in order to arrive at realis-

tic extrapolations to geologic heating rates, the de-scription of gas generation must involve a set of

Ž .parallel reactions ‘reaction complex’ with an acti-Žvation energy distribution Juntgen and van Heek,¨

.1970; Braun and Burnham, 1987 . The experience

from kinetic modelling of hydrocarbon generation

has so far found only relatively little application in

the investigation of the associated isotope fractiona-

tion processes.ŽSeveral authors Galimov, 1988; Clayton, 1991;

.Berner et al., 1992, 1995; Rooney et al., 1995 used

Ž .Rayleigh distillation formulae Rayleigh, 1896 tocompute isotopic fractionation processes of natural

gas components. Isotope partitioning between reac-

tant and reaction product as a function of the extentŽ .of gas generation transformation ratio and initial

isotope ratio of the precursor material was simulated

using a fractionation coefficient termed kinetic iso-Ž .tope effect KIE . The kinetic isotope effect KIE is

defined as ratio of the reaction rate coefficients of Ž 12 .the isotopically light k and the isotopically heavyC

Ž 13 .compound k :C

k 12

CKIE s . 1Ž .13

k C

Ž .Galimov 1974 showed that the KIE concept

applied to generation of hydrocarbon gases from a

set of parallel reactions predicts significantly differ-

ent isotope ratios than for a single generation reac-

tion. In consequence he combined a model of

methane generation from a set of parallel first-orderŽreactions with Rayleigh isotope fractionation Gali-

.mov, 1988 . Here, the generation of hydrocarbonsŽ .was simulated based on temperature-dependent

chemical reaction kinetics, but the temperature de-Žpendence of the isotope fractionation itself as re-

ported from laboratory experiments for example, byŽ . Ž ..Galimov et al. 1972 and Sackett 1978 was not

taken into consideration.

Rate coefficients of chemical reactions are usually

strongly temperature-dependent. If k 12

and k 13

haveC C

even slightly different temperature dependences,Ž .then, according to Eq. 1 the KIE will also be

temperature-dependent. Based on experimental evi-

dence from non-isothermal open system pyrolysis we

present a conceptual model which explicitly takes

into account the temperature dependence of the KIE.

In this context it was our main objective to combine

the reaction kinetic fractionation concept for a set of Ž .parallel first-order reactions Galimov, 1974, 1988

Ž .with the idea of Berner et al. 1995 to predict

isotope composition of natural gas components from

laboratory pyrolysis experiments.

The second objective of this work was to test the

hypothesis on thermogenic generation of methane

during early source maturation in northern West

Siberia. Immature organic matter from the Lower

Cretaceous Pokur formation in which the giant gas

accumulations of northern West Siberia are concen-

trated was used for the pyrolytic studies and thecombined isotope measurements.

2. Samples and experimental

2.1. Rock samples

Nine source rock samples from the Pokur forma-

tion in northern West Siberia were selected for the

evaluation of kinetic parameters for methane genera-Ž .

tion Schaefer et al., 1998, in press . For pyrolysisexperiments combined with isotope studies, two of

these nine samples were chosen. The samples se-

lected for this study were cored in borehole 105 in

the gas field Yuzhno Russkoe approximately 150 km

east of the Urengoy gas field which contains theŽlargest known accumulation of gas on earth Grace

.and Hart, 1990 . The 1000-m thick Pokur formation



( ) B. Cramer et al.r Chemical Geology 149 1998 235–250 237

Table 1

Organic geochemical characteristics of the pyrolysed rock samples

of the Pokur formation

Sample Pk1 Pk2

Ž .Depth m 1250 1450Ž .TOC % 41 63

Ž .VR % 0.51 0.52

Ž .S1 mg HCrg 2.2 18.1Ž .S2 mg HCrg 54.6 130.2Ž .S3 mg CO rg 17.0 12.12

Ž .T 8C 422 426max

Ž Ž ..PI S1r S2qS3 0.04 0.12Ž .HI mg HCrgTOC 134 207Ž .OI mg CO rgTOC 42 192

13 Ž .Initiald C ‰ y24.1 y23.3OM13 Ž .Final d C ‰ y23.8 y23.1OM

was deposited from Upper Aptian to Cenomanian

times and predominantly consists of sandstones with

coaly organic matter. The two rock samples repre-sent the Cenomanian section of the Pokur formation

Ž .with one sample from the top of the formation Pk1Ž .and the other Pk2 from a section 200 m deeper.

General organic geochemical characteristics of the

organic matter are summarized in Table 1. Accord-Ž . Žing to the concentration of organic carbon TOC 41

.and 63 wt.% the rock samples can be described as

coaly sandstones or sandy coals. Vitrinite reflectance

and T -values clearly indicate that the organic mat-max

Ž .ter of these rocks is immature Table 1 . Hydrogen

Ž .indices HI of 134 and 207 mg HCrgTOC aretypical of humic organic matter in coals at low levels

Ž .of maturation Tissot and Welte, 1984 .

2.2. Pyrolysis experiments

A 200 mg rock sample was pyrolysed using the

open-system pyrolysis apparatus previously de-Ž .scribed by Krooss et al. 1995 . Open-system pyroly-

sis allows the continuous registration of hydrocarbon

formation rates as a function of temperature that

constitute the most common data base for kinetic

modelling of non-isothermal simulation experimentsŽ .Schenk et al., 1997 . Although even under open-sys-

tem conditions a certain overlap of primary gas

generation with secondary cracking of high molecu-

lar weight primary petroleum compounds cannot be

avoided, this method provides probably the closest

approach to primary cracking reactions.

Special tests were performed to control the ovenŽtemperature during the experiments Schaefer et al.,

.1998, in press . Samples were heated from 208C up

to 8008C each at heating rates of 0.1, 0.3 and 2.0 K

miny1. About 40 ml miny1 helium were flushed

through the reactor as carrier gas. Gaseous hydrocar-Ž .bons were separated by gas chromatography GC

Ž .and quantified by a flame ionisation detector FID .

These measurements were carried out every 3 min

during each pyrolysis experiment. More details about

the analytical procedure are found in Schaefer et al.Ž .1998, in press . The evaluation of the experimental

data was performed according to the scheme de-Ž .scribed by Schaefer et al. 1990 and yielded an

activation energy distribution and one common pre-

exponential factor for the entire set of parallel reac-

tions.

For isotope analyses, gas samples were taken

off-line from experiments performed at a heating rateof 2.0 K miny1. During time intervals when no

GC-measurements were made gaseous pyrolysis

products together with helium were flushed throughŽ .a glass sampling container 250 ml equipped with

two stopcocks. After 20 min the flask was closed and

the gas was expanded into an evacuated 70 ml

stainless steel container. For every sample a new

glass flask was installed. For carbon isotope analysis

the gas was injected from the container into a GC

interfaced to an isotope ratio mass spectrometer.

Measurements were carried out using the method of continuous flow.

3. Experimental results

3.1. Methane generation

Characteristics of methane generation during py-

rolysis experiments from the two rock samples were

very similar. As a result, the activation energy distri-butions and pre-exponential factors differ onlyŽ .slightly Fig. 1 . The total methane generation poten-

tial of approximately 29 mgrgTOC determined for

the two samples corresponds to 22% of the total

hydrocarbon generation potential measured by

Rock–Eval pyrolysis for sample Pk1 and to 14% forŽ .sample Pk2 Table 1 . Methane generation is de-




Fig. 1. Reaction kinetic parameters for methane generation from rocks of the Pokur formation evaluated by the gross kinetic model of Ž .Schaefer et al. 1990 .

scribed by 39 parallel reactions for sample Pk1 andŽ .42 reactions for Pk2 Fig. 1 . The highest methane

generation potentials were calculated for activation

energies of 243 kJ moly1

for Pk1 and 247 kJ moly1

for Pk2 at pre-exponential factors of 9.06P1013 sy1

Ž . 13 y1 Ž .Pk1 and 3.20P10 s Pk2 . Both activation

energy distributions show a nearly symmetrical ap-y1 y1 Žpearance from 167 kJ mol to 352 kJ mol Fig.

.1 .

Methane generation during both pyrolysis experi-

ments started at 3008C, reached a maximum genera-Ž .tion at 4908C, and ceased at 8008C Fig. 2 . Mod-

elled methane generation for a geological heating

rate of 2 K Myry1 results in small differences

between both samples. As shown in Fig. 2 modelled

methane generation starts at about 708C. Generally,

the generation curve of sample Pk1 is shifted by 5 K

to higher temperatures in comparison to Pk2. Maxi-

mum methane generation rate from Pk1 occurs at

1878C and from Pk2 at 1818C. Under these condi-

tions, the potential for methane generation of bothŽ .rocks is exhausted at 4008C Fig. 2 .

3.2. Stable carbon isotope Õalues

The stable carbon isotope composition of methane

during pyrolysis experiments is summarized in Table2. Because of the fast volume exchange in the glass

flask with a rate of about 20%rmin the measured

d 13

C-values mainly represent the highest temperatureŽof the respective sampled temperature interval Table

.2 . The comparatively low reproducibility of the13 Žd C-measurements with 1s ranges between 0.5

.and 1.25‰, Table 2 is regarded as a result of low

methane concentrations in the carrier gas collected

during the pyrolysis experiments.

Measured carbon isotope ratios of methane from

both rock samples display similar trends. These mea-

sured d 13

C-values of methane as a function of tem-

perature and extent of methane generation are com-Ž .pared with those of Berner et al. 1995 for methane

pyrolytically generated from xylite and kukersite in

Fig. 3. Interestingly, neither their results nor our

results show a steady increase in carbon isotopeŽ .values over the entire temperature range Fig. 3A .




Ž y1 . Ž y1 .Fig. 2. Methane generation rates for the laboratory experiment 2 K min and a geological heating rate 2 K Myr as a function of

temperature calculated from kinetic parameters for the two rock samples of the Pokur formation.

Our experiments resulted in increasing d 13

C-values

with increasing temperature only for limited temper-

ature ranges, whereas within two temperature inter-

Table 2

Carbon isotope values of methane generated during pyrolysis

experiments at a heating rate of 2 K miny1 , reproducibility of

d 13

C measurements given as 1s range13 13

Temperature c-Pk1 d CH -Pk1 c-Pk2 d CH -Pk24 4

Ž . Ž . Ž .8C ‰ ‰

260 –300 0.001 y50.0"1.25 0.001 y53.5"1.25

300 –340 0.006 y43.0"1.25 0.005 y41.9"1.0

340 –380 0.027 y39.5"1.25 0.023 y38.2"1.0

380 –420 0.097 y40.1"0.75 0.087 y39.0"0.50

420 –460 0.256 y37.4"0.50 0.239 y37.6"0.50

460 –500 0.468 y33.0"0.50 0.454 y33.8"0.50

500 –540 0.664 y31.2"0.50 0.658 y31.0"0.50540 –580 0.812 y29.5"0.50 0.816 y28.7"0.50

580 –620 0.902 y25.3"0.50 0.911 y25.6"0.50

620 –660 0.950 y27.3"0.75 0.959 y29.0"0.75

660 –700 0.978 y31.7"0.75 0.982 y29.9"0.75

700 –740 0.992 y29.7"1.0 0.993 y33.2"0.75

740 –780 0.998 y26.5"1.0 0.998 y31.1"1.0

c denotes the realized methane potential.

vals decreasing13

C y concentrations were observed.

Starting with d 13

C-values below y50‰ at 3008C

and a degree of conversion of less than 1% of the

Ž .methane generation potential Fig. 3B , methane fromPk1 and Pk2 became isotopically heavier to valuesŽ . Ž .of about y39.5‰ Pk1 and y38.2‰ Pk2 at

Ž . 133808C Fig. 3A . At 4208C a slight decrease of d C

of methane was observed for both samples. From

460 to 6208C d 13

C-values increased with increasing

temperature up to values of y25.3‰ for Pk1 andŽ .y25.6‰ for Pk2 Fig. 3A . At this temperature

Ž .about 90% of the methane was generated Fig. 3B .

During generation of the last 10% of methane, car-

bon isotope ratios decreased to values of y31.7‰Ž . Ž .Pk1 and y29.9‰ Pk2 . The last measured isotope

values above 99% methane generated again showed

slightly higher values.Ž .Berner et al. 1995 measured carbon isotope

values of methane generated during open-system py-

rolysis with a heating rate of 5 K miny1 from a

xylite representing terrestrial organic matter and from

an algae-derived kukersite. Due to the different heat-








The ratio of the pre-exponential factors denotesŽ .the minimum kinetic isotope effect for the limit of

high temperatures. The rate of decrease in isotope

fractionation with increasing temperature depends onŽ .the difference in activation energies D E of thea

two isotopic product species.

Although this temperature dependence may not

hold for all types of kinetic isotope effects theoreti-

cal calculations show that most reactions involving

stable carbon isotopes can be described with suffi-Žcient precision using this approach Huang et al.,

.1968; Vogel and Stern, 1971 . In the present work

the ratio A r A was assumed to be equal to 1 in12 13C C

accordance with results by Wolfsberg and SternŽ .1964 for secondary kinetic isotope effects. This

assumption implies that isotope fractionation van-

ishes at high reaction temperatures.

Fig. 4 shows the temperature dependence of the

kinetic isotope effect for a single first-order reactionŽ .and different D E -values according to Eq. 4 . Witha

increasing difference in activation energy, both the

absolute value of the KIE and its temperature depen-

dence increase. The strongest isotope fractionation

will occur at low temperatures of gas generation in

geological systems. During pyrolysis experiments the

temperature dependence can be observed over a wide

temperature range, but the change of KIE with tem-

perature is much weaker than under geological con-

ditions. Therefore, if an isotope effect determined

from pyrolysis experiments is assumed to be temper-

ature-independent conversion of the reaction to geo-

logical heating rate would probably result in incor-

rect interpretations.

4.3. Justification of the model

Ž .The isotope fractionation during hydrocarbon gas

generation is attributed to small differences in the

reaction rate coefficients for the different isotopeŽ .species which, according to Eq. 4 reflect differ-

ences in the activation energies of the formation

reactions. The properties of molecules differing onlyby isotopic substitution are qualitatively the same but

Ž .quantitatively different Hoefs, 1996 . It can be

shown that, as a result of quantum mechanical ef-

fects, different isotope species in a given chemical

Fig. 4. Kinetic isotope effect defined by a difference in activation energy D E as a function of temperature.a




Žbond will have different zero-point energies cf..Hoefs, 1996 and that, due to an inverse relationship

between vibrational frequency and molecular mass

of bonded atoms, a chemical bond involving a heav-

ier isotope species will have a lower zero-point

energy than the same bond with the light isotope.

The slight difference in bond energy is considered to

influence reaction kinetics by affecting the thermal

cleavage of the covalent bonds which represents the

rate-determining reaction in kerogen transformation

and hydrocarbon generation processes. This reason-

ing provides the justification for attributing a differ-

ence in activation energies to the formation reactions

of different isotope species. The qualitative and to

some extent speculative character of this approach is

recognized and should be kept in mind. However, it

represents, in our opinion, a useful and necessary

step from predominantly empirical relationships to-

wards mechanistic models.

4.4. Kinetic equations for parallel reactions

As pointed out above, a description of hydrocar-

bon generation kinetics by one single reaction yields

unrealistic temperature predictions for hydrocarbon

generation on the geologic time scale. Therefore, theŽ .thermal generation of hydrocarbons methane from

sedimentary organic matter is represented by a set of

n first-order reactions with discrete activation ener-

gies and initial generation potentials f 0

. For non-iso-i

Žthermal systems e.g., geologic systems, non-isother-. Ž .mal pyrolysis the temperature T and, accordingly,

Ž .the rate coefficient k are functions of timei

Ž Ž Ž ... Ž .k T t . The reaction rate r for reaction i ati i

time t is given by:

d c d f i ir t s s y s k T t P f i s 1 . . . nŽ . Ž . Ž .Ž .i i id t d t

6Ž .

with

c t s f 0 y f t 7Ž . Ž . Ž .i i i

Here, c denotes the amount of reaction product ati

time t and f is the residual generation potential,i

which can be obtained by integration according to:

t 0 f t s f exp y k T t d t 8Ž . Ž . Ž .Ž .Hi i iž /

0

so that

d c t i 0r t s s k T t f exp y k T t d t Ž . Ž . Ž .Ž . Ž .Hi i i iž /d t 0

9Ž .

The total residual generation potential for all n

parallel reactions at time t is given by the sumn

f t s f t 10Ž . Ž . Ž .Ý i

is1

and, correspondingly, the total amount of reaction

product is:

n

c t s c t 11Ž . Ž . Ž .Ý i

is1

The overall generation rate at time t is

n

r t s r t 12Ž . Ž . Ž .Ý iis1

4.5. Isotope fractionation

The computation of the isotope fractionation ef-Ž .fects is performed in terms of isotope ratios R . For

each of the parallel reactions the isotope ratio of

product precursor sites in the organic matter is de-

fined as:

f 013i C

0 R s 13Ž .i 012 f i C

Correspondingly, the precursor isotope composition

for all reactions is given by:

n

013 f Ý i C

is10 R s 14Ž .n

012 f Ý i C

is1

This value is not necessarily identical with theŽ 0 .

initial bulk isotope ratio of the organic matter R .OMIt is determined from the cumulative product isotope

composition after complete conversion. For sedimen-

tary organic matter an isotopic homogeneity of

methane precursor sites cannot be presumed. Never-

theless, we presently see no possibility to attribute a

specific initial isotope ratio to each of the n parallelŽ .first-order pseudo reactions. Therefore, the precur-




sor sites of all parallel reactions are assumed to have

the same initial isotope composition:

R0 s R0 i s 1 . . . n 15Ž . Ž .i

The input data for the isotope fractionation model

are the kinetic parameters for gas generation ob-

tained from the non-isothermal pyrolysis experi-

Žments number of parallel reactions, total generationpotential; activation energy distribution, pre-ex-

.ponential factor; cf. Figs. 1 and 2 and the isotope

composition of the gas sampled at different stages of

the pyrolysis experiment. The activation energy dis-

tribution from this procedure is assumed to representŽ12 .the predominant isotope species C . Based on the

activation energy distribution and the precursor iso-Ž 0 .topic composition R generation potentials for the

isotopically light and the isotopically heavy species

are determined for each individual reaction:

f 0

f 0

P R0

i i i0 012 13 f s ; f s i s 1 . . . n 16Ž . Ž .i C i C0 01 q R 1 q Ri i

These generation potentials are used to compute

the residual generation potentials, the amount of

product generated and the generation rate for the two

isotope species as a function of timertemperature for

each individual reaction. The generation rates of 12

C13 Ž .and C species e.g., methane , respectively, from

reaction i at time t are:

d c 12i C 012 12 1 2r t s s k T t f Ž . Ž .Ž .i C i C i C

d t

=t

12exp y k T t d t Ž .Ž .H i Cž /0

17aŽ .

d c 13i C 013 13 1 3r t s s k T t f Ž . Ž .Ž .i C i C i C

d t

=t

13exp y k T t d t Ž .Ž .H i Cž /0

17bŽ .

From the two reaction rates the ‘instantaneous’

isotope composition of the product at time t can becomputed:

n

13r t Ž .Ý i C

is1 R t s 18Ž . Ž .ninst

13r t Ž .Ý i C

is1

The cumulative isotopic product composition at

time t and the isotopic composition of the residual

precursor sites can be calculated in a similar way.

The differences in reaction rates of the isotope

species and, in consequence, in the product and

residual isotope ratios arise from the difference inŽ .activation energies D E . To simplify the calcula-a

tion procedure we assumed identical D E for all na

Žreactions constant offset of the activation energy of 13 .C generation to higher values . This model parame-

ter is varied to match the measured and calculated

‘instantaneous’ isotope ratios determined in the py-

rolysis experiments.The conversion of carbon isotope

ratios to the usual d -notation is performed with the

carbon isotope standard ratio R referenced to PDBstd

standard:

Rd ‰ s y 1 1000 19Ž . Ž .

ž / Rstd

This set of equations models the time- and tem-

perature-dependent isotope distribution between or-Ž .ganic source material and hydrocarbon gas methane

generated from the organic matter. The method

avoids the isotope fractionation concept of a temper-

ature-independent isotope effect.

This procedure also allows extrapolation of mea-

sured isotope values of methane generated pyrolyti-

cally in laboratory experiments to geological temper-

ature histories. Thus, carbon isotope values of

methane only depend on time and temperature, theinitial isotope ratio of methane generating reaction

sites, and on the difference in activation energy

between12

C- and13

C-methane generation.

4.6. Determination of model parameters

Non-isothermal pyrolysis experiments were per-

formed with the Pokur samples at three different

heating rates to evaluate the kinetic parameters of

methane generation. According to the gross kineticŽ .

model of Schaefer et al. 1990 , a set of n parallelreactions with different activation energies was as-

sumed. This procedure yielded the distribution of

activation energies and the pre-exponential factor for

methane generation. The kinetic parameters were

used to compute the generation of methane during

the separate laboratory experiments conducted for

the carbon isotope measurements.




Each of the n methane generating reactions was

attributed a generation potential with the same initial

carbon isotope ratio. This carbon isotope ratioŽ .y33.2‰ was derived from the total methane quan-

tity and the isotope ratios of methane measured in

the experiments. The isotope fractionation model

was matched to the measured carbon isotope values

of methane by varying the difference in activation

energy between12

C- and13

C-methane generation

until the square of the difference between model and

measured values had reached its minimum. The ac-

tual computations were performed in a spreadsheet

using a discretized time-temperature history com-

posed of sufficiently small isothermal time steps. To

relate the stable carbon isotope ratio of methane to

the maturation of organic matter an EASY%Ro ele-Ž .ment Sweeney and Burnham, 1990 was integrated

into the program.

5. Results of the modelling of isotope fractionation

The carbon isotope ratios of methane calculated

with the new model are shown in Fig. 5. In principle

all trends of carbon isotope ratios of methane from

pyrolysis experiments, increasing and decreasing

d 13

C-values, are reproduced by the model. Especially

the temperature interval of main methane generation

Ž .between 400 and 6008C Fig. 2 shows good concur-rence of measured and predicted value. Generally,

only the measured minimum and maximum valuesŽ .are not matched Fig. 5 . The modelled trends shown

in Fig. 5 were obtained with almost identical D E -a

values of y103 J moly1 for Pk1 and y102 J moly1

for Pk2. The D E y values are in the same range asa

the differences in zero-point energies between C–C

bonds in isotopically substituted and non-substitutedŽorganic molecules D E between y80 and y250 Jzp

y1 .mol modelled with ab initio quantum chemistryŽ .calculations by Tang and Jenden 1995 . Once again

it should be emphasized that the isotope trends from

pyrolysis experiments were fitted with one common

D E -value for all parallel reactions. The D E con-a a

cept was introduced to account for the differences in

bond strength between12

C–12

C and12

C–13

C bonds

of precursor structures. Although one could argue

that the D E value may not be the same for alla

reactions, a definition and computation of individual

D E values for each reaction is not justified with thea

present database. Such an approach would corre-

spond to a gross over-interpretation of the existing

database.

The modelled D E -values for methane generationa

from rocks of the Pokur formation correspond to

KIE’s between 1.013 and 1.023 for temperatures of Ž .laboratory pyrolysis Fig. 4 and 1.020 and 1.038 for

the temperature range of methane generation at geo-Ž .logical heating rates Fig. 4 .

No realistic results were achieved when applying

the measured carbon isotope ratios of total organicŽ . 13

carbon Table 1 as initial d C-values of methane

precursors. Generally, the slope of the modelledŽ .carbon isotope trend of methane Fig. 5 is deter-

mined by the difference in activation energy. A

parallel shift of the general trend to isotopically

lighter or heavier methane can be realized by chang-ing the initial carbon isotope ratios of the methane

Ž .precursors as shown by Clayton 1991 . The devia-

tions of isotope trends during methane generation

from monotonously increasing isotope ratios must be

seen as a pure result of the dynamics of methane

generation. At the beginning of methane generation

only some reactions of the whole set are involved in

generation processes. At these hypothetical reaction

sites initial carbon isotope fractionation leads to min-

imum carbon isotope ratios of methane. During our

pyrolysis experiments this stage was reached at tem-Ž .peratures of about 3008C Fig. 5 where less than 1%Ž .of total methane was generated Fig. 3 . With in-

creasing temperature the number of participating re-

actions increases. The measured average isotope

composition of methane during this main stage of

generation can be described as a mixture of gener-

ated methane from a maximum number of active

reaction sites. A more or less steady increase of d 13

C

of methane must be expected and actually is ob-

served. In our pyrolysis experiments this stage wasŽ .reached between 400 and 6008C Fig. 5 . At 5008C

the steady isotope trend of both experiments showsŽ .an inflexion Fig. 5 , indicating that the number of

reactions contributing to isotope fractionation de-

creases and methane generation rates have reachedŽ .maximum values Fig. 2 . The maximum values of

carbon isotope ratios at 380 and 6208C also coincide

fairly well with the inflexion of methane generation




Fig. 5. Measured and calculated carbon isotope ratios of methane generated during dry open-system pyrolysis experiments from rock

samples of the Pokur formation.

Ž .rate vs. temperature Figs. 2 and 5 . Towards the end

of methane generation the number of contributing

reactions decreases and the remaining reaction sites

are almost exhausted in12

C methane. They produce

an isotopically heavy ‘rest’ of methane. Thus, thestable carbon isotope ratio during the main phase of

methane generation obviously reflects the generation

dynamics.Ž .Berner et al. 1995 modelled carbon isotope ra-

tios of methane, ethane, and propane generated dur-

ing open-system pyrolysis experiments using

Rayleigh equations with constant KIE’s. They were

not able to describe deviations from monotonously

increasing d 13

C-values. They presumed that different

groups of methane generating reactions are involved

in gas generation. A first group producing isotopi-

cally heavier gas would be continuously over-

whelmed by isotopically lighter gas from a secondŽ .group of reactions Fig. 3A .

We also modelled our data set with RayleighŽ .equations, but in contrast to Berner et al. 1995 and

Žother authors Clayton, 1991; Berner et al., 1992;.Rooney et al., 1995 we applied Rayleigh fractiona-

tion with a temperature-independent kinetic isotope

effect to a set of methane generating reactions asŽ . Ž .defined in Eqs. 6 – 12 and as suggested by Gal-

Ž .imov 1974, 1988 . By this approach the general

trend of stable carbon isotope variations of methanefrom open-system pyrolysis experiments was mod-

elled successfully. This finding supports our general

conclusion on the influence of generation dynamics

on isotope distribution. With a temperature-indepen-

dent KIE the slope of the isotope trend was not

matched and the conversion to geological tempera-

ture histories led to unrealistic results. The applica-

tion of a temperature-dependent KIE as defined inŽ .Eq. 4 to Rayleigh distillation resulted in almost

exactly the same trend as reported for the pure

reaction kinetic approach Fig. 5. The calculation

procedure however was much more complicated with

Rayleigh distillation than with our new model.Ž .One of our reviewers M. Rooney asked about

the possibility and necessity to model isotope effects

for ethane, propane, and other gaseous maturation

products. In principle stable isotope ratios of allŽ .other pyrolysis products N , CO , C , C . . . can2 2 2 3




be computed with our model, if reaction kinetic

parameters are available and isotope ratios were

measured during the pyrolysis experiments. Espe-

cially for the determination of source maturity of

natural gas it appears to be useful to know the

isotope trends of these non-methane gas compounds.

The present work was limited to methane, because

the main goal was to resolve the controversy on the

source of methane in reservoirs of the Pokur forma-

tion. Few additional measurements were made forŽ .ethane and propane Cramer, 1997 , but the database

is much weaker than for methane. In future this type

of measurement and modelling will be performed.

6. Case history northern West Siberia

12 3 Ž .With 40P10 m gas Khartukov et al., 1995about one third of known conventional natural gas

reserves on earth have been found in the northern

part of the West Siberian basin. 95% of this gas

accumulated in the rocks of the Pokur formationŽ .Rovenskaya and Nemchenko, 1992 . It consists of

Žalmost pure methane about 98 vol.% of methane,. 13

less than 1.5 vol.% of C -components with d C-2q

values between y42 to y54‰ and d D-values be-Ž .tween y250 and y180‰ Cramer, 1997 . The ori-

gin of this methane has been discussed extensively

since the first gas pools were discovered in the late1960s. In general three models of methane genera-

tion have been developed. The purity of methane and

its light carbon isotope ratio is consistent with aŽbacterial methane origin Nesterov et al., 1970;

. Ž .Vasil’ev et al., 1970, Schoell, 1995 . Prasolov 1990

presumed a thermogenic methane formation from

highly mature organic matter in deeply buried Trias-

sic and Jurassic sediments, requiring vertical migra-Žtion over large distances to the trap. Galimov 1988,

..1995, Galimov et al., 1990 championed an olderŽidea e.g., Nesterov et al., 1978; Nemchenko and

.Kramarenko, 1985 explaining the methane as ther-

mogenic gas, in situ generated from coaly organic

matter in the Pokur formation during early matura-Ž .tion. More recently Mango 1996 used the isotope

composition of the West Siberian gas to promote his

idea of a thermocatalytic rather than thermogenic or

bacterial gas generation.

In Fig. 6, carbon isotope ratios of methane from

different reservoirs within the Pokur formation of the

Geologicheskaya field are plotted vs. vitrinite re-

flectance. Vitrinite reflectance of the associated PokurŽ .coal was measured by Cramer 1997 . Examples of

empirical relationships between d 13

C of methane and

maturity of source organic matter and our modelled

isotope trends are also plotted in this figure. The

Geologicheskaya field is located adjacent to the

Yuzhno Russkoe field, where the rock samples for

our experimental work were cored. The modelled

d 13

C trend of methane for source organic matter

maturity above 1.5% vitrinite reflectance follows the

general trend of the earlier published empirical rela-

tionships. It is situated between the trend of type IIŽ . Žkerogen Fig. 6, line A and type III kerogen Fig. 6,

. Ž .line C both developed by Faber 1987 . The mod-Ž .elled trend is similar 1 to 2‰ lighter to that

predicted by the empirical relationship of Shen et al.Ž . Ž .1988 for coal-derived methane Fig. 6, line B . For

low maturity levels, however, our model calculates

much lighter carbon isotope ratios of methane than

predicted by empirical relationships for type III kero-Ž . 13

gen Fig. 6 . d C-values of methane are as low as

y44‰ at 0.6% vitrinite reflectance. The fluctuations

in modelled carbon isotope compositions below a

vitrinite reflectance of about 0.6% result from the

small number of reactions contributing at the earliest

stage of methane generation. The modelled carbon

isotope ratios of methane for low maturation matchthe isotope ratio of methane from natural gas as

observed today within the reservoirs of the PokurŽ .formation Fig. 6 . The modelled stable carbon iso-

tope ratio of the cumulative methane generated in the

Pokur formation is y46‰.

These results confirm that early thermogenic

methane generated within the Pokur formation should

have an isotopic signature similar to methane within

the large gas accumulations. In this respect the model

of early thermogenic gas generation of GalimovŽ . Ž .1988, 1995 , Galimov et al. 1990 is neither contra-

dicted nor supported. In the Pokur formation only

about 1% of the methane potential is realized up to

now and only this ‘early’ thermogenic methane has

the isotopic signature matching the gas within the

reservoirs. Clearly, the possibility of mixing with

bacterial methane characterized by a similar light

carbon isotope signature is not discarded by these




Fig. 6. Carbon isotope composition of methane in natural gas from Geologicheskaya field in the Pokur formation as a function of sourceŽ .organic matter maturity compared with modelled trends and empirical relationships. Empirical relationships for type II A and type III

Ž . Ž . Ž . Ž .kerogen C taken from Faber 1987 for type III kerogen B from Shen et al. 1988 .

data. The influence of a release of methane from

deep groundwater on reservoir filling in northernŽ .West Siberia is discussed elsewhere Cramer, 1997 .

7. Conclusion

A new concept is presented to describe stable

carbon isotope fractionation during generation of

natural gas. The model simulates kinetic isotope

effects as differences in activation energy between

reactions involving12

C- and13

C-methane genera-

tion. This approach is based on established and

widely used concepts of hydrocarbon generation ki-

netics and inherently implies a temperature depen-

dence of the kinetic isotope effect. Methane genera-

tion and isotope fractionation during open-system

pyrolysis experiments are calculated from a set of

parallel first-order reactions. Laboratory experiments

were carried out with two rock samples of the Pokur

formation from northern West Siberia. Measured

carbon isotope ratios of methane generated during

pyrolysis experiments were converted to the geologi-

cal temperature history of the area. The main find-

ings of this work can be summarized as follows.v Isotope values of methane measured during

open-system pyrolysis experiments can be explained

by temperature-dependent kinetic isotope fractiona-

tion from a set of parallel first-order reactions with

assumed equal initial carbon isotope compositions of

methane precursors.The best match between mea-

sured carbon isotope ratios of methane generated

during open-system pyrolysis experiments and model

predictions was obtained by applying a difference in

activation energy between12

C- and13

C-methane

generation of D E s E y E s y102 and y103a a a12 C 13C

J moly1 for the two rock samples. This difference in

activation energy was assumed to be equal for all

parallel reactions.

v Methane precursors in organic matter of coaly

sandstones from the Pokur formation show a carbonŽ .isotope composition evidently lighter y33.2‰ than

Ž .bulk organic matter y23.5‰ .




v Because of its direct relation to kinetic parame-

ters the new isotope fractionation concept can be

incorporated into numerical basin models to simulate

carbon isotope ratios of methane from individual

source rocks and for individual basin histories.

v We hope that our new model will develop into

a proper tool for hydrocarbon exploration. For this

purpose it will be necessary to model hydrocarbon

generation and associated isotope fractionation from

many well studied source rocks around the world.

v Application of the model to source bed organic

matter of the Pokur formation from northern West

Siberia provides an explanation of light methane

within the gas accumulations of the Pokur formation

as in situ generated thermogenic gas derived from

the low mature coaly organic matter.

Acknowledgements

The authors thank Dr. R.G. Schaefer and A.

Kolloff for support with the pyrolysis experiments

and the interpretation of kinetic parameters. We are

grateful to Dr. N.V. Lopatin, O.I. Simonenkova and

P. Gerling who offered isotope data of natural gas

from northern West Siberia. The authors thank M.

Rooney and an anonymous reviewer for important

and specific improvements. The study benefitted

considerably from substantial, in particular financial

sup port by R uhrga s, E ssen , V EB A O il,Gelsenkirchen, and Wintershall, Kassel. Financial

support by the Bundesministerium fur Bildung, Wis-¨Ž .senschaft, Forschung und Technologie BMBF ,

Kennziffer GAS 1000, is gratefully acknowledged.

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Modeling Isotope Fraction During Primary Cracking of Natural Gas

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