Isotopic evidence for quasi-equilibrium chemistry in thermally mature natural gases

Isotopic evidence for quasi-equilibrium chemistry in

thermally mature natural gases

Nivedita Thiagarajan

a,1

, Hao Xie

, Camilo Ponton

, Nami Kitchen

, Brian Peterson

, Michael Lawson

, Michael Formolo

Yitian Xiao

, and John Eiler

Department of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125;

Geology Department, Western Washington

University, Bellingham, WA 98225;

ExxonMobil Corporate Strategic Research, Annandale, NJ 08801;

ExxonMobil Upstream Business Development, Spring,

TX 77389; and

ExxonMobil Upstream Research Company, Spring, TX 77389

Edited by Mark H. Thiemens, University of California San Diego, La Jolla, CA, and approved January 17, 2020 (received for review April 25, 2019)

Natural gas is a key energy resource, and understanding how it

forms is important for predicting where it forms in economically

important volumes. However, the origin of dry thermogenic natural

gas is one of the most controversial topics in petroleum geochem-

istry, with several differing hypotheses proposed, including kinetic

processes (such as thermal cleavage, phase partitioning during

migration, and demethylation of aromatic rings) and equilibrium

processes (such as transition metal catalysis). The dominant para-

digm is that it is a product of kinetically controlled cracking of long-

chain hydrocarbons. Here we show that C

+

n

-alkane gases (ethane,

propane, butane, and pentane) are initially produced by irreversible

cracking chemistry, but, as thermal maturity increases, the isotopic

distribution of these species approaches thermodynamic equilib-

rium, either at the conditions of gas formation or during reservoir

storage, becoming indistinguishable from equilibrium in the most

thermally mature gases. We also find that the pair of CO

and C

(methane) exhibit a separate pattern of mutual isotopic equilibrium

(generally at reservoir conditions), suggesting that they form a sec-

ond, quasi-equilibrated population, separate from the C

to C

com-

pounds. This conclusion implies that new approaches should be

taken to predicting the compositions of natural gases as functions

of time, temperature, and source substrate. Additionally, an isotopi-

cally equilibrated state can serve as a reference frame for recogniz-

ing many secondary processes that may modify natural gases after

their formation, such as biodegradation.

stable isotopes

|

compound-specific isotope analysis

|

clumped isotopes

|

natural gas

|

methane

atural gas is primarily composed of volatile alkanes contain-

ing five or fewer carbon atoms and is widely distributed in the

subsurface. It is a key resource (1), and is increasingly viewed as

a transition fuel that can reduce CO

emissions relative to coal

and oil as the world

’

s economies move toward carbon-free en-

ergy systems. However, the utilization of natural gas poses en-

vironmental risks, as leakage contributes significantly to total

atmospheric methane, a significant greenhouse gas. Ethane,

propane, and butane have short atmospheric lifespans, but they

also increase the production of tropospheric ozone, a respiratory

hazard and pollutant (2, 3).

Understanding the mechanisms of natural gas formation is

critical for predicting where it forms in economic volumes and

for recognizing its release to the environment. Hydrocarbons in

natural gas are believed to come from two sources, one from

biological processes (

“

biogenic gas

”

) (4) and the other from the

thermal cracking of kerogen and oil (

“

thermogenic gas

”

). There

is disagreement over the origin of thermogenic gas. The pre-

dominant view is that it is created by irreversible, thermally acti-

vated breakdown of hydrocarbon solids and liquids, with reactions

dominated by the cleavage of carbon

−

carbon bonds (or

“

crack-

ing

”

) (5, 6) (Fig. 1

). However, laboratory experiments involving

heating of hydrocarbons generally produce hydrocarbon gases that

differ in molecular composition from natural gases. Natural gas

reservoirs tend to have greater than 80% methane, while pyrolysis

experiments only produce 10 to 65% methane (7

–

10). Additionally

hydrocarbons exist in geologic environments at temperatures that

are much greater than their predicted stability based on experi-

mentally derived models of catagenesis (11, 12).

Most explanations for this discrepancy argue that natural gas

is generated with a chemistry more similar to products of crack-

ing experiments, but its molec

ular proportions are then modi-

fied by secondary processes, such as methane enrichment by

buoyancy-driven fractionation during the migration of gas from its

source reservoir (13, 14) or methane enrichment from exception-

ally high-temperature catagenesis at equivalent thermal maturities

far in excess of those explored by most experiments (12). Addi-

tionally, methane-rich thermogenic gases are often suspected of

containing a component of biogenic gas (e.g., ref. 15). None of

these processes challenge the fundamental view of catagenesis as a

family of irreversible reactions that break down larger hydrocarbon

molecules to form smaller ones (Fig. 1

One alternative hypothesis holds that thermogenic gases are

generated through catalytic equilibrium processes. Previous work

has suggested that hydrocarbons, water, and authigenic minerals

in hydrocarbon reservoirs are in a metastable equilibrium (16

–

19),

while other laboratory experiments have suggested that methane,

ethane, and propane are in a metathetic equilibrium (20). Support

for the metastable equilibrium hypothesis comes from theoretical

calculations (16) as well as laboratory experiments that mix pre-

cursor hydrocarbons with catalysts, which, upon heating, produce

low-molecular weight

-alkane gases with molecular proportions

Significance

The mechanisms of natural gas formation are important to the

carbon cycle and predicting where economical amounts of nat-

ural gas form. However, the formation mechanisms of natural

gas are not clear, with hypotheses including both irreversible

chemical processes such as thermal cracking of long-chain hy-

drocarbons and thermodynamic equilibrium processes such as

transition metal catalysis. Here we show that hydrocarbon spe-

cies in natural gases are initially produced by irreversible cracking

chemistry, but, as thermal maturity increases, the H and C iso-

topic distributions within and among coexisting light

n

-alkanes

approach thermodynamic equilibrium, either at the conditions of

gas formation or during reservoir storage. Our finding has sig-

nificant implications for natural gas exploration.

Author contributions: N.T., H.X., C.P., and J.E. designed research; N.T., H.X., C.P., N.K., B.P.,

M.L., M.F., and Y.X. performed research; N.T

., H.X., C.P., and J.E. analyzed data; and

N.T., H.X., C.P., B.P., M.L., M.F., and J.E. wrote the paper.

The authors declare no competing interest.

This article is a PNAS Direct Submission.

Published under the

PNAS license

To whom correspondence may be addressed. Email: nivedita@caltech.edu.

This article contains supporting information online at

https://www.pnas.org/lookup/suppl/

doi:10.1073/pnas.1906507117/-/DCSupplemental

First published February 11, 2020.

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more closely resembling natural gases (21

–

23). Finally, another

hypothesis is that thermogenic gases are created by a network of

radical chain reactions among the gas species, dominated by fast

radical transfer reactions and beta-scission leading to thermody-

namic equilibrium (Fig. 1

). If these equilibrium hypotheses are

correct, it implies that natural gases are products of thermal

breakdown of larger hydrocarbons, but form gases in proportions

governed by the free energies of formation of alkanes and related

alkenes and radicals, rather than the rate constants for irreversible

cracking of large molecules. This difference would substantially

change how we predict and interpret the chemistry of natural gases

as functions of temperature, time, and compositions of source

substrates.

The distributions of naturally occurring stable isotopes (princi-

pally

C and D) within and between the molecular constituents of

natural gases offer tests of whether thermogenic gas production

is controlled by irreversible cracking or equilibrium processes.

Cracking chemistry yields products having isotopic contents that

depend on the compositions of the substrates and the kinetic

isotope effects (KIEs) associate

dwithirreversiblereactions,

whereas systems in a metastable equilibrium have isotopic distri-

butions closely resembling thermodynamic equilibrium, which can

be predicted based on the partition function ratios of the com-

pounds of interest. It has been previously shown that methane,

ethane, and propane in some natural gases have molecular

proportions and

C ratios that resemble thermodynamic

equilibrium and not thermal cleavage (21).

Here we extend that argument in three ways: 1) We have

measured or compiled C and H isotopic compositions of methane

), ethane (C

), propane (C

), butane (C

), pentane (C

), and

for 119 gases from 20 conventional, unconventional, oil-

associated, and nonassociated natural deposits around the world.

This extended database provides a far wider sampling and allows

us to use stricter tests of the equilibrium hypothesis than have been

previously considered. 2) Additionally, we include methane clumped

isotope compositions (

values) for a large subset of the gases

we examine (24

–

26). The

value principally reflects enrich-

ment (or depletion) in

D relative to a stochastic distri-

bution of

C and D among all methane isotopologues, and, in

isotopically equilibrated systems, the

value is a function of

temperature. 3) We compare measured isotopic compositions to

a comprehensive set of theoretically predicted equilibrium and

nonequilibrium fractionations between CO

and C

to C

spe-

cies. Our equilibrium models are based on new ab initio calcu-

lations of molecular partition function ratios (see

SI Appendix

for details). Models of nonequilibrium carbon and hydrogen

isotope fractionations are based on previous estimates of KIEs

associated with homolytic cleavage and beta-scission of methyl,

ethyl, propyl, butyl, and pentyl radicals from an

-alkane pre-

cursor (27, 28) (

SI Appendix

Results and Discussion

We find that our most thermally immature samples (R

<

0.8) are

consistent with stable isotope distributions controlled by KIEs.

However, natural gases of moderate or greater maturity (R

>

0.8)

have C

+

gases (ethane, propane, butane, and pentane) that are

consistent with thermodynamic equilibrium for carbon (Fig. 2 and

SI Appendix

,Fig.S1

) and hydrogen isotopes (

SI Appendix

,Fig.S2

considering the combined analytical and model uncertainties. This

pattern is also seen in a global compilation (29) of natural gases

(

SI Appendix

,Fig.S3

). There are three important exceptions to

this pattern which we discuss in the following paragraphs.

One subset of gases that are significant exceptions to this

generalization have

e

C(C

-C

) values greater than 5

‰

and do

not fall on or near the thermodynamic equilibrium fractionation

line in Fig. 2. These samples are shaded in Fig. 2 and

SI Appendix

Fig. S2

and share several other traits: All have low apparent

temperatures and relatively low

Cand

DofCH

, and tend to

have higher than average values for

CofCO

. These isotope

signatures are all suggestive of biodegradation of oil and/or gas

and resemble isotopic signatures previously seen in natural gases

from the Antrim Shale, Michigan

—

a biodegraded natural gas

deposit (30, 31).

Another subset of gases that are not in isotopic equilibrium

are the hydrogen isotopes of

-butane and

-pentane (

SI Appen-

dix

, Fig. S4

). This deviation could be an analytical artifact, as it is

difficult to separate

-alkanes from

-alkanes. Another possibility

is that these species are actually not in equilibrium, and branched

-alkanes do not form in the same manner that

-alkanes do.

Third, we observe that methane and CO

generally are not

coequilibrated with the C

to C

hydrocarbons in natural gases

from most basins (

SI Appendix

, Fig. S5

). Instead, we find that this

pair of compounds exhibits its own pattern of isotopic signatures

that suggest a second quasi-equilibrated population, separate

from the C

to C

compounds. This feature is best illustrated in a

plot of

e

C(CO

−

) vs. the methane clumped isotope ap-

parent temperature, which shows that 73% of gas samples having

/(C

+

)

<

20 (in the thermogenic range) are consistent with

mutual thermodynamic equilibrium for the methane

value and

the intermolecular equilibrium for

C exchange between CO

and CH

(Fig. 3). It has been previously suggested that transition

metal catalysts can facilitate carbon isotope equilibrium between

and CH

(18). A notable exception to this trend is the suite of

2CH

Fig. 1.

(

) A schematic showing examples of butane degradation through

irreversible cracking reactions, and (

) a reversible radical reaction network.

*, radical.

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Thiagarajan et al.

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Eagle Ford gases, which have

e

C(CO

−

)valuesof40to

‰

, consistent with equilibration at temperatures of 100 °C to

140 °C

—

similar to the reservoir temperature of

∼

140 °C

—

but

methane clumped isotope compositions suggesting apparent tem-

peratures of

≥

200 °C, and, in some cases, exceeding the nominal

upper bound of thermogenic gas generation of 250 °C (24, 26, 32).

Several hypotheses have been put forward to explain the high

apparent methane clumped isotope temperatures of Eagle Ford

gases, including analytical artifacts and KIEs related to secondary

cracking (30). Thus, the deviation of Eagle Ford gases from this

pattern of CH

−

equilibrium may reflect the fact that they are

an unusual case where thermogenic methane clumped isotope

apparent temperat

ures do not approach methane formation

temperatures (26).

Some gas samples with C

/(C

+

)

>

—

generally considered

indicative of biogenic gas or supermature thermogenic gas

—

show

e

C(CO

−

) fractionations greater than, equal to, and less than

equilibrium values at the temperatures corresponding to methane

value (Fig. 3). The Santa Barbara Basin seep samples have an

e

C(CO

−

) much greater than expected for equilibrium val-

ues, reflecting unusually high

CofCO

(

∼

‰

) with moderate

CofCH

(

∼−

‰

) and elevated [CO

]. We suggest that the

high

CofCO

values as well as the large

e

C(CO

−

) (which

corresponds to a temperature of

∼

10 °C) in this suite is due to

methanotrophic processes increasing CO

concentrations and

driving CO

and C

to equilibrate, possibly associated with sulfate-

dependent methane oxidation in shallow sediments at bottom-

water temperatures. A second noteworthy exception of this kind

is the coal-derived gases in the Rotliegend field, which have

e

(CO

−

) values much lower than values predicted for thermo-

dynamic equilibrium and have the highest

CofCH

values of

the suite. These coal-derived gas s

amples (33) could h

ave a different

set of precursors than the gases derived from marine source rocks,

which are the bulk of the rest of the suite. The high-maturity

Haynesville Shale formation in addition to the biodegraded gases

(Nebo Hemphill and Olla) have C

+

ratios greater than 20, but

e

C(CO

−

) values generally consistent with thermodynamic

equilibrium. We speculate that, in these fields, methane was

introduced to the basin but has had sufficient time and/or exposure

to catalysts to approach C isotopic equilibrium with CO

The relationship between methane and the higher order

-alkanes

is further illuminated by the ob

servation that 88% of measured

hydrogen isotope fractionations between methane and higher-

order hydrocarbons are consiste

nt with thermodynamic equi-

librium at their corresponding methane clumped isotope ap-

parent temperature (

SI Appendix

,Fig.S6

). However, only 30%

of these gas samples are in carb

on isotope equilibrium between

methane and C

to C

species at that same temperature (Fig.

4). Specifically, gas

samples with a low methane clumped iso-

tope apparent temperature (0 °C to 120 °C) tend to have car-

bon isotope fractionations between methane and C

to C

alkanes

that are greater than equilibrium at that methane apparent tem-

perature and near the predicted compositions of products of ho-

molytic cleavage or beta-scission, whereas samples with higher

methane clumped isotope apparent temperatures tend to lie closer

to the equilibrium fractionation line (Fig. 4

). Additionally, sam-

ples with low methane clumped isotope apparent temperatures

tend to have lower methane

C values, in the range commonly

associated with biogenic gas, whereas samples with higher meth-

ane temperatures have higher methane

C values, consistent

with common ranges for thermogenic gas. These patterns of var-

iation can be explained if the carbon isotope composition of

thermogenic methane begins in or near equilibrium with coex-

isting C

to C

hydrocarbons when it first forms, but then sub-

sequent addition of biogenic methane without subsequent

participation in

“

metastable equilibrium

”

reactions involving the

to C

hydrocarbons, lowers the

C of methane, increasing

values of

e

C(C

-C

) value (where x

=

2 to 5). In the case of

biogenic addition of methane, hydrogen isotope exchange

among all hydrocarbons must keep pace with addition of this

exotic methane, and the newly formed methane must generally

be capable of exchanging carbon with coexisting CO

,asthese

quasi-equilibria are maintained (Fig. 3 and

SI Appendix

, Figs. S2

and S6

). Hydrogen exchange in

-alkanes has previously been

documented to occur within approximately year timescales (34).

So, in effect, only the methane carbon pool appears to remain

048

-5



C (butane-ethane)



C (butane-ethane)



C (propane-ethane)

048



C (propane-ethane)



C (butane-ethane)



C (pentane-propane)

-5



C (pentane-propane)

Thermodynamic Fractionation

Homolytic C-C Cleavage Instantaneous

Homolytic C-C Cleavage Cumulative

Homolytic C-C Cleavage Rayleigh

Beta Scission Instantaneous

Beta Scission Cumulative

Hadrian/Keathley Canyon

Hoover-Diana

Walker Ridge

Green Canyon

Galveston

SYU

Rotliegend

Sleipner Vest

Eagle Ford

La Barge

Santa Barbara Basin

Above Haynesville

Nebo Hemphill

Olla

Scotian Basin

Potiguar

020



C (butane-ethane)

020

UNCONVENTIONAL

NONASSOCIATED

AND ASSOCIATED

CONVENTIONAL

NONASSOCIATED

CONVENTIONAL OIL

ASSOCIATED &

SOLUTION GAS

<0.5

1.5

2.5+

<0.5

1.5

2.5+

Fig. 2.

e

C (butane

−

ethane) vs.

e

C (propane

−

ethane), and

e

C(pentane

−

propane) vs.

e

C (propane

−

ethane), color-coded by (

and

) reservoir name or (

and

, a proxy for thermal maturity calculated via

C of ethane (46). Eighty-eight percent of measured carbon isotopes of C

-C

species and 68% of pentane

species are consistent with being in thermodynamic equilibrium. Hydrocarbons initially form through homolytic cleavage (yellow and blue lines) or

-scission (brown

lines) mechanisms, as seen in the most-immature reservoirs in our datasets,

such as Walker Ridge and Keathley Canyon. As maturity (time and temperature) in-

creases, a radical reaction network chemistry or catalytic chemistry begins to operate, and the reservoirs approach isotopic equilibrium. The appr

oach to equilibrium

is seen in moderate-maturity reservoirs such as Green Canyon and SYU. The reservoirs that are the most mature, such as Sleipner Vest, Galveston, Above

Haynesville,

and Hogsback, show compositions characteristic of having reached isotopic equilibrium (red solid line). The shaded gases are gases associated with

biodegradation.

Thiagarajan et al.

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isolated from the carbon pool in the C

to C

species once an

exotic, low-

C methane source has been introduced.

We also reexamined previously published isotopic data mea-

sured on products of pyrolysis experiments (both catalyzed and

not) to see whether those systems also provide evidence for

equilibrium processes (35

–

39). We confirm the previous sug-

gestion that catalyzed pyrolysis generates gas components that

approach equilibrium (35) (

SI Appendix

, Fig. S7

); moreover, we

find that noncatalyzed pyrolysis, despite producing gases with

molecular proportions that differ from natural gases, also com-

monly exhibit intermolecular C and H isotope fractionations that

approach equilibrium and differ from expectations for homolytic

cleavage and beta-scission (

SI Appendix

, Fig. S8

). This agreement

is relatively close for lower-te

mperature noncatalyzed pyroly-

sis experiments (

≤

400 °C). Large departures from equilibrium

are observed at the highest tem

peratures, generally falling to

progressively larger intermole

cular fractionations at higher

temperatures

—

a pattern that contrasts with natural gases (

Appendix

,Fig.S9

), equilibrium predictions, and models of well-

defined kinetically co

ntrolled processes.

In summary, we find evidence that the distribution of stable

isotopes among the C

to C

hydrocarbons and CO

in natural

gas generally conform to two families of mutual quasi-equilibria:

one being the C isotope contents of the C

to C

species plus the

H isotope contents of all C

to C

species, and the second being

C isotopes in methane and CO

. Moreover, equilibrium in-

termolecular isotopic distributions are also observed in catalyzed

pyrolysis experiments and noncatalyzed pyrolysis experiments

conducted at relatively low temperatures (

≤

400 °C).

Radical Reaction Network Model.

Most of the compounds present in

natural gas (alkanes, aromatics, thiols, etc.) are thermodynamically

metastable for the temperatures and pressures where they exist

(16, 40). We explore whether our findings could reflect the at-

tainment of a

“

metastable cyclic equilibrium,

”

through a network

of radical chain reactions among the gas species, dominated by fast

radical transfer reaction and beta-scission leading to metastable

equilibrium as has been previous

ly suggested (28). We tested

the plausibility of this hypothe

sis by constructing a model that

tracks the distribution of

C among coexisting hydrocarbons that

participate in free radical chain reactions. We do not address

H isotope exchange in the model, as hydrogen in hydrocarbon

molecules is more susceptible to isotope exchange than carbon

under conditions seen in natural gas fields on timescales of days

(34). Therefore, the equilibrium signature that we see in hydrogen

isotope fractionation can be explained by an intermolecular hy-

drogen isotope equilibration, without implying a significant re-

vision to common understanding of cracking reactions. Our carbon

isotope model includes 24 species and 79 reactions, including

initiation, H transfer, radical decomposition, radical termination,

and radical addition reactions. We acquired kinetic parameters

(activation energy and preexponential factor) for each reaction

from the literature (41

–

43). We find that, when a

C spike is in-

troduced in any of the species present at the outset of the model

(methane, ethane, propane, and butane), that spike is transferred

to all of the other hydrocarbon species, and, once steady state is

reached, the

C ratio of each species equals the equilibrium

value. This finding is true regardless of which species contains the

C spike when the model is initiated (

SI Appendix

,Fig.S10

). At

500 K, our model comes to equilibrium within a year. We are

unable to run the model at 423 K, due to limitations in compu-

tational power. However, in our model, the exchange rate is

100

200

300

400

Methane Temperature

100

200

300

400

Methane Temperature

100

200

300

400

Methane Temperature

C (butane-methane)

Deviation of

C (butane

-methane) from equilibrium

C (butane-methane)

-60

-50

-40

-30

C of C

-60

-50

-40

-30

C of C

-10

=0.7

Fig. 4.

e

C(butane

−

methane) vs. methane clumped isotope apparent tem-

perature for gases considered in this study color-coded by the corresponding

C of methane for each (

)gasor(

) reservoir. Gas samples with low

methane clumped isotope apparent temperatures also have low

Cof

methane and tend to lie above the equilibrium line in this figure, near the

curves for homolytic cleavage or

-scission, whereas gases with higher methane

apparent temperatures have higher

C of methane values and lie closer to

the equilibrium fractionation line. This correlation is depicted in

and is con-

sistent with an input of biogenic methane with very low

C values at low

methane temperatures, although we cannot rule out a contribution of low

C values via kinetic processes. The red circles in

indicate binned averages

over 50 °C intervals. We excluded the Eagle Ford gases for this calculation, as

they are known to have a KIE affecting the methane temperatures. (See Fig. 2

for legend.) The measurement errors for carbon isotopes of butane and CH

are 0.5

‰

, and errors plotted for methane temperatures are 1

100

200

300

400

Methane Temperature

Thermodynamic Fractionation

Haynesville

Marcellus

Walker Ridge

Green Canyon

Galveston

SYU

Rotliegend

Sleipner Vest

Eagle Ford

La Barge

Santa Barbara Basin

Above Haynesville

Nebo Hemphill

Olla

Searcy

50+

C (CO

-methane)

C (CO

-methane)

)

100

200

300

400

Methane Temperature

Fig. 3.

e

C(CO

−

methane) of carbon isotopes vs. methane temperature

for gases in the study subdivided by (

) basin name and (

) gas wetness.

Seventy-three percent of samples having C

/(C

+

) values of less than 20

(excluding Eagleford) are consistent with the thermodynamic equilibrium

fractionation (red solid line). Gases associated with biodegradation are

shaded. The Eagle Ford gases are also shaded, as they are suspected to be

influenced by a KIE in clumped isotopes of methane (26). The measurement

errors for carbon isotopes of CO

and CH

are 0.5

‰

, and errors plotted for

methane temperatures are 1

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limited by the radical initiation steps that have activation energies

ranging from 51 kcal/mol to 88 kcal/mol (41). If we apply an

Arrhenius relationship, the rate of those reactions decreases by a

factor of 10

to 10

when the temperature changes from 500 K to

423 K. Therefore, we expect that the timescale of equilibration

at geological temperatures will range from 10 kya to 10 Mya.

Given these timescales, these reactions are geologically plausible

and relevant. We propose that, similarly to our radical reaction

model network, natural gas components exchange carbon with one

another through multiple radical reactions, allowing their

contents to approach equilibrium with one another.

Model for Natural Gas Formation.

The preceding discussion and

model of metastable cyclic equilibrium attempts to explain the

pattern of equilibrium isotopic fractionations seen in C

to C

components of natural gases; but the exceptions to that pattern are

equally significant (see

SI Appendix

for additional discussion on

clumped isotopologues of small

-alkanes). We propose that

three separate processes are responsible for the isotopic varia-

tions observed in natural gas components, and that the isotopic

“

fingerprint

”

of any one gas source reflects the unique combina-

tion of these processes.

First, we argue that the H isotope compositions of C

to C

hydrocarbons and C isotope compositions of C

to C

hydro-

carbons often reflect an approach to metastable cyclic equilib-

rium during gas generation and/or deep subsurface storage. It has

been previously argued that such metastable equilibrium requires

catalysts to occur (27), although our reaction network model

achieved the same end state over geologically relevant tempera-

tures and times. We conclude that a metastable cyclic equilibrium

might be aided by solid catalysts, but they are not required. An

important point to note here is that the hydrocarbons in low-

maturity systems are not generated in equilibrium, as seen in the

two least-mature reservoirs in our dataset (Keathley Canyon and

Walker Ridge), which fall near the

-scission fractionations and

not near thermodynamic equilibrium. As maturity increases, the

hydrocarbons fall closer to the equilibrium fractionation line. The

approach to equilibrium is seen in moderate-maturity gases such

as Santa Ynez Unit (SYU) and Green Canyon, while the attain-

ment of equilibrium is seen in our most mature gases such as

Hogsback, Above Haynesville, Sleipner Vest, and Galveston

(Fig. 5).

Second, because we find that the CO

−

pair generally

attains carbon isotope equilibrium without either species nec-

essarily being in C isotope equilibrium with C

+

hydrocarbons,

we suggest that oxidation of methane to form CO

and reduction

of CO

to form methane provides a second, effectively separate

reaction network that allows these two species to maintain equi-

librium without efficient C exchange with other species (18). This

is reasonable because CH

is the slowest species to react in our

model of hydrocarbon metastable cyclic equilibrium chemistry, for

example, its hydrogen abstraction reactions being an order of

magnitude slower than for other hydrocarbons (the k of reaction

78 listed in

SI Appendix

is one order of magnitude slower than

reactions 53, 47, and 49). Therefore, it is easy to imagine cases

where methane will react more quickly with oxidants than with

hydrocarbon radicals. Additionally, C

−

C bonds in C

+

species are

weaker and relatively easy to cleave compared to C

−

HorC

−

bonds in CH

and CO

. It is noteworthy that the CO

−

system

often approaches equilibrium at temperatures lower than estab-

lished thermogenic gas generation temperatures and similar to

reservoir conditions. For this reason, we suspect gases often enter

shallow reservoirs near metastable cyclic equilibrium with respect

to isotopic distributions among all molecular species, but, while gas

is stored at shallower depths, methane oxidation and CO

re-

duction quickly redistribute

C between these two species. This

redistribution could be driven by biological cycling of carbon

between methanogens and methanotrophs, or it could reflect a

catalyzed abiotic reaction (18).

Third, we see that the most marked departures from quasi-

equilibrium isotope distributions among gas components, in-

cluding highly aberrant C isotope fractionations among the C

+

species and/or between methane and C

+

species, are associated

with recognized signatures of biodegraded gas (especially low

C of methane). This feature is seen in reservoirs such as Olla

and Nebo Hemphill. We suggest that this signature becomes

dominant when biogenic production of CH

and destruction of

+

hydrocarbons has altered a large fraction of the initial gas

charge, overwhelming the earlier signature of metastable cyclic

equilibrium and sometimes outstripping the process that pro-

motes quasi-equilibrium of C isotopes between CO

and CH

The mechanisms we propose for hydrocarbon equilibration or

−

equilibration are similar to previous suggestions that

-alkanes (and other small organic molecules) are in a metastable

equilibrium with water in hydrocarbon reservoirs (16, 40). How-

ever, Helgeson et al. (16) suggested C

-C

hydrocarbons, in par-

ticular, would not participate in these equilibrating reaction

networks at the conditions of natural gas sources or reservoirs.

This conclusion was largely a consequence of his estimates of

reservoir [O

] concentrations. Our finding that these species

commonly participate in metastable equilibrium with respect to

C isotope distributions would be consistent with Helgeson et al.

’

treatment of metastable equilibria if log

(g) in hydrocarbon

source rocks were

∼

0.5 lower than Helgeson et al. calculated.

Implications.

Our primary finding, that natural gas formation

generally occurs via reaction networks that incorporate meta-

stable equilibrium between some subsets of species, has signifi-

cant implications for central questions regarding the origins and

fates of geological hydrocarbons: Where and when do natural

gases form? What are the chemical proportions of major natural

gas components, and how do they vary in time and space? These

Thermal maturity/burial

(OLLA)

OIL, GAS

(HAYNESVILLE

MARCELLUS )

OIL, GAS

GAS

(GREEN CANYON

& SYU)

(

WALKER RIDGE

& KEATHLEY CANYON)

NON

EQUILIBRIUM

CRACKING

Rock

Diagenesis

Early

ene

sis

tag

ene

Depos.

SOURCE ROCK

HARGED

RESERVOIRS -

METASTABLE CYCLIC

EQUILIBRIUM

(

)

RESERVOIR

SCALE

CYCLING

OIL+

GAS

GAS MIGRATION

BIOGENIC ADDITION

Ro< ~1

Ro ~1-2

Ro> ~2

Fig. 5.

Our model for

-alkane generation in natural gas reservoirs. Hy-

drocarbon species are initially produced by cracking mechanisms. This

cracking signature is seen in very immature reservoirs such as Walker Ridge

and Keathley Canyon. As maturity increases, the hydrocarbons fall closer to

the equilibrium fractionation line. The approach to equilibrium is seen in

moderate-maturity gases such as SYU and Green Canyon, while the attainment

of equilibrium is seen in our most-mature gases such as Above Haynesville,

Hogsback, Sleipner Vest, and Galveston. Ro indicates vitrinite reflectance, while

green in the charged reservoirs indicates oil and red indicates gas.

Thiagarajan et al.

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questions are generally approached by merging models of basin

thermal evolution with kinetic models for hydrocarbon generation

that are based on extrapolations to geological conditions of the

rates of gas and oil production in high-temperature, laboratory-

timescale experiments. This method may still be the appropriate

approach to predicting the onset of petroleum formation (i.e., as

we find the least-mature natural gases express kinetically con-

trolled fractionations), but, as petroleum systems deepen and

thermally mature, the spatial and temporal distributions and

chemical compositions of gases will be more strongly controlled

by the relative thermodynamic stabilities of major components

and their possible breakdown products; that is, high abundances

of components may be buffered indefinitely where temperature,

pressure, and fugacities of reactive species (e.g., O

and H

) permit

their persistence and destroyed where other compounds become

more energetically favorable. Helgeson et al. (16) suggested that

proportions of liquid, gas, and solid in petroleum-forming systems

should be evaluated in a way analogous to how we use thermo-

dynamic analysis of other quasi-equilibrium processes, such as

partial fusion of rocks. The findings here extend this argument,

suggesting that the partial pressures of gases of moderately to

highly mature systems also follow thermodynamic principles. For

example, one practical implication of this line of reasoning is that

the conversion of

“

wet

”

+

-rich) to

“

dry

”

(methane-dominated)

gas is controlled by thermodynamic conditions (e.g., T, fO

,and

) and not only source rock maturity as it is conventionally

understood. As such, any effort to predict the possible range in the

abundance of economically and environmentally important vola-

tile hydrocarbons should incorporate thermodynamic models

alongside the thermal history of the source and reservoir interval

in which they are generated and stored.

Methods

Methane Analysis.

Methane (CH

) was purified from mixed-gas samples using

previously described methods (44).

C, and

of methane were measured

using the Ultra, using previously described methods (44), and reported in

Dataset

S1.

Dand

C values are expressed as

=

((R

VSMOW

)

−

1)*1,000, and

=

((R

VPDB

)

−

1)*1,000, where R

=

[D/H], R

=

[

C)]),

VSMOW is Vienna Standard Mean Ocean Water, and VPDB is Vienna Pee Dee

Belemnite. Clumped isotope compositions are expressed using

notation,

where

=

((

R*)

−

1)*1,000,

=

[

+

[

]/[

], and 18R*

=

(6*[R

)

+

(4*R

H*R

C); 18R* is the 18R value expected for a random in-

ternal distribution of isotopologues given the

Cand

D value of the sample

(11). The specified isotope ratios are measured from the corresponding ion

beam current ratios, standardized by comparison with a standard of known

composition.

data are reported as per mil (

‰

), where 0

‰

refers to a

random distribution of methane isotopologues. We present measurement

uncertainties for individual samples as 1 SE of the internal measurement

variability for a single measurement. Reported uncertainties for inferred

temperatures are propagated from the 1

errors for

values. Finally,

values can be related to formation t

emperature (K) via the equation

=

−

0.0117*(10

)

+

0.708*(10

)

−

0.337 (25).

Higher

n

-alkane Stable Isotope Measurements.

Compositional analysis of gas

samples was perfomed using gas chromatography (GC) as well as thermal

conductivity and flame ionization detectors in Isotech Laboratories in

Champaign, Illinois. Stable isotope values for gas components are measured

using isotope ratio mass spectrometers and reported in

Dataset S2

. The gas

samples are separated into individual components using a GC system. A

cupric oxide furnace then combusts each component into CO

and H

After purification, CO

is analyzed directly, whereas the H

O is reacted with

zinc to generate H

gas. We use error bars of 0.5

‰

for carbon isotopes and

‰

for hydrogen isotopes for all measured hydrocarbons (45).

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no. 8

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AND PLANETARY SCIENCES

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