Directory UMM :Data Elmu:jurnal:O:Organic Geochemistry:Vol31.Issue6.2000:

Organic Geochemistry 31 (2000) 553±575
www.elsevier.nl/locate/orggeochem

The kinetics of in-reservoir oil destruction and gas
formation: constraints from experimental and
empirical data, and from thermodynamics
Douglas W. Waples *
9299 William Cody Drive, Evergreen, CO 80439, USA
Received 10 May 1999; accepted 9 February 2000
(returned to author for revision 2 September 1999)

Abstract
Experimental kinetic data on the reactions of pure chemicals, destruction of heavy hydrocarbons, and gas formation
have been combined with thermodynamic theory and empirical data on oil and gas occurrences to constrain the range of
plausible activation energies and frequency factors for oil destruction and gas formation in nature. It is assumed explicitly
here that the kinetics of oil destruction and gas formation can be adequately described using a set of parallel ®rst-order
reactions. At geologic temperatures and pressures the mean activation energy for oil destruction and gas generation is about
59 kcal/mol (246.9 kJ/mol), with a frequency factor of about 1014.25 sÿ1 (1.78.1014 sÿ1). A narrow distribution of activation
energies [=1.5 kcal/mol (6.3 kJ/mol)] for destruction of oil seems intuitively more reasonable than a single activation
energy, and also seems to ®t empirical data on high-temperature occurrences of condensate slightly better. No large or
systematic variation in cracking rates or kinetics is apparent for di€erent oil types. Using these recommended kinetic

parameters, the maximum temperature at which oil can be preserved as a separate phase varies from about 170 C at geologically very slow heating rates to slightly over 200 C at geologically extremely fast heating rates. Using this model, oil
destruction occurs at slightly higher temperatures than those predicted by older kinetic models, but at considerably lower
temperatures than those suggested by some recent studies. Di€erences in predicted levels of cracking obtained from the
various models in use today can a€ect exploration decisions. # 2000 Elsevier Science Ltd. All rights reserved.
Keywords: Cracking; Kinetics; Thermodynamics; Gas generation; Oil destruction; Activation energy; Frequency factor; First-order;
Distributed kinetics

1. Introduction
In recent years the similar but nonidentical issues of
the kinetics of oil cracking and the kinetics of gas formation from oil have received some attention (e.g. Braun
and Burnham, 1988; Quigley and Mackenzie, 1988;
Ungerer et al., 1988; DomineÂ, 1989, 1991; Domine et al.,
1990, 1998; Enguehard et al., 1990; Domine and
Enguehard, 1992; Hors®eld et al., 1992; Kuo and
Michael, 1994, 1996; Pepper and Dodd, 1995; Behar and
Vandenbroucke, 1996; Waples, 1996; Schenk et al., 1997;
Burnham et al., 1997, 1998; McKinney et al., 1998).
Despite the variety of experimental systems employed, raw
* Tel.: +1-303-670-5114; fax: +1-303-670-5114.
E-mail address: dwaples@compuserve.com (D.W. Waples).

laboratory-pyrolysis data from those studies show many
important consistencies. However, the kinetic parameters
extracted by those workers from their raw data show much
greater variations than do the overall reaction rates. I
believe that those large di€erences in kinetic parameters
are neither supported by the raw data, nor consistent
with the mechanisms proposed for those reactions or
with the requirements of thermodynamics (Glasstone et
al., 1941; Benson and O'Neal, 1970; Benson, 1976).
It is normally assumed either that cracking follows
®rst-order kinetics, or that it can be described adequately
as the sum of a small set of ®rst-order reactions that run
in parallel. Arrhenius plots derived from isothermal
kinetics experiments carried out under high-temperature
laboratory conditions are generally consistent with the
idea of simple ®rst-order kinetics with a single activation

0146-6380/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.
PII: S0146-6380(00)00023-1

554

D.W. Waples / Organic Geochemistry 31 (2000) 553±575

energy (e.g. Burnham et al., 1997, 1998; McKinney et
al., 1998). Other workers, however, have disputed this
assumption. Domine and Enguehard (1992) and Domine et al. (1998) believe that cracking follows half-order
kinetics at geologic temperatures, and that the reaction
order increases with temperature. Still other investigators (e.g. Hors®eld et al., 1992; Schenk et al., 1997) have
used distributed kinetics and parallel ®rst-order reactions
to ®t their data from nonisothermal pyrolysis. Resolution of these issues would greatly improve both our
understanding of the chemical processes that control oil
destruction and our ability to model oil destruction
under geologic conditions.
A second problem is that many of the Arrhenius A factors (also called pre-exponential factors or frequency factors) proposed to date for the ®rst-order reactions in oil
cracking are, in my opinion, too high. Errors in estimating
A factors will lead to compensating errors in estimates of
activation energies, and ®nally to potentially serious errors
when those incorrect parameters are applied in maturity

modeling under geologic conditions. This paper, therefore, attempts to unify the various data sets into a more
appropriate and internally consistent kinetic model for oil
destruction and concomitant gas generation.

2. Raw experimental data
Behar et al. (1988), Ungerer et al. (1988), Hors®eld et al.
(1992), Schenk et al. (1997), Burnham et al. (1997, 1998)
and McKinney et al. (1998) have provided raw laboratory
data on the rates of decomposition of individual heavy nalkanes or C13+ hydrocarbons, or on the rates of gas
generation from oil. The remarkable similarity of the

measured reaction-rate constants for all those experiments indicates that we can indeed reproducibly measure important aspects of oil destruction and gas
generation in the laboratory. Table 1 shows that with
one exception the rate constants for the decomposition
of individual n-alkanes and of C13+ hydrocarbons vary
by less than a factor of three among experiments carried
out by three di€erent research groups on several di€erent types of oils. This excellent agreement clearly indicates that variations in oil composition play only a
secondary role in controlling the rates of these processes, at least in the laboratory.
Data on decomposition rates of n-alkanes and C13+
fractions (Behar et al., 1988; Ungerer et al., 1988; Burnham

et al., 1997; McKinney et al., 1998) actually refer to
similar phenomena, since both reactions monitor the
loss of irreplaceable oil-like material. However, none of
those experiments directly measured oil destruction, since
individual n-alkanes and C13+ hydrocarbons can be
cracked to other oil molecules as well as to gas and residue.
Nor did those studies attempt to measure gas generation.
Table 2 shows kinetic data obtained by direct measurement of the rates of formation of gas from oil. Once
again, the rate constants are almost identical for gas
generation from ®ve di€erent oils, including oils of very
di€erent compositions.
Comparison of the data in Tables 1 and 2 shows that
the median rate constant for gas generation at 350 C
(4.0.10ÿ8 sÿ1) is less than one-®fth that for decomposition of heavy hydrocarbons (22.10ÿ8 sÿ1). This result is
not surprising, since destruction of a particular heavy
hydrocarbon does not necessarily lead to the formation
of gas. Moreover, only about 40±45% of the mass of oil
cracked is converted into gas; the greater part forms

Table 1

Observed and calculated rates of decomposition of individual n-alkanes and C13+ hydrocarbons in oils at 350 C
Reaction

Medium
a

n-C16 disappearance
n-C16 disappearanceb
n-C16 disappearancea
n-C16 disappearanceb
n-C16 disappearancea
n-C16 disappearanceb
n-C25 disappearanceb
n-C25 disappearancea
C13+ disappearancea
C13+ disappearancea
C14+ disappearancea
C14+ disappearancea
a
b

c
d
e
f
g

North Sea oil
North Sea oil
High-paran oile
High-paran oile
High-sulfur oilf
High-sulfur oilf
Ardjuna oile
Arabian oilf
Boscan oilf
Pematang oile
Boscan oilf
Pematang oile

E (kcal/mol)

51.81
51.81
63.59
63.59
63.57
63.57
67.9
67.5
64.8
69.4
57.34
58.15

E (kJ/mol)
216.8
216.8
266.1
266.1
266.0
266.0

284.1
282.4
271.1
290.4
239.9
243.3

A (sÿ1)

Measured k (sÿ1)
11

2.710
2.71011
4.11015d
4.11015d
4.71015
4.71015
3.41017
1.31017

2.811016
5.091017
1.111014
6.511013

ÿ7c

1.7310
2.0810ÿ7c
1.9610ÿ7c
1.7310ÿ7c
2.5410ÿ7c
2.1910ÿ7c
5.0610ÿ7
2.5910ÿ7
5.0510ÿ7g
2.2210ÿ7g
8.2910ÿ7g
2.5310ÿ7g

Autoclave experiment.
MSSV experiment.
Recalculated from dayÿ1 in original reference.
Corrected from typesetting error in original reference (A.K. Burnham, personal communication, 1999).
High-wax oil.
High-sulfur oil.
Calculated from A and E.

Reference
Burnham et al. (1997)
Burnham et al. (1997)
Burnham et al. (1997)
Burnham et al. (1997)
Burnham et al. (1997)
Burnham et al. (1997)
McKinney et al. (1998)
McKinney et al. (1998)
Ungerer et al. (1988)
Ungerer et al. (1988)
Behar et al. (1988)
Behar et al. (1988)

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D.W. Waples / Organic Geochemistry 31 (2000) 553±575
Table 2
Observed and calculated rates of gas generation from oils at 350 C
Reaction

Reactant
a

C1±C4 generation
C1±C4 generation a
C1±C4 generation a
C1±C4 generation a
C1±C4 generation a
a
b
c
d
e
f

North Sea oil
Tualang oild
Mahakam oild
Tuscaloosa oil
Smackover oile

E (kcal/mol)
b

67.1
73.1b
72.6b
68b
68b

E (kJ/mol)
280.7
305.9
303.8
284.5
284.5

Calculatedf k (sÿ1)

A (sÿ1)
16

1.110
8.321017
5.701017
2.671016
2.671016

ÿ8

c
c
c
c

4.0010
2.7610ÿ8
4.5610ÿ8
3.5010ÿ8
5.2910ÿ8

Reference
Hors®eld et al. (1992)
Schenk et al. (1997)
Schenk et al. (1997)
Schenk et al. (1997)
Schenk et al. (1997)

MSSV experiment.
Mean activation energy calculated from distribution.
Recalculated from minÿ1 in original reference.
High-wax oil.
High-sulfur oil.
Rate calculated using activation-energy distribution.

dead carbon or pyrobitumen (Behar et al., 1988, 1991;
Burnham, 1989; Hors®eld et al. 1992; Schenck et al.,
1997). Stoichiometric considerations alone account for
nearly half of the di€erence between the rates of gas
generation and n-alkane decomposition.

3. Kinetic parameters from laboratory measurements
Although there is excellent agreement among reaction
rates determined in the various laboratory studies, the
kinetic parameters derived from those raw data show
extremely wide variations (see Tables 1 and 2). Several
possible explanations for the similarities in the raw data
and the simultaneous discrepancies in the derived kinetic
parameters are discussed in the following sections.
3.1. Compensation e€ect
Lakshmanan et al. (1991) have noted in their discussion of kerogen kinetics that a wide range of activation
energies and frequency factors will generally ®t a given
set of nonisothermal laboratory data, because an
increase in activation energy (E) can be directly compensated by an increase in frequency factor (A). This
phenomenon, called the compensation e€ect, has been
recognized for a long time. All points along the compensation line have the same reaction rate at the average
temperature at which they were derived (that is, they all
predict the same reaction rate under laboratory conditions).
However, they will have di€erent reaction rates at any other
temperatures (for example, under geologic conditions).
The compensation e€ect arises because the measurement errors during nonisothermal pyrolysis (see Jarvie,
1991; Burnham, 1994), though small, are large enough
to interfere with the mathematical reduction of the pyrolysis data. These problems will be exacerbated by any
kind of technical diculties encountered during the
pyrolysis analysis, such as larger-than-average errors in
temperature control. Because it cannot overcome these
analytical errors, the standard method used to deconvolve

the raw nonisothermal pyrolysis data into kinetic parameters is not well suited to the tasks we have set for it
(Lakshmanan et al., 1991; Sundararaman et al., 1992)
unless special measures are taken.
Alan Burnham (personal communication, 1999) has
pointed out that if multiple runs are made at the lowest
and highest heating rates, and if the mathematical analysis is performed using all combinations of heating-rate
data, the average kinetic parameters thus obtained will
be reliable, provided that all combinations of pyrolysis
data yield activation energies that di€er by no more than
about 2 kcal/mol (8.4 kJ/mol). However, most commercial laboratories carrying out kinetic determinations do
not follow such stringent quality control. Consequently,
we usually cannot, on the basis of ordinary laboratory
data alone, decide with con®dence which A/E combination along the compensation line is correct.
In fact, as Lakshmanan et al. (1991) have noted, it is
possible to obtain wildly disparate kinetic parameters
from deconvolution of very similar pyrolysis data.
Dembicki (1992), who pyrolyzed the same kerogen in a
variety of concentrations mixed with several di€erent
minerals, inadvertently provided one example. His
derived modal activation energies varied from 48 to 56
kcal/mol (200.8±234.3 kJ/mol), despite the fact that
Tmax values for all mixtures were, within experimental
error, essentially identical.
In a more-extreme example, I acquired data from
kinetic analyses performed on two kerogen samples that
were geochemically almost identical (Rock-Eval, visual
kerogen analysis, atomic H/C ratio, geologic age, location, organic facies). Although those two samples also
yielded nearly identical raw pyrolysis data (yields, temperatures) during the kinetic analysis, the standard
deconvolution software selected mean activation energies that di€ered by more than 16 kcal/mol (67 kJ/mol),
and frequency factors that di€ered by more than four
orders of magnitude. One of those samples was assigned
a mean activation energy of 75.8 kcal/mol (317.1 kJ/
mol) and a frequency factor of 1021.1 sÿ1! However, if
the same frequency factor had been assigned to both

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D.W. Waples / Organic Geochemistry 31 (2000) 553±575

samples during the mathematical treatment of the raw
pyrolysis data, the activation energies would have been
virtually identical (see Pelet, 1994).
Isothermal kinetic measurements of the type
employed by Behar et al. (1988), Ungerer et al. (1988),
Burnham et al. (1997, 1998), and McKinney et al. (1998)
can also su€er from the compensation e€ect. In isothermal experiments A and E are usually determined
using an Arrhenius plot rather than by ®tting the calculated pyrolysis yield curves to the measured ones. Errors
in measurements of reaction rates or temperatures, or in
experimental design (see Burnham, 1998), will lead to
errors in the slope of the Arrhenius plot (which yields E)
and the intercept (which gives A).
For kerogen-kinetics data obtained at the temperatures and heating rates typically used in nonisothermal
pyrolysis experiments (maximum pyrolysis yields obtained
between about 420 C and 480 C at heating rates of about
25 C/min), the empirical relationship between E and A
resulting from the compensation e€ect is
log A ˆ 0:3E ÿ 2:0

…1A†

log A ˆ 0:072E ÿ 2:0

…1B†

In Eq. (1A) E is in kcal/mol; in Eq. (1B) E is in kJ/
mol. A is in sÿ1 in both equations (Waples, unpublished
data). The compensation line for kerogens is shown in
Fig. 1.
The frequency factor A is also known to vary imperfectly with E in the reactions of pure chemical compounds (Fig. 1). However, the cause for the covariance
of E and A for the pure chemical reactions is thermodynamics itself. As Eqs. (2) and (3) show, the frequency
factor for a chemical reaction depends on the entropy of

Fig. 1. Log of the frequency factor plotted vs. activation
energy for all reactions of pure chemicals reported by Benson
(1976). Also shown for reference is the compensation line corresponding to log A/E pairs derived for a large number of
kerogens (Waples, unpublished data). The equation for the
compensation line is log A=0.3Eÿ 2.0, where E is in kcal/mol
and A is in sÿ1.

ÿ


activation
S6ˆ , whereas the activation
ÿ

energy
depends on the enthalpy of activation
H6ˆ (Benson,
1976, p. 86).
ÿ


A ˆ …ekT=h† exp
S6ˆ =R
…2†
E ˆ
H6ˆ ‡ RT
…3†
In these equations e is the base of the natural logarithm, k is Boltzmann's constant, h is Planck's constant,
R is the gas constant, and T is the absolute temperature.

S6ˆ and
H6ˆ represent the di€erence in entropy and
enthalpy, respectively, between the ground state of the
reactants and the transition state. Because
S6ˆ and

H6ˆ both depend to a large degree on the same structural characteristics of the transition state (in particular
to the looseness of the chemical bonds), they will almost
inevitably covary.
Regression of all the laboratory data compiled by Benson (1976) for many types of unimolecular and bimolecular reactions (Fig. 1) yields the empirical relationship
log A ˆ 0:086E ‡ 9:4

…4†

This relationship is approximately valid for a wide
variety of reaction types over a very wide range of E and
A values, although as Fig. 2 shows, each type of reaction has a unique E/A relationship that may be very
di€erent from the average one characterized by Eq. (4).
In comparing Eqs. (4) and (1), and the data points and
compensation line in Fig. 1, we see that the thermodynamically induced increase in A as E increases is much less
than it is when the compensation e€ect is operative [that
is, the slope of Eq. (1) is much greater than that of Eq.
(4)]. This discordance between the two empirical A-E relationships shows that the compensation e€ect is an artifact
of our work-up of the raw kinetics data, and not a phenomenon intrinsic to kerogen chemistry (see Pelet, 1994).
As we saw earlier, the compensation e€ect can be
large. It can also be very dangerous: although the various E/A pairs derived from mathematical deconvolution all may ®t laboratory data, they will make very
di€erent predictions when used in geologic modeling
(see also Lewan, 1998b). Following Occam's Razor, the
simplest explanation for why the various decomposition
reactions of oil, n-alkanes, and kerogen all have similar
reaction rates is that they all have similar activation
energies and frequency factors. This explanation, as
Pelet (1994) also noted, is much more attractive than
one that invokes greatly di€erent E/A pairs whose
e€ects fortuitously cancel each other, as do the parameters in Tables 1 and 2. However, Occam's Razor is
not a proof. It merely recommends the simplest
hypothesis until evidence to the contrary emerges.
The compensation e€ect, as noted earlier, is a problem endemic to kinetic parameters determined by
standard mathematical analysis of nonisothermal kinetics (Lakshmanan et al., 1991; Sundararaman et al.,
1992). Although nonisothermal kinetic analysis is

D.W. Waples / Organic Geochemistry 31 (2000) 553±575

557

the experimental data considerably better than any
other A/E combination). While it is useful to know that
those particular pairs gave relatively better ®ts to the
experimental data, it is more crucial to know in an
absolute sense how good the ®ts were. Unfortunately,
Schenk et al. (1997) did not show those data. If the ®t
between calculated and measured curves is acceptable
over a considerable range of values (as Lakshmanan et
al., 1991, showed to be generally true for kerogen
kinetics and as my own experience has con®rmed), then
choosing some set of parameters other than the absolute
statistical best ®t could also represent a satisfactory
solution. An alternative to the statistical best ®t would
be particularly attractive if the alternative parameters
were in better agreement with other facts (for example,
with empirical observations in real basins (e.g. Pelet,
1994) or with the requirements of thermodynamics, as
discussed below). Schenk et al. (1997) themselves noted
that the intrinsic errors in closed-system pyrolysis were
somewhat larger than those for an open system, suggesting another reason why statistical best ®ts might not
be the best ®nal choice in their interpretation.
Therefore, in spite of the good agreement in reaction
rates among the four samples analyzed by Schenk et al.
(1997), I believe there may be a systematic problem in
extraction of the kinetic parameters from their raw pyrolysis data. In fact, the discrepancy between the consistent raw data and the inconsistent kinetic parameters
derived therefrom (Tables 1 and 2) is similar to what we
often observe for kerogen kinetics.
3.2. Errors in measured data

Fig. 2. Log of the frequency factor plotted vs. activation
energy for three di€erent types of chemical reactions. Top:
simple ®ssion reactions (data from Benson, 1976, p. 98). Middle: ®ve- and six-center reactions (data from Benson, 1976, p.
114). Bottom: bimolecular metathesis reactions (data from
Benson, 1976, p. 157).

mainly used in deriving Rock-Eval-type kerogen kinetics, it was also employed by Hors®eld et al. (1992) and
Schenk et al. (1997) in their study of gas generation. The
compensation e€ect, which could therefore also a€ect
their results, might well explain why the frequency factors in those two studies vary from sample to sample by
nearly two orders of magnitude, and the activation
energies vary by 5±6 kcal/mol (21±25 kJ/mol), in spite of
the very similar reaction-rate constants (Table 2).
Schenk et al. (1997) suggested that their frequency factors were robust because they represented distinct minima
in the error function (that is, their chosen parameters ®t

Errors in the measured data may be responsible for
additional problems in at least some of the kinetic
parameters compiled in Tables 1 and 2. Two of the three
sets of kinetic parameters provided by Burnham et al.
(1997) are similar to those published by Ungerer et al.
(1988), Hors®eld et al. (1992), Schenk et al. (1997), and
McKinney et al. (1998). Those derived by Burnham et
al. (1997) for the North Sea oil, however, are quite different (Table 1). A probable explanation for this large
di€erence in kinetic parameters is that one of the raw
data points used to derive the North Sea-oil parameters
is wrong. Use of an incorrect reaction-rate constant in
an Arrhenius plot would then give an incorrect slope (E)
and intercept (A).
The rate constant of 0.0009 dayÿ1 reported by Burnham et al. (1997) for n-hexadecane disappearance in the
North Sea oil at 310 C is much higher than the rates
observed for the other two oils at the same temperature
(0.0005 and 0.0006 dayÿ1). At the other temperatures, in
contrast, the cracking rates in the North Sea oil were
comparable to those in the other oils. This single data
point is thus suspect, and may be responsible for the
greatly di€erent activation energy and frequency factor

558

D.W. Waples / Organic Geochemistry 31 (2000) 553±575

for the North Sea oil (Table 1). On the other hand, the
data for the North Sea oil also appear to be di€erent at
350 C, suggesting that the kinetics for the North Sea oil
may in fact be somewhat di€erent from the other two
oils studied by Burnham et al. (1997).
In actuality, data from the runs at 310 C for all three
oils studied by Burnham et al. (1997) appear to be
uncertain, since all are reported to only one signi®cant
®gure. Unfortunately, the 310 C data points are keys in
constructing the Arrhenius plots for all three oils, because
the remaining data come from too narrow a temperature
range (6 C in two oils, 16 C in the North Sea oil) to
yield reliable Arrhenius plots.
Moreover, Burnham et al. (1997) obtained two sets of
rate data at 350 C for each oil. Because di€erences in
rates for the two di€erent experiments are about 15%,
the true rate of n-hexadecane decomposition at that
temperature (and by inference at all other temperatures)
is uncertain by the same amount.
Finally, the rate data in the Arrhenius plots do not fall
precisely on a straight line. If the nonlinearity is due to a
substantial error in one measurement, rather than to
minor random errors in each measurement, the activation energy and frequency factor obtained from a leastsquares ®t to the data plots could be considerably in error
(see discussion below for McKinney et al., 1998). Burnham et al. (1997) themselves and McKinney et al. (1998)
have already noted the potential for up to 30% error in
the experimental data of Burnham et al. (1997).
In contrast, McKinney et al. (1998) characterized
their own analytical techniques as highly accurate, and
their Arrhenius plots, derived over a somewhat broader
range of temperatures, yield excellent straight lines.
However, McKinney et al. (1998) did not address the
question of systematic errors. For example, the temperature control during the pyrolysis experiments may
not have been as accurate as McKinney et al. (1998)
believed (‹1 C). As will be discussed later, errors of a
few degrees in measured temperatures could greatly
change the calculated activation energies and frequency
factors derived from Arrhenius plots.
Finally, Domine et al. (1998) have pointed out that if
Arrhenius plots for cracking of n-hexane are constructed using large numbers of data points, and if those
plots are viewed in detail, they are actually nonlinear. If
this observation of Domine et al. (1998) is correct, then the
activation energy and frequency factor derived by
McKinney et al. (1998) from an assumed-linear Arrhenius
plot is in error.

problems. First, we must decide whether to model
cracking as a ®rst-order or half-order process (see Domine et al., 1998). Second, we must decide which type of
data (disappearance of heavy hydrocarbons or formation
of gas) is more appropriate for modeling oil destruction.
Third, we must choose between modeling oil destruction
using a single activation energy or a distribution of activation energies. Finally, we must select frequency factors
and activation energies to describe cracking.

4. Alternative methods of constraining kinetic parameters

4.3. Activation energies: single activation energy vs.
distributed

If we assume for the moment that reaction-rate constants shown in Tables 1 and 2 are substantially correct
(except as noted above), we are faced with four additional

4.1. Reaction order
The conclusion of Domine (1989), Domine and
Enguehard (1992), and Domine et al. (1998) that oil
cracking follows half-order kinetics in the concentration
of oil may be correct. However, it is almost universally
accepted today, on the basis of abundant laboratory
and empirical data, that oil generation can be adequately described using simple ®rst-order kinetics or a
set of parallel ®rst-order reactions. Moreover, because
today's commercial software (GenexTM, BasinModTM,
etc.) only allows cracking to be modeled as a ®rst-order
process, most modelers can only use ®rst-order kinetics.
In this paper I will therefore assume that for exploration
purposes cracking reactions can be adequately described
by ®rst-order kinetics, and that the chemical steps in a
reaction sequence that leads to cracking are those
required to yield ®rst-order kinetics.
4.2. Which reaction to use as a model?
The kinetics of which we are speaking here are traditional cracking kinetics, in which the only components
are oil, gas, and residue. Until oil becomes gas or residue,
it is considered to be oil, regardless of its molecular
weight. Therefore, in the traditional system oil destruction is synonymous and synchronous with gas formation.
The kinetics of oil destruction in the traditional system
are thus better obtained by following gas formation
than by following the cracking of a particular heavy
compound or class of heavy compound, whose decomposition products may still be considered to be oil.
An alternative is to treat oil as several distinct fractions and calculate the reactions of each fraction separately. This method, often called ``compositional
kinetics'', is not discussed further in this paper (see for
example Forbes et al., 1991). However, the conclusions
of this paper will be applicable in deriving kinetic parameters for use in compositional kinetics as well as traditional kinetics.

It is generally assumed that oil cracking occurs via
chain reactions involving free radicals. A radical chain

559

D.W. Waples / Organic Geochemistry 31 (2000) 553±575

mechanism is consistent with the general values of activation energies that are found for oil and gas formation
and oil cracking [50±70 kcal/mol (210±290 kJ/mol)].
Indeed, a chain reaction is the only plausible explanation for cracking of hydrocarbon molecules, since the
observed overall activation energies are so much lower
than activation energies for simple carbon±carbon bond
cleavage.
The potential complexity of the chain process, with
numerous initiation, propagation, and termination
steps, and the fact that bond energies vary by position
and substituents (Patience and Claxton, 1993), strongly
suggest that oil destruction is most accurately modeled
using a distribution of activation energies. Oil Ð even
an oil that consists mainly of saturated hydrocarbons Ð
consists of a variety of bond types. Moreover, the presence of various types of free-radical initiators and
quenchers will ensure that any cracking system o€ers a
variety of di€erent chain sequences with di€erent overall
kinetic parameters.
Empirical data support this view. For example, Alan
Burnham (personal communication, 1999) has suggested that the di€erence in cracking rate between the
North Sea oil and other oils studied by Burnham et al.
(1997) might be the result of a broader distribution of
activation energies for that oil. In reviewing numerous
studies of cracking, Braun and Burnham (1988) concluded that the process of destruction of a complex
mixture like oil could not be adequately modeled using a
single activation energy. Their solution, and that adopted by the French workers (e.g. Forbes et al., 1991) was
to divide oil into several fractions and use a single activation energy and frequency factor for each fraction.
The solution adopted by Hors®eld et al. (1992), Pepper
and Dodd (1995), and Schenk et al. (1997), in contrast,
considers oil to be a single material, but one that can
crack via several di€erent reactions whose activation
energies are similar but not identical. The two methods
are, of course, not mutually exclusive: oils could be split
into fractions, and each fraction assigned a distribution
of activation energies.
In practice, the decision to model oil destruction using
a single activation energy or a distribution of activation
energies depends more on the experimental setup for
deriving the kinetics than on what is actually happening
in nature. Nonisothermal analyses of the type employed
by Hors®eld et al. (1992) and Schenk et al. (1997) yield
distributions of activation energies, whereas Arrhenius
plots used by Burnham et al. (1997) and McKinney et
al. (1998) to analyze their isothermal data can only give
a single activation energy for each process being monitored. Pepper and Dodd (1995) used isothermal pyrolysis but analyzed their data by curve ®tting, and thus
obtained distributed activation energies. Because the
nonisothermal analysis can be used conveniently to study
gas formation, because gas formation is the reaction we

want to measure, and because distributed kinetics seem
intuitively more realistic, oil destruction should be measured and described using a distribution of activation
energies.
4.4. Frequency factors and activation energies
The question of how to choose frequency factors and
activation energies is much more complex. Eq. (4) and
Figs. 1 and 2 show that for chemical reactions in the
laboratory the frequency factor increases slowly and
irregularly as the activation energy increases. As noted
earlier, the theoretical explanation for this relationship
is that thermodynamics requires the entropy and
enthalpy of activation to covary to a signi®cant degree.
The irregularity of the relationships in Figs. 1 and 2
merely re¯ects the imperfection in the correlation
between
S6ˆ and
H6ˆ .
However, the cracking reactions with which we are
concerned are normally presumed to be chain reactions.
It is thus important to understand the trends and values
of activation energies and frequency factors for chain
reactions as well as for simple reactions.
Chain reactions will always have lower activation
energies and will usually have lower frequency factors
than those of the slowest step in the chain sequence. The
slow step in turn will have the highest activation energy
and frequency factor of all the reactions in the sequence.
We can estimate overall ®rst-order kinetic parameters
for a simple chain reaction like that formulated by
Hansford 1953, (p. 212), which consists of …† unimolecular initiation, …† bimolecular hydrogen transfer,
…
1 † unimolecular decomposition, and …† bimolecular
recombination.

Initiation

M1 ! R1 ‡ R2 …†

Hydrogen transfer

R1 ‡ M2 ! R1 H ‡ R3 …†

Unimolecular decomposition R3 ! R1 ‡ M3 …
1 †
Recombination

R1 ‡ R3 ! M4 …†

R1, R2, and R3 are free radicals, while M1, M2, M3,
M4, and R1H are molecular species. The calculated
order for the overall reaction depends critically on the
species that participate in the recombination step (Rice
and Herzfeld, 1934; Hansford, 1953; Benson, 1976, p.
230). Kinetics are ®rst-order when the two recombining
radicals are di€erent. Hansford 1953, (p. 213) showed
that the overall ®rst-order frequency factor A for the
process outlined above is given by
ÿ

1=2
A ˆ A A A
=2A

…5†

560

D.W. Waples / Organic Geochemistry 31 (2000) 553±575

where the various An are the frequency factors for the
individual reactions in the chain sequence.
Although activation energies and frequency factors
for a given reaction are normally assumed to be independent of temperature, Eqs. (2) and (3) show that they are in
fact temperature dependent. In the following discussion I
shall ®rst consider kinetic parameters for reactions
occurring in the gas phase under high-temperature
laboratory conditions. In the subsequent sections I will
then discuss kinetic parameters for the same reactions in
the liquid phase under lower-temperature, high-pressure
geologic conditions.

normally involve the relatively unreactive alkanes, but
rather the more-labile species (e.g. ethers, dialkylsul®des
and, as noted earlier, alkylbenzenes) that have lower
activation energies (Table 3, step  ). Lewan (1998a) has
suggested a similar phenomenon for participation of
sulfur compounds in hydrocarbon generation from
kerogen. Frequency factors calculated from the best-®t
line (log A=0.02E+15.0) to the data in Fig. 2 (top)
suggest a frequency factor of about 1016.5 sÿ1 for chain
initiation that does not involve hydrocarbons (reactions
with activation energies between about 72 and 77 kcal/
mol (300±320 kJ/mol): Enguehard et al., 1990; DomineÂ
et al., 1990).
Domine (1989) used 1016.8 sÿ1 for the chain-initiation
step for cracking of n-hexane. Domine and Enguehard
(1992) and Domine et al. (1998), in contrast, preferred
1016.5 sÿ1.
Although step
1 also represents unimolecular
decomposition, it has a much lower frequency factor
than does step a . The lower frequency factor is a consequence of the tight transition state, which lacks signi®cant long-distance interaction between the newly
forming fragments (a molecule and a radical) and has an
entropy of activation near zero. Benson (1976, pp. 95±
96) suggests that A will be in the neighborhood of 1013.5
to 1014 sÿ1 at typical pyrolysis temperatures. Allara and
Shaw (1980) reported values between 1012.6 and 1013.5
sÿ1 for the most-rapid decomposition of alkyl radicals
(that is, when both products had at least two carbon
atoms). Domine (1989) preferred 1013.5 sÿ1, while
Domine and Enguehard (1992) and Domine et al. (1998)
used a range of values between 1013 and 1014.2 sÿ1. I
have chosen 1013.2 sÿ1, the median value from Allara
and Shaw (1980), as the best estimate.

4.4.1. High-temperature laboratory conditions: gas
phase
Table 3 summarizes observed ranges and most-probable values for frequency factors for high-temperature
chain reactions leading to alkane cracking in the gas
phase. Frequency factors for the initiation step, if it
involves saturated hydrocarbons (step  in Table 3),
average about 1016.8 sÿ1, with 1017.5 sÿ1 as an upper
limit (Benson, 1976, p. 98; Allara and Shaw, 1980).
However, alkylaromatics, which form benzylic radicals,
may also participate in oil cracking. Reactions leading
to formation of benzylic radicals have lower frequency
factors because their transition states are sti€er, as a
consequence of the delocalization of the unpaired electron through the  system (Benson, 1976, pp. 99±100).
The average frequency factor for all initiation steps in oil
cracking may therefore be slightly lower than 1016.8 sÿ1 if
initiation involves saturated hydrocarbon molecules. I
have used 1016.7 sÿ1 for step  .
However, Enguehard et al. (1990) and Domine et al.
(1990) have suggested that initiation reactions do not

Table 3
Ranges and best estimates of activation energies and frequency factors for steps in a chain reaction leading to cracking of large saturated hydrocarbonsa
Activation energy Ð kcal/mol (kJ/mol)

Log frequency factor (sÿ1)d

Step

Range

Best estimate

Range

Best estimate

 b
 c

1 (unimolecular)
2 (bimolecular)


79±86 (331±360)
72±77 (301±322)
10±25 (42±105)
26±29 (109±121)
10±20 (42±84)
0 (0)

82 (343)
76 (318)
12.5 (52)
28.5 (119)
15 (63)
0 (0)

16.4±17.5
16.47±16.52
7.7±9.0
12.6±13.5
11.0±11.5
9.5±10.0

16.7
16.5
8.2
13.2
11.25
9.9

a
All values taken from Allara and Shaw (1980) except for bimolecular step
2 , which is from Benson (1976, p. 230), and activation
energies for step  , which are from Domine and Enguehard (1992) and Domine et al. (1998). Frequency factors for step  were
calculated from the equation describing the trend in Fig. 2 (top). Activation energies for step  are assumed to be zero (Benson, 1976,
p. 164; Domine et al., 1998). Frequency factors for step  were then calculated from rate constants reported by Allara and Shaw
(1980).
b
Chain initiation involving saturated hydrocarbons.
c
Chain initiation involving the most labile species in oil (see text for discussion).
d
All frequency factors are in units of sÿ1 except for bimolecular steps ,
2 , and , which are in units of l molÿ1 sÿ1.

D.W. Waples / Organic Geochemistry 31 (2000) 553±575

Typical frequency factors for bimolecular reactions
(steps  and ) are much lower than for unimolecular
steps  and
1 . The frequency factor for step  is about
probably 108.2 l molÿ1 sÿ1 when both reacting species
are saturated and both are larger than methyl (Allara
and Shaw, 1980). Those for bimolecular recombination
by collision of two radicals (step ) are likely to be about
109.9 l molÿ1 sÿ1 when both species have two or more
carbon atoms (Allara and Shaw, 1980). The values used
by Domine (1989), Domine and Enguehard (1992), and
Domine et al. (1998) of 108 to 109 l molÿ1 sÿ1 for step ,
and 109.8 l molÿ1 sÿ1 for step  seem about right. The
value of Domine (1989) of 1011 l molÿ1 sÿ1 for step 
appears to be too high.
Benson (1976, p. 230) has noted that in the decomposition of acetaldehyde, step
is actually bimolecular,
with a catalyst acting as the second species:
Bimolecular
decomposition

R2 ‡ catalyst ! R1
‡ M3 ‡ catalyst

…
2 †

Although the inclusion of a catalyst in this step does
not change the overall order of the reaction sequence, it
does change the kinetic parameters for step g and for the
overall reaction. If we assume that for hydrocarbon
cracking step
is actually bimolecular, the frequency
factor for step
2 is considerably lower (probably about
1011 to 1011.5 l molÿ1 sÿ1) than for a unimolecular reaction (see Table 3).
Using the most-probable values in Table 3 for
A ÿ A , we obtain A  1014.0 sÿ1 when step
1 is
unimolecular (regardless of whether initiation involves
saturated hydrocarbons or other species), and A1013.0
sÿ1 for bimolecular step
2 . Even if we select the mostextreme values (those that will yield the maximum value
for A), A is only 1015.2 sÿ1 using step
1 or 1014.2 sÿ1
using step
2 . These maximum values are considerably
lower than the frequency factor for the slow step, which
is formation of the initial radical (1016.5±1016.7 sÿ1).
The activation energy E for the overall chain reaction
can also be calculated easily. From Hansford 1953, (p.
214) we ®nd that
ÿ


E ˆ E ‡ E ‡ E
ÿ E =2
…6†
Table 3 shows ranges and best-estimates of activation
energies for steps ÿ at laboratory temperatures.
Using the best-estimate activation energies for each step,
Eq. (6) yields calculated overall activation energies ranging from 51.75 kcal/mol (216.5 kJ/mol) for bimolecular
step g2 initiated through non-hydrocarbon radicals, to
61.5 kcal/mol (257.3 kJ/mol) for unimolecular step g1
initiated via hydrocarbon radicals. From Eq. (6) it is
easy to see that the activation energy E for the overall
reaction will always be smaller than that for the slow
step in the process.

561

Domine et al. (1998) have calculated the overall activation energy for cracking of n-hexane in an analogous
fashion, and found it to be about 70 kcal/mol (293 kJ/
mol) for their proposed half-order reaction. The activation energies and frequency factors they used are very
similar to the ``best estimates'' in Table 3. The di€erence
between their estimate of 70 kcal/mol (293 kJ/mol) for
the overall activation energy and those calculated above
[51.75 to 61.5 kcal/mol (216.5±257.3 kJ/mol)] is a consequence of di€erences in the mechanistic details of the
proposed chain reactions, rather than of di€erences in
the activation energies used for the individual steps in
the chain sequence.
We can now re®ne these initial theoretical estimates
of E and A using an independent source of laboratory
data: the kinetic parameters derived for destruction of
heavy hydrocarbons by Behar et al. (1988), Quigley and
Mackenzie (1988), Ungerer et al. (1988), Burnham et al.
(1997), and McKinney et al. (1998). Fig. 3 shows that
when the values for log A and E from those studies are
crossplotted, they all fall very close to a straight line. At
350 C the equation1 for this ``compensation'' line1 is
log A ˆ 0:351E ÿ 6:62

…7†

If we constrain the true kinetic parameters at laboratory temperatures to also fall along this line, and if we
assume that the thermodynamic analysis above gives
us better estimates of the frequency factors than of the
activation energies (Benson, 1976, p. 190), then we can
use the assumed frequency factors and Eq. (7) to

Fig. 3. Log of the frequency factor plotted vs. activation
energy for reactions involving destruction of heavy hydrocarbons. Data are from Quigley and Mackenzie (1988) and
Table 1. Equation for the best-®t line through the data points is
log A=0.351E ÿ 6.62, where E is in kcal/mol and A is in sÿ1.

1
Eq. (7) is actually a rearrangement of the Arrhenius equation, in which the coecient of E is equal to 1/(2.303RT) (1=
in Benson's 1976 terminology). The intercept is the log of the
median reaction-rate constant at 350 C, computed from data in
Table 1.

562

D.W. Waples / Organic Geochemistry 31 (2000) 553±575

calculate the activation energies. Inserting the four frequency factors calculated above for Eq. (7) yields activation energies ranging from 58.5±58.8 kcal/mol (244.8±
246 kJ/mol) using unimolecular step
1 to 55.8±56.0
kcal/mol (233.5±234.3 kJ/mol) using bimolecular step
2 . These values fall within a much narrower range [< 3
kcal/mol (12.6 kJ/mol)] than those obtained by purely
theoretical analysis, but otherwise are consistent with
the theoretical values.
As we noted above, even after taking stoichiometry
into account, gas formation in the laboratory proceeds
slightly more slowly than destruction of heavy hydrocarbons (compare the reaction-rate constants in Tables
1 and 2). Therefore, either the activation energy for gas
formation must be higher, or the frequency factor must
be lower, or both. From Eq. (6), we see that the overall
activation energy E for the chain reaction will be higher
if E , E , or E
is higher, or if E is smaller.
Some of the reactions involved in gas formation
probably have di€erent activation energies than the
reactions involved in cracking of heavy hydrocarbons.
Gas formation probably involves formation of many
methyl radicals, since natural gas typically contains at
least 75% methane. Using data from Allara and Shaw
(1980) for reactions that involve methyl radicals (as
opposed to those involving ethyl and larger radicals,
whose activation energies are shown in Table 3), assuming that chain initiation does not involve saturated
hydrocarbons, and assuming that step
is unimolecular
…
1 †, I estimate the typical activation energies for steps
ÿ shown in Table 4. The ®rst column in Table 4 shows
the activation energy if only methyl radicals are involved;
the second column represents a weighted average of the
values from Table 3 and column 1 of Table 4, in an
e€ort to simulate gas formation as a mixture of 75%
methane and 25% higher hydrocarbons. Inserting these
new values for E ÿE into Eq. (6), I estimate the overall

activation energy for gas formation at laboratory temperatures to be 59.4 kcal/mol (248.5 kJ/mol).
Using this overall activation energy E for gas formation, we can then calculate the overall frequency factor
A from the trend of experimental data. A plot of log A
versus E for the experimental data on gas formation
(taken from Table 2) yields a straight line very similar to
that for kerogen decomposition or heavy-hydrocarbon
cracking [Eqs. (1) and (7)]. The slope (0.292 at 477 C, the
average temperature at which maximum cracking rates
occurred during the experiments) can be calculated as
illustrated in the previous footnote, and the intercept
(ÿ3.11) is the log of the rate constant (recalculated using
the median activation energy and median frequency
factor in Table 3) at that temperature:
log A ˆ 0:29E ÿ 3:11

…8†

If we insert E=59.4 kcal/mol (248.5 kJ/mol) for gas
formation into Eq. (8), we obtain log A=14.23 sÿ1.
We can address the uncertainties in these estimates
indirectly by calculating the activation energy and frequency factor in an alternate way, starting with the frequency factors for the individual steps instead of the
activation energies. This calculation method is actually
better, since it is easier to predict frequency factors than
activation energies (Benson, 1976, p. 190). Table 4
shows anticipated frequency factors for steps ÿ when
they involve methyl radicals (column 3), as well as a
weighted average of the values in column 3 and those
from Table 3 (calculated in the same manner as we did
above with activation energies).
Using Eq. (5) and the values in column 4 of Table 4,
we calculate the overall frequency factor as 1014.28 sÿ1.
Inserting this frequency factor in Eq. (8), the calculated
activation energy comes out to be 59.4 kcal/mol (248.5
kJ/mol). These parameters are essentially identical to

Table 4
Best estimates of activation energies and frequency factors for steps in a chain reaction leading to formation of gasa
Log frequency factorb

Activation energy Ð kcal/mol (kJ/mol)
Step


1 (unimolecular)

a

CH3. only
c

76 (318)
10.5 (44)
33 (138)
0(0)d

75% CH3.
c

76 (318)
11.0 (46)
31.8 (133)
0 (0)d

CH3. only
e

16.5
8.8
14
10.2

75% CH3.
16.5e
8.65
13.8
10.1

All values interpreted from Allara and Shaw (1980).
All frequency factors are in units of sÿ1 except for steps  and , which are in units of l molÿ1 sÿ1.
c
Values are the same as for cracking of heavy hydrocarbons because the initiation step, which does not involve formation of
hydrocarbon radicals, is the same.
d
Activation energies for step  are assumed to be zero (Benson, 1976, p. 164; Domine et al., 1998). Frequency factors for step 
were then calculated from rate constants reported by Allara and Shaw (1980).
e
Estimated from Allara and Shaw (1980) and the slope of the data trend in Fig. 2 (top).
b

D.W. Waples / Organic Geochemistry 31 (2000) 553±575

those calculated starting with the activation energies.
These calculations show clearly that frequency factors
greater than 1015 sÿ1, such as those reported by Ungerer
et al. (1988), Hors®eld et al. (1992), Burnham et al.
(1997), Schenk et al. (1997), and McKinney et al. (1998),
are not thermodynamically compatible with an overall
®rst-order kinetic model for hydrocarbon destruction.
4.4.2. Geological conditions
The preceding discussion has provided theoretical and
experimental support for activation energies near 59.4
kcal/mol (248.5 kJ/mol) and frequency factors near
1014.25 sÿ1 for oil destruction and gas formation in the
gas phase under laboratory conditions. The next steps
are (1) to estimate, from thermodynamic data and theory, the activation energy and frequency factor under
geologic conditions (that is, in the liquid phase at lower
temperatures and high pressures), and then (2) to test this
model with empirical data recording high-temperature
occurrences of liquid hydrocarbons in nature.
4.4.2.1. Temperature effects. Although it is usually
assumed that activation energies and frequency factors
do not vary with temperature, it is well known that
thermodynamics does indeed require a small and direct
temperature dependence [see Eqs. (2) and (3)]. Moreover, there is also a hidden temperature dependence in
each of those equations, because both the entropy of
activation and the enthalpy of activation are themselves
functions of temperature (see Benson, 1976, pp. 32±77,
85±86, 100±104). A detailed theoretical analysis o