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 1014.25sÿ1(1.78.1014sÿ1). 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 dierent oil types. Using these recommended kinetic parameters, the maximum temperature at which oil can be preserved as a separate phase varies from about 170C at
geo-logically very slow heating rates to slightly over 200C 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. Dierences in predicted levels of cracking obtained from the various models in use today can aect 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 for-mation 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
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 dierences 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
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energy (e.g. Burnham et al., 1997, 1998; McKinney et al., 1998). Other workers, however, have disputed this assumption. Domine and Enguehard (1992) and Dom-ine et al. (1998) believe that cracking follows half-order kinetics at geologic temperatures, and that the reaction order increases with temperature. Still other investiga-tors (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. Resolu-tion 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 ArrheniusA tors (also called pre-exponential factors or frequency fac-tors) proposed to date for the ®rst-order reactions in oil cracking are, in my opinion, too high. Errors in estimating Afactors 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, there-fore, 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 heavyn -alkanes or C13+ hydrocarbons, or on the rates of gas generation from oil. The remarkable similarity of the
measured reaction-rate constants for all those experi-ments indicates that we can indeed reproducibly mea-sure 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 individualn-alkanes and of C13+hydrocarbons vary by less than a factor of three among experiments carried out by three dierent research groups on several dier-ent types of oils. This excelldier-ent agreemdier-ent clearly indi-cates that variations in oil composition play only a secondary role in controlling the rates of these pro-cesses, 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 mea-surement of the rates of formation of gas from oil. Once again, the rate constants are almost identical for gas generation from ®ve dierent oils, including oils of very dierent compositions.
Comparison of the data in Tables 1 and 2 shows that the median rate constant for gas generation at 350C
(4.0.10ÿ8sÿ1) is less than one-®fth that for decomposi-tion of heavy hydrocarbons (22.10ÿ8sÿ1). 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 individualn-alkanes and C13+hydrocarbons in oils at 350C Reaction Medium E(kcal/mol) E(kJ/mol) A(sÿ1) Measured k (sÿ1) Reference
n-C16disappearancea North Sea oil 51.81 216.8 2.71011 1.7310ÿ7c Burnham et al. (1997) n-C16disappearanceb North Sea oil 51.81 216.8 2.71011 2.0810ÿ7c Burnham et al. (1997) n-C16disappearancea High-paran oile 63.59 266.1 4.11015d 1.9610ÿ7c Burnham et al. (1997) n-C16disappearanceb High-paran oile 63.59 266.1 4.11015d 1.7310ÿ7c Burnham et al. (1997) n-C16disappearancea High-sulfur oilf 63.57 266.0 4.71015 2.5410ÿ7c Burnham et al. (1997) n-C16disappearanceb High-sulfur oilf 63.57 266.0 4.71015 2.1910ÿ7c Burnham et al. (1997) n-C25disappearanceb Ardjuna oile 67.9 284.1 3.41017 5.0610ÿ7 McKinney et al. (1998) n-C25disappearancea Arabian oilf 67.5 282.4 1.31017 2.5910ÿ7 McKinney et al. (1998) C13+disappearancea Boscan oilf 64.8 271.1 2.811016 5.0510ÿ7g Ungerer et al. (1988) C13+disappearancea Pematang oile 69.4 290.4 5.091017 2.2210ÿ7g Ungerer et al. (1988) C14+disappearancea Boscan oilf 57.34 239.9 1.111014 8.2910ÿ7g Behar et al. (1988) C14+disappearancea Pematang oile 58.15 243.3 6.511013 2.5310ÿ7g Behar et al. (1988)
a Autoclave experiment. bMSSV experiment.
cRecalculated from dayÿ1in original reference.
dCorrected from typesetting error in original reference (A.K. Burnham, personal communication, 1999). eHigh-wax oil.
f High-sulfur oil.
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 dierence between the rates of gas generation andn-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 eect
Lakshmanan et al. (1991) have noted in their discus-sion 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 com-pensated by an increase in frequency factor (A). This phenomenon, called the compensation eect, has been recognized for a long time. All points along the com-pensation 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 dierent reaction rates at any other temperatures (for example, under geologic conditions).
The compensation eect arises because the measure-ment errors during nonisothermal pyrolysis (see Jarvie, 1991; Burnham, 1994), though small, are large enough to interfere with the mathematical reduction of the pyr-olysis data. These problems will be exacerbated by any kind of technical diculties 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 para-meters 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 ana-lysis 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 dier by no more than about 2 kcal/mol (8.4 kJ/mol). However, most commer-cial 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 whichA/E combina-tion along the compensacombina-tion 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 dierent 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, loca-tion, organic facies). Although those two samples also yielded nearly identical raw pyrolysis data (yields, tem-peratures) during the kinetic analysis, the standard deconvolution software selected mean activation ener-gies that diered by more than 16 kcal/mol (67 kJ/mol), and frequency factors that diered 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 Table 2
Observed and calculated rates of gas generation from oils at 350C
Reaction Reactant E(kcal/mol) E(kJ/mol) A(sÿ1) Calculatedfk (sÿ1) Reference
C1±C4generationa North Sea oil 67.1b 280.7 1.11016 4.0010ÿ8 Hors®eld et al. (1992) C1±C4generationa Tualang oild 73.1b 305.9 8.321017 c 2.7610ÿ8 Schenk et al. (1997) C1±C4generationa Mahakam oild 72.6b 303.8 5.701017 c 4.5610ÿ8 Schenk et al. (1997) C1±C4generationa Tuscaloosa oil 68b 284.5 2.671016 c 3.5010ÿ8 Schenk et al. (1997) C1±C4generationa Smackover oile 68b 284.5 2.671016 c 5.2910ÿ8 Schenk et al. (1997)
a MSSV experiment.
b Mean activation energy calculated from distribution. c Recalculated from minÿ1in original reference. d High-wax oil.
e High-sulfur oil.
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 suer from the compensation eect. In iso-thermal experiments A and E are usually determined using an Arrhenius plot rather than by ®tting the calcu-lated 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 givesA).
For kerogen-kinetics data obtained at the tempera-tures and heating rates typically used in nonisothermal pyrolysis experiments (maximum pyrolysis yields obtained between about 420C and 480C at heating rates of about
25C/min), the empirical relationship betweenE andA
resulting from the compensation eect is
logA0:3Eÿ2:0 1A logA0:072Eÿ2:0 1B
In Eq. (1A)Eis in kcal/mol; in Eq. (1B)Eis in kJ/ mol.Ais in sÿ1in both equations (Waples, unpublished data). The compensation line for kerogens is shown in Fig. 1.
The frequency factorAis also known to vary imper-fectly with E in the reactions of pure chemical com-pounds (Fig. 1). However, the cause for the covariance ofE andAfor the pure chemical reactions is thermo-dynamics itself. As Eqs. (2) and (3) show, the frequency factor for a chemical reaction depends on the entropy of
activation ÿS6
, whereas the activation energy depends on the enthalpy of activationÿH6
(Benson, 1976, p. 86).
A ekT=hexp ÿ S6=R
2
EH6RT 3
In these equations eis the base of the natural loga-rithm,kis Boltzmann's constant,his Planck's constant, Ris the gas constant, andTis the absolute temperature.
S6 andH6 represent the dierence in entropy and
enthalpy, respectively, between the ground state of the reactants and the transition state. Because S6 and H6both depend to a large degree on the same
struc-tural 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 Ben-son (1976) for many types of unimolecular and bimole-cular reactions (Fig. 1) yields the empirical relationship
logA0:086E9:4 4
This relationship is approximately valid for a wide variety of reaction types over a very wide range ofEand Avalues, although as Fig. 2 shows, each type of reac-tion has a unique E/A relationship that may be very dierent 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 thermodyn-amically induced increase inAasEincreases is much less than it is when the compensation eect is operative [that is, the slope of Eq. (1) is much greater than that of Eq. (4)]. This discordance between the two empiricalA-E rela-tionships shows that the compensation eect is an artifact of our work-up of the raw kinetics data, and not a phe-nomenon intrinsic to kerogen chemistry (see Pelet, 1994).
As we saw earlier, the compensation eect can be large. It can also be very dangerous: although the var-ious E/A pairs derived from mathematical deconvolu-tion all may ®t laboratory data, they will make very dierent 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 dierent E/A pairs whose eects fortuitously cancel each other, as do the para-meters 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 eect, as noted earlier, is a pro-blem endemic to kinetic parameters determined by standard mathematical analysis of nonisothermal kinet-ics (Lakshmanan et al., 1991; Sundararaman et al., 1992). Although nonisothermal kinetic analysis is Fig. 1. Log of the frequency factor plotted vs. activation
mainly used in deriving Rock-Eval-type kerogen kinet-ics, it was also employed by Hors®eld et al. (1992) and Schenk et al. (1997) in their study of gas generation. The compensation eect, which could therefore also aect their results, might well explain why the frequency fac-tors 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 fac-tors were robust because they represented distinct minima in the error function (that is, their chosen parameters ®t
the experimental data considerably better than any otherA/Ecombination). 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, sug-gesting 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 pyr-olysis data. In fact, the discrepancy between the con-sistent raw data and the inconcon-sistent kinetic parameters derived therefrom (Tables 1 and 2) is similar to what we often observe for kerogen kinetics.
3.2. Errors in measured data
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 dif-ferent (Table 1). A probable explanation for this large dierence 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 dayÿ1reported by Burn-ham et al. (1997) forn-hexadecane disappearance in the North Sea oil at 310C 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 dierent activation energy and frequency factor Fig. 2. Log of the frequency factor plotted vs. activation
for the North Sea oil (Table 1). On the other hand, the data for the North Sea oil also appear to be dierent at 350C, suggesting that the kinetics for the North Sea oil
may in fact be somewhat dierent from the other two oils studied by Burnham et al. (1997).
In actuality, data from the runs at 310C 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 310C data points are keys in
constructing the Arrhenius plots for all three oils, because the remaining data come from too narrow a temperature range (6C in two oils, 16C in the North Sea oil) to
yield reliable Arrhenius plots.
Moreover, Burnham et al. (1997) obtained two sets of rate data at 350C for each oil. Because dierences in
rates for the two dierent 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 activa-tion energy and frequency factor obtained from a least-squares ®t to the data plots could be considerably in error (see discussion below for McKinney et al., 1998). Burn-ham 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 tem-perature control during the pyrolysis experiments may not have been as accurate as McKinney et al. (1998) believed (1C). 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 con-structed 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.
4. Alternative methods of constraining kinetic parameters
If we assume for the moment that reaction-rate con-stants shown in Tables 1 and 2 are substantially correct (except as noted above), we are faced with four additional
problems. First, we must decide whether to model cracking as a ®rst-order or half-order process (see Dom-ine 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 acti-vation energies. Finally, we must select frequency factors and activation energies to describe cracking.
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 ade-quately 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 tradi-tional 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 destruc-tion is synonymous and synchronous with gas formadestruc-tion. 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 decom-position products may still be considered to be oil.
An alternative is to treat oil as several distinct frac-tions and calculate the reacfrac-tions of each fraction sepa-rately. 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 para-meters for use in compositional kinetics as well as tra-ditional kinetics.
4.3. Activation energies: single activation energy vs. distributed
mechanism is consistent with the general values of acti-vation 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 explana-tion 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 pre-sence of various types of free-radical initiators and quenchers will ensure that any cracking system oers a variety of dierent chain sequences with dierent overall kinetic parameters.
Empirical data support this view. For example, Alan Burnham (personal communication, 1999) has sug-gested that the dierence 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) con-cluded 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 adop-ted by the French workers (e.g. Forbes et al., 1991) was to divide oil into several fractions and use a single acti-vation 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 dierent 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 mon-itored. Pepper and Dodd (1995) used isothermal pyr-olysis 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 mea-sured 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 betweenS6andH6.
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 unim-olecular initiation, bimolecular hydrogen transfer,
1
unimolecular decomposition, and bimolecular recombination. 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 dierent. Hansford 1953, (p. 213) showed that the overall ®rst-order frequency factor A for the process outlined above is given by
A AAA=2A
ÿ 1=2
where the variousAnare 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 indepen-dent 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.
4.4.1. High-temperature laboratory conditions: gas phase
Table 3 summarizes observed ranges and most-prob-able 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 stier, as a consequence of the delocalization of the unpaired elec-tron 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 1016.8sÿ1if initiation involves saturated hydrocarbon molecules. I have used 1016.7sÿ1for step.
However, Enguehard et al. (1990) and Domine et al. (1990) have suggested that initiation reactions do not
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 1016.5sÿ1for 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; Domine et al., 1990).
Domine (1989) used 1016.8sÿ1for the chain-initiation step for cracking ofn-hexane. Domine and Enguehard (1992) and Domine et al. (1998), in contrast, preferred 1016.5sÿ1.
Although step 1 also represents unimolecular
decomposition, it has a much lower frequency factor than does stepa. The lower frequency factor is a
con-sequence of the tight transition state, which lacks sig-ni®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 thatAwill be in the neighborhood of 1013.5 to 1014sÿ1at typical pyrolysis temperatures. Allara and Shaw (1980) reported values between 1012.6 and 1013.5 sÿ1for 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.
Table 3
Ranges and best estimates of activation energies and frequency factors for steps in a chain reaction leading to cracking of large satu-rated hydrocarbonsa
Activation energy Ð kcal/mol (kJ/mol) Log frequency factor (sÿ1)d
Step Range Best estimate Range Best estimate
b 79±86 (331±360) 82 (343) 16.4±17.5 16.7
c 72±77 (301±322) 76 (318) 16.47±16.52 16.5
10±25 (42±105) 12.5 (52) 7.7±9.0 8.2
1(unimolecular) 26±29 (109±121) 28.5 (119) 12.6±13.5 13.2
2(bimolecular) 10±20 (42±84) 15 (63) 11.0±11.5 11.25
0 (0) 0 (0) 9.5±10.0 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 stepwere
calculated from the equation describing the trend in Fig. 2 (top). Activation energies for stepare assumed to be zero (Benson, 1976, p. 164; Domine et al., 1998). Frequency factors for stepwere 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 sÿ1except for bimolecular steps,
Typical frequency factors for bimolecular reactions (steps and) are much lower than for unimolecular stepsand
1. The frequency factor for stepis 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 109.9l molÿ1sÿ1when 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 108to 109l molÿ1sÿ1for step, and 109.8 l molÿ1 sÿ1for stepseem about right. The value of Domine (1989) of 1011l molÿ1 sÿ1for step appears to be too high.
Benson (1976, p. 230) has noted that in the decom-position of acetaldehyde, stepis actually bimolecular, with a catalyst acting as the second species:
Bimolecular decomposition
R2catalyst ! R1 M3catalyst
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 stepgand for the overall reaction. If we assume that for hydrocarbon cracking step is actually bimolecular, the frequency factor for step2is considerably lower (probably about
1011to 1011.5l molÿ1sÿ1) than for a unimolecular reac-tion (see Table 3).
Using the most-probable values in Table 3 for AÿA, we obtain A 1014.0 sÿ1 when step 1 is
unimolecular (regardless of whether initiation involves saturated hydrocarbons or other species), andA1013.0 sÿ1for bimolecular step
2. Even if we select the
most-extreme values (those that will yield the maximum value for A), A is only 1015.2sÿ1 using step
1 or 1014.2sÿ1
using step2. These maximum values are considerably
lower than the frequency factor for the slow step, which is formation of the initial radical (1016.5±1016.7sÿ1).
The activation energyEfor the overall chain reaction can also be calculated easily. From Hansford 1953, (p. 214) we ®nd that
E EEEÿE
ÿ
=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 ran-ging from 51.75 kcal/mol (216.5 kJ/mol) for bimolecular step g2initiated 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 energyEfor the overall reaction will always be smaller than that for the slow step in the process.
Domine et al. (1998) have calculated the overall acti-vation energy for cracking ofn-hexane in an analogous fashion, and found it to be about 70 kcal/mol (293 kJ/ mol) for their proposed half-order reaction. The activa-tion energies and frequency factors they used are very similar to the ``best estimates'' in Table 3. The dierence 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 con-sequence of dierences in the mechanistic details of the proposed chain reactions, rather than of dierences in the activation energies used for the individual steps in the chain sequence.
We can now re®ne these initial theoretical estimates ofEandAusing 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 logAandEfrom those studies are crossplotted, they all fall very close to a straight line. At 350C the equation1for this ``compensation'' line1is
logA0:351Eÿ6:62 7
If we constrain the true kinetic parameters at labora-tory 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 hydro-carbons. Data are from Quigley and Mackenzie (1988) and Table 1. Equation for the best-®t line through the data points is logA=0.351Eÿ6.62, whereEis in kcal/mol andAis in sÿ1.
1 Eq. (7) is actually a rearrangement of the Arrhenius equa-tion, in which the coecient ofEis equal to 1/(2.303RT) (1= in Benson's 1976 terminology). The intercept is the log of the median reaction-rate constant at 350C, computed from data in
calculate the activation energies. Inserting the four fre-quency factors calculated above for Eq. (7) yields acti-vation 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 hydro-carbons (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 energyEfor the chain reaction will be higher ifE,E, orEis higher, or ifEis smaller.
Some of the reactions involved in gas formation probably have dierent 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), assum-ing that chain initiation does not involve saturated hydrocarbons, and assuming that stepis unimolecular
1
, I estimate the typical activation energies for steps
ÿshown 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 eort to simulate gas formation as a mixture of 75% methane and 25% higher hydrocarbons. Inserting these new values forEÿEinto Eq. (6), I estimate the overall
activation energy for gas formation at laboratory tem-peratures to be 59.4 kcal/mol (248.5 kJ/mol).
Using this overall activation energyEfor gas forma-tion, we can then calculate the overall frequency factor Afrom the trend of experimental data. A plot of logA 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 477C, 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:
logA0:29Eÿ3:11 8
If we insert E=59.4 kcal/mol (248.5 kJ/mol) for gas formation into Eq. (8), we obtain logA=14.23 sÿ1.
We can address the uncertainties in these estimates indirectly by calculating the activation energy and quency factor in an alternate way, starting with the fre-quency 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 stepsÿwhen 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 1014.28sÿ1. 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 Activation energy Ð kcal/mol (kJ/mol) Log frequency factorb
Step CH3.only 75% CH3. CH3.only 75% CH3.
76 (318)c 76 (318)c 16.5e 16.5e
10.5 (44) 11.0 (46) 8.8 8.65
1(unimolecular) 33 (138) 31.8 (133) 14 13.8
0(0)d 0 (0)d 10.2 10.1
a All values interpreted from Allara and Shaw (1980).
b All frequency factors are in units of sÿ1except for stepsand, which are in units of l molÿ1sÿ1.
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 stepare 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).
those calculated starting with the activation energies. These calculations show clearly that frequency factors greater than 1015sÿ1, 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 1014.25sÿ1for oil destruction and gas formation in the gas phase under laboratory conditions. The next steps are (1) to estimate, from thermodynamic data and the-ory, 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)]. More-over, 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 of oil cracking, which would be extremely dicult, will not be attempted in this paper. However, it is still possible to make some reasonably con®dent general comments about the temperature dependence of kinetic parameters for oil destruction.
In order to analyze the eect of temperature on the overall activation energy and frequency factor for a chain reaction, we must ®rst analyze the temperature eect for each individual step. According to data and arguments presented by Benson (1976, pp. 100±104), frequency factors for ®ssion reactions of complex mole-cules (step) increase slightly as temperature decreases from laboratory to geologic temperatures. I estimate that at geologic temperatures the frequency factor for step, a unimolecular decomposition reaction, is about
100.2sÿ1higher than at laboratory temperatures. Lack-ing speci®c data, I assume that the frequency factor for step 1, which is also a unimolecular decomposition
reaction, is higher by about the same amount at geologic temperatures.
In contrast, Benson's (1976, p. 158) data for bimole-cular reactions that are similar in character to step b suggest that the frequency factor for stepat geologic temperatures is about 100.4sÿ1lower than at laboratory temperatures. Data for the recombination of radicals
(step ), however, are somewhat inconsistent (Benson, 1976, p.164), and do not show any clear temperature dependence greater than the uncertainty in the labora-tory experiments. I therefore assume that the frequency factors for step d are about equal at laboratory and geologic temperatures.
When we insert the frequency factors appropriate for each of these four steps at geologic temperatures into Eq. (5), we discover that these various temperature eects cancel. Thus the overall frequency factor for oil destruction under geologic conditions fortuitously turns out to be essentially the same as in the laboratory.
As Benson (1976, p. 190) has noted, prediction of activation energies from theory alone is very dicult. Unfortunately, experimental data on the temperature dependence of activation energies are not abundant. We can, however, make a few useful comments. The activa-tion energy for step, recombination of radicals, which is zero under laboratory conditions, is surely not aec-ted by temperature. In contrast, the activation energy for step a* appears to increase by about 0.3 kcal/mol (1.3 kJ/mol) in going from laboratory temperatures to geologic temperatures (see relevant examples in Benson, 1976, pp. 102±103). We might cautiously estimate that the activation energy for unimolecular step 1 follows
this trend, but data to test this hypothesis are lacking. Step, in contrast, appears to have a large decrease in activation energy [about 1.5 kcal/mol (6.3 kJ/mol) based on the example in Benson, 1976, p. 158] in going from laboratory to geological temperatures.
Inserting these modi®ed activation energies into Eq. (6), we ®nd that the overall activation energy for oil destruction at geological temperatures should be about 0.45 kcal/mol (1.9 kJ/mol) lower than the activation energy at laboratory conditions. Thus the overall acti-vation energy for gas-phase destruction of oil at geolo-gic temperatures and atmospheric pressure is probably about 59 kcal/mol (247 kJ/mol). It should be noted, however, that the calculated temperature dependence of EandAfor the various steps in the oil-cracking chain is uncertain. The reactions analyzed by Benson (1976) may not in all cases provide ideal models for the reactions we are attempting to describe. Thus the estimate of 59 kcal/ mol (247 kJ/mol) is not extremely well constrained. The true value might be slightly higher or lower, and the uncertainty may be on the order of 0.5 kcal/mol (2.1 kJ/mol).
by Enguehard et al. (1990) and Domine et al. (1998) are the result of hypothesized changes in reaction order with temperature.
4.4.2.2. Liquid-phase kinetics. The overall rates of cracking reactions are similar in the liquid and gas pha-ses. Stein et al. (1982), for example, found that cracking reactions in the gas phase were only about two to three times faster than in the liquid phase at temperatures of 350C. They noted, however, that other workers had
reported that some reactions were slightly faster in the liquid phase.
Nevertheless, despite the overall similarity of the reaction rate constants in liquid and gas phase for cracking of 1,2-diphenylethane in two dierent inert solvents, Stein et al. (1982) found that both the activa-tion energy and frequency factor were both considerably higher for the liquid-phase reactions. The overall acti-vation energy increased by about 5 kcal/mol (21 kJ/ mol), and log(A) by a factor of about 1.5. They attrib-uted the slightly lower reaction rates in the liquid phase to cage eects, which promoted recombination of the newly formed free radicals before they could form a chain reaction. The magnitude of the cage eects, they noted, is very sensitive to solvent viscosity. The changes in E and A were presumably a consequence of the change in relative importance of the various steps in the chain sequence (especially bimolecular steps in compe-tition with unimolecular steps) in changing from a gas phase to a denser liquid phase.
However, these results are probably not relevant to oil cracking in hot reservoirs. First, since oil viscosity is not low, molecules can move rather freely out of their cage. Second, in an oil reservoir the molecules surrounding the cracking species are reactive rather than inert. For both these reasons cage eects are probably of negligible importance in oil cracking. Thus it does not appear that there will be major dierences in kinetic parameters between gas-phase and liquid-phase cracking of oil (see also Domine et al., 1990).
4.4.2.3. Pressure effects. Although high pressure increases the rate of cracking at the high temperatures normally used in laboratory experiments (e.g. Khora-sheh and Gray, 1993), there is empirical evidence and theoretical support for the idea that high pressure retards cracking at geologic temperatures (DomineÂ, 1991; Jackson et al., 1995). Pressure eects on reaction rates take three forms. There is a concentration eect that leads to a greater proportion of bimolecular reac-tions at high pressure (Khorasheh and Gray, 1993; Jackson et al., 1995). There is also an activation-volume eect (DomineÂ, 1989, 1991; Domine et al., 1990; Freund et al., 1993). Finally, there are radical addition reac-tions, which are favored at high pressure and which lead to formation of larger compounds rather than cracked
products (Khorasheh and Gray, 1993). Bimolecular propagation reactions, which have relatively high acti-vation energies, are more positively aected at high tem-peratures than are bimolecular termination reactions, which have activation energies of zero and are thus only slightly sensitive to temperature. Consequently, high pressures, which increase both types of bimolecular reaction, will lead to greater rates of cracking at high temperatures. At low (geologic) temperatures, in con-trast, an increase in pressure will lead to a greater increase in termination reactions than propagation reactions, and thus will retard the overall reaction rate.
In mechanistic terms a positive activation volume represents the work required to expand a molecule and its surrounding solvent molecules to its transition-state form (e.g. Jenner, 1975), although Freund et al. (1993) have suggested that for complex systems it is better con-sidered simply as the pressure sensitivity of the system. Most unimolecular reactions have positive activation volumes. Bimolecular reactions, in contrast, generally have negative activation volumes, since the transition states represent a decrease in total reactant volume. A positive activation volume increases the activation energy by an amount equal to the product of the pres-sure and the activation volume, and thus slows the reaction, while a negative activation volume decreases the activation energy.
For chain reactions at high pressures the increased proportion of bimolecular reactions should lead to a decrease in overall activation volume. However, the overall pseudo-activation volumes for cracking pro-cesses still seem to be positive, indicating that high pressures will lead to an overall decrease in reaction rates.
Free-radical-recombination reactions lead to formation of heavy compounds rather than lighter ones, and thus decrease overall cracking rates. As bimolecular processes, the rates of recombination are increased at high pressure, thus decreasing the overall rate of cracking.
In part because some of these eects cancel, the overall eect of pressure on cracking rates seems to be small. Freund et al. (1993) calculated an increase of 1 kcal/mol (4.2 kJ/mol) in activation energy of kerogen decomposition when the pressure was increased from 138 to 1380 bar. Jackson et al. (1995) estimated that rates of oil cracking are typically reduced by about a factor of two at high pressure. Domine (1989, 1991) reported similar pressure eects. If we attribute all this dierence to an increase in activation energy, the acti-vation energy for oil cracking at high pressure would be about 0.9 kcal/mol (3.6 kJ/mol) higher than at atmo-spheric pressure.
feet (4600 m) is about 450 bar, whereas the experiments of Domine and Enguehard (1992) used pressures up to 15,000 bar. Since the eect of pressure on activation energy depends linearly on pressure (Domine and Enguehard, 1992; Freund et al., 1993), the eect of pres-sure on activation energy will be much smaller than the 0.9 kcal/mol (3.6 kJ/mol) suggested above for laboratory conditions. Considering the other uncertainties in our estimates of the typical activation energy for oil cracking, no pressure correction seems necessary.
4.4.3. Activation-energy distributions
A narrow distribution of activation energies probably provides a more-realistic description of oil destruction than does a single activation energy. In fact, wherever experimental design has permitted, pyrolysis experi-ments have yielded activation-energy distributions in preference to single activation energies. Quigley and Mackenzie (1988) suggested a Gaussian distribution with =1.2 kcal/mol (5.0 kJ/mol). Hors®eld et al. (1992) and Schenk et al. (1997) used asymmetric and decidedly non-Gaussian distributions, but virtually all the activation energies in their distributions were within 2 kcal/mol (8.4 kJ/mol) of the mean. Pepper and Dodd (1995) used broader Gaussian distributions [ varying between 1.7 and 4.8 kcal/mol (7.1±20.1 kJ/mol)], but their parameters referred to cracking within the source rock, and as those workers themselves noted, may not be directly applicable in reservoir rocks.
There are some dierences in predicted cracking between the models employing single and distributed activation energies. Fig. 4 compares oil destruction using a single activation energy of 59 kcal/mol (246.9 kJ/mol) with cracking using a Gaussian distribution centered at 59 kcal/mol (246.9 kJ/mol) with=1.5 kcal/ mol (6.3 kJ/mol) (Fig. 5). Although the disappearance of liquid oil (approximately 50±65% cracking, as explained in the next section) occurs at about the same temperature (because oil disappearance occurs near the midpoint of the cracking process, where the eective activation energy is near the mean, which is the same in both models), cracking begins a little earlier and ends a little later using the distributed kinetics.
4.4.4. Frequency factors: constant or variable?
If we work with distributed activation energies, we must also decide whether to use a single frequency fac-tor for the entire distribution (the solution normally employed), or to vary the frequency factor system-atically with the activation energy. Thermodynamic considerations and Eqs. (1), (4), (7) and (8), which are derived from empirical data, all suggest that frequency factors increase as activation energies increase. More-over, experimental data on cracking of n-alkanes have been interpreted to support a variation of activation energy with chain length (Voge and Good, 1949). It
therefore appears that the frequency factor should vary as a function of activation energy. Some previous work has attacked this problem (Braun and Burnham, 1988; Burnham, 1989).
We can calculate the dependence of A on E using laboratory data. If we assume that dierences in the initiation step are responsible for the dierences in activation energy within the distribution, then the var-iation in frequency factor with activation energy will be related to the variation ofAwithEfor step(Fig. 2, top). The best-®t line to those data, logA=0.02E+15.0, shows that a change in 2 kcal/mol (8.4 kJ/mol) in the activation energy for step will result in a change of 100.04 sÿ1 in the frequency factorA
for that step. A Fig. 5. Distribution of activation energies for oil cracking. Distribution is Gaussian, with mean activation energy of 59 kcal/mol (246.9 kJ/mol) and=1.5 kcal/mol (6.3 kJ/mol). Fig. 4. Calculated temperature (C) at which oil will disappear
as a separate phase (62.5% cracking) plotted vs. the log of the heating rate (C/my) for two dierent kinetic models. Dotted
change of 2 kcal/mol (8.4 kJ/mol) inEalso results in a
change of 1 kcal/mol in the overall activation energyE [see Eq. (6)]. A change of 100.04sÿ1inA
in turn results in
a change of 100.02sÿ1in overallA[see Eq. (5)]. Thus as we increase E within the activation-energy distribution, Awill increase at the rate of 100.02sÿ1per kcal/mol.
Table 5 contains frequency factors calculated in this way for a range of activation energies that may fall within activation-energy distributions. However, as Fig. 6 shows, there is essentially no dierence between cracking pro®les calculated using a single frequency factor and a distribution of frequency factors based on the values in Table 5. Therefore, it is of no practical importance whether we varyAas a function ofEwithin an activation-energy distribution.
4.4.5. Cracking kinetics of dierent types of oils Although dierences in cracking rates have some-times been observed for dierent types of oils (Ungerer et al., 1988; Burnham et al., 1997; McKinney et al., 1998), those dierences are always small. High-sulfur oils seem to crack slightly faster than high-paran oils, which in turn seem to crack at a similar rate to ``nor-mal'' oils (see Tables 1 and 2). The intrinsic dierences in cracking rates from one oil type to another are, how-ever, much smaller than our uncertainties about the broad range of activation energies and frequency factors reported by the various investigators (for example, compare in Table 1 data for the Boscan and Pematang samples measured by Behar et al. (1998) and Ungerer et al. (1988). The entire range of activation energies among
all the oil types analyzed in Table 1 is only 2 kcal/mol (8.4 kJ/mol) when the same frequency factor is used (Table 6).
Moreover, only the high-sulfur oils seem to be sub-stantially dierent, and they are not consistently dierent in all studies. Alan Burnham (personal communication, 1999) has noted that the Boscan oils that crack rapidly are asphaltic oils, whereas the slower-cracking high-sul-fur oil of Burnham et al. (1997) is a free-¯owing oil in which the sulfur-bearing compounds have a very dier-ent structure. Further work is obviously necessary to understand cracking parameters in high-sulfur oils.
4.4.6. A kinetic model for oil destruction and gas formation
I propose that oil destruction in reservoirs be descri-bed by a narrow discrete distribution of activation energies with a Gaussian shape and a mean activation energy of 59 kcal/mol (246.9 kJ/mol) and a standard deviation of about 1.5 kcal/mol (6.3 kJ/mol). Frequency factors can either be the same for all activation energies (1.78.1014sÿ1), or else can vary slightly with activation energy (increasing by about 5% for each 1 kcal/mol (4.2 kJ/mol) increase in activation energy). The mean acti-vation energy can be decreased by up to about 1.5 kcal/ mol (6.3 kJ/mol) for at least some high-sulfur oils. These parameters dier radically from those reported by some workers, but agree well with those proposed by Pepper and Dodd (1995) and Behar et al. (1988).
Table 5
Frequency factor as a function of activation energy for oil cracking and gas formation. Values to be used for distributed kinetics
Activation energy (E) LogA
(kcal/mol) (kJ/mol) (sÿ1)
52 217.5 14.11
53 221.8 14.13
54 225.9 14.15
55 230.1 14.17
56 234.3 14.19
57 238.5 14.21
58 242.7 14.23
59 246.9 14.25
60 251.0 14.27
61 255.2 14.29
62 259.4 14.31
63 263.6 14.33
64 267.8 14.35
65 272.0 14.37
66 276.1 14.39
67 280.3 14.41
Fig. 6. Degree of cracking as a function of temperature at a heating rate of 1C/my for two oils whose cracking is described
4.4.7. Empirical tests of the kinetic model
We can now test our kinetic model for oil destruction at geologic temperatures by comparing predictions of the model with empirical observations of the occurrence and composition of oils and condensates in reservoirs at high temperatures. First, however, we must de®ne what we mean by ``oil'' and ``condensate''.
According to Hunt (1996, p. 52), the transition from oil to gas in a reservoir occurs when the GOR exceeds about 5000 scf/bbl. This level of cracking corresponds to about 62.5% destruction of oil (the rest of the uncracked oil is taken into the gas phase), as calculated using the formula of Claypool and Mancini (1989):
CGOR= 3000GOR 9
where C is the fraction of original oil that has been destroyed and GOR is in scf/bbl. Although Eq. (9) takes into account the stoichiometry of the oil-gas/residue transformation, it is only approximate. The value 3000 in the denominator is an assumed average; the actual value depends upon the density and average molecular weight of the oil. Moreover, dierent oils will yield slightly dierent amounts of gas upon cracking (e.g. Behar et al., 1988, 1991; Hors®eld et al., 1992; Schenk et al., 1997); dierent PVT conditions can result in dier-ences in mutual solubilities (Pepper and Dodd, 1995); gas can leak away after it is generated; or gas can come from other sources besides oil destruction.
Other workers, however, have proposed that a GOR of about 3200 scf/bbl is the maximum at which a free oil phase can exist in the reservoir (e.g. McCain and Bridges, 1994). Under this de®nition liquid oil dis-appears when C=0.51, which corresponds to 51% cracking. The dierences between these two de®nitions of maximum GOR are not extreme, despite the apparently large dierences between GORs of 3200 and 5000. George Claypool (personal communication, 1999) believes that a
GOR of 5000 is probably more appropriate when repor-ted GOR values refer to cumulative production, but that a GOR of 3200 may be better if the reported values are for initial production (e.g. McCain and Bridges, 1994).
It is important to note that according to either of these de®nitions, a large proportion of oil-like molecules can still exist after the separate liquid phase we call ``oil'' has disappeared (Pepper and Dodd, 1995). WhenC> 0.625 (or 0.51, depending on one's preference for interpreting GOR values) a separate liquid phase does not exist in the reservoir. Under these conditions cracking involves changes in the proportion of condensate in a gas, as heavy hydrocarbons in the gas phase are progressively transformed into gas-size molecules.
The issue of oil stability is a highly controversial one today (e.g. Quigley and Mackenzie, 1988; Hayes, 1991; Mango, 1991; Price, 1993; Pepper and Dodd, 1995; Claypool et al., 1996; McNeil and BeMent, 1996). Whatever assumptions I make here about the hottest occurrences of oil will therefore meet with strong dis-agreement in one laboratory or another. The empirical evidence I cite below is based only on occurrences of signi®cant amounts of oil or condensate.
Modeling results show clearly that the temperature at which oil disappears depends on the heating rate (Table 7 and Fig. 7). Pepper and Dodd (1995) observed the same phenomenon. Using the kinetics developed above, at the most-typical geological heating rates (2C/my to
5C/my) oil will disappear at between 182 and 188C if
the maximum GOR is 5000 scf/bbl, and between 179 and 185C if the maximum GOR is 3200 scf/bbl. Thus
the choice of a GOR of 3200 scf/bbl or 5000 scf/bbl for the disappearance of oil does not strongly aect the cal-culated limits for oil preservation. These predictions are reasonably concordant with the ideas of George Clay-pool (personal communication, 1999), who believes that there are very few cases where oil is preserved at tem-peratures above 180C. However, Neogene petroleum
Table 6
Recalculated activation energies for destruction of heavy hydrocarbons assuming A =1014.0sÿ1
Reaction Medium E(kcal/mol) E(kcal/mol) Reference
Normal oils
n-C16disappearance North Sea oil 59.1 247.3 Burnham et al. (1997)
n-C25disappearance Arabian oil 59.0 246.9 McKinney et al. (1998)
High-wax oils
n-C16disappearance High-paran oil 59.0 246.9 Burnham et al. (1997)
n-C25disappearance Ardjuna oil 57.8 241.8 McKinney et al. (1998)
C13+disappearance Pematang oil 58.8 246.0 Ungerer et al. (1988)
C14+disappearance Pematang oil 58.7 245.6 Behar et al. (1988)
High-sulfur oils
n-C16disappearance High-sulfur oil 58.8 246.0 Burnham et al. (1997)
C13+disappearance Boscan oil 57.8 241.8 Ungerer et al. (1988)
