An Appropriate Kinetic Model for Well-Preserved Algal Kerogens

Energy & Fuels 1996, 10, 49-59

49

An Appropriate Kinetic Model for Well-Preserved Algal Kerogens Alan K. Burnham,* Robert L. Braun, and Thomas T. Coburn Lawrence Livermore National Laboratory, Livermore, California 94551

Erik I. Sandvik and David J. Curry Exxon Production Research, Houston, Texas 77252-2189

Birthe J. Schmidt Statoil, 4035 Stavanger, Norway

Rohinton A. Noble Arco E&P Technology, Plano, Texas 75023 Received July 18, 1995. Revised Manuscript Received October 2, 1995X

While the broadness of the pyrolysis profile of most kerogens is described well by a parallel reaction model, the pyrolysis profile at a constant heating rate for certain well-preserved algal kerogens is narrower than can be described by a single first-order reaction. Further, these kerogens show an acceleratory period under isothermal conditions that is inconsistent with any parallel or nth-order reaction model. Three different models (serial, Bouster, and three-parameter) are tested against isothermal and nonisothermal pyrolysis data for a few samples, with the conclusion that the three-parameter model fits well and is the most stable and reliable. The three-parameter model reduces to a first-order model when the acceleration parameter is zero. The overall activation energy and frequency factor from this model are very close to those of the Tmax-shift method recommended earlier.

Introduction Most aspects of the global kinetics of coal and kerogen pyrolysis and maturation have been successfully modeled with either a first-order reaction, as in the case of Anvil Points Green River shale,1 or a system of parallel first-order reactions, as in the case of most marine and terrestrial kerogens.2-6 For isothermal pyrolysis conditions, these samples have their maximum generation rate as soon as they are heated up.5 The reaction rate of the first-order kerogens follows an exponential decay with time, while the parallel-reaction kerogens and coals have a long time tail, which gives a semilog plot that is concave upward rather than linear. For pyrolysis at a constant heating rate, the reaction profile shape and width of the first-order kerogens is compatible with the activation energy (E) and frequency factor (A) determined from the shift in the profile Tmax with heating rate, while the reaction profile width of the parallelreaction kerogens and coals is broader than calculated from the E and A determined from the Tmax shift with Abstract published in Advance ACS Abstracts, November 15, 1995. (1) Campbell, J. H.; Koskinas, G. J.; Stout, N. D. Fuel 1978, 57, 372376. (2) Ungerer, P.; Pelet, R. Nature 1987, 327, 53-54. (3) Burnham, A. K.; Braun, R. L.; Gregg, H. R.; Samoun, A. M. Energy Fuels 1987, 1, 452-458. (4) Burnham, A. K.; Oh, M. S.; Crawford, R. W.; Samoun, A. M. Energy Fuels 1989, 3, 42-55. (5) Braun, R. L.; Burnham, A. K.; Reynolds, J. G.; Clarkson, J. E. Energy Fuels 1991, 5, 192-204. (6) Tegelaar, E.; Noble, R. A. Org. Geochem. 1994, 22, 543-574. X

0887-0624/96/2510-0049$12.00/0

heating rate. The broader constant-heating-rate profile and isothermal concave upward semilog shape can be mimicked to some extent by an nth-order reaction with order greater than 1. However, the parallel reaction model is sounder theoretically, because there is a significant change in product composition during pyrolysis, and because individual species have different Tmax values. Even though these kinetic analysis methods work for most coal and kerogen samples, some kerogens and coals, usually made up of well-preserved algal material, have pyrolysis characteristics that are incompatible with either first-order or parallel-reaction models. For isothermal pyrolysis, these kerogens have an acceleratory phase so that the reaction rate does not reach its maximum until some time after reaching pyrolysis temperature.5,7,8 For a constant heating rate, the reaction profile is narrower than that calculated from the first-order E and A derived from the shift in Tmax with heating rate. Consequently, the A and E derived from nonlinear regression of reaction profiles are significantly higher than the A and E derived from the shift in Tmax. This behavior correlates with the presence of dominant (7) Klomp, U. C.; Wright, P. A. Org. Geochem. 1990, 16, 49-60. (8) Bar, H.; Ikan, R.; and Aizenshtat, Z. J. Anal. Appl. Pyrolysis 1988, 14, 73-79. (9) Delvaux, D.; Martin, H.; LePlat, P.; Paulet, J. Org. Geochem. 1990, 16, 175-187. (10) Charlesworth, J. M. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 1117-1125; 1125-1132. (11) Young, D. A. Decomposition of Solids; Pergamon: Oxford, U.K., 1966.

© 1996 American Chemical Society

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Table 1. Properties of the Samples Investigated in This Work sample

age

deposition

TOC, wt %

HI, mg/g

Tmax, °C

AP24 OLS-1 GGU24 Frejus Autun

Eocene Oligocene Permian Carboniferous Permian

lacustrine lacustrine marine lacustrine lacustrine

10.8 8.3 2.8 49.1 44.4

850 448 621 932 926

443 448 439 449 439

amounts of telalginites,6,8 which are microscopically recognizable as thick cell-walled algal colonies of the tasmanites (marine) and botryococcus (lacustrine) familes. Other types of well-preserved algal kerogens may also exhibit similar behavior as discussed in this article. Although the anomalous kinetic behaviors of these materials have been observed by several workers attempting to derive kinetic parameters,5-10 an appropriate kinetic model has not been widely adopted. Acceleratory kinetic behavior has been observed for many years in both the solid-state reaction and polymer decomposition literature. It is distinguished from induction, a term that we have used improperly for acceleration in the past,5 in that induction describes a period where the rate is nearly constant at a low value, whereas acceleration describes a period during which the reaction is accelerating toward its maximum rate.11 While acceleratory behavior can occur either from a lack of heat dissipation from exothermic reactions or from heat transfer limitations for a sample being brought up to temperature, the more relevant case is when the reaction is accelerated due to autocatalytic, chain branching, or expanding reaction-interface effects. A simple-minded view presented earlier5,8 is that the wellpreserved kerogens consist of long-chain polymers that require multiple bonds to be broken in order to form fragments small enough to volatilize, while most kerogens are sufficiently branched that bond breakage usually results in a volatile fragment from the outset, but it is difficult to derive detailed mechanistic interpretations with any confidence. In any event, the literature is full of potential kinetic models. From the solid-state reaction literature come nucleation models11-17 and from the polymer literature come various simplified chain reaction models.18-27 The objective of this work is to test and adapt these models to appropriate cases of kerogen decomposition. Samples and Experiments The samples used in this work are described in Table 1. They have HI values that range from 448 to 932 mg/g TOC, which are typical of algal kerogens. Photomicrographs of four of the samples are shown in Figure 1. AP24 is a blend (24 US gal/ton) of mine-run Green River oil shale from the Anvil Points mine near Rifle, CO, and was chosen as a kinetic reference material. It is a fine-grained calcareous sample, and its organic matter is mostly liptinite with a very few vitrinite particles. The liptinite is largely structureless at the petro(12) Bamford, C. H.; Tipper, C. F. H., Reactions in the Solid State, Comprehensive Chemical Kinetics, Vol. 22; Elsevier: Amsterdam, 1980. (13) Erofeev, B. V. C. R. Dokl. Akad. Sci. URSS 1946, 52, 511514. (14) Erofeev, B. V. In Reactivity of Solids, Proceedings of the 4th International Symposium (Amsterdam, 1960); Elsevier: Amsterdam, 1961; pp 273-282. (15) Avrami, M. J. Chem. Phys. 1939, 7, 1103-1112; 1940, 8, 212224; 1941, 9, 177-184 . (16) Prout, E. G.; Tompkins, F. C. Trans. Faraday Soc. 1944, 40, 488-498.

graphic microscope scale, with green-yellow fluorescence. GGU24 is a marine shale with moderate organic content from the upper Permian Ravnefjeld Formation in Greenland. Its organic matter is primarily liptinite, with minor amounts of vitrinite and inertinite. The liptinite occurs mainly as alginite of the Tasmanites type (well preserved) with greenish-yellow fluorescence and very small amounts of bituminite. OLS-1 is an Oligocene lacustrine source rock from Indonesia. It has moderate organic content dominated by liptinite, with only a few vitrinite and inertinite particles. The liptinite occurs as small liptodetrinites (60%) and Botryococcus-like algal material (40%) and a few cutinites. The Botryococcus-like algal remains show yellow fluorescence, and the internal structure is poorly visible. Frejus is a boghead coal from the “Mines de Boson” region in France. It is dominated (82%) by liptinite with minor content of vitrinite (desmocollinite) and a few percent of inertinite. The liptinite occurs as densely packed large Botryococcus-like algal colonies with yellow fluorescence. Some of the algal bodies show slight oxidation, with orangebrown fluorescence. The Autun sample is a boghead coal from St. Hilaire, France, that is highly dominated by liptinite (94%), with minor vitrinite and inertinite. The liptinite occurs as densely packed large Botryococcus-like algal colonies with greenish-yellow fluorescence. Some of the algal bodies show slight oxidation, with brown-yellow fluorescence. A rough estimate of the degree of preservation from microscopic appearance is GGU24 > Autun>Frejus > OLS-1 > AP24. Extracted rock samples were also characterized by pyrolysis-gas chromatography and mass spectrometry (Py-GC-FID and Py-GC-MS) at Exxon Production Research. Earlier PyGC work6 indicates that samples displaying very clean algal signatures with very little contribution from other organic precursors (such as detrital woody material or bacterial reworking) are the most likely to display the acceleratory kinetic behavior discussed in this article. The FID chromatograms of four of our samples are shown in Figure 2. The samples are all very rich in aliphatic pyrolysis products, which is characteristic of algal-rich kerogens. Some differences in peak abundances are apparent in the pyrograms, which is consistent with the compositional differences observed by petrography. The highest prist-1-ene content is in the Green River shale, AP24, whereas the highest concentration of C25C30 components is in the OLS-1 sample. The highest alkene/ alkane ratios are found in the Frejus and AP24 samples, but a large alternating variation in the alkene/alkane ratio with carbon number in the C20+ region is observed only for AP24. The highest concentrations of diolefins, perhaps suggestive of multiple bond breaks being required to form a volatile product, are in the OLS-1 and Frejus samples. The shortest normal chain length and highest concentration of benzene, toluene, and xylene are observed in sample GGU24, consistent with its marine origin. The Autun sample (not shown) had a normal carbon distribution similar to GGU24 and a BTX content about twice that of Frejus. The clear algal nature of the OLS-1 fingerprint is in contrast to its HI of 448 mg/g TOC, suggesting a major content of dead carbon, which may be associated with the liptodetrinite identified by microscopy. (17) Gadalla, A. M. M. Thermochim. Acta 1984, 74, 255-272. (18) Jellinek, H. H. G. Aspects of Degradation and Stabilization of Polymers; Elsevier: Amsterdam, 1978. (19) Jellinek, H. H. G. Degradation and Stabilization of Polymers; Elsevier: Amsterdam, 1983. (20) David, C. In Comprehensive Chemical Kinetics, Vol 14; Bamford, C. H., Tipper, C. F. H., Eds.; Elsevier: Amsterdam, 1975; Chapter 1. (21) Madorsky, S. L. Thermal Degradation of Organic Polymers; Interscience: New York, 1964. (22) Wall, L. A.; Madorsky, S. L.; Brown, D. W.; Straus, S.; Simha, R. J. Phys Chem. 1954, 76, 3430-3437. (23) Wall, L. A.; Straus, S. J. Polym. Sci. 1960, 44, 313-323. (24) Simha, R. J. Chem. Phys. 1956, 24, 796-802. (25) Bouster, C.; Vermande, P.; Veron, J. J. Anal. Appl. Pyrolysis 1980, 1, 297-313. (26) Polymer Degradation Mechanisms, National Bureau of Standards Circular 525, U.S. Department of Commerce, 1953. (27) Gordon, M. Trans. Faraday Soc., 1957, 53, 1662-1675.

Kinetic Model for Well-Preserved Algal Kerogens

Energy & Fuels, Vol. 10, No. 1, 1996 51

Figure 1. Photomicrographs of blue-light induced fluorescence from four samples investigated in this work (180 × 265 µm): (a) AP24; (b) OLS-1; (c) Frejus; and (d) GGU24. The Frejus and GGU24 photos show particularly clear images of Botryococcus (lacustrine) and Tasmanites (marine) algal bodies, respectively. The samples were also pyrolyzed in two kinds of kinetic apparatus at Lawrence Livermore: a Pyromat II kinetic analyzer and a fluidized-bed apparatus. In both cases, temperatures were measured by type K thermocouples that had been carefully calibrated against a platinum resistance thermometer or platinum-rhodium thermocouple that had been verified to be within 1 °C of the correct absolute temperature. The three shale samples were extracted with CS2 prior to pyrolysis to remove volatile bitumen that masked the acceleratory kinetic behavior in initial experiments. The boghead coals were not extracted because they did not show evidence of a major volatile bitumen peak. Minerals were not removed from any of the samples, but we have not seen significant differences between whole rocks and isolated kerogens in previous comparisons.28 Isolated macerals were not used because our samples were dominated by one maceral type and because they cannot be used in our fluidized bed due to their small particle size. For the Pyromat II kinetic analyzer, 4-12 mg of powdered sample was placed in a silica crucible containing silica wool and pyrolyzed in flowing helium. Sample temperature was monitored by a thermocouple in contact with the sample, and the rate of product evolution was measured by a flame ionization detector. A minimum of three experiments at 50 °C/min, two experiments at 1 °C/min, and one experiment at 7 °C/min were done to ensure reproducibility of (1 °C, thereby ensuring a reproducibility in activation energies of about 1 kcal/mol. An additional experiment at 5 °C/min was done to facilitate a comparison with the fluidized-bed experiments. In the fluidized-bed system, samples (sieved to 0.3-1.0 mm) were dropped into a preheated bed of 0.18-0.30 mm sand that (28) Reynolds, J.; Burnham, A. K. Org. Geochem. 1995, 23, 11-19.

was fluidized by argon. Sample sizes were 0.3 g for the shales and 0.04 g for the coals. The pyrolysate was converted to CO2 and H2O in a catalytic burner, and the rate of product formation was monitored by mass spectrometry. Baseline corrections were made for ambient CO2 and H2O and, when appropriate, for CO2 from slowly decomposing carbonate minerals. The fluidizing gas contained a small amount of H2 to give a constant water background and to minimize tailing. Experiments were conducted isothermally at nominal temperatures of 470, 490, and 510 °C as well as at a roughly constant heating rate of about 6 °C/min. The reaction dispersion function and lag time were measured by injecting a short pulse of krypton or N2 into the reactor and monitoring the broadened pulse in the effluent by the mass spectrometer. The nonisothermal temperature-rate data were corrected for the time lag between generation and detection.

Acceleratory Kinetic Models The conceptual basis of polymer decomposition models was developed mostly in the early 1950s,26 resulting in kinetic models containing initiation, propagation, transfer, and termination reactions. Unfortunately, these early polymer models are difficult to apply to kerogen. The detailed models have far too many parameters, and the simple models still contain parameters that are welldefined for polymers but unknown for kerogen. Also, the derivations of the simple models involve many assumptions, and the simple forms usually apply to only part of the reaction history. Their greatest importance is to establish a qualitative explanation for an initial finite rate and acceleratory period, including the plau-

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Burnham et al.

Figure 2. Pyrolysis-GC chromatograms of the four samples investigated in this work.

sibility of a rate equation that is related to the product of the extent of reaction times the amount of remaining material at early times. From these considerations, along with analogous nucleation theories for solids, we developed the simple three-parameter model

form a volatile fragment. It is represented by the kinetic equations

dx/dt ) -kx(1 - 0.99x)m

dB/dt ) k2A - k3B

(1)

The details of its derivation are given in the Appendix. An alternative simple expression comes from Bouster et al.25 They studied the pyrolysis of polystyrene by thermogravimetry in the temperature range of 300400 °C and found that it obeys the kinetic law

dx/dt ) -kx(1 - x2b)1/2

(2)

and b ≈ In order to where k ) establish the validity of this law in the very large range 0.1 < x < 0.95, they assumed that the pyrolysis involves three steps: random initiation, depolymerization, and termination by disproportionation or combination. For another alternative, we have previously explored the use of serial and alternate pathway models for kerogen decomposition.5,29 These models are represented by A1e-E1/RT

A2e-E2/RT.

A

2

1

B 3

dA/dt ) -k2A

dC/dt ) k3B

(3)

Of course, a true random scission model produces some volatiles with only one bond break and forms others through n bond breaks, but the two-stage serial model contains much of the required functional form. The alternate pathway model also describes a different structure in which the final product can be formed either directly from the starting material or via a reaction intermediate. One example of such a model is a branched kerogen (A) that typically takes only one bond break to form a volatile product (C) but also contains some weak links that independently convert the starting material into a nonvolatile, soluble intermediate (B, bitumen). The second end member model results if the A f C and B f C rate constants are identical, as might be expected if the breakdown of the weak links and branched hydrocarbon structure are independent, and the formation of product is described by a first-order reaction (no acceleratory period):

C

and form the end members of two end members of kerogen structure. The first end member model, a serial pathway of A f B f C, represents a long-chain structure in which multiple bonds must be broken to (29) Burnham, A. K.; Braun, R. L.; Taylor, R. W.; Coburn, T. T. Prepr.sAm. Chem. Soc., Div. Pet. Chem. 1989, 34, 36-42.

dx/dt ) -kx

(4)

Kinetics Analysis Software All kinetic data was analyzed by the Lawrence Livermore program KINETICS, version 3.2, which includes the new nucleation kinetic models described



for the serial reaction model. Our earlier experience has found that because of the high mathematical correlation between A and E, nonlinear regression fails to give reliable results when both A and E are allowed to vary for two reactions unless the data provide a clear basis for decoupling the two sets of parameters. In one case when both A’s were determined independently for the parallel reaction model, the first reaction had such a low activation energy that it occurred rapidly in geologic time at a temperature lower than at which the sample was actually recovered. Obviously, this is impossible. All nonlinear regression models are implemented using numerical integration of the kinetic equations over an arbitrary temperature history, so kinetic analysis is not restricted to either isothermal or constantheating-rate conditions. All models can also be convoluted with reactor dispersion functions in order to properly account for measurement artifacts that affect the observed reaction profiles. Both features are essential for separating the intrinsic acceleratory reaction characteristics from sample heatup and gas dispersion effects during the first few seconds of nominally isothermal experiments. KINETICS v. 3.2 also contains a 10-parameter free-radical reaction model, but it was not investigated in detail for this work. Detailed Kinetic Analysis

Figure 3. Comparison of three model fits (lines) with Pyromat data (points) for the Frejus boghead coal at heating rates of 1, 7, and 50 °C/min. The Tmax-shift parameters are determined from eq 5, and the first-order nonlinear regression (nlr) parameters used eq 4. The first-order nlr analysis improves the fit of the profile width at the expense of Tmax. The threeparameter model, eq 1, matches the entire reaction profile well.

in the previous section.30 The first-order reaction, eq 4, is the simplest form of a model in KINETICS that is capable of fitting three parallel nth-order reactions with a Gaussian activation energy distributions by nonlinear regression. First-order kinetic parameters are also determined for multiple constant-heating-rate experiments from linear regression of the shift in Tmax with heating rate:

ln(H/Tmax2) ) -E/RTmax + ln(AR/E)

(5)

KINETICS also fits, using nested linear regressionconstrained linear regression, a discrete distribution of first-order reactions with the same frequency factor and evenly spaced activation energies. The simplest resulting distribution, of course, is a single first-order reaction. The serial reaction, eq 3, is implemented by fitting only to the appearance of product C. While not required by the program, we have found in practice that it is necessary to constrain the frequency factors to be equal (30) Braun, R. L.; Burnham, A. K. KINETICS: A Computer Program to Analyze Chemical Reaction Data; Lawrence Livermore National Laboratory Report UCRL-ID-21588 Rev. 2, Livermore, CA, 1994.

Table 2 summarizes the results from the various kinetic models applied to the Pyromat data. (Autun was measured at one heating rate only in the Pyromat, so no kinetic parameters are available.) As a good example of the problem identified earlier,5,28 the kinetic parameters determined from the Tmax-shift model (eq 5) are systematically lower than those determined from nonlinear regression of all reaction profiles to a single firstorder reaction (eq 4) and to the discrete activation energy distribution model. As shown in Figure 3 for the Frejus sample, the Tmax-shift parameters fit the Tmax shift but predict too broad a reaction profile, while the first-order parameters determined from the entire profile fit the profile better but do not match the shift in Tmax. These results are characteristic of well-preserved algal kerogens, in which the reaction profile is narrower than a first-order reaction. The difference is smallest for sample AP24, which is the least-well preserved of the samples investigated. In contrast, the activation energies from the threeparameter model (eq 1) and the serial first-order model (eq 3) agree well with those from the Tmax-shift model. They also fit the profile well, as shown for the threeparameter model in Figure 3 for the Frejus sample. The three-parameter model has the lowest residual sum of squares for the OLS-1, GGU24, and Frejus samples. It is less advantageous for sample AP24 because that sample has some diversity of reactivity, with some branched and cyclic materials generated earlier than the bulk. The Bouster four-parameter model (eq 2) typically had the next lowest residuals, but it did not reliably converge and the A2 and E2 parameters varied widely and unpredictably. These results suggest that the three-parameter model is the best choice when a narrow reaction profile is observed. While the Pyromat technique is widely used to measure pyrolysis kinetics for petroleum source rocks, constant heating rate experiments are not well suited

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Table 2. Summary of Kinetic Parameters Derived from the Pyromata AP24

OLS-1

GGU24

Frejus

Pyromat

Aapprox Eapprox σ, % of E

Tmax-Shift Model 5.74Eb+13 1.70E+14 2.96E+14 53 414 55 262 56 065 0.00 0.00 0.00

5.26E+14 57 491 0.00

A E residuals

First-Order Model 7.96E+13 1.47+E15 3.56+E15 53 731 58 332 59 595 0.61 0.56 1.06

1.25+E16 62 033 1.11

Discrete Model 1.92E+14 1.17+E15 4.76+E15

1.22+E16

Adisc E and % at E 41 45 46 47 48 50 51 55 58 59 60 62 63 64 66 residuals

0.5 0.1 0.3 0.5

0.8 2.8 0.9 92.3 98.4 0.9 96.7 100.0 1.7 1.8 0.34

1.05

1.11

A E1 E2 residuals

Serial First-Order Model 3.63E+14 3.72E+14 53 152 54 135 56 259 56 111 0.50 0.64

7.85E+14 56 041 57 686 0.26

A E m residuals

Three-Parameter Model 1.12E+14 2.97E+14 3.72E+14 54 265 55 748 55 891 -0.03 0.19 0.28 0.54 0.23 0.43

8.22E+14 57 551 0.32 0.10

A1 E1 A2 E2 residuals

Bouster Four-Parameter Model 8.97E+13 3.63E+15 7.48E+13 53 916 59 522 53 769 1.13E+10 3.86E-11 1.43E+02 -77 171 -36 716 6 186 0.55 0.30 0.63

6.29E+15 60 759 7.46E-05 -14 720 0.22

a A is in s-1, E is in cal/mol, and the discrete energy distribution is given in percent of total potential. b E+n ≡ ×10n.

to observe nucleation kinetic behavior, as distinct from shrinking core kinetic behavior, because both mechanisms give reaction profiles narrower than a first-order reaction. Consequently, we used the fluidized-bed experiments to achieve nearly isothermal conditions, which can definitely distinguish between shrinking core and nucleation kinetics, because only nucleation kinetics have an initial acceleratory period. As a preliminary step, the fluidized-bed and Pyromat data are compared directly in Table 3 for similar heating conditions, 5.7 °C/min constant heating rate, to assess any ambiguities related to differences in equipment, such as temperature calibration. For a more complete assessment of these potential differences, Table 3 includes results for Kukersite, an Estonian oil shale, but its kinetic parameters will not be discussed in this paper. In general, both the Tmax and profile width values agree for the two types of experiments. The worst agreement is the Tmax for sample G24. This fluidized-bed experiment had the poorest quality data, as a small sample size was used because the sample was nearly gone. Overall, the data from the two apparatus agree quite well.

a

fluidized bed

sample

Tmax

fwhm

Tmax

fwhm

AP24 OLS-1 GGU24 Frejus Autun Kukersite

453 457 458 465 453 443

39 36 29 31 44 46

453 457 452 466 451 442

38 41 33 30 40 47

a

0.6

1.6 0.56

Table 3. Comparison of Fluidized Bed and Pyromat Results for a Heating Rate of 5.8 °C/min, Where Fwhm Is the Full Width at Half-Maximum of the Pyrolysis Curve

Tmax in °C.

A more complete comparison between Pyromat kinetics and fluidized bed data is shown in Figure 4 for sample AP24. The calculated curve used a threereaction approximation of the Pyromat discrete distribution parameters. The agreement is excellent, confirming that there is little intrinsic difference in the kinetics from the Pyromat and fluidized bed. Further, a single first-order rate law fits the fluidized bed experiments well and gives A ) 2.7 × 1014 s-1 and E ) 55.4 kcal/mol, in good agreement with the Pyromat parameters. The agreement between the Pyromat and fluidized-bed experiments might have been expected, in that both are conducted in flowing helium. More important is that the isothermal and nonisothermal kinetic behavior are self-consistent. The need for an acceleratory kinetic model for some samples is demonstrated convincingly in Figure 5 for the Frejus sample. While the initial rise in reaction rate for sample AP24 (see Figure 3) is consistent with the finite heatup time (7 s to final T) and reactor dispersion, an analogous first-order fit to the Frejus boghead coal is unsatisfactory. Although the single derived activation energy of 55.4 kcal/mol explains the global change in reactivity with temperature, the first-order reaction does not have the correct functional form to fit the shape of the pyrolysis curves. The measured reaction profile is substantially narrower than the first-order profile at a constant heating rate, and the measured maximum reaction rate is displaced substantially from the initial time for constant temperature. These deviations from first-order behavior are very similar to those shown in Figure 8 for the nucleation models. The parameters derived for various kinetic models from the fluidized-bed experiments are summarized in Table 4. For the four samples showing acceleratory behavior, the three-parameter model was clearly the best. It had the lowest residuals in two of the four cases. An example of the ability of the three-parameter model to fit the measurements is given in Figure 6 for the Frejus sample and in Figure 7 for the GGU24 and OLS-1 samples. The serial reaction model fits nearly as well as the three-parameter model and gives physically reasonable parameters, so it is clearly the second choice. The Bouster four-parameter had the lowest residuals in two cases, but the parameters are physically unreasonable. The Bouster model sometimes took several initial guesses to successfully reach convergence, and the parameters vary unpredictably. Another area of concern is the low activation energies for sample GGU24. This may be due to the poor quality of the constant heating rate data. The parameters probably have less absolute reliability, but the relative qualities of fit for the different models are instructive neverthe-



Figure 4. Comparison of the Pyromat discrete model parameters for sample AP24 (lines) with fluidized-bed data (points) for the same sample. The discrete model distribution in Table 2 was approximated by 4% at 50 kcal/mol, 94% at 55 kcal/mol, and 2% at 63 kcal/mol.

Figure 5. Failure of a first-order reaction model to fit the shape of the fluidized-bed rate curves for the Frejus boghead coal sample. The dashed line is calculated from the Pyromat Tmax-shift parameters, and the solid line represents a first-order fit to the fluidized-bed data. The success of a first-order model in Figure 3 combined with the long acceleratory phase here is strong evidence for the need of a nucleation kinetic model.

less. The Autun sample has a smaller nucleation parameter than Frejus, seemingly at odds with the estimated degree of algal preservation estimated from

petrography, but consistent with the higher BTX content in its Py-GC fingerprint and its broader profile width (Table 3). Even with the frequency factors tied

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Burnham et al.

Figure 6. Fit of the three-parameter model to the fluidized-bed data for the Frejus boghead coal sample. The parameters are given in Table 4. This should be contrasted to the failure of the first-order reaction model shown in Figure 4. Table 4. Summary of Kinetic Parameters Derived from the Fluidized-Bed Experimentsa sample

AP24

OLS-1

GGU24

Frejus

Autun

Single First Order 2.72E+14 1.02E+14b 3.84E+12 1.13E+14 4.38E+14 A1 55 391 54 772 45 918 55 378 56 477 E2 residuals 0.391 0.377 2.94 4.47 0.90 Parallel First Order A E1 f1 E2 residuals

2.59E+14 48 775 0.043 55 387 0.188

A E1 E2 residuals A E m residuals

6.84E+14 56 883 -0.09 0.300

A1 E1 A2 E2 residuals

5.48E+14 56 395 1.62E+05 -208 080 0.353

Serial First Order 1.29E+14 4.73E+12 51 289 47 367 54 985 49 426 0.235 1.01

1.42E+14 54 356 54 562 0.322

5.26E+14 53 113 56 618 0.433

Three Parameter 1.01E+14 3.17E+12 54 366 48 553 0.17 0.31 0.153 0.623

1.24E+14 54 489 0.44 0.224

3.84E+14 55 927 0.17 0.430

Bouster Four Parameter 3.26E+14 9.90E+11 3.85E+19 53 197 47 122 73 490 2.48E+01 1.22E+02 5.80E-17b 13 268 5 895 -55 734 0.235 0.962 0.150

8.88E+15 60 732 4.54E-15 -52 116 0.234

a The frequency factor is in s-1, the energies are in cal/mol, and the residuals are a normalized residual sum of squares. b E+n ≡ ×10n and E-n ≡ ×10-n.

together, the serial reaction model failed to converge on an answer for sample AP24, probably because of the inappropriateness of the model for that sample. Two parallel first-order reactions gives a superior fit to any of the nucleation models for AP24, as might be expected from its lack of well-preserved algal bodies. An important issue for using these kinetic parameters

to estimate geologic oil formation temperatures is how much difference in prediction there is between the various models. As a rough rule of thumb, a each kcal/ mol shift in activation energy with its compensating twofold shift in A to maintain the same reactivity at the measurement temperature will cause a 3 °C shift in the generation temperature at typical geologic heating rates. For sample AP24, the A and E values are fairly close, and the geologic prediction of 50% generation at a hypothetical heating rate of 1 °C/million years using Table 2 parameters for the various models varies only from 141 to 144 °C. In contrast, the relatively large differences in the Frejus kinetic parameters result in predictions at the same heating rate of 154 and 169 °C for the three-parameter and first-order nonlinear regression models, respectively. Similarly, the threeparameter model predictions are lower by 9 and 13 °C, respectively, for the OLS-1 and GGU24 samples. However, the predictions of the simple Tmax-shift parameters are within 4 °C of the three-parameter model for all four samples, which is probably within the precision of the method. Discussion and Conclusions The problem with the activation energies derived from the discrete activation energy model for well-preserved algal kerogens has been known for nearly 6 years,29 but a well-examined alternative did not exist. In earlier work,5,29 we recommended that the A and E values determined from the shift in Tmax were the most likely to extrapolate to geological maturation conditions, but the calculated width of the pyrolysis profile was significantly broader than measured. An nth-order reaction with order less than 1 gave a narrower profile and an



in Tegelaar and Noble,6 to predict when it is likely. The true test is in the reaction characteristics: (1) for multiple heating rate data, when nearly all of the reactivity distribution in a discrete activation energy distribution analysis is in one energy and the discretemodel activation energy is more than two kcal/mol higher than the Tmax-shift energy, or (2) when isothermal data shows a shoulder or peak delayed from the time that the sample has reached the final temperature. It is important from an applications standpoint that the appropriate kinetic model be used to derive A and E for a well-preserved algal source rock, since the resulting values may vary significantly from conventional first-order analysis. Unreasonable predictions of geological temperatures for kerogen breakdown may result from the 1st-order kinetic scheme compared with the more appropriate three-parameter nucleation model. Consequently, it is the model we now recommend for determining A and E from high-temperature pyrolysis of these kerogens.

Figure 7. Comparison of the ability of the first-order and three-parameter reaction models to fit the fluidized-bed data at nominally 470 °C for samples GGU24 and OLS-1. The threeparameter model (solid line) clearly fits the GGU24 data much better than the first-order model (dashed line) due to its 30 s acceleratory phase. The model shows less improvement the OLS-1 sample because of an apparent second component at the longer times. A slight high-temperature shoulder also appears on the OLS-1 reaction profile at a constant heating rate.

activation energy closer to that from the Tmax shift, but it missed other details of the reaction profile. A serial reaction seemed most compatible with the reaction details, but the regression analysis method was not broadly available. Nucleation models had been considered only briefly.10 This work has shown that the serial reaction model works well, but not as well as a new three-parameter nucleation model. The functional form of the nucleation model is consistent with earlier theoretical work on polymers and inorganic crystals, and it converges easily and reliably upon nonlinear regression to obtain an activation energy nearly equal to that determined from the shift in Tmax of multiple constant-heating-rate experiments. In addition, the frequency factor divided by 1 minus the nucleation parameter equals the frequency factor determined from the shift in Tmax. Furthermore, it reduces to a ordinary first-order reaction when the nucleation parameter is zero. It should be understood that the acceleratory kinetic behavior treated in this paper is observed only for a small fraction of all kerogens and that the nucleation kinetic models are certainly not required for all kerogens with high Rock-Eval hydrogen indices. We have not attempted an exhaustive study of many kerogens with the objective of being able to predict with certainty from petrographic or pyrolysis-gas chromatography data that an acceleratory kinetic model is required, but enough data is available in the literature, particularly

Acknowledgment. This work was performed under the auspices of the Department of Energy by the Lawrence Livermore National Laboratory under contract no. W-7405-ENG-48. It was supported by the DOE Basic Energy Sciences Program (Office of Geosciences) and a group of industrial sponsors: Agip, Arco, Amoco, Conoco, Exxon, IKU, Mobil, Norsk Hydro, Saga Petroleum, and Statoil. We thank Dr. E. Tegelaar (TOTAL, France) and Prof. H. Kerp (U. Muenster, Germany) for providing samples. Appendix: Background Information on Nucleation Models The three-parameter model, while motivated by empirical and practical considerations, has a foundation in more rigorous kinetic models for nucleation phenomena. Three distinct theoretical approaches, one from the polymer literature and two from the solid-state literature, have come to this general functional form. These models are presented here in order to justify, at least in a qualitative sense, the precise functional form of the three-parameter model used in this work. Polymer Decomposition Models. The conceptual basis of polymer decomposition models was developed mostly in the early 1950s. An exceptionally good summary of early results is contained in the National Bureau of Standards Circular 525,26 which contains measurements of polystyrene and polyethylene decomposition by Madorsky and detailed polymer decomposition kinetic models by Jellinek and Simha containing initiation, propagation, transfer, and termination reactions. Much of this work was published in modified form later.17,18,21-24 Polystyrene, a linear polymer, was shown to have an acceleratory period during the early stages of reaction such that the maximum rate of volatilization did not occur until a conversion of roughly 40%.21,26 Similarly, linear polyethylene showed a maximum conversion rate at 10-20% conversion.21-23 Simha’s random initiation theory24 showed qualitative agreement with this acceleratory behavior. In simplified form, Simha’s model says

58


Burnham et al.

Figure 8. Calculated reaction rates for idealized reactions having A ) 1E+13 s-1 and E ) 51 kcal/mol and various values of the nucleation parameter. The top figures give the rate at a constant heating rate of 10 °C/min, and the bottom reactions occurred at a constant temperature of 460 °C.

dC/dt ) k(L - 1)[(1 - C) - (1 - R)L(N - L)/N] ≈ RL2 (1 - C) (A1) (1 + RL) where C is the conversion to volatiles, R is the fraction of polymer bonds broken (R ) 1 - e-kt at constant T), N is the chain length, L is the minimum chain length for pyrolysis rather than evaporation, and k is an overall rate constant proportional to the concentration of radicals. At t ) 0, the rate is proportional to L(L - 1)/N; for both small R and C, the rate is proportional to R(1 - C); for large R, the rate is proportional to (1 - C). For the purposes of this work, the most important conclusions are that the initial reaction rate is proportional to the product of two quantities, one proportional to conversion and the other proportional to 1 minus conversion, and that there is an initial non-zero rate. Wall et al.22 and Wall and Straus23 demonstrated that the random initiation theory fits the acceleratory period in linear polyethylene and that the acceleratory period in polyethylene decreases in importance with an increase in branching. These models considered an initial monodisperse molecular weight, but Gordon27 showed polydisperse (exponential chain-length distribution) linear polymers undergoing unzipping should also have a maximum volatilization rate at about 30% conversion, using simple rate expressions that depend on either 1/N or 1/N1/2, depending on whether the termination is a first- or second-order process. These results suggest that the degree of acceleratory behavior will depend on the details of the kerogen structure. Solid-State Nucleation Models. A variety of models have been used in the solid-state reaction literature that have profiles narrower than a first-order reaction.12,17 They can generally be grouped into two classes: (1) shrinking core reactions and (2) nucleation (expanding core) models. The shrinking core models are

described by an nth-order reaction, dx/dt ) -kxn, where x is the fraction remaining (equal to 1 - R in the conventional notation, where R is the fraction reacted). The reaction order, n, equals 2/3 for a shrinking sphere and 1/2 for a shrinking cylinder. These models are unsatisfactory for the kerogen pyrolysis aspects studied in this paper, however, because they cannot have an acceleratory period and they reach complete reaction under a constant heating rate with a rapid, finite rate. The nucleation reactions are of the Avrami-Erofeev (AE) type13-15 or the Prout-Tompkins (PT) type.16 They are based on the concept that the reaction starts at various nuclei that react at an accelerating rate as their reaction interface grows until the reaction spheres coalesce as the reaction nears completion. These models have the correct reaction profile attributes for both linear polymer and narrow profile kerogens. The Prout-Tompkins model, named after those who used it to describe the decomposition of potassium permanganate,16 is of the form

dx/dt ) -kx(1 - x)

(A2)

where x again is the fraction unreacted. The functional form was initially adopted, according to Prout and Tomkins,16 because it had the correct mathematical shape, but it has since been derived more rigorously.11 Because the rate is identically zero for x ) 0, any numerical integration of eq A2 must start with a finite amount of reaction. Considering that the polymer acceleratory theories predict that the initial rate should be nonzero,18-20,24 we first change the quantity in the parentheses from (1 - x) to (1 - 0.99x). Second, so we can have an equation that can reduce to the conventional first-order reaction, we add an adjustable exponent to the equation so that


dx/dt ) -kx(1 - 0.99x)m


(A3)

We define this equation as the three-parameter model (A and E defining k, along with m). The Avrami-Erofeev models13-15 were derived from more fundamental considerations about how a reaction nucleus grows. The general functional form is

dx/dt ) -m′kx[ln(x)]1-1/m′

(A4)

Again, the rate of reaction is identically zero for x ) 1. In this case, all numerical integrations started with x ) 1 - 10-10. Erofeev14 has shown that a numerical expansion and regrouping of eq A4 gives

dx/dt ) -kxn(1 - x)m

(A5)

where specific values of m′ in eq (A4) correspond to specific values of m and n in eq A5. For example, m′ )

2, 3, and 4 correspond to n ) 0.500, 0.667, and 0.750 and m ) 0.774, 0.700, and 0.664, respectively. The reaction profile shapes of eqs A2 and A4 are given in Figure 8 for isothermal and constant heating rate conditions. The calculations used a standard activation energy of 51 kcal/mol and a frequency factor of 1013 s-1. Note that an increase in the nucleation parameter for the P-T model causes Tmax to increase. The P-T model can have Tmax independent of nucleation parameter if we define a new frequency factor, APT ) A/(1 - mPT). If we make this substitution, Figure 8 shows that the PT and AE models become numerically very close, as might be expected from eq A5. The main difference is that eq A4 starts with a significant initial rate and eq A4 starts with a near-zero initial rate for isothermal pyrolysis. Similarly, if the Avrami-Erofeev rate is divided by m′, the resulting plots become nearly equivalent to those for eq A3. EF950142S

An Appropriate Kinetic Model for Well-Preserved Algal Kerogens

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