A chemical kinetic model of vitrinite maturation and reflectance

00167037/89/53.00

Geochimrca n Cosmcchimica Acta Vol. 53, pp. 2649-2651 Copyright @ 1989 Ptxgamon Res pk. Printed in U.S.A.

+ .lIO

A chemical kinetic model of vitrinite maturation and reflectance ALAN K. BURNHAMand JERRY 3. SWEENEY Lawrence Livermore National Laboratory, Livermore, CA 94550, U.S.A. (Received December 28, 1988; accepted in revisedform July 14, 1989)

Abstract-A chemical kinetic model is presented that uses Arrhenius rate constants to calculate vitrinite elemental composition as a function of time and temperature. The model uses distributions of activation energies for each of four reactions: ehmination of water, carbon dioxide, methane, and higher hydrocarbons. The resulting composition is used to calculate vitrinite reflectance via correlations between elemental composition and reflectance. The correlations are derived from published measurements. The model is valid for %Ro values from slightly less than 0.3 to slightly greater than 4. Model calculations are compared to published vitrinite data from both laboratory experiments and sedimentary columns where adequate thermal histories are available. Calculated and measured %Ro values generally agree within 0.1 at low rank and 0.4 at high rank, which is comparable to uncertainties in the experimental values. This confirms our starting premise that vitrinite reflectance is properly described by standard chemical kinetics with activation energies that extrapolate from laboratory to geological maturation temperatures. The model indicates that the relationship between the extent of oil generation and vitrinite reflectance is nearly independent of heating rate. INTRODUCIlON

then calculates vitrinite reflectance from correlations of reflectance with carbon content and with H/C and O/C atomic ratios. Derivation of the composition-reflectance correlations is given first, development of the compositional kinetic model is given next, followed by comparisons of measured vitrinite reflectance with values calculated from thermal histories.

VITRINITEREFLECTANCE IS A major indicator of thermal maturity for oil and gas exploration (HUNT, 1979; WAPLES, 1981; TISSOT and WELTE, 1984; TISSOT et al,, 1987). It has been recognized for many years that vitrinite reflectance correlates with coal rank, which is primarily a function of time and temperature (VAN KREVELEN, 1961; TSCHAMLERand DE RUITER, 1963). The first popular “kinetic” model of vitrinite maturation related to petroleum exploration ( WAPLES, 1980) used the Lopatin approach ( LOPATIN, 197 1 ), which assumes that the rate of maturation doubles every 10°C. Although this rule of thumb is stated in some elementary chemistry texts, it is generally not very accurate. In particular, it implies that the activation energy for the reaction is a function of temperature and equal to 20 kcal/mol at 103°C. Some early kinetic models of oil generation in sedimentary columns also used very low activation energies (TISSOT, 1969; CONNAN, 1974), but these erroneously low values arise because they did not account for a dist~bution of reactivity ( HANBABA,1967, quoted in JUNTGENand VANHEEK, 1970; BRAUNand BURNHAM, 1987). The distribution ofreactivity is usually treated by using a distribution of activation energies, and it is now generally accepted that the correct mean activation energy for oil generation is about 50 kcal/mol (UNGERER and PELET, 1987; TISSOT et al., 1987; SWEENEYet al., 1987; BURNHAM et al., 1987; QUIGLEY et al., 1987; MACKENZIEand QUIGLEY, 1988 ) . The correct activation energy for vitrinite maturation is less well established, but LARTER ( 1989) has shown that vitrinite maturation is also consistent with an activation energy distribution model using chemicaily meaningful parameters. This paper presents a related but more comp~hensive model for vitrinite maturation and reflectance. We caJculate vitrinite composition from a chemical kinetic model that considers separate reactions for elimination of water, carbon dioxide, methane, and higher hydrocarbons from the structure, and

RELA~ONS~IP

BETWEEN VITIUNITE ~OMPOS~ON AND REPLECIANCE

The underlying assumption of our model is that reflectance of vitrinite (or any other maceral) is related to its chemical composition. Reflectance of light at any interface is related to the refractive and absorption indices by the Fresnel-Beer equation ( TSCHAMLERand DE RUITER, 1963 ) . Both indices are a function of the material’s density and electronic structure, both of which are determined by the material’s chemical structure. If the detailed chemical structure of vitrinite were known as a function of maturity, the refractive index could be estimated, at least at low rank, from correlations that have been developed for the refractive index of organic liquids and polymers f VAN REEVELEN,1976). Estimations at higher rank would have to take into consideration the fact that the polarizability per carbon atom becomes larger as the aromatic rings become larger due to the higher mobility of the rr electrons (SCHUYERet al., 1953). However, estimating %Ro from such correlations requires more structural inFo~ation than is presently available, especially considering that absorption constants would have to be estimated as well as refractive indices. Furthermore, to achieve the object of this work, we would need some way of calculating the detailed vitrinite structure as a function of time and temperature. A more tractable approach is to assume that the electronic properties of vitrinite vary smoothly with elemental composition. MCCARTNEYand ERGUN ( 1958) showed that the logarithm of vitrinite reflectance correlated strongly with the H/C atomic ratio of vitrinite. NEAVEL( 198 1) later attributed the relation 2449

2650

A. K. Bumbam and .I. .J.Sweeney %Ro = 15.64 exp[-3.6(H/C)J

(I)

to MCCARTNEYand ERCUN ( 1967 ), where OioRois the percent of reflected tight in oil immersion. This is logical because the polar&ability densities (molar refractivity divided by molar volume) of aromatic groups are higher than those of aliphatic groups (VAN KREVELEN, 1976 1. However, it is evident in MCCARTNEYand ERGUN ( 1958 ) as well as in a later figure in MCCARTNEYand TEICHM~LLER( 1972 f that there is some curvature in the reIationship. An improved correlation can be obtained by recognizing that oxygen content also tends to reduce the refractive index. The average polarizability density of carboxylate groups is about the same as that of methylene groups, and ethers and hydroxyl groups are substantially less poiarizable (VAN KREVELEK 1976 ). We derived by inspection the relation “oRo = 12 exp[-3.3(H/C)]

- (O/C!.

(2)

which is compared in Fig. 1 with the MCCARTNEY and TEKHM~LLER ( 1972) results. We have used an average relation between O/C and H/C to derive our curve. It may look as though this oxygen correction is too huge, but evidence presented in the next section indicates that it is approximately correct. Any improvement in this correlation would require more extensive data at low reflectance, possibly by including individual O/C ratios in a multiple regression analysis. Correlations between reflectance and carbon content have also been presented (VAN KREVFLEN, 196 I ; TKHAMLER and DE RUIWR, 1963; MCCARTNEY and TEI~HMULLER. 1972: DAVIS, 1978; HUNT, 1979). We derived by inspection an equation based on results given by DAVIS ( 1978 ). %Ro

= exp(-1.25

+ 4.58

+ 3OO.I’ + 1.6 ‘q 10x~“).

(3)

where A = (wt% C -

65)/ 100. This equation is compared with his data in Fig. 2. Again, it is doubtful that the data warrants more rigorous curve fitting.

...___. ,

c i-

‘OIL--: * 70 75

:

-_-I-_~___

80 85 Carbon, % ~~~~F,

__.

90

_

9s

Parr)

FIG. 2. Comparison of Eqn. (3) to the vitnnite retlectance data oi DAVIS ( 1978 ) to which it was calibrated.

It is important to recall that vitrinite reflectance can be anisotropic. When maturation occurs under hthostattc QreSsure, the aromatic rings tend to reorient along the bedding planes. Since the rings are more polarizable along the ring than orthogonal to it, the reflectance will be greater along the bedding plane. This anisotropy is insignificant for PRO less than 1, but it is about a factor of two when “PRO reaches 4 f SHARKEYand MCCARTNEY, 1963 ) ~Our correlations have been derived for the maximum reflectance orientation COMF’OSITIONAL MODEL OF VITRINITE MATURATION To take advantage of the relationship in the preteens section, we need a chemical kinetic model that can calculate the carbon content and H/C and O/C atomic ratios of vi. trinite as a function of time and temperature. The van Krec’ elan diagram (H/C versus O/C) is commonly used to plot changes in composition with maturation (VAN ~EVELEk. 1961; TSAI, 1982; TISSOT and WELTE, 1984; Mo~T~I~~I~ et al., 1985; SAXBY et al., 1986 j. It is evident from these plots that coal, which is dominated by vitrinite, and vitrinite. when analyzed separately, preferentially eliminate water and carbon dioxide during the early maturation stages and eliminate hydrocarbons in the later stages. This can be treated most simply by considering four independent paraltel reactions: vitrinite + residual vitrinite + HZ0 vitrinite -c residual vitrinite + CO1 vitrinite --* residual vitrinite T i.‘H, vitrinite --) residuat vitrinite t C’H,

0.2

/

0.4

1

0.6 H/C,

/

0.8

1 .O

1.2

.A

1.4

atomic ratio

Frc. 1. Comparison of vitrinite reflectance data ( MCCARTNE’I and TEICHMULLER,1972) to that calculated with E&s. ( I ) and (2 ) The syrnboIs retain their original meaning: 0.0 European v&kites: 3 U.S. coals.

The third reaction, generation of higher hydrocarbons iCEi,)_ is not essential for calculation of vitrinite reflectance. However, we have included it for generality because the same kinetic model could be used to calculate compositional maturation trends for other mace&i that may generate signifi~n~ amounts of higher hydrocarbons. The material balance

2651

Kinetics of vitrinite maturation equations presented in this section are general and could therefore be applied to other macerals or mixtures. By the application of simple conservation relations, it is possible to derive equations giving the composition of the residual vitrinite as a function of the initial vitrinite composition and the extent of each of the four reactions above. We start by writing the reaction U-LO, -

C,-&-dH*-za_nr_4dOp2ti+ a

Hz0

+bC02+cCH,+dCH4. The compositional properties of the residual solid can be calculated easily from its empirical formula. Time dependence is added by merely replacing the factors u-d with the product of the maximum possible yield and the fraction reacted for each species. We define (Yand @as the fraction of initial oxygen that is removed as H20 and C02, respectively, and y and 6 as the fraction of initial carbon removed as CH, and CH4, respectively. A concern is to choose the maximum yields so that the hydrogen and oxygen contents do not become negative. There is ordinarily enough hydrogen for all the water to be removed without depleting hydrogen, and the yield of CH, is usually small enough that it does not exceed hydrogen availability. In contrast, methane is a major fate of hydrogen and the last product to be evolved in this model. Therefore, we derive an equation to calculate the maximum possible methane yield assuming values for the other products and the desired end state. If we define x as the desired residual H/C atomic ratio after all of the above reactions are complete, it can be shown that 6 = [x - 2Ycu - 2y - X( 1 - yp/2 - y)]/(4

- X).

(4)

If we defined as the fraction of the jth species evolved, then the composition of the remaining material as a function of conversion is given by H/C = (x - 2ycvL - nrf

- 4%)l (1 - YPf/2 - Yf, - %),

O/C = Y( 1 - 4

- PXdl( 1 - yPfs/2 - rf, - G),

(5)

+ 16(0/C)]

- 1.5.

k = A exp(-EIRT)

(8)

where k is the rate “constant,” A is the frequency factor, and E is the activation energy. We assume that each of the four reactions above is really a complex set of reactions that can be described by a set of parallel first-order reactions: dCiJdt

= -kiCi,

(9)

where C represents the precursor of H20, C02, CH, , or CH., , and i represents the ith component of that precursor. We also assume that the ki’s for a given precursor have different E’s but share a common A. There is insufficient information in the literature to uniquely define the required rate parameters for vitrinite. The kinetic parameters are given in Table 1 from trial-anderror matching of the model to results from both geological maturation ( TSAI, 1982; POLASTROand BARKER, 1986 ) and laboratory pyrolysis ( DURAND-SOURONet al., 1982; MONTHIOUXet al., 1985; SAXBYet al., 1986). The methane kinetic parameters are taken with minor modification from a mass spectrometric investigation of coal pyrolysis ( BURNHAM et

(6)

and wt% C = 1200/[12 + (H/C)

a maximum carbon content of 93.3%, which results in a maximum reflectance of 4.62%. We need chemical kinetic expressions to calculate the extent of the above reactions. In general, maturation reactions can be a function of time, temperature, and pressure. High pressure is required in laboratory experiments to simulate geological maturation of low rank coals ( MONTHIOUXet al., 1985 ). In low-pressure laboratory experiments, oxygen-containing tars are evolved during the early stages of reaction, the ratio of water to CO2 increases, and other oxygen is converted to refractory cross-linking bonds, thereby causing the coal to follow a more direct path to the origin of the van Krevelen diagram. For simplicity, we chose not to include pressure explicitly in our model. However, our model does assume that the pressure is high enough so that time and temperature are the only important variables. We further assume that this dependence is described adequately by the Arrhenius equation

(7)

The constant of 1.5 in Eqn. (7) accounts for nitrogen and other elements, which we assume are eliminated from the vitrinite structure at a rate such that their ratio to carbon does not change. This approximation is supported by analyses of both naturally (SENFTLE et al., 1986) and artificially ( MONTHIOUX et al., 1985 ) matured samples. Most calculations in the next section used an initial atomic H/C(x) of 0.9, an initial atomic O/C(Y) of 0.35, and a residual atomic H/C(X) of 0.28. The fractions of oxygen evolved as H20( (Y) and CO,(p) were 0.25 and 0.7, respectively, and 1% of the carbon was evolved as CH,(7), with n = 1.7. Using these parameters in Eqns. (4) and (5) gives a methane yield of 12.5% of the initial carbon and a residual atomic O/C of 0.024. Substituting the residual H/C and O/C atomic ratios into Eqn. (2) reveals a maximum calculated reflectance of 4.74%. Similarly, substituting them into Eqn. (7), one obtains

Table 1. Kinetic constams used in the compositional model of vitrinite maturati0n.a Energy kcal/mol

% of soecies characterized bv eiven E

H20

38 40 42 44

20

46 48 50 52

20 15 10 5

Co;?

CH,

CH4

1: 15

5 15 5 ;: 15 10 S

:: 2 62 : 68 70 72 74 aA is 2~013 s-1 for

:: 2: 10 5

7 12 14 13 12 11 9 7 : ; 1

cH,

and 1~1013s-1 for others

A. K. Bumham and J. J. Sweeney

2652

al., 1989). At atmospheric pressure, molecular hydrogen continues to evolve after methane evolution is complete ( BURNHAMet al., 1989). Extension of the present model to higher reflectance would require kinetics for elimination of this additional residual hydrogen. The kinetic parameters in Table 1 were used in a spreadsheet implementation of our maturation model. Integration of the kinetic equations, which is required in order to calculate the jj in Eqns. (5) and (6), is done by using the algorithms given by BRAUN and BURNHAM ( 1987) for a series of sequential time segments with constant but independent heatin rates. The results from Eqns. ( 5 )-( 7 f were then used in Eqns. [ 2 f and (3) to calculate vitrinite reflectance. Calculation of all parameters including vitrinite reflectance took about 0.5 second per segment on a ~-MHZ IBM AT with a math coprocessor.

VERIFICATION OF THE MATURATIONREFLECTANCE

:

8

4

cj ;

i(!,i

I-

.

-,_.-------

WC correlation -- - - C correlation

4

=tz

?!

2 I/

t ‘62

/

/

/ .I-.

70

---

_-_-_-“___.,_i

78 86 Carbon content, wt%

94

FIG. 4. Further comparison of calculated maturation trends wtth data given by SENRLE (1986). The H/C and O/C atomic ratios and vitrinite reflectance are c&dated at lO”F/Ma.

formalism used in this paper. They attributed 20% of the reaction to an activation energy of 52 kcalimol, 40% to 54 kcal/mol, 20% to 56 kcal/mol, plusother minor components. They gave a generation midpoint of 150°C at a heating rate of 3.3*C/Ma, which corresponds to a frequency factor of 1.1. lOI s-‘. QUIGLEYet al. ( 1987) presented rate constants for gas generation from “refractory” kerogen derived from wood. Their parameters are A = 1.8 - 10 ‘s s _ ’ and a Gaussian distribution of energies with a mean of 66.7 kcalimol and a dis~bution width of 3 kcal/mol. We calculate a gas gener-

Geologic temperature,’

__..__._ ___^._:_-. -._

I

4

3

MQDEL

‘The kinetic and stoichiometric parameters were initially verified by comparing crossplots of various compositional variables with published data ( TSAI, 1982; SENFTLE et al.. 1986). These calculations assumed a constant heating rate of 1O°C/ Ma. A few examples of these comparisons are given in Figs. 3 and 4 for vitrinite com~sitions published by SENFTLE et al. ( 1986). The calculated maturation curve in Fig. 3 ends at H/C = 0.32 because not all methane has been generated by 280°C at lO”C/Ma. While these plots verify that both the relative rates of reiease of the four species at geological conditions and the compositional relationships to reflectance are adequate, they do not address the absolute rates of release. The extent of the four reactions as a function of temperature at typical geologic and laboratory heating rates is given in Eig. 5. We compare these results to published data and models, keeping in mind that all published kinetic data are for coal, not vitrinite, and that our model does not correspond exactly to other matumtion models. We first consider geologic maturation. TLSSOTet al. ( 1987 ) presented a kinetic model for hydrocarbon generation from Type III kerogen, which they seem to imply is mostly for oil generation. They used the same discrete activation energy 1

0.61

Z_:

180

100

c: 0 0.6 c

calcutation 1

i

0.4 [I o.30

/

I 0.1

1

/ 0.2

.-i_i 0.3

0.4

O/C, atomic ratio FIG. 3. Calculated van Kreveten maturation path of vitrinite compared to data given by SE-E et al. ( 1986). The calculation was from 20 to 28O’C at IO’C/Ma.

300

400

!iOo

600

Laboratory temperature, “62

FIG. 5. Cumulative amount of&O, COz, CH.. and CH4 evolveu from coal for reaction at 3.3”C/Ma and 4”C/min

2653

Kinetics of vitrinite maturation

from these parameters. For comparison, our generation midpoints at 3.3”CjMa are 143°C for higher hydrocarbons and 192°C for methane. We noted earlier that our methane generation kinetics were derived from laboratory experiments on coal ( BURNHAMet al., 1989). The parameters were calibrated by comparison to experiments at a single heating rate of 4”C/min, so they agree by design at that heating rate. Because of an assumed mean activation energy, however, they do not necessarily extrapolate to geologic conditions. Therefore, the agreement with Quigley’s refractory kerogen kinetics at 3.3’C/Ma is important because it indicates that our methane parameters are good. The comparison of our hi8her hydrocarbon kinetics to laboratory experiments is complicated by the pressure effects mentioned above. We chose our mean kinetic parameters to be close to those for Green River (lacustrine) kerogen (SWEENEYet al., 1987; BURNHAMet al., 1987). The generation of dkanes from coal occurs at roughly the same temperature as from Green River shale f BURNHAMet al., 1989 ) . The water and carbon dioxide generation kinetics are also not well-constrained. DURAND-SOURONet al. ( 1982 ) report that when very immature terrestrial kerogen is pyrolyzed at S”C/min in a vacuum, both are evolved over a wide temperature range with a maximum rate at about 300°C which is slightly lower than for our calculated evolution rates. For all species, the temperature of maximum evolution rate for laboratory pyrolysis increases with coal rank, which is consistent with the predictions of an activation energy distribution model. Finally, an overall test of the kinetics is provided in Fig. 6, where we compare our calculated H/C and O/C atomic ratios to the measured values from hi&r-pressure sealed-tube experiments of MONTHIOUXet al. ( I985 ) . Their results indicate slightly faster hydrocarbon generation kinetics and slightly broader distributions for the oxygen species, but the overall agreement is very good. The preceding paragraphs indicate that our calculated rates of product release and our correlations between composition and reflectance are inde~ndently valid. A more stringent

.

ation midpoint of 180” at 3.3”C/Ma

jr-55

I

,

,

I

I

me Calculated q 0 Measured

ii

I i

I

1

0.9 f

D---m 250 “C

0.8

u 0.7 E

p I’;‘Og: 200 “C

=----a 300%

2 0.6 i _

0

0.1

0.3

0.2 O/C, atomic tatlo

0.4

FIG. 7. van Krevelen diagram comparing data of SAXBY et al. ( 1986) for brown coal heated at IT/week with our model calculations for the same thermal history. The initial H/C and O/C atomic ratios for the calculations are equal to those of the brown coal.

test is whether the model can accurately calculate the reflectances of a series of samples heated for different, known times. We now present such a comparison for both laboratory and geolog_ical series. SAXBY et al. ( 1986) heated samples of a brown coal and a torbanite in sealed glass tubes from 100 to 400°C at a heating rate of 1“C/week. At 50°C intervals, a tube of each material was removed and analyzed. The measured compositions of the brown coal are compared with our model calculations in Fig. 7. The agreement is good, except that hydrogen is eliminated in Saxby’s experiments a little fmter relative to oxygen. The vitrinite reflectance from both samples is compared with our model calculation in Fig. 8. The agreement is generally excellent. However, the reflectance of vitrinite in their torbanite sample seems to start at an anomalously high value, possibly because the vitrinite in the torbanite is recycled organic matter from a more mature coal. LEWAN ( 1985) reported vi~nite-re~e~n~ data for two source rocks and two coals pyrolyzed under subcritical water at various temperatures for 72 hours. Unlike Saxby, Lewan found that vitrinite reflectance in coal increased much faster with initial heating than vitrinite mixed with a larger amount of hydrogen-rich kerogen. Our calculated values are compared

6.8 -

: ae $

5 5 5L

Ia / C&i” sample

/

00

l*.”

0 g 460 366 Temperature,%

Q

$ 500

d

A Torbanite V Brown coal 3

2

07

i

I

I

I

I

100

150

200

250

300

350

J

400

Final temperature,“C

FIG. 6. Comparison of measured atomic ratios of residual coal from high-pressure pyrolysis (MONTHIOLJXet al., 1985) with those calculated for 24.hour exposure at the indicated temperature.

FIG. 8. Vitrinite reflectsnce data Of SAXBY et al. ( 1986) compared to that calculated with our kinetic model and Eqns. (2) and ( 3 ).

4. K. Bumham and J. J. Sweeney

2654

with his data in Fig. 9. Initially, our calculated values are intermediate between his coal and marine source-rock values. but our calculations agree very well with his marine sourcerock values at higher temperatures. The difference in Lewan’s results for his two samples may be due to different types of vitrinite ( TISSOT et al., 1987 ) or to the hydrogen-rich environment of the Phosphoria shale (PRICEand BARKER,1985 ) In any event, it appears that the difference between Saxby’s and Lewan’s results is more significant than the difference between our calculations and either data set. We next compare our model with vitrinite reflectance data from sedimentary columns where the thermal histories are known fairly well. LARTER( 1989) demonstrated that his kinetic model was consistent with vitrinite reflectance for the COST #1 well in the Gulf of Mexico. Thermal history and vitrinite reflectance data for the COST #1 well is given by WAPLES( 198 1). Our model calculations using Wapfes’ thermal history model are compared in Fig. 10 with both the experimental data and with Larter’s model. Our H/C correlation, Eqn. (2), works somewhat better than our carbon correfation, Eqn. (3). Our H/C correlation agrees with Larter’s method over the range that his is valid, but our calcutation works over a larger range. The disagreement between our calculations and the measured data at depths above 2000 m could be due to the thermal model used, as well as to the limitations of our model. A similar comparison IS shown in Fig. 1I for the Wagon Wheel well in Wyoming. The thermal history for this calculation was derived from the burial history of POLLASTROand BARKER ( 1986) by assuming that all stratigraphic levels follow parallel burial histories and by using a geothermal gradient of 23.7’C/km (SPENCER, 1987). Here the correspondence is good over the entire range of data. QWGLEY et al. ( l987) presented vitrinite data for three basins

Original sample

Vltrlnlte reflectance,

Y&o

Larter

C corr.

__-..__a-_--.

; * \ . \ ‘\

._i_ _.i

j

JI H/C corr.

i_..._ . .

.

. _ -..

FIG. f 0. A comparison of vitrinite reflectance data fmm WAPLES ( 198 I ) for theCOST #I welt, Gutfcoast, U.S.A.. with that calculated by various kinetic equations. All calculations used Waples’ thermal history.

with different but roughly constant heating rates. Our model calculations using our H/C correiation at the extreme healing rates bracket the data, as shown in Fig. 12. The calculated curves are not quite linear, and there is too much scatter XI the data to test whether they should be linear. The curves from the carbon correlation are similar but tend to be more nonlinear.

, 1 -r

Vitrinite reflectance, O/of30

1.1 I-__r

d

0.2

3.0 4.0 -T--‘ weti l

2000

C

Measured

C

E

360

t 0.2

1.0

Vltrinite reflectance,

1.8 %Ro

FOG. 9. Vitrinite reflectance data of LEWAN( 1985) for hydrous pyrolysis of Phosphoria ( 0) and Woodford ( 0) shales and Wilcox

Fairfield (A) and Blackhawk coals (m) compared to our model calculations ( 72 h at indicated temperature 1.

FIG. 1I. Similar comparison as in Fig. IO for the Wagon Wheel well, Wyoming. Also shown is a calculation using Ihe TTI formalism and the correlation between TTI and reflectance given by WAPI.ES (19811.

2655

Kinetics of vitrinite maturation

$ 2.0E s l.Og = s 0.5 .Z C & 0.3 > c. I

0

50

4

I

150 loo maximum T, “C

/

200

250

FIG.12. Effect of geological heating rate on vitrinite reflectance. The lines represent calculations of our kinetic model and Eqn. (3), and the data comes from QUIGLEYet al. ( 1987) for the Scotian Shelf (A,0.5”C/Ma),North!Sea(O, l”C/Ma),andPannonianBasin(+, 30-50”C/Ma).

We present one final comparison that tests the upper range of our present model parameters. Figure 13 compares measured and calculated vitrinite reflectance values from the Cerro Prieto geothermal field. The measured values come from BARKER and ELDERS (198 1) and were obtained by comparing vitrinite vs. depth data in their Fig. 2 with the T25 profile of present-day temperature vs. depth in their Fig. 3. The solid line is their correlation for vitrinite versus temperature. The broken lines were calculated with our model by using a heating rate of lOO’C/Ma, which corresponds to reaching 3OO’C in 3 Ma. Even though we assumed a constant heating rate, our model calculations agree with the measured values at least as well as the correlation of BARKER and ELDERS (198 1 ), and our model was developed completely independent of their data. Any rigorous statistical comparison is hindered by scatter in the data. Part of the scatter, in fact, may be due to differences in the exact thermal history paths for each depth. RELATIONSHIP BETWEEN VITRINITE REFLECTANCE AND OIL GENERATION It is normally assumed that intense oil generation from typical marine source rocks starts at a vitrinite reflectance of 0.5-0.65% and oil generation is completed (oil concentrations at their maximum) at 0.85-l. 1% ( WAPLES, 1981; TISSOT and WELTE, 1984). If we calculate reflectance and the extent of oil generation as a function of time for the same thermal history, we can construct the relationships shown in Fig. 14. For these calcuiations, we used a frequency factor of 5 - 10 I2 s-’ and an activation energy dist~bution of 5, 20, 50, 20, and 5% of the reaction, respectively, at energies of 47-51 kcal / mol. These kinetic parameters predict a maximum rate of oil generation of 128°C at a heating rate of 3.3”C/Ma, which is near the average of temperatures predicted by several kinetic models for marine kerogens ( BURNHAMet al., 1987; TISSOT et al., 1987; YOKLER, 1987; MACKENZIE and QUIGLEY, 1988). There are two points of interest concerning Fig. 14. First, the reflectance calculated from the H/C correlation seems to agree better with prevailing wisdom concerning the onset

Oka

150 Present-day

100

200

250

300

350

temperature,%

FIG. 13. Comparison of measured and calculated vitrinite reflectance values for the Cerro Prieto geothermal field.

of oil generation. We do not know why the carbon correlation does not work quite as well. Second, the calculations for Fig. 14 used a constant heating rate of 3.3’C/Ma, but calculations at heating rates from 0.1 to SO”C/Ma yielded curves that were nearly identical. This disagrees with the suggestion of YUKLER and KOKESH ( 1984) that the ~lation~ip between vi&mite reflectance and oil generation depends on heating rate. Their arguments were based on differing, but obviously erroneous, effective activation energies for the two processes. Our calculations agree with the result of LARTER( 1989) that the effective mean activation energy for vitrinite maturation near the oil window is close to the approximately 50 kcal/ mol for oil generation. DISCUSSION While there is no rigorous argument that the Arrhenius equation should extrapolate well from laboratory to geological conditions, the results in this paper provide ad~tion~ con-

1-

1

I

.

0.8 B X 8 5 0.6 01 % = 0.4 -

WC eorr. (Eq. 2)

-

$ ZZ 8 g 0.2-

Vitrinite reflectance,

%Ro

RG. 14. Relationship between vitrinite reflectance and oil gcueration cakulated by our model. The temperatures indicated are for a heating rate of 3.3’C/Ma, but the retkctanceconvemion relationship is essentially independent of heating rate for heating rates from 0.1 to SO”C/Ma.

2656

A. K. Bumham and J. J. Sweeney

firmation that it works quite well as long asgood, appropriate data are properly analyzed. Earlier pessimism (SNOWDON, 1979) was a result of poor data or poor data analysis. The word “appropriate” is particularly important for vitrinite. While pressure does not appear to be particularly important for Type I and II kerogens, the higher oxygen content of Type III kerogens (e.g., vitrinite) appears to require data at high pressures to derive correct, effective rate constants. Alternatively, a detailed chemical kinetic model that includes both transport processes and secondary reactions might be able to predict the pressure effects from more basic phenomena. A key eiement in deriving kinetic expressions that extrapolate over wide temperature ranges is the use of activation energy distribution models. The very low effective activation energy that corresponds to the Lopatin method is an artifact of neglecting the diversity of reactions involved. In a similar vein, it is possible to derive chemically realistic activation energies for biomarker generation if an activation energy distribution model is used ( BURNHAM, 1989). The use of a single frequency f&or with the activation energy ~~bution is an obvious simplification of reality, but there is usually not enough data available over a wide enough temperature range to determine distributions in both A and E. Altemalively, a conve~ionde~ndent A and E is easily derived (FRIEDMAN, 1963), but it is more difficult to apply in complex kinetic models. The compositional model presented here is obviously more complex than the kinetic model presented previously by LARTER ( 1989 1. If one is interested only in geological maturation within the range of0.5 to 1.4 %Ro, his model is more convenient. However, our model, especially with the H/C correlation, appears to be valid from 0.3 to about 4 %Ro. Moreover, ours is based on correlating reflectance with compositional properties that are more directly related to those causing reflectance. Latter’s is based on phenol yield upon pyrolysis, which correlates directly with vitrinite rank only over a narrow range. Methoxy- and dioxy-aromatics are formed instead of phenols at very low ranks (WATCHERet al., 1988), and there is an insufficient amount of the right kind of oxygen left in high-rank coal to form significant amounts of phenols. It is important not to confuse the model presented in this paper with the model input parameters. Adjustments in the input parameters could certainly improve agreement between the model calculations and experiments for any given limited set of conditions, and perhaps for all vitrinite reflectance data as a whole. However, the principal objective of this work is to show that a relatively simple kinetic model with reasonable reaction parameters can achieve semi-quantitative agreement with much data over a very wide range of conditions. A major impediment to improving the model for more global application is the inconsistency among various data sets. There are issues in addition to inaccurate me~uremen~ and thermal histories. First, there are two different types of organic matter that are commonly identified as vitrinite, but they differ in hydrogen content and reflectance ( TIZ+OTet al., 1987, pp. 1447-1449). Second,it has been proposed that increases in vitrinite reflectance can be inhibited by reaction with bitumen from other hydrogen-rich macerals (PRICEand BAR.,

KER, 1985). Third, the dependence of reflectance on particte orientation, which becomes important for reflectances greatei than l%, is not always taken into account. Kinetic expenments on isolated vitrinites also would aid in model devel. opment. We believe that other vitrinite reflectance models not ba.5e.d on the Arrhenius equation have significantly less merit be cause they are valid only over relatively narrow heating rate ranges. The weaknesses of the Lopatin method have been discussed previously ( QUIGLEY et al., 1987; WOOD. 1988 1: The time-temperature relationship used by LERCXE et a: ( t984), k = A exp[( T - r,),/rp], also has little theoreticai basis. Combining previous results for oil ( BURNHAMet al. 1987; UNGEBER and PELET, 1987) and biomarker (BURIZ. HAM, 1989) generation with the vitrinite results discussed in this paper, it becomes obvious that the Arrhenius equation with an activation energy distribution is a superior approach Acknowledgments-This work was perfom~ed under the auspices 01 the U.S. Department of Energy by the Lawrence Livermore National

Lahoratorv under Contract W-7~5-~n~~8. Financial sunnort came from the &I& of Basic Energy Sciences and a group o‘f;ndustrial sponsors (Exxon, Arco, Norsk Hydro, IKU, Chevron, Stat&l, and JNOC). Editorial hu~df~~g:R. P. Philp REFERENCES BARI(ER C.

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