Kinetics of gaseous hydrocarbon generation with constraints of natural gas composition from the Barnett Shale

Organic Geochemistry xxx (2014) xxx–xxx

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Kinetics of gaseous hydrocarbon generation with constraints of natural gas composition from the Barnett Shale Xinyu Xia ⇑ Hess Corporation, Houston, TX 77010, USA

a r t i c l e

i n f o

Article history: Received 18 October 2013 Received in revised form 31 January 2014 Accepted 8 February 2014 Available online xxxx

a b s t r a c t A kinetic compositional model covering the generation of methane through pentanes is calibrated with both experimental and field data. A continuous distribution of activation energy (E = E0 + yEs) is applied to describe the heterogeneity of hydrocarbon generation kinetics, with E0 (activation energy E at conversion y = 0) as the location parameter and Es as the scale parameter. The best fit gives E0 = 53.0 kcal/mol and Es = 4.0 kcal/mol for methane generation with frequency factor A = 3  1011 s1. The values of E0 and Es for the generation of ethane, propane, n-butane and n-pentane decrease with carbon chain length, with a constant A value. The generation of branched alkanes (isobutane and isopentane) has higher E0 and narrower Es values compared with the generation of their n-alkane isomers. The model adequately describes natural gas compositional properties with thermal maturation, including: (1) decreased wetness, (2) a log-log relation between the C2H6 through C5H12 concentration, and (3) increased i-C4H10/nC4H10 and i-C5H12/n-C5H12 with thermal maturity. The contribution of secondary-cracking gas at higher maturity, which may change the above trends, was also quantified. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Hydrocarbon composition is the most important geochemical characteristic of natural gas. Compositional parameters (1) determine other physical and chemical properties under geological conditions; (2) reflect hydrocarbon generation mechanisms; (3) can be applied as proxies to estimate the distribution and composition of oil and condensates; and (4) can be used to estimate the economic value of a gas reservoir. Despite these significant factors, chemical composition has not been as fully investigated as gas stable isotopic compositions. Isotopic data have been applied as proxies for hydrocarbon generation (Stahl et al., 1977; Schoell, 1983; Tang et al., 2000), source rock organic facies and hydrocarbon potential (Schoell, 1983; Galimov, 2006), reservoir alteration (e.g., thermochemical sulfate reduction, Mankiewicz et al., 2009), and hydrocarbon migration (Prinzhofer and Pernaton, 1997; Xia and Tang, 2012). Some chemical compositional parameters (such as wetness, CH4/C2H6, C2H6/C3H8 and i-C4H10/i-C4H10) have been applied (e.g. Schoell, 1983; Prinzhofer and Pernaton, 1997; Zumberge et al., 2012). But these applications are normally descriptive; the variation of these relations with source rock thermal maturity has been poorly quantified.

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A quantified estimate of natural gas chemical composition and its quantified relationship with petroleum system features (especially thermal maturity) requires calibration of a theoretical mechanistic model with laboratory and field data. Empirical models of hydrocarbon generation are usually based on the assumption of parallel first-order reactions (Burnham et al., 1987). Hydrocarbon generation includes primary cracking (cracking of kerogen) and secondary cracking (cracking of larger hydrocarbon molecules into smaller ones). Theoretically, an empirical model can be applied to simulate the generation of each gaseous hydrocarbon (methane, ethane, propane, n-butane, isobutane, n-pentane and isopentane), but there has been no ideal data to calibrate such a model. Laboratory pyrolysis data are commonly not suitable for compositional calibration, because the yield of C2–C5 (ethane through propane) is seriously affected by secondary cracking at high temperatures, making it impossible to get unique and accurate solutions. Ideal field data for model calibration should correlate with source rock maturity and the gas composition should not be altered by migration. Such correlated and unaltered data are difficult to obtain from conventional reservoirs. The recent intensive exploration for shale gas provides an unprecedented opportunity to conduct detailed geochemical studies of natural gas generation mechanisms. Zumberge et al. (2012) reported detailed chemical compositions of natural gas from the Barnett Shale. The gas samples cover a continuous range of source rock thermal maturity (vitrinite reflectance Ro from 1.3% to greater

http://dx.doi.org/10.1016/j.orggeochem.2014.02.009 0146-6380/Ó 2014 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Xia, X. Kinetics of gaseous hydrocarbon generation with constraints of natural gas composition from the Barnett Shale. Org. Geochem. (2014), http://dx.doi.org/10.1016/j.orggeochem.2014.02.009

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X. Xia / Organic Geochemistry xxx (2014) xxx–xxx

than 2.0%). Because of the gas retained in the source rock, compositional fractionation due to migration (from source rock to reservoirs) is minimal. Furthermore, the geological and geochemical characteristics of the Barnett Shale were studied in detail (Hill et al., 2007a,b; Jarvie et al., 2007). In this paper, the kinetics of natural gas generation were investigated using published data. Specifically, a continuous activation energy distribution was applied in the empirical kinetic model, so that the calibration is more rigorous, and the solutions for each kinetic parameter are more unique than the model using discrete kinetic energy distributions. Laboratory and field data were applied for the calibration. The work aimed to provide more detail needed to understand natural gas generation and an improved method with more accurate parameters to estimate hydrocarbon properties in oil and gas reservoirs.

2. Data and model 2.1. Geochemical background of Barnett Shale gas Shale gas is generated and reservoired in the Mississippian Barnett Shale in the Fort Worth Basin, Texas, United States. The source rock has average TOC of 4% with Type II kerogen (Hill et al., 2007b; Jarvie et al., 2007). Gas is produced from the eastern part of the basin, where the source rock is currently in the gas window. Residual gas in the source rock is estimated to be 100–350 standard cubic feet (scf) per short ton of rock or 3–11 m3/t rock (Zumberge et al., 2012). Carbon isotopic compositions of ethane and propane in the Barnett Shale gas show reverse trends with respect to maturity at Ro > 1.5% (Zumberge et al., 2012), which can be explained by mixing of primary and secondary generated gas (Xia et al., 2013). 2.2. Data for model calibration The laboratory gas yield data are from the pyrolysis of a mature Barnett Shale kerogen (Ro = 1.15%) in a closed system (Hill et al., 2007a). The thermal maturity of the unheated kerogen surpasses the oil-generation window; therefore, the contribution of oil cracking to gas generation during pyrolysis is minimal, making the data suitable to calibrate the kinetics of primary gas generation. The field data of gas composition (molar percentage) includes all C1–C5 alkanes (Zumberge et al., 2012). Additionally, the conversion of kerogen under geological thermal conditions is also applied to constrain the calibration. The conversion is represented by the decrease of hydrogen index (HI, in mg hydrocarbon/g TOC) as a function of equivalent Ro (measured or derived from Rock-Eval pyrolysis Tmax). Two sets of Rock-Eval results were applied. One is composed of over 20 Barnett Shale samples at different thermal maturity (Jarvie et al., 2005, 2007; Bernard et al., 2012). The other set is from systematic measurements on Paleozoic source rocks with type II kerogen in the Canadian Arctic Islands (Dewing and Obermajer, 2009), with over 300 samples. The large sample set of the latter set is beneficial to reduce the uncertainty. The difference of the HI–Ro relations between the two sets of source rocks is expected to be minimal in the gas window. In the gas window, kerogen (especially for type I and type II kerogens) chemical structure is largely homogenized, where methyl groups and short C–C chains are the dominant precursor for gas generation (Hunt, 1996). 2.3. Kinetic model The generation of each hydrocarbon component is regarded as a first-order reaction, therefore, the rate equation is:

dy ¼ kð1  yÞ dt

ð1Þ

Here y is the conversion of the precursor (dimensionless), t is time (in s), and k is reaction rate constant (in s1):

  E k ¼ A exp  RT

ð2Þ

Here A is the pre-exponential factor (in s1), E is activation energy (in J/mol or kcal/mol; 1 kcal = 4184 J), R is the gas constant (8.314 J mol1 K1), and T is temperature (in K). Due to the complexity of kerogen, a single E value cannot accurately describe the cracking of side chains over a wide range of thermal maturity. In most previous work, a group of discrete E values are assigned to account for the cracking of the various precursors. Such a discrete energy distribution makes the model easier to match with the laboratory data; but it is often difficult to obtain a unique solution. In contrast, a continuous energy distribution is applied in this work:

EðyÞ ¼ E0 þ yEs

ð3Þ

Here E0 is the location parameter (E at y = 0); Es is the scale parameter (the difference of the E values at y = 0 and y = 1). The distribution has a clear physical meaning with only two variables to optimize. Such a linear energy distribution has been widely applied to describe chemical processes having mathematical similarity to kerogen cracking, i.e., gas adsorption on energetically heterogeneous surfaces. The adsorption energy is assumed to decrease linearly with the coverage of gas molecules on the surfaces and the popular Temkin isotherm is derived (Lyklema, 1995). The theoretical Ro values are calculated with the EasyRo method (Sweeney and Burnham, 1990). The parameters to be optimized include the fraction of each hydrocarbon precursor in the kerogen, kinetic parameters (A, E0 and Es) for cracking, and the precursor ratio between primary and secondary cracking.

2.4. Fitting the model In the fitting, different geological heating rates (from 1 K/ma to 10 K/ma) were tested. Initial estimated values were assigned to kinetic parameters (A, E, and Es) and precursor concentration, so that the Ro values and each species amount were calculated at any given time point with the kinetic model described in Section 2.3. Then a group of relations were obtained, for example, HI–Ro relation, or CH4/C2H6–CH4/C3H8 relations for field data. The relations for the field data are independent of heating rate within a reasonable geological heating rate for the Barnett Shale (between 1 K/ma to 4 K/ma before the maximum burial depth; Montgomery et al., 2005; Ewing, 2006). The objective function for best-fit is based on the x–y relations. For each x value of the observed data, there is an observed y value (yobs) and a calculated y value (ycal). The objective function Q is defined as

Q¼

mj n X X ðycal;i;j  yobs;i;j Þ2 j

i

mj  max ðyobs;i;j Þ2

ð4Þ

Here i and j refer to the ith data point in the jth relation; mj is the amount of total observed data points in the jth relation; n is the amount total relations. Best-fitting parameters are obtained when Q is minimized. The numerical calculation is performed using Mathworks MATLAB R2013b.

Please cite this article in press as: Xia, X. Kinetics of gaseous hydrocarbon generation with constraints of natural gas composition from the Barnett Shale. Org. Geochem. (2014), http://dx.doi.org/10.1016/j.orggeochem.2014.02.009

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3. Results and discussion 3.1. Constraint of gas yield Modeling results of gas yield from primary cracking are constrained by both the laboratory and field data. The constraint from laboratorial pyrolysis results (Hill et al., 2007a) is the relation between cumulative CH4 yield and temperature at two different heating rates (2 K/h and 20 K/h, Fig. 1A). Only the data for T < 500 °C are applied to avoid interference from cracking of C2– C5 components. The constraint from natural thermal evolution is the HI–Ro relation for source rocks (Jarvie et al., 2005, 2007; Dewing and Obermajer, 2009; Fig. 1B). The decrease of HI (in mg/g TOC) for Ro > 1.1% is assumed to result from the generation of gas components. The best-fit results will be discussed in the next section. 3.2. Constraint of gas composition 3.2.1. Field data The chemical composition of natural gas, which can be converted to the ratios between different hydrocarbons, does not directly indicate the yield of these components from source rock without knowing the total amount of hydrocarbon generated. On the other hand, chemical composition provides more constraints on the relations between gas generation kinetic parameters. During optimization of the model, the following relations are applied: 1. The volumetric ratios of CH4/C2H6, CH4/n-C4H10 and CH4/nC5H12 as functions of the CH4/C3H8 ratio. 2. The volumetric ratios of isomers (i-C4H10/n-C4H10 or i-C5H12/nC5H12) as a function of wetness. Each of the two relations has a reversal trend at high thermal maturity (Zumberge et al., 2012). 3. Wetness versus Ro (Xia et al., 2013):

Ro ð%Þ ¼ 0:33 lnðwetness=100Þ þ 2:2 Wetness of natural gas is defined as the ratio between the molar sum of C2 through C5 hydrocarbons and the molar sum of total gaseous hydrocarbons. The cross plots in Fig. 2 are based on the theoretical values that will be discussed in the following subsections. Remarkably, there are reverse trends of butane and pentane isomer ratios with respect to wetness (Fig. 2C). Reversals can also be distinguished in Fig. 2A and B. The reversals occur at high maturity; therefore, they may be related to the contribution of secondary-cracking gas, as

140

dlnðDCH4 =DC2 H6 Þ 1  kC2 H6 =kCH4 ¼ dlnðDCH4 =DC3 H8 Þ 1  kC3 H8 =kCH4

ð5Þ

For the derivation of Eq. (5) see the appendix. This transient slope value varies in a narrow range of 0.42–0.65 within modeling thermal maturity (Ro 1.1–2.0%), with an average of 0.51. Because the ‘‘transient’’ slope does not change remarkably, the slope of the overall curve is nearly constant. As a result, the trend line appears to be a straight line on the logarithm plot, and the slope is determined by the k values. 3.2.2. Barnett Shale as an ‘‘instantaneously’’ cumulating reservoir To use the above ratios (especially wetness) for calibration, it is necessary to know whether they result from a ‘‘cumulative’’ or an ‘‘instantaneous’’ reservoir history. A reservoir that trapped both the early- and late-stage products from the source rock is referred to as ‘‘cumulative’’; while a reservoir that only trapped late-stage products is referred to as ‘‘instantaneous’’. The fraction of C2 through C5 hydrocarbons in natural gas generated from source rock decreases with its thermal maturity. Consequently, gas wetness is higher for the cumulative than for the instantaneous case. For gas shale (which is both source and reservoir), an ‘‘instantaneous’’ reservoir will have a higher expulsion yield than a cumulative reservoir. The current geochemical data suggest that the gas in Barnett Shale is most likely instantaneous. If it was cumulative, that means, the C2 through C5 components (mainly ethane and propane) generated at all earlier maturity stages could be preserved in the reservoir. Cracking of ethane and propane in the reservoir is unlikely to happen, because isotopic compositions do not suggests any remarkable cracking of ethane and propane at Ro < 2.4% (Zumberge et al., 2012). Consequently, the decrease of wetness with increasing maturity (Fig. 2D) should be accompanied by an increase in methane generation in order to ‘‘dilute’’ the preserved ethane and propane. Because of constraints imposed by the kerogen conversion rate (Fig. 1B), there is no solution matching the relation between wetness and maturity (Fig. 2D). Therefore, the shale reservoir should be ‘‘instantaneous’’ and early products were expelled. This is consistent to the observation that the Barnett

400

A

B

100 80

300

100

HI (mg/g TOC)

Gas yield (mL/g TOC)

120

suggested by the isotopic reversal of ethane and propane at high maturity (Rodriguez and Philip, 2010; Xia et al., 2013). One interesting phenomenon is that there are linear logarithm relations between methane to C2–C5 component ratios (Fig. 2A and B). This is a strict constraint to fit the kinetic parameters. Taking the CH4/C2H6 versus CH4/C3H8 line (on logarithm plot) as an example, at each time point the ‘‘transient’’ slope is approximately

80 60 40

60 40

200

20 0

1

1.5

2

2

2.5

2.5

100

20 0 300

350

400 o

T ( C)

450

500

0 0.5

1

1.5

3

Ro (%)

Fig. 1. (A and B) Experimental data, field data and theoretical values accounting for gas yield. Plot A: Cumulative methane yield during laboratory pyrolysis at different heating rates: circle (experimental, Hill et al., 2007a) and solid line (theoretical curve of this study) – 2 K/h; triangle (experimental, Hill et al., 2007a) and dashed line (theoretical curve of this study) – 20 K/h. Plot B: Residual hydrocarbon index: circle—field data from the Barnett Shale (Jarvie et al., 2005, 2007); cross - field data from the Paleozoic source rock in the Canadian Arctic Islands (Dewing and Obermajer, 2009); solid line—theoretical curve of this study.

Please cite this article in press as: Xia, X. Kinetics of gaseous hydrocarbon generation with constraints of natural gas composition from the Barnett Shale. Org. Geochem. (2014), http://dx.doi.org/10.1016/j.orggeochem.2014.02.009

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X. Xia / Organic Geochemistry xxx (2014) xxx–xxx 5

6

10

4

5

10

CH4/n-C5H12

CH4/C2H6, CH4/n-C4H10

10

3

10

2

10

10

4

10

3

10

A

1

10 1 10

2

3

10

10

B

2

10 1 10

4

10

2

10

CH4/C3H8

4

10

10

CH4/C3H8

3

15

2.5

Wetness (%)

i-C4H10/n-C4H10, i-C5H12/n-C5H12

3

2 1.5 1 0.5 0

5

10

15

20

5

D

C 0

10

0

25

1.2

1.4

1.6

1.8

2

2.2

2.4

Ro (%)

Wetness (%)

Fig. 2. Field data (Barnett Shale gas, Zumberge et al., 2012) and theoretical values that constrain the gas compositions. The best-fitting results (solid lines) are for an instantaneous case, where a reservoir is charged for a time interval corresponding to DRo = 0.3% or 0.5%. (A) Volumetric ratios of CH4/C2H6 (triangle) and CH4/n-C4H10 (square) against CH4/C3H8; (B) CH4/n-C5H12 (square) against CH4/C3H8; (C) the volumetric ratios of i-C4H10/n-C4H10 (dots) and i-C5H12/n-C5H12 (cross) against wetness; (D) wetness against Ro.

A = 3.85  1016 s1 from Behar et al. (2008) for light oil cracking is applied, and a best fit of E = 65.5 kcal/mol is obtained, which is close to the value derived from experimental pyrolysis of light oil (67.2 kcal/mol; Behar et al., 2008). The y0 values are best-fit values (Table 1). The fitting curves show that the kinetic model accurately describes the primary cracking for Ro < 1.7% (wetness > 5%, and CH4/C3H8 < 1000). At higher maturity, mixing of secondary cracking gas can explain the deviation from the trend. The original ratio between secondary and primary precursors is low (1.5  103 in carbon weight ratio), but secondary cracking gas strongly influences the hydrocarbon composition at high thermal maturity because secondary cracking has higher activation energies and occurs later. Notably, the reversed trends of i-C4H10/n-C4H10 and i-C5H12/n-C5H12 with respect to wetness can be explained by secondary gas having low values of these ratios. In secondary cracking, the precursor fractions of the two isoalkanes are remarkably lower than their n-alkane isomers. This indicates that secondary gas generation involves the cracking of i-C4H10 and i-C5H12.

Shale is the source rock of some conventional gas reservoirs in the Fort Worth Basin (Ball and Perry, 1996). The following theoretical results are calculated for two instantaneous scenarios: DRo = 0.3% or 0.5%. Here DRo signifies an Ro interval where only the gas generated in the maturity range between (Ro–DRo) and Ro is preserved in the shale. The initial Ro value is 1.1% for the modeling. 3.3. Best-fit results The parameters are obtained by fitting theoretical results to the real data. The best-fit results for primary cracking are listed in Table 1. The theoretical results are shown in Figs. 1 and 2. There is no significant difference between the scenarios of DRo = 0.3% and 0.5%. The deviation in the trend at high maturity indicates that secondary cracking should be taken into account. Compared with the fit to primary cracking, there are not enough constraints and no unique solution exists for secondary cracking parameters. Here

Table 1 Best-fit results of kinetic parameters and precursor fraction (in mg C of product/mg C of precursor) for gaseous hydrocarbon generation from Barnett Shale assuming an instantaneous reservoir history (DRo = 0.3%). Products

CH4 C2H6 C3H8 i-C4H10 n-C4H10 i-C5H12 n-C5H12 a

Kinetic parameters (primary cracking)

Precursor composition (mol C%)

A (1013 s1)

E0 (kcal/mol)

Es (kcal/mol)

Primary cracking

Secondary crackinga

0.03 1 1 1 1 1 1

51.0 52.9 52.5 53.2 52.3 53.0 52.0

4.0 2.8 2.5 1.6 2.4 1.5 2.4

83.29 10.71 3.57 0.95 0.95 0.29 0.24

74.07 22.22 2.96 0.04 0.56 0.04 0.11

A = 3.85  1016 s1 (Behar et al., 2008) and E = 65.5 kcal/mol; ratio of secondary cracking to primary cracking precursors is 1.5  103 (in carbon weight).

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The frequency factor for methane generation (A = 3  1011 s1) is about two orders of magnitude lower than most of the values in basin modeling (for example, Pepper and Corvi, 1995; Hill et al., 2007a,b). The corresponding of E value (51–55 kcal/mol) is also lower. This is related to a key point for kinetic fitting: to separate the contributions of A and E to variations in k values. A good separation requires a wide temperature range, as indicated by Eq. (2). The above A and E values in this work are constrained by remarkably different temperatures (100–200 °C under geological conditions and 300–500 °C under laboratory conditions). This large temperature difference improves the separation of the effects of A and E on the reaction rate, making solutions more rigorous. If the A value is in the range of 1013 s1 with E fitted by laboratory results, then the gas generation window under geological conditions is postponed to Ro > 1.8%, which is inconsistent with observations of low residual hydrocarbon potential in high maturity source rocks (Fig. 1B). The above A and E values are similar to those for recent gas generation experiments on model methyl aromatic compounds (Fusetti et al., 2010), which are A = 9  1011 s1 and E = 53 kcal/mol. This consistency suggests that demethylation is the main mechanism for late gas generation. The value of A = 1013 s1 for C2–C5 generation is confined by the wetness (Fig. 2D), the determined kinetic parameters for methane generation, and the relation between the kinetic parameters for generation of different hydrocarbons (Fig. 2A and B). If A is set close to methane generation (1011 s1) and E is fitted by Fig. 2A and B, then C2–C5 gas generation under geological conditions terminates too early, and the wetness around Ro  1.6% cannot be fitted. Overall, the fit for the primary generation of different gas components are rigorously constrained.

precursor amount or the accumulation extent. Consequently, the slope of the correlation line in Eq. (5) should be ‘‘universal’’ for different gas fields. Fig. 3 compares more data sets of CH4, C2H6 and C3H8. The organic types include Type II (Barnett, Fayetteville and Bossier shales) and Type III (Lewis Shale and Xujiahe Coal Formation). The data points are all close to the Barnett Shale gas trend, indicating that Eq. (5) is rather general for hydrocarbon distributions in natural gas. The similarity of kinetics can be attributed to the structural similarity of kerogens in gas window; residual kerogens are characterized by short alkyl chains on the inert core structure (Hunt, 1996). Most of the data points from conventional reservoirs are located to the upper-left of the line for Barnett Shale gas, which means that for any ethane concentration, the Barnett Shale has more propane content than other reservoirs. This suggests that the Barnett Shale trapped more products formed at lower thermal maturity than most of the conventional reservoirs and nearly all the reservoirs are instantaneously trapped. The two sets of data points close to the two ends of the trend line in Fig. 3 deviate from the trend. The cluster of points in the low CH4/C2H6 and CH4/C3H8 region represents the associated gas generated from Barnett Shale (Hill et al., 2007b). These points probably are a ‘‘reversed’’ trend at early thermal maturity, i.e., the CH4/C2H6 and CH4/C3H8 ratios decrease with increasing maturity. This reversal can be explained by early generation of methane. The other deviation in the high CH4/C2H6 and CH4/C3H8 region consists of the data from the Fayetteville shale gas (Zumberge et al., 2012). This deviation is attributed to mixing of secondary-cracking gas (Xia et al., 2013). It is also a reversed trend because the CH4/ C2H6 and CH4/C3H8 ratios decrease with increasing maturity.

3.4. Applications for natural gas generation and accumulation

3.4.2. Dry gas indicating instantaneous reservoir history Table 1 suggests that while the precursor of methane dominates in the gas-prone kerogen, if all of the gas accumulates in a single reservoir and the ethane and propane do not crack, then the ultimate wetness is still about 7%. Dry gas (wetness < 5%) in shale reservoir forms by expulsion of early generated wet gas in addition to the accumulation of late methane. Therefore, a dry gas reservoir indicates instantaneous reservoir history. This can be illustrated by the transient, instantaneous and cumulative wetness calculated using the parameters in Table 1, as shown is Fig. 4. An instantaneous charging history means that only a small part of the total generated gas is trapped in shale. In other words, the

3.4.1. General applicability of the kinetics Gas composition reflects the relationship between the generation kinetics of different hydrocarbons. Eq. (5) suggests that the CH4/C2H6 and CH4/C3H8 relation is independent of the amount of 1,000

CH4/C2H6

100 15

Wetness (%)

10

1

10

5

1

10

100

1,000

10,000

100,000

CH 4/C3H8 Fig. 3. The relation between the CH4/C2H6 and CH4/C3H8 volume ratios of natural gas from different basins. Solid line: Cross and trend line (ln y = 0.504 ln x + 0.45) for Barnett Shale gas (Zumberge et al., 2012); triangle: Barnett Shale gas of low maturity (Hill et al., 2007b); closed circle: Mississippian Fayetteville shale gas of Arkoma Basin, USA (Zumberge et al., 2012); open circle: gas from Upper Cretaceous Lewis Shale, Washakie Basin, USA (U.S. Geological Survey, 2009); open diamond: gas from Upper Jurassic Bossier Formation, East Texas Basin, U.S.A. (U.S. Geological Survey, 2009); closed diamond: gas from Upper Triassic Xujiahe Formation, Sichuan Basin, China (Dai et al., 2012); dots: all data from U.S. Geological Survey, 2009.

0

1.2

1.4

1.6

1.8

2

2.2

Ro (%) Fig. 4. Comparison between cumulative wetness (solid line), instantaneous wetness (dotted–dashed line for DRo = 0.3% and dashed line for DRo = 0.5%) and transient wetness (dotted line) of primary-cracking products.

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scribe the compositional properties of natural gas, including decreasing wetness with thermal maturity, the logarithmic relation between the concentrations of the C2–C5 components, and the increase of i-C4H10/n-C4H10 and i-C5H12/n-C5H12 with thermal maturity. The calibrated kinetic parameters reveal new details on gaseous hydrocarbon generation and accumulation. This work may improve estimates of hydrocarbon amounts and compositions for oil and gas exploration.

-24

13C(i-C

4H 10)

-27

-30

Appendix A. Derivation of Eq. (5) Assume c1, c2 and c3 are the concentrations of methane, ethane and propane. Here the subscripts refer to carbon number in any hydrocarbon molecule. From Eq. (1), the relation between the transient concentration increase of methane and propane is

-33

-36 -36

-33

-30 13C(n-C

-27

-24

4H 10)

Fig. 5. Comparison of carbon isotopic compositions (d13CPDB, ‰) between isobutane and n-butane in natural gas samples (circle; data from U.S. Geological Survey, 2009). The dashed line shows equivalent d13C values for isobutane and n-butane.

ln

Dc 1 k1 1  y1 ¼ ln þ ln Dc 2 k2 1  y2

ðA1Þ

The derivative of Eq. (A1) over t is

d Dc 1 d k1 1 dy 1 dy ln ¼ ln þ  2  1 dt Dc2 dt k2 1  y2 dt 1  y1 dt

ðA2Þ

Substitute dy/dt with Eq. (1), amount of generated gas exceeds the storage capacity of the shale. Consequently, forming a commercial dry gas reservoir requires high TOC. For the instantaneous case presented in Fig. 4 and considering wetness lower than 5% at Ro = 1.7% for DRo = 0.5%, only the gas generated between 1.2% and 1.7% is trapped. In this maturity range, the decrease of HI is about 50 mg/g TOC (Fig. 1B). If the original gas in place reaches 100 scf per short ton rock (3.1 m3/ton), then the TOC of the shale at Ro 1.3% should be more than 4.4%. 3.4.3. Mechanisms of isoalkane generation The kinetic parameters reveal some unusual characteristics for isoalkane generation compared with normal alkanes. The precursor for the C2–C5 components decreases with increasing carbon number. From ethane to n-pentane, the precursor amount decreases evenly by a factor of four to five with each additional carbon number in the normal alkanes. However, the amounts of precursors for the isoalkane and n-alkane isomers are rather similar in primary cracking. This similarity may indicate that the pair of precursors, iso-alkyl and its corresponding n-alkyl, may have some relation in gas generation, as discussed below. The activation energy is slightly higher for isoalkanes than for the corresponding n-alkanes (Table 1). This accounts for the increase of i-C4H10/nC4H10 and i-C5H12/n-C5H12 with thermal maturity when wetness > 5% (Fig. 2C and D). Because the precursors of isoalkanes (isoalkyl radicals) have lower Gibbs free energy than the corresponding normal isomers under geological conditions, the higher activation energy for isoalkane formation is unlikely to be caused by the energy difference for isoalkyl cleavage from kerogen. Rather, it is likely due to the formation of isoalkyl groups from normal alkyl groups in kerogen (for example, by methyl shift). That is to say, normal alkane are a primary product, while isoalkanes are a secondary product of kerogen in the gas generation window. This is consistent with the observation that isobutane is usually more depleted in 13 C than n-butane in natural gas (Fig. 5). The more negative isotopic composition of isobutane may be caused by isotopic fractionation during methyl shift. 4. Conclusions This work demonstrates a hydrocarbon generation model with a simple energy distribution that fits the gas yields under both laboratory and geological heating conditions. The model can also de-

d Dc 1 d k1 ln ¼ ln þ k2  k1 dt Dc2 dt k2

ðA3Þ

Calculation   based on the numerical intermediate results show   that dtd ln kk12   jk2  k1 j when neither of the conversions is extremely close to 0 or 1. Therefore,

d Dc 1 ln ¼ k2  k1 dt Dc2

ðA4Þ

Similarly

d Dc 1 ln ¼ k3  k1 dt Dc3

ðA5Þ

d lnðDc1 =Dc2 Þ k2  k1 ¼ d lnðDc1 =Dc3 Þ k3  k1

ðA6Þ

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Please cite this article in press as: Xia, X. Kinetics of gaseous hydrocarbon generation with constraints of natural gas composition from the Barnett Shale. Org. Geochem. (2014), http://dx.doi.org/10.1016/j.orggeochem.2014.02.009