Compositional and stable carbon isotopic fractionation during non-autocatalytic thermochemical sulfate reduction by gaseous hydrocarbons

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ScienceDirect Geochimica et Cosmochimica Acta 139 (2014) 472–486 www.elsevier.com/locate/gca

Compositional and stable carbon isotopic fractionation during non-autocatalytic thermochemical sulfate reduction by gaseous hydrocarbons Xinyu Xia a, Geoffrey S. Ellis b, Qisheng Ma c, Yongchun Tang c,⇑ a Hess Corporation, Houston, TX 77010, USA U.S. Geological Survey, Denver, CO 80225, USA c Power Environmental Energy Research Institute, Covina, CA 91722, USA b

Received 25 February 2014; accepted in revised form 3 May 2014; Available online 23 May 2014

Abstract The possibility of autocatalysis during thermochemical sulfate reduction (TSR) by gaseous hydrocarbons was investigated by examination of previously reported laboratory and field data. This reaction was found to be a kinetically controlled nonautocatalytic process, and the apparent lack of autocatalysis is thought to be due to the absence of the required intermediate species. Kinetic parameters for chemical and carbon isotopic fractionations of gaseous hydrocarbons affected by TSR were calculated and found to be consistent with experimentally derived values for TSR involving long-chain hydrocarbons. Model predictions based on these kinetic values indicate that TSR by gaseous hydrocarbon requires high-temperature conditions. The oxidation of C2–5 hydrocarbons by sulfate reduction is accompanied by carbon isotopic fractionation with the residual C2–5 hydrocarbons becoming more enriched in 13C. Kinetic parameters were calculated for the stable carbon isotopic fractionation of gaseous hydrocarbons that have experienced TSR. Model predictions based on these kinetics indicate that it may be difficult to distinguish the effects of TSR from those of thermal maturation at lower levels of hydrocarbon oxidation; however, unusually heavy d13C2+ values (>10&) can be diagnostic of high levels of conversion (>50%). Stoichiometric and stable carbon isotopic data show that methane is stable under the investigated reaction conditions and is likely a product of TSR by other gaseous hydrocarbons rather than a significant reactant. These results indicate that the overall TSR reaction mechanism for oxidation of organic substrates containing long-chain hydrocarbons involves three distinct phases as follows: (1) an initial slow and non-autocatalytic stage characterized by the reduction of reactive sulfate by long-chain saturated hydrocarbons; (2) a second autocatalytic reaction phase dominated by reactions involving reduced sulfur species and partially oxidized hydrocarbons; (3) and a final, or late-stage, TSR reaction in which hydrocarbon oxidation continues at a slower rate via the non-autocatalytic reduction of sulfate by gaseous hydrocarbons. Ó 2014 Elsevier Ltd. All rights reserved.

1. INTRODUCTION Thermochemical sulfate reduction (TSR) is the abiotic stepwise reduction of sulfate to sulfide by hydrocarbons or other organic compounds, and is commonly observed in ⇑ Corresponding author.

E-mail address: [email protected] (Y. Tang). http://dx.doi.org/10.1016/j.gca.2014.05.004 0016-7037/Ó 2014 Elsevier Ltd. All rights reserved.

high-temperature carbonate petroleum reservoirs. Understanding the reaction mechanisms involved in the overall sulfate reduction pathway is essential for developing predictive models of H2S risk for application to oil and gas exploration (Machel, 2001). However, studies of the details of the chemical reactions involved in TSR are hampered by the difficulty of simulating TSR in the laboratory under conditions resembling those where it occurs in nature. Whereas

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thermodynamics predicts that sulfate reduction by hydrocarbons is favorable at temperatures encountered in most near-surface geologic settings (Goldstein and Aizenshtat, 1994), extensive experimental (Goldhaber and Orr, 1995, and references therein) and field observations (Machel, 1987; Heydari and Moore, 1989; Worden et al., 1995) indicate that the minimum temperature for the onset of TSR is approximately 100–140 °C. This leads to the conclusion that the overall TSR reaction mechanism is kinetically controlled, and that determining the extent of TSR requires accurate knowledge of the rate of reaction (Machel, 2001). In one of the first reported laboratory simulations of TSR, Toland (1960) noted that organics were not oxidized when sulfate was the only reductant present, but that even as little as 0.1 mol of H2S (or other reduced sulfur species) was able to initiate sulfate reduction. Subsequent experimental studies showed that the rate of TSR is directly proportional to the amount of reduced sulfur present in the system (see Goldhaber and Orr, 1995, for a summary of this work). Based on geochemical evidence obtained from sour gas fields in the Big Horn Basin, Orr (1974) proposed that TSR is an autocatalytic reaction with H2S generated by sulfate reduction catalyzing further sulfate reduction. For decades following Toland’s (1960) early work, the presence of reduced sulfur was considered essential for initiating and sustaining TSR reactions (Machel, 2001). More recently, a theoretical study of the TSR reaction mechanism explained the apparent non-reactivity of sulfate by showing that free aqueous sulfate ions (SO2 4 ) are very stable; however, sulfate is significantly more reactive when it occurs as bisulfate ions (HSO 4 ) or in association with magnesium ions as contact ion-pairs ([MgSO4]CIP) (Ma et al., 2008). The presence of reduced sulfur species in experimental simulations of TSR leads to the formation of aqueous bisulfate which is readily reduced by hydrocarbons. Zhang et al. (2012) demonstrated that TSR can occur under laboratory conditions without the initial presence of any reduced sulfur species by using aqueous sulfate solutions (CaSO4) buffered to pH conditions <4. The authors note that such acidic conditions are not likely to occur in natural settings where TSR is observed, because carbonate rocks buffer the pH of formation waters at higher values. They propose that in natural TSR reactions [MgSO4]CIP is the reactive form of sulfate (Zhang et al., 2012). Importantly, Zhang et al. (2012) showed that while reduced sulfur is not required to initiate the TSR reaction, the presence of H2S does enhance the rate of TSR. They proposed a twostage reaction scheme, whereby the initial sulfate reduction reaction is slow and non-autocatalytic until a threshold concentration of H2S is reached, at which point the catalyzed sulfate reduction reaction becomes dominant. The details of how reduced sulfur propagates sulfate reduction are not well understood, but it is thought that H2S reacts with hydrocarbons to form labile sulfur compounds (LSC) (e.g., thiols, sulfides, polysulfides, etc.) that in turn propagate TSR (Amrani et al., 2008; Zhang et al., 2008). Amrani et al. (2008) conducted a series of controlled TSR experiments and observed that LSC were significantly more effective at catalyzing the TSR reaction than either elemental S or H2S (on a mole S basis). The authors

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considered several possible explanations for their observations including: (1) the thermal degradation of LSC to form H2S, (2) the formation of unsaturated hydrocarbons, and (3) the generation of S radicals; however, they were able to discount all of these mechanisms. Ultimately, they concluded that direct reaction of thiol with sulfate to form a sulfate ester was one viable mechanism for catalysis of TSR, but conceded that further work is needed to understand the chemistry of the catalyzed TSR reaction (Amrani et al., 2008). Other factors are known to affect the rate of sulfate reduction, perhaps most importantly, the type of organic compound being oxidized. Zhang et al. (2007) conducted a series of TSR simulation experiments using a variety of model organic compounds and found that unsaturated hydrocarbons and oxygen-containing organic compounds (i.e., alcohols and ketones) were more reactive than normal alkanes, whereas carboxylic acids and aromatic hydrocarbons were less reactive. Field observations of known TSR occurrences show gasoline-range normal and branched alkanes to be the most easily oxidized followed by cyclicand mono-aromatics (Krouse et al., 1988; Manzano et al., 1997). The net effect of TSR on residual petroleum is to lower the API gravity, the C15+ hydrocarbon content, and the saturated to aromatic hydrocarbon ratio, while increasing the gas to oil ratio (GOR) (Orr, 1974; Claypool and Mancini, 1989). Of all of the possible organic reactants for TSR, methane is the most stable (Orr, 1990), and would be the least oxidized component in petroleum reservoirs experiencing TSR (Machel, 2001). Most published experimental studies of TSR have involved liquid-phase organic compounds (Zhang et al., 2012, and references therein), and TSR in nature is generally observed in petroleum accumulations that contain crude oil, condensate, or wet gas (Machel, 2001). However, there are some notable exceptions to these circumstances where TSR involving dry gas has been documented (Krouse et al., 1988; Worden and Smalley, 1996; Cai et al., 2003; Hao et al., 2008; Mankiewicz et al., 2009). Two recent studies (one experimental and one fieldbased) of TSR involving gaseous hydrocarbons are of particular interest because of the detailed molecular and stable isotopic compositional data that are available for these systems (Pan et al., 2006; Mankiewicz et al., 2009). Pan et al. (2006) used a novel experimental approach to generate natural gas from kerogen, expose this gas to TSR at 350 °C, and then observe the effect on the molecular and stable carbon isotopic composition of the gases. Mankiewicz et al. (2009) reported the molecular and stable carbon isotopic composition of produced natural gases from 29 wells in the Mobile Bay gas field, offshore Alabama, Gulf of Mexico, where present-day reservoir temperatures are as high as 215 °C. These wells contain hydrocarbons that were originally generated by the thermal alteration of liquid petroleum (“oil cracking”) and then experienced variable amounts of TSR. Both of these studies demonstrated that little to no methane was oxidized under the observed conditions, whereas the heavier hydrocarbon components (C2+) were nearly completely oxidized by sulfate reduction. A significant enrichment in 13C in the residual ethane and

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propane was also observed in these studies, with the heaviest stable carbon isotopic compositions of ethane (d13C2) and propane (d13C3) being 10& and 0&, respectively. These values are significantly more enriched in 13C than the heaviest values previously reported for TSR associated ethane and propane, which did not exceed 15& (Krouse et al., 1988; Cai et al., 2003). These two studies (Pan et al., 2006; Mankiewicz et al., 2009) not only broaden the knowledge of stable isotopic fractionations related to TSR processes, but also provide an opportunity to study the mechanisms of TSR. The gas geochemistry data from the Mobile Bay gas field and the experimental work of Pan et al. (2006) can be used to develop a predictive model of the kinetics of gas generation and associated stable carbon isotopic fractionation of TSR reactions involving gaseous hydrocarbons. In contrast to TSR involving liquid hydrocarbons, TSR by purely gaseous hydrocarbons likely involves fewer side reactions (most notably less hydrocarbon cracking), and consequently the mechanism of TSR may be more easily distinguished under these conditions. Moreover, the temperatures at which TSR occurred in these two studies are widely separated, which greatly reduces the uncertainties of kinetic fittings to the data. In this paper, we present a conceptual model for the autocatalytic and non-autocatalytic reduction of sulfate by gaseous hydrocarbons. Based on these two distinct reaction pathways, we quantitatively evaluate the chemical and stable isotopic fractionation of gaseous hydrocarbons from field (Mankiewicz et al., 2009) and laboratory (Pan et al., 2006) observations of TSR. The model results are then used to determine if TSR involving gaseous hydrocarbons follows an autocatalytic or non-autocatalytic pathway. Although the uncertainty surrounding the details of the chemistry of the TSR reaction mechanism prohibits the development of a generalized predictive model of stable isotopic fractionation related to TSR, the work presented herein does provide a viable approach for constructing such a model at a point when the chemistry is better understood. Moreover, our model results can also be directly applied to future research efforts directed at understanding the complexities of the TSR reaction mechanisms by constraining the potential reaction pathways with valid isotopic fractionations. 2. METHODS 2.1. Kinetic models 2.1.1. Autocatalytic and non-autocatalytic TSR reactions As discussed above, the oxidant in TSR reactions has been shown to be reactive sulfate species such as bisulfate ions (HSO 4 ) or magnesium sulfate contact ion pairs [MgSO4]CIP (Zhang et al., 2012). However, TSR occurring in natural petroleum systems may involve a wide variety of different organic compounds. Though in many instances TSR may be initiated by reactions involving pure saturated hydrocarbons (alkanes) and reactive sulfate, some cases may involve nitrogen-, sulfur-, or oxygen-containing organic compounds (NSO) in oil, in particular labile organic sulfur compounds (Amrani et al., 2008). However, in natural gas reservoirs the concentration of NSO compounds is typically

quite low; therefore, the initiation step is generally the redox reaction between sulfate and alkanes. Based on previous experimental (Amrani et al., 2008; Zhang et al., 2008, 2012), theoretical (Ma et al., 2008), and field-based observations (Orr, 1974; Worden and Smalley, 1996; Machel, 2001), we propose the conjectural TSR reaction model shown in Scheme 1. Scheme 1 consists of four distinct reactions, each of which has been observed in, or indicated by, laboratory TSR simulation. Reaction rI is initiation, the reaction between hydrocarbon and activated sulfate, generating partially oxidized and reduced intermediates (Ma et al., 2008; Zhang et al., 2012). Sulfate ions are converted to a series of reduced intermediates (RI), such as sulfite, elemental sulfur, etc.; and alkanes are converted to oxidized intermediates (OI), such as alcohol by oxygen insertion, or alkenes by dehydrogenation (Goldstein and Aizenshtat, 1994; Ma et al., 2008). The reduction of sulfate by OI (reaction rII) and the oxidation of alkanes by RI (reaction rIII) are generalized reactions, and each of these reactions (rII and rIII) necessarily consists of multiple elementary steps. For example, rII may involve alcohol oxidation to aldehydes, ketones and carboxylic acids, and the subsequent decarboxylation of a carboxylic acid may form CO2 and an alkane compound with a shorter C–C chain. If the intermediates from alkane oxidation are further converted to organosulfur compounds (such as thiols) by reaction with H2S, then the reduction of sulfate by OI (rII) is fast (Amrani et al., 2008). Experimental evidence has shown that the oxidation of alkanes by RI (reaction rIII) is significantly faster than hydrocarbon oxidation by sulfate (Zhang et al., 2008); consequently, reactions rII and rIII form a propagation loop of an autocatalytic reaction. But if the rate of reaction rII is considerably slower than that of rI, then the reaction path is dominantly non-autocatalytic. Inhibition of the autocatalytic loop occurs when the RI is further reduced by an organic compound other than an alkane. The reductant may be any OI species, and the inhibiting reaction pathway is shown in Scheme 1 as rIV. As a self-redox reaction, the disproportionation of partially reduced sulfur species (RI) is also covered by rIV. 2.1.2. Rate equations and solutions The contribution of an autocatalytic path can be quantitatively explained by reaction kinetics. We consider two conditions depending on the significance of initiating reaction rI in Scheme 1. If rI is significantly faster than rII and rIII, then the contribution of the autocatalytic loops is minimal, and the rate-limiting step (rI) determines the rate of overall reaction. As a second order reaction, its reaction rate equation is given by: dcHC ca ¼ k  cHC dt c

ð1Þ

where, c is the concentration in aqueous solution (mol dm3), t is time (s), k is rate constant (s1); subscripts “a” refers to as activated sulfate ion, c° = 1 mol dm3 is the standard concentration. Note that according to the Henry’s law and considering the quasi-equilibrium of fast solution/ dissolution processes, Eq. (1) is also valid when we substitute cHC with the partial pressure pHC of a gaseous hydrocarbon.

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RI

HC

CO2, H2O

H2S

SO42rIV rII

SO42-

rIII

rI

H2S CO2, H2O

HC

OI

Scheme 1. Generalized reaction path of thermochemical sulfate reduction. HC, saturated hydrocarbons; RI, reductive intermediates from sulfate (such as sulfite); OI, oxidative intermediates from alkane (such as alcohol). Reactions rI (initiation) and rII + rIII (propagation) form an autocatalytic path; rIV is an inhibition step for the autocatalytic path.

Assuming that the supply of sulfate is sufficient and does not change significantly during the reaction, Eq. (1) becomes a pseudo-first order reaction, with a solution of:  c  cHC a ð2Þ ¼ exp k  t cHC;ini c Here the subscript “ini” denotes the initial state. If there are at least two data groups from different temperature (T) or heating rate conditions, the frequency factor A and activation energy DE can be derived from the Arrhenius equation:   DE ð3Þ k ¼ A exp  RT If rIV is omitted, then the rate equations for Scheme 1 are: 8 dcHC ca > > < dt ¼ k I c cHC  k III cHC cRI dcOI ð4Þ ¼ k I cca cHC þ k III cHC cRI  k II cca cOI dt > > : dcRI ¼ k ca c  k c c þ k ca c dt

Ic

HC

III HC RI

II c

OI

where, “HC” refers to alkanes, “OI” refers to oxidized intermediates (such as alcohol), and “RI” refers to reduced intermediates (such as sulfite). Eq. (4) can be solved with numerical methods, but an analytical solution is available considering a quasi-steady state approximation of the active species (Boudart, 1968). The solution demonstrates that the net reaction rate of Scheme 1 is determined by reaction rI, when reaction rII is much slower than rI (kII  kI, meaning a non-autocatalytic mechanism), or when rII is much faster than rI (kII  kI, meaning an autocatalytic mechanism) but the overall conversion is small. For the derivation see Appendix 1. 2.1.3. Chemical compositional and carbon isotopic fractionation Because ethane, propane, and butane isomers may have different activity reacting with sulfate, their relative concentrations change during TSR by natural gas, which is referred to as compositional fractionation. A 12C–H bond and a 13C–H bond in hydrocarbons have different activities in gas generation from kerogen and oil cracking (Tang et al., 2000), and this same effect has been shown to produce carbon isotopic fractionation in gaseous hydrocarbons

during TSR (Krouse et al., 1988). Solving for the chemical compositional or stable isotopic fractionation for the autocatalytic loop requires a numerical method, based on Eq. (4). The analytical solutions for the non-autocatalytic paths can be derived for fractionation. From Eq. (1), the fractionation between hydrocarbon compounds A and B gives: dcA k A cA ¼  dcB k B cB

ð5Þ

It indicates that the fractionation is independent of activated sulfate concentration. From Eq. (5), ln

cA kA cB ¼ ln cA;ini k B cB;ini

ð6Þ

Eq. (6) indicates that the logarithms of two residual hydrocarbon concentrations are proportional under isothermal conditions (this is demonstrated in Section 3.3). Reaction rI in Scheme 1 brings about the oxidation of a carbon atom in the hydrocarbon molecule. Substitution of a 12C atom with a 13C atom at this position will change the reaction rate (kinetic isotope effect, or KIE). Suppose the rate constant changes from k to k* (superscript “*” refers to a molecule with a 13C atom), then d13 Cn  d13 Cn;ini ¼ ð1  k Cn =k Cn Þ lnðcn =cn;ini Þ  1000

ð7Þ

Here n refers to the number of carbon atoms in the hydrocarbon molecule (n = 2 refers to ethane, and n = 3 refers to propane); d13Cn refers to the carbon isotopic composition of compound Cn at some time t, and d13Cn,ini refers to its initial carbon isotopic composition. The details of the derivation are provided in Appendix 2. The KIE is due to the change in the transition state properties, A and DE in Eq. (3), by stable-isotopic substitution (Tang et al., 2000). A general expression for the reduction of [MgSO4]CIP by hydrocarbons, whereby two adjacent carbon atoms are involved in Reaction rI of Scheme 1, is shown in Eq, (8) (Ma et al., 2008): ½MgSO4 CIP þ R-CH2 -C0 H2 -R0 ! MgSO3 þ R-CH2 -C0 HOH-R0 0

ð8Þ

Here R- and R - may be hydrogen atoms or alkyl groups. The C0 carbon atom is oxidized by the oxygen insertion, and the KIE is only significant for this C0 carbon

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atom, because it is directly connected to the reacting chemical bonds (Tang et al., 2000). We define the values of A and DE to be A* and DE* if a 12C atom at the C0 position is substituted with a 13C atom. Considering an alkane molecule with n carbon atoms, when one 12C atom is substituted with a 13C atom, the probability of the substitution occurring on the C0 atom versus the probability on another carbon atom is 1:(n  1), if we omit the a priori intra-molecular carbon isotopic fractionation. Therefore, the overall rate constant of alkane conversion as a weighted average considering the probability is:   1 A DDE n1 k Cn þ k Cn ¼  exp  ð9Þ k Cn n A RT n Eq. (9) is essential to derive the kinetic isotopic fractionation factors of A*/A and DDE. Here we have omitted the isotopic fractionation between hydrocarbons in gas phase and in dissolved phase, because this fractionation is minimal under reservoir temperatures (<0.5& for methane at T > 80 °C, see Fig. 3 in Xia and Tang, 2012). 2.2. Data for model calibration As introduced in Section 1, the models will be calibrated by one group of laboratory data and one group of natural data. The laboratory TSR experiments involved sulfate solutions and experimentally generated gaseous hydrocarbons, conducted in sealed gold-tube reactors at a constant temperature of 350 °C and pressure of 500 bar (Pan et al., 2006). The natural data are from Lower Jurassic Norphlet reservoirs in the Mobile Bay area, Gulf of Mexico (Mankiewicz et al., 2009; U.S. Geological Survey, 2009). Compared with reservoirs in other areas in the Gulf of Mexico region, the Mobile Bay reservoirs have a unique 13 C-enriched ethane and propane signature (Fig. 1), which has been recognized as the result of TSR reactions (Mankiewicz et al., 2009). These TSR-affected reservoirs are confined to an area of 22 km by 47 km with a depth interval between 6350 and 6931 m. The reservoir temperature is about 215 °C and the source rock is expected to be highly mature (vitrinite reflectance Ro% = 2.2). 3. RESULTS AND DISCUSSION 3.1. Determining initial values The initial values of chemical and isotopic compositions are necessary to calibrate the kinetic models. For the laboratory data, the initial values are well defined by the blank experiment (Pan et al., 2006). For the field data, the determination of the initial values must take into consideration the effect of variation in source rock thermal maturity. Although the variations of d13C2 and d13C3 are significant, the d13C1 values are rather stable (average 37.6&; standard deviation 1.2&), and have no obvious relation to the d13C2 composition (Fig. 1). The value of d13C1 is influenced by source rock thermal maturity and TSR reactions. Pan et al. (2006) reported that the value of d13C1 becomes enriched by 6& during laboratory TSR experiments. The enrichment of 13C in methane is not due to methane

10 0 -10 δ13C1 and δ13C3(‰)

476

Jurassic reservoirs, Mobile Bay region

-20 -30 -40 -50 -60 -40

-30

-20 -10 δ13C2(‰)

0

Fig. 1. d13C1 (circles) and d13C3 (squares) versus d13C2 of natural gas from the Gulf of Mexico region. Data source: Mankiewicz et al. (2009) (solid circles and squares); U.S. Geological Survey (2009) (open circles and squares). Field data points within the dashed line are only from Upper Jurassic reservoirs of the Mobile Bay area. Diamonds show laboratory simulation results of d13C1 versus d13C2 (Pan et al., 2006).

depletion (methane yield increased with TSR extent); rather, it is most likely due to methane that is a product of TSR by larger hydrocarbons with more enriched d13C values. This TSR effect on d13C1 is pronounced in these experimental data (Pan et al., 2006) because of the high concentration of C2+ hydrocarbons (wetness = 32.5%) in the reactant gas. But this effect is rather weak for the Mobile Bay reservoir because of its much lower gas wetness (0–15%). Consequently, d13C1 values in the Mobile Bay gases are mainly determined by the thermal maturity of their precursors, and the consistent d13C1 values reflect a homogeneous precursor thermal maturity and a narrow charging time window for the reservoir (Mankiewicz et al., 2009). Because the amount of methane in the reservoirs is dominantly determined by gas charging within a narrow maturity window, methane concentration (volume specific molar amount) can be regarded as constant. Therefore, the molar ratio of C2–4 to CH4 reflects the variation in the amount of C2–4 components during TSR. The maximum C2H6 concentration and C2H6 to CH4 molar ratio, along with the most negative d13C2 value, are assumed to be the initial (nonTSR) values in the Mobile Bay reservoirs (they are the values the sample from lease SL624#4, Well 114-4 in Mankiewicz et al., 2009). All the initial values are summarized in Table 1. 3.2. Activated sulfate concentration in aqueous solution To calibrate Eqs. (1), (2), (4), it is essential to know the concentration of activated sulfate ca. The TSR experiments used by Pan et al. (2006) contained 600 mg magnesium sulfate heptahydrate (2.4 mmol MgSO47H2O) with 100 mg deionized water. Under the experimental conditions used, aqueous magnesium sulfate precipitates as a magnesium– hydroxide–sulfate–hydrate complex (“MHSH 0.625”) (Janecky and Seyfried, 1983):

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477

Table 1 Initial values of TSR reactions.

C2H6 C3H8 i-C4H10 n-C4H10 H2S

d13C (&)

Mobile Bay* concentration (mol/mol CH4)

d13C (&)

3.31 1.30 n.a. n.a. 0.00

30.8 20.5 n.a. n.a. n.a.

0.0985 0.0509 0.0166 0.0122 0.00

26.4 22.9 20.3 18.5 n.a.

The initial values are presented by the sample from lease SL624#4, Well 114-4 in Mankiewicz et al. (2009). n.a. – not applicable.

þ 5Mg2þ þ 4H2 O þ 4SO2 4 ¼ MgðOHÞ2  4MgSO4  2H2 O þ 2H

ð10Þ

Following a mass balance calculation, the aqueous phase contained 0.48 mmol residual SO2 4 and 0.37 g water; and the reaction generated 0.97 mmol H+. Due to the extremely low dissociation constant of HSO at 350 °C 4 (3.85  107, Marshall and Jones, 1966), the solution contained roughly 1.3 mol dm3 of HSO 4 . During the TSR reaction, the total consumed carbon atom in hydrocarbon compounds was less than 0.05 mmol, or 10 times lower than the initial amount of SO2 4 in the solution. Additionally, the concentration of HSO 4 in the system was buffered by the existence of the magnesium–hydroxide–sulfate–hydrate complex; and therefore, the concentration of HSO 4 can be regarded as constant. Pan et al. (2006) also performed experiments on gaseous hydrocarbon oxidation using a mixture of magnesium sulfate heptahydrate and hematite (Fe2O3), and these experiments showed a much lower TSR rate. Apparently the solid hematite as a Lewis base consumed the proton generated by magnesium sulfate hydrolysis, so the activated sulfate concentration was much less than in the absence of hematite. Brine from the Norphlet Formation in the Mobile Bay area is closely related to the Louann Salt (Mankiewicz et al., 2009), which is characterized by a high Mg2+ concentration (Kharaka et al., 1987). We calculated the concentration of [MgSO4] complex with two data groups: (1) a typical brine sample from the Norphlet reservoirs in the Mobile Bay area (Yuan et al., 2003); and (2) 17 brine samples from the central Mississippi Salt Dome Basin (concentrations reported by Kharaka et al. (1987)). The complex concentration calculations were based on aqueous thermodynamics using the software package PHREEQE version 3 (Parkhurst and Appelo, 2013). The concentrations of [MgSO4] and HSO 4 for the Norphlet reservoir sample at T = 180–215 °C are calculated to be 0.24 mmol/L and 0.66  104 mmol/L, respectively. At these temperatures, the dominant species of all [MgSO4] complexes is the contact ion pair (Rudolph et al., 2003; Akilan et al., 2006). This indicates that [MgSO4], rather than HSO 4 , is the dominant active sulfate species in the Norphlet reservoir brine. For comparison, we also calculated the [MgSO4] complex concentration for 17 brine samples from the central Mississippi Salt Dome Basin, where the brine is also closely related to the Louann Salt. In these samples, the [MgSO4] complex concentration is between 5.5  103 mmol/L and 1.1 mmol/L, with a geometric mean of 0.22 mmol/L, which is close to the value calculated for the Norphlet Reservoir

sample (for complete results see Appendix 3). Therefore, we use ca = 0.24 mmol/L to represent the concentration of activated sulfate in the Mobile Bay reservoirs. 3.3. Contribution of autocatalytic path The autocatalytic and non-autocatalytic paths are expected to have different patterns of temporal variation of hydrocarbon concentration, as predicted by Eqs. (4) and (2). In the non-autocatalytic path, the logarithm of residual hydrocarbon concentration is directly proportional to the reaction time, whereas in the autocatalytic path the value increases significantly more rapidly. The experimental data of Pan et al. (2006) more closely follow the proportional trend, indicating that the contribution of the autocatalytic path is not significant (Fig. 2). As discussed in Section 2.1, an extensive amount of TSR without an obvious contribution from autocatalytic processes indicates that the rate of reaction rII in Scheme 1 is low. This is different from late-stage TSR involving oil, and it might be attributed to the differences in the sizes of the hydrocarbon molecules found in oil and gas. A possible explanation is that on average hydrocarbon molecules in oil have longer carbon-chain lengths, so the oxidation by

8 4

6

-ln(cHC/cHC,ini)

*

Laboratory Concentration (mmol/gTOC)

3

2

4 1

2

0 0

2

4

6

8

o

k1(ca/c )t Fig. 2. Comparison of temporal variation of hydrocarbon concentration between autocatalytic (dashed lines) and non-autocatalytic (solid line) TSR paths. The kII/kI values are 0, 0.1, 1 and 10 for curves 1, 2, 3, and 4, respectively. Data points show ethane (circles) and propane (triangles) from laboratory TSR experiments (Pan et al., 2006) with best-fitting of Eq. (2) (kI = 4.30  106 s1 for ethane and 4.90  106 s1 for propane), respectively.

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sulfate has a higher probability to induce cleavage of C-C bonds in the middle of the carbon chain. The cleavage may produce unsaturated compounds and other active species, which are more reactive to reduce sulfate than the alkanes are. The cleavage of hydrocarbons during TSR has been indicated by the generation of shorter chain-length hydrocarbons as byproducts of TSR by larger hydrocarbons (Zhang et al., 2007, 2012). 3.4. Chemical kinetics

Table 2 Kinetic and isotopic fractionation factors of thermochemical sulfate reduction by C2–4 alkanes. Kinetics

C2H6 C3H8 i-C4H10 n-C4H10 a b

Both the laboratory and the natural data show that methane is not enriched in 13C as a result of TSR, and the controlled laboratory experiments confirm that methane is not significantly oxidized by sulfate under the observed conditions. A possible explanation is that the most favorable transition state for the kinetically controlled TSR reaction mechanism requires a C–C bond (Ma et al., 2008), and that significantly more energy is required to reach the transition state for sulfate reacting with methane since it lacks a C–C bond. Therefore, TSR involving methane is considerably more difficult than with other hydrocarbons, and we will not discuss its kinetics. Because the contribution of autocatalysis is limited for TSR involving purely gaseous hydrocarbons, we will only calibrate the non-autocatalytic kinetic model based on Eq. (1). Taking the experimental data into Eq. (2) gives kC2 = 4.30  106 s1 and kC3 = 4.90  106 s1 at T = 350 °C (Fig. 2). From Eq. (3),   DEC2 AC2 ¼ 4:30  106 s1 exp ð11Þ 5:18 kJ=mol   DEC3 ð12Þ AC3 ¼ 4:90  106 s1 exp 5:18 kJ=mol The butane isomers (isobutane and n-butane) are more reactive than ethane and propane during the TSR reactions, and their residual amounts in the laboratory TSR experiments are too small for a reliable kinetic fitting. The kinetic parameters for ethane, propane, iso- and n-butane are summarized in Table 2. Compared with laboratory conditions, making accurate determinations of the thermal history and the sulfate concentration in gas reservoirs in nature is much more difficult, which complicates the calibration of the model for the Mobile Bay reservoir data. Although the charging history and gas maturity in the reservoirs throughout Mobile Bay are quite similar (Section 2.2), the ethane and propane concentrations vary significantly. The variation can be readily attributed to differences in the sulfate concentrations (ca) in various reservoirs, as is explained by Eq. (2). Additionally, the Mobile Bay data show linear chemical compositional fractionation between the different components (Fig. 3). This behavior is well described by Eq. (6) when applied over a relatively narrow temperature range. The values of A and E for ethane and propane are determined by calibrating Eq. (2) with the Mobile Bay reservoir data and applying the constraints of Eqs. (11) and (12). Given an initial guess of DE, we can calculate the residual ratio of c2/c2,0 at each time point during the thermal history

c d

Using Based Using Based

Isotopic fractionation

A(1016 s1)

DE (kJ/mol)

A*/A

DDE (J/mol)

6.4 1.9 1.9a 1.9a

264.5 257.6 256.9b 257.0b

1.024 1.024c 1.024c 1.024c

178.1 207.1d 169.0d 205.9d

the same value as for propane. on the estimated A value. the same value as for ethane. on the estimated A*/A value.

(starting from 100 Ma), with Eqs. (2), (3), (11), and (12). The initial value of c2,0/c1 = 0.0985 is explained in Table 1 and in Section 3.1. We applied the geometric mean of c2/c1 = 0.0451 to represent the field data of c2/c2,0 for the present day. When the calculated present-day c2/c2,0 ratio matches the field data (c2/c2,0 = 0.0451/0.0985 = 0.46), the unique solutions are obtained. The fitted kinetic parameters are DEC2 = 264.5 kJ/mol (63.23 kcal/mol) and AC2 = 6.4  1016 s1. Because the error associated with the propane concentration is larger than that of the ethane concentration, we applied the relation between ethane and propane concentrations shown in Fig. 3A as a constraint, rather than the present c3/c3,ini ratio, for the fitting of the kinetic values for propane. The rest of the procedure is the same as for ethane. The fitted kinetic parameters are DEC3 = 257.6 kJ/mol (61.56 kcal/mol), and AC3 = 1.9  1016 s1. The final calculated c3/c1 ratio (0.27) is close to the geometric mean of the field data (0.30). The smaller value of AC3 < AC2 reflects a larger steric barrier of an extra methyl group in the transition state for propane, and the smaller value of DEC3 < DEC2 reflects the fact that the presence of adjacent alkyl groups as electron-donors is beneficial for TSR reactions. Because of the limitations of the experimental data, we cannot derive the constraints for n-butane and isobutane as were done for ethane and propane with Eqs. (11) and (12). For comparison of reactivity, we apply AC4 values identical to AC3 and take into account the constraints of the relations shown in Fig. 4B and C, then DE values of 256.9 kJ/mol (61.40 kcal/mol) and 257.0 kJ/mol (61.42 kcal/mol) are determined for isobutane and n-butane, respectively. The DEC4 values for butane isomers are slightly lower than DEC3, indicating an enhanced electron-donor effect. Compared with TSR by C21-C35 paraffin without autocatalysis (A = 4.0  1014 s1 and DE = 246.6 kJ/mol, Zhang et al., 2012), the A value is higher by two orders of magnitude and DE is higher by 7–18 kJ/mol for TSR by the gaseous hydrocarbons. These differences reflect a similar reaction mechanism (the ratedetermining step is the reaction between alkane and activated hydrocarbon), but relatively lower steric barrier and higher activation energy in the transition state for TSR involving gaseous hydrocarbons. The DE values are higher

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479

3.5. Kinetic carbon isotope fractionation

1.4

A 1.2

-ln(c3/c3,ini )

1 0.8 0.6 0.4 0.2 0 0

0.2

0.4

0.6

0.8

1

-ln(c2/c2,ini ) 2

B

-ln(c4/c4,ini )

1.6

1.2

0.8

0.4

0 0

0.2

0.4

0.6

0.8

1

-ln(cn2/cn2,0)

2

C

-ln(ci4/ci4,ini )

1.5

1

0.5

0

The relation between chemical and isotopic fractionations during TSR involving gaseous hydrocarbons is shown in Fig. 4. This linear relationship can be explained with Eq. (7) within a narrow temperature range. The linear covariance is pronounced in the TSR reservoirs, but not observed in the reservoirs without TSR (Fig. 4E and F). Similar to chemical fractionation, the isothermal laboratory TSR data provide constraints to the isotopic fractionation of ethane. The experimental data give a slope of 5.19& for the linear covariance of d13C2  d13C2,ini a nd ln(c2/c2,ini) (Fig. 4A). According to Eq. (7), k*C2/kC2 = 1  5.19& = 0.9948. Taking this value into Eq. (9) and simplifying,   DDEC2 ð13Þ AC2 =AC2 ¼ 0:9896 exp 5:18 kJ=mol As discussed in Section 3.3, Eq. (2) for ethane isotopologues is calibrated with the Mobile Bay reservoir data and the constraints of Eq. (13). We applied the most depleted d13C2 value (26.4&) as the initial value and an average of 18.7& to represent the current d13C2 value, then the unique solution is A*C2/AC2 = 1.024 and DDEC2 = 178.1 J/mol (42.6 cal/mol). Due to the large uncertainty of their chemical and isotopic compositions in the experimental results, it is not appropriate to derive the kinetic fractionation factors of propane and butanes. But by assuming a ratio of frequency factors for substituted and unsubstituted reactants equivalent to that of ethane (A*/A = 1.024), and taking into account the constraints of the relations in Fig. 4B–D, we obtain DDE = 207.1 J/mol (49.5 cal/mol), 169.0 J/mol (40.4 cal/ mol) and 205.9 J/mol (49.2 cal/mol) for propane, isobutane and n-butane, respectively. The values are summarized in Table 2. Generally, DDE increases with DE (Tang et al., 2000), but the ethane data do not follow the trend: though DEC2 > DEC3, we have DDEC2 < DDEC3; that is, ethane does not have as strong of an isotopic fractionation as expected. This deviation is probably due to the fact that ethane, as a short alkane, is partly an intermediate of TSR by longer chain-length hydrocarbons (Zhang et al., 2012), and this process brings about depletion of 13C in ethane. 3.6. Application to the Mobile Bay gas field

0

0.5

1

1.5

2

-ln(cn4/cn4,0)

Fig. 3. Compositional fractionation of natural gas components during TSR under reservoir conditions. (A) C3H8 v. C2H6 (C3H8 > 1.0%); (B) n-C4H10 v. C2H6 (n-C4H10 > 0.15%); (C) i-C4H10 v. n-C4H10. Legends: circles – field data from Mobile Bay (Mankiewicz et al., 2009; U.S. Geological Survey, 2009); dashed line – theoretical values explained in Section 3.3.

than the theoretical DFT results calculated for C2 oxidation (Ma et al., 2008), and this difference could be attributed to solvent effects from the brine in the natural system.

The kinetic parameters derived for chemical and stable isotopic compositional fractionation (Table 2) were combined with the thermal history reported by Mankiewicz et al. (2009, Fig. 3) to model the history of alkane depletion by TSR in Mobile Bay reservoirs as shown in Fig. 5. A [MgSO4]CIP concentration of 0.241 mmol/L was assumed for these calculations (see Section 3.2 and Appendix 3 for [MgSO4] calculations). It should be noted the final values predicted by the model do not correspond to the Mobile Bay gas samples with the maximum conversion, because the [MgSO4]CIP concentration applied here is the geometric mean of the concentration in the Mobile Bay reservoir brines; the samples with maximum conversion may reflect

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X. Xia et al. / Geochimica et Cosmochimica Acta 139 (2014) 472–486 30

35

B

A 30

25 δ13C3 - δ13C 0,3 (‰)

δ13C2 - δ13C2,0 (‰)

25 20 y = 5.19x R² = 0.98

15 10

20 15 10 5

5

0

0 0

1

2

3 4 -ln(c2/c2,0)

5

6

0

7

C

20

0.5

1

1.5 2 2.5 -ln(c3/c3,0)

3

3.5

0.5

1

1.5 2 2.5 -ln(cn4/cn4,0)

3

3.5

D

25

δ13Cn4 - δ13Cn4,0 (‰)

δ13Ci4 - δ13Ci4,0 (‰)

20 15

10

5

15 10 5 0

0 0

1

2 3 -ln(ci4/ci4,0)

4

0

5

25

4

E

F

20 δ13Ci4 - δ13Cn4 (‰)

δ13C n4 - δ13C2 (‰)

0

y = -6.99x - 9.75 R² = 0.74

15

10

5

-4

-8 y = 5.39x - 3.04 R² = 0.93

0

-12

-5

-4

-3 -2 ln(cn4/c2)

-1

0

-2

-1

0

1

ln(ci4/cn4)

Fig. 4. Isotopic fractionations of hydrocarbon during TSR as functions of reaction extent (A–D) or functions of chemical fractionation (E and F). Legends: triangles – TSR at T = 350 °C under laboratory conditions (Pan et al., 2006, data at 144 h omitted due to large variation between three samples obtained for this time point); circles – TSR Lower Jurassic Norphlet reservoirs in the Mobile Bay area (Mankiewicz et al., 2009; U.S. Geological Survey, 2009); squares – the whole Gulf of Mexico region other than Mobile Bay area for comparison (U.S. Geological Survey, 2009); dashed lines – linear trends; solid lines – theoretical values based on parameters in Table 2. Subscript “0” refers to initial values.

a much higher [MgSO4]CIP concentration. The results show that a significant depletion of C2–4 alkanes and enrichment of 13C in the residual alkanes occurred within the most recent 30 Ma, as the temperature increased more rapidly.

Moreover, with increasing reaction extent, there might be an isotopic reversal between propane and isobutane (d13C3 > d13Ci4). This phenomenon is consistent with some Mobile Bay gas samples (Mankiewicz et al., 2009).

X. Xia et al. / Geochimica et Cosmochimica Acta 139 (2014) 472–486 1

A

220

0.8

210

0.6

200

0.4

190

0.2

180 -100

c/c0

Reservoir temperature(oC)

230

481

0 -80

-60 -40 Time (mybp)

-20

-5

0

B

δ 13C (‰)

-10 -15 -20 -25 -30 -100

-80

-60 -40 Time (mybp)

-20

0

Fig. 5. Modeling the history of alkane depletion (A) and carbon isotopic fractionation (B) during TSR in Mobile Bay reservoirs, using the kinetic parameters in Table 2 and [MgSO4]CIP concentration of 0.241 mmol/L. Legends: solid line – reservoir thermal history from Mankiewicz et al. (2009); dotted–dotted–dashed line – ethane; dotted dashed line – propane; dashed line – n-butane; dotted line – isobutane.

3.7. Extrapolation to geologic conditions Based on the kinetic parameters in Table 2, we calculated a general relation between hydrocarbon conversion (oxidation), sulfate concentration, reservoir thermal history, and isotopic fractionation during TSR. Fig. 6A shows the conversion as a function of thermal history and the concentration of [MgSO4]CIP. We use calculated vitrinite reflectance values (Sweeney and Burnham, 1990) to represent the reservoir thermal history, because the relation between conversion and the calculated Ro is independent of temperature and heating rate. We calculated two scenarios with different [MgSO4]CIP concentrations: 0.1 mol/L and 1 mol/L, which cover the range for the Norphlet brine. For the higher concentration of [MgSO4]CIP (1 mol/L), TSR by natural gas starts at Ro 1.5%; at Ro around 2.5%, half of C2–4 is consumed; when Ro reaches 3.0%, nearly all the wet components are oxidized (Fig. 6A). The thermal maturity for the onset of TSR by gas is earlier than the range of secondary cracking of propane (Ro up to 2.5%, based on the shale gas isotopic compositions in the Arkoma Basin, Zumberge et al., 2012), though the ranges may overlap. But if the concentration of [MgSO4]CIP is 10 times lower (0.1 mol dm3), then the thermal maturity must increase by about 0.5% Ro in order to produce an amount of hydrocarbon conversion equivalent to that which occurred at the higher [MgSO4]CIP.

Carbon isotopic fractionation (d13C increase during reaction) of each of the C2–4 alkanes as a function of its conversion is shown in Fig. 6B. With any given conversion, the isotopic fractionation extent is ethane > propane > n-butane > isobutane. When conversion is less than 40%, isotopic fractionation is limited (<5&), which is difficult to distinguish from fractionation associated with thermal maturation. An extreme isotopic fractionation (>10&) happens when conversion is above 60%. Overall, unusually heavy d13C2 and d13C3 values (>10&) in TSR reservoirs may clearly indicate extensive amounts of C2+ conversion (>80%) due to oxidation by sulfate. On the other hand, when d13C2 and d13C3 values are still in the typical thermogenic range (30& to 20&), a C2+ conversion as great as 50% is still possible, because carbon isotopic fractionation is moderate when TSR conversion is below this value. Application of these model results to natural TSR occurrences must be made very cautiously. The limited amount of data used to calibrate the models and the uncertainties surrounding the details of the reaction mechanism undoubtedly lead to the potential for large inaccuracies in the model predictions. Nevertheless, it is instructive to examine some field observations of TSR involving natural gas accumulations in light of these new model results. In particular, we look at data from the Western Canadian Sedimentary Basin (Krouse et al., 1988) and the Sichuan Basin, in southwestern China (Cai et al., 2003) to determine

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X. Xia et al. / Geochimica et Cosmochimica Acta 139 (2014) 472–486

100

30

B 25

80 [MgSO4]CIP =

60

δ13Cn - δ13Cn,ini (‰)

Conversion due to TSR(%)

A

1 mmol/L

40

15 10 5

[MgSO4]CIP =

20

20

0.1 mmol/L

0

0 1.5

0

2

2.5 EasyRo (%)

3

3.5

20

40

60

80

100

Conversion due to TSR (%)

Fig. 6. Projecting conversion of C2–4 hydrocarbon during TSR under geological conditions. (A) Conversion as a function of thermal history and concentration of [MgSO4]CIP. (B) Carbon isotope fractionation as a function of conversion (the curves are not sensitive to thermal history). Legends: solid line – ethane; dotted–dashed line – propane; dotted line – isobutane; dashed line – n-butane.

if these model predictions may help to understand the TSR process in some other gas fields. In the Western Canadian Sedimentary Basin, Krouse et al. (1988) reported d13C2 and d13C3 increases of about 10& accompanied by TSR. Thermal maturation may have influenced the observed isotopic variation, because d13C1 values also become more enriched along with the d13C2 and d13C3 values. Our model predicts that the oxidation of ethane and propane could be as great as 70%, if the fractionation is solely due to TSR. Even more significant fractionation is observed in C5–8 hydrocarbons (up to 10& for pentanes in the Brazeau PA #1644 well, Whiticar and Snowdon, 1999), indicating that the conversion of pentanes is above 80% in some reservoirs, assuming that the isotopic fractionation of pentanes is less extensive than butanes at a given conversion. Large isotopic fractionations of ethane and propane are reported in some other reservoirs (d13C2 = 13& and d13C3 = 0& in Gething Formation in the Ojay and Belloy wells, Tilley and Muehlenbachs, 2006). Such unusual d13C2 and d13C3 values in natural gas are comparable to the Mobile Bay gases, reflecting a potential conversion of >90% for ethane and propane. In the Carboniferous strata in the eastern Sichuan Basin, China, the maximum temperature is up to 220 °C and the %Ro is as high as 3.0% in some H2S-bearing reservoirs where TSR accompanied by oil cracking has been reported (Hao et al., 2008). The d13C2 values vary from 39& to 31& and the d13C1 values span a narrower range, from 35& to 31& (Huang et al., 1997). In this case, it is difficult to distinguish the fractionation due to TSR from that of thermal cracking, because an increase of gas derived from oil-cracking may decrease the d13C2 and d13C3 values by 10& or more (Xia et al., 2013). Nevertheless, >50% consumption of gaseous hydrocarbons by TSR is quite likely based on the model predictions shown in Fig. 7. The kinetic values reported herein (Table 2) should be taken as an approximation due to the limited amount of calibration data and the uncertainties surrounding the details of the overall reaction mechanism of TSR. However,

the A and DE values determined from this study of TSR via gaseous hydrocarbons are consistent with recently published data on the kinetics of TSR involving a mixture of long-chain hydrocarbons (Zhang et al., 2012). 3.8. Further considerations The finding that TSR by gaseous hydrocarbon is dominantly through a non-autocatalytic process is contrary to the long-held view that all TSR reactions are autocatalytic (Goldstein and Aizenshtat, 1994), and adds a new dimension to the recent proposal that the overall TSR process involves a two-stage mechanism (Zhang et al., 2012). Integration of the results from the present study with the previous work of Zhang et al. (2012) suggests that the overall TSR reaction mechanism for oxidation of organic substrates containing long-chain hydrocarbons involves three distinct phases, and this conceptual model is illustrated in Fig. 7. With the possible exception of the very earliest or latest TSR reactions, the autocatalytic and the non-autocatalytic reaction mechanism are expected to occur simultaneously throughout TSR. The identification of the three distinct reaction stages is based on which mechanism is dominant. The first stage is dominantly characterized by the reduction of reactive sulfate by long-chain saturated hydrocarbons, which is slow and non-autocatalytic due to the limited presence of reduced sulfur species. This initial stage produces more stable hydrocarbons (short-chain alkanes, cyclic alkanes and aromatics) in addition to intermediate reduced sulfur species (e.g., sulfite, thiosulfate, and elemental sulfur) and partially oxidized organic compounds (e.g., alcohols, ketones, carboxylic acids). These reaction intermediates are significantly more reactive than the initial reactants (i.e., sulfate and alkanes), and once the concentration of the intermediates reaches some threshold level an autocatalytic reaction pathway becomes dominant. The second stage of TSR is defined by an autocatalytic reaction mechanism predominantly involving intermediate oxidized organic compounds and partially reduced sulfur species. As has been previously discussed (Section 1), longer chain-length

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Extent of Reaction

Late-stage nonautocatalytic reaction Limit of long-chain hydrocarbons

Autocatalytic reaction

H2S threshold

Initial non-autocatalytic reaction Time Fig. 7. Conceptual model of TSR reaction over time when the initial organic reductant contains long-chain hydrocarbons. The initial reaction is non-autocatalytic due to limited supply of reduced sulfur, and the intermediate stage is autocatalytic due to abundant long-chain hydrocarbons and reduced sulfur (Zhang et al., 2012). Once the long-chain hydrocarbons are consumed, the reaction becomes predominantly non-autocatalytic and the rate of reaction slows.

hydrocarbons are preferentially oxidized by TSR and this leads to an increase in the proportion of shorter hydrocarbons. If TSR proceeds to the point where most of the longer chain-length hydrocarbons are consumed, then the fraction of TSR following the autocatalytic pathway will be significantly reduced. This would be the final, or late-stage, TSR reaction in which hydrocarbon oxidation continues at a slower rate via the non-autocatalytic reduction of sulfate by gaseous hydrocarbons. It is important to note that not all instances of TSR are expected to experience all phases of this TSR mechanism, and where a particular occurrence would plot along this curve will depend on the availability of reaction intermediates and long-chain hydrocarbons. It is also worth noting that the novel three-stage reaction mechanism that we propose for the overall TSR process predicts slow reduction of sulfate by gaseous hydrocarbons at high temperatures. Based on empirical observations of natural occurrences of TSR, the potential existence of an upper thermal limit for the TSR reaction has been suggested beyond which the reaction no longer proceeds (Machel et al., 1995). Our results may explain these field observations by demonstrating that as long-chain hydrocarbons are exhausted in high-temperature settings that have undergone extensive TSR, the rate of reaction slows significantly, giving the appearance of a thermal maximum for the reaction. Finally, this study provides a framework for further kinetic studies on TSR. As additional field and laboratory data become available for the reduction of sulfate by gaseous hydrocarbons, the kinetic parameters for this reaction can be better constrained. Additionally, this approach has applications to studies of the details of the chemical mechanisms of TSR by constraining viable mechanisms with valid isotopic fractionations.

483

4. CONCLUSIONS This study was designed to evaluate the potential for the autocatalytic and the non-autocatalytic reduction of sulfate by gaseous hydrocarbons. A combination of laboratory (Pan et al., 2006) and field (Mankiewicz et al., 2009) data was used to develop a kinetic model for chemical and isotopic fractionation related to TSR. The results of this work lead to the following conclusions: 1. TSR by gaseous hydrocarbons is a kinetically controlled non-autocatalytic process. It is proposed that the lack of apparent autocatalysis is due the absence of the required intermediate species or their non-reactivity with active sulfate. 2. Kinetic parameters were calculated for the chemical compositional fractionation of gaseous hydrocarbons from field (Mankiewicz et al., 2009) and laboratory (Pan et al., 2006) observations of TSR. The activation energies (DE) for TSR by ethane, propane, isobutane and n-butane are 264.5, 257.6, 256.9, 257.0 kJ/mol (63.2, 61.6, 61.4, 61.4 kcal/mol), respectively. The respective frequency factors (A) for these reactions are 6.4  1016, 1.9  1016, 1.9  1016, 1.9  1016 s1. 3. Model predictions based on these kinetic values indicate that TSR by gaseous hydrocarbon requires high-temperature conditions (typically Ro > 2.0%, depending on the concentration of activated sulfate). This results in significantly higher onset temperatures for TSR in gas reservoirs compared with oil reservoirs. 4. The oxidation of C2–5 hydrocarbons by sulfate is accompanied by carbon isotopic fractionation and the residual C2–5 hydrocarbons are more enriched in 13C. Kinetic parameters were calculated for the stable carbon isotopic fractionation of gaseous hydrocarbons based on field (Mankiewicz et al., 2009) and laboratory (Pan et al., 2006) observations of TSR. The activation energy difference DDE is 178.1, 207.1, 169.0, 205.9 J/mol (42.6, 49.5, 40.4 and 49.2 cal/mol) for ethane, propane, isobutane and n-butane, respectively, accounting for a frequency factor ratio of A*/A = 1.024. 5. TSR-induced carbon isotopic fractionation of gaseous hydrocarbons may be difficult to distinguish from thermal maturity effects at lower levels of hydrocarbon oxidation; however, unusually heavy d13C2+ values (>10&) can be diagnostic of high levels of conversion (>50%). 6. We propose that the overall TSR reaction mechanism for oxidation of organic substrates containing longchain hydrocarbons involves three distinct phases as follows: (1) an initial slow and non-autocatalytic stage characterized by the reduction of reactive sulfate by long-chain saturated hydrocarbons; (2) a second autocatalytic reaction phase dominated by reactions involving reduced sulfur species and partially oxidized organic intermediates; and (3) a final, or late-stage, TSR reaction in which hydrocarbon oxidation continues at a slower rate via the non-autocatalytic reduction of sulfate by gaseous hydrocarbons (if earlier TSR reactions have consumed most of the longer chain-length hydrocarbons).

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X. Xia et al. / Geochimica et Cosmochimica Acta 139 (2014) 472–486

ACKNOWLEDGMENTS The authors wish to thank Tongwei Zhang from The Bureau of Economic Geology, Austin, Texas, for many helpful discussions relate to this work. Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government.

Eq. (A5) is similar to Eq. (2), reflecting a pseudo first-order reaction and no autocatalysis. The only difference is a factor of 2 in Eq. (A5); this is introduced by the differences in stoichiometry.

APPENDIX 1. Approximation of Eq. (4) to a first-order reaction In TSR, the most reactive species are the RI species; the quasi-steady state approximation (dcRI/dt) gives: ca ca k III cHC cRI ¼ k I  cHC þ k II  cOI ðA1Þ c c Substituting Eq. (4) with Eq. (A1), ( dc HC ¼ 2k I cca cHC  k II cca cOI dt dcOI dt

ðA2Þ

¼ 2k I cca cHC

Eq. (A4) reflects a higher hydrocarbon conversion rate than Eq. (2). But when conversion is very small, that is, the reaction is at a very early stage, then the second factor on the right-hand side of Eq. (A4) is close to 1; Eq. (A4) is approximated to the form similar to Eq. (2). When kII  kI, Eq. (A3) is approximated to:  cHC ca  ðA5Þ ¼ exp 2k I  t cHC;ini c

The solution of Eq. (A2) is: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  k I sin 2k I k II  k 2I cca t  7 cHC ca 6 2 ca 7 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q 2k ¼ exp k I  t 6 k  k t cos  I II I  5 cHC;ini c 4 c 2k I k II  k 2I 

ðA3Þ

Note that the solution is still valid when kII < kI/2, with the relation of cos(ix) = cosh(x) and isin(ix) = sinh(x). Eq. (A3) and its following approximations are valid when hydrocarbon conversion is not extremely close to 1. For the autocatalytic conditions, kII  kI, Eq. (A3) is approximated to  pffiffiffiffiffiffiffiffiffiffiffiffi c  cHC ca  a 2k I k II  t ðA4Þ ¼ exp k I  t  cos cHC;ini c c

2. Derivation of Eq. (7) The definition of d13C is: d13 C ¼ ðRsample =RPDB  1Þ  1000

ðA6Þ

with RPDB = 0.011237 refers the molar ratio between 13C and 12C atoms in the PDB standard; Rsample is the molar ratio between 13C and 12C atoms in a sample. This definition is straightforward for methane, which has only one carbon atom in a molecule. For other gaseous molecules with n carbon atoms in each molecule, there are two types isotopologues of 12CnH2n+2 and 12Cn113CH2n+2 (the isotopologues with more than one 13C atoms is ignored due its extremely small probability), with concentration of c and c*, respectively. By definition of Eq. (A6), the carbon isotopic compositions d at beginning of a reaction and at any time points during the reaction are: 8 cini < dini ¼ 1 1000 RPDB ½ðn1Þcini þncini ðA7Þ c : d ¼ 1 RPDB ½ðn1Þc þnc 1000 By rearranging Eq. (A7), we have: 8  cini < ¼ nRPDB ðdini =1000þ1Þ cini 1ðn1ÞRPDB ðdini =1000þ1Þ

ðA8Þ

: c ¼ nRPDB ðd=1000þ1Þ 1ðn1ÞRPDB ðd=1000þ1Þ c

Table A1 [MgSO4] concentration in brine samples from the central Mississippi Salt Dome basin. Sample

84-MS-1 84-MS-2 84-MS-3 84-MS-4 84-MS-5 84-MS-6 84-MS-7 84-MS-8 84-MS-10 84-MS-11 84-MS-12 84-MS-13 84-MS-14 84-MS-15 84-MS-16 84-MS-19 84-MS-20

Water analysis results (mg/L, Kharaka et al., 1987) +

+

pH

Na

K

5.89 5.82 6.59 5.65 5.7 5.4 5.37 5.5 5.73 5.08 5.59 5.3 5.36 4.73 5.42 5.48 5.16

56,700 56,900 52,300 65,400 67,500 56,700 57,200 57,100 55,600 61,700 53,100 69,300 69,200 67,900 63,600 54,800 54,600

678 609 395 691 1095 713 1000 803 449 990 430 5960 5790 10,700 4920 6500 6240

2+

2+

[MgSO4] (mmol/L) 2+

Mg

Ca

Sr

SO2 4

2250 1610 1280 1850 1880 1390 2310 2440 1610 3050 1330 3010 2950 6180 2560 3350 3380

23,700 13,600 6600 30,100 30,700 22,800 31,700 28,300 12,800 48,600 8400 29,300 28,900 32,900 26,100 33,900 33,900

967 609 828 1860 1940 1920 1460 1300 620 1920 775 1250 1260 1190 1040 1670 1730

129 114 44 15 19 13 68 89 49 64 2 182 197 166 175 161 169



Cl

140,000 120,000 94,900 166,000 169,000 127,000 158,000 159,000 116,000 198,000 105,000 184,000 190,000 201,000 165,000 170,000 171,000

Br



1040 685 468 1040 1060 554 1030 1070 673 2020 495 1740 1760 2190 1670 2080 2080

0.466 0.341 0.113 0.045 0.057 0.033 0.251 0.342 0.151 0.278 0.006 0.775 0.836 1.052 0.670 0.746 0.797

X. Xia et al. / Geochimica et Cosmochimica Acta 139 (2014) 472–486

The quotient of each side of the two equations in Eq. (A8) gives: c =cini d=1000 þ 1 ¼ dini =1000 þ 1 c=cini 1  ðn  1ÞRPDB ðdini =1000 þ 1Þ  1  ðn  1ÞRPDB ðd=1000 þ 1Þ

ðA9Þ

Taking the logarithm of both sides of Eq. (A9), considering |RPDB|  1, |dini/1000 + 1|  1, and an approximation formula of ln(1 + x) = x when |x|  1, we have: ln

c c d  dini d  dini  ln ¼  ðn  1ÞRPDB cini cini 1000 1000

ðA10Þ

Because |RPDB|  1, we have: ln

c c  ln ¼ d  dini cini cini

ðA11Þ

Substituting Eq. (6) with (A11), with “c*” in Eq. (A11) referring to cA in Eq. (6) and “c” in Eq. (A11) referring to “cB” in Eq. (6), we have: kA c c d  dini ln  ln ¼ cini k B cini 1000

ðA12Þ

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