Thermodynamic Analysis of Organic / Inorganic Reactions Involving Sulfur : Implications for the Sequestration of H 2 S in Carbonate Reservoirs

Thermodynamic Analysis of Organic/Inorganic Reactions Involving Sulfur: Implications for the Sequestration of H2S in Carbonate Reservoirs — A thermodynamic analysis has been made of water-gas-rock-hydrocarbon interactions involving sulfur in carbonate reservoirs. Mineral-solution equilibria calculations indicate that formation waters produced from carbonate reservoirs at temperatures between 40°C and 160°C in the Paris Basin, Alberta Basin, and the North Sea are saturated with respect to calcite and dolomite, but undersaturated with respect to anhydrite. The calculations also suggest that increasing the activity of dissolved H2S (aH2S(aq)) in the reservoirs favors the formation of elemental sulfur, which constitutes a potential sequestration reaction for H2S. It is also shown that high partial pressures of H2S generated by thermochemical sulfate reduction in carbonate reservoirs may be controlled by metastable equilibrium states between hydrocarbons, organic Gas-Water-Rock Interactions ... / Interactions gaz-eau-roche ... IFP International Workshop Rencontres scientifiques de l’IFP Oil & Gas Science and Technology – Rev. IFP, Vol. 60 (2005), No. 2 sulfur compounds, elemental sulfur, and H2S at partial pressures which are 4 to 6 orders of magnitude higher than in clastic reservoirs where the H2S partial pressures are controlled by pyrite and iron carbonates. Depending on the H/C ratios of the hydrocarbons and organic sulfur compounds, H2S may be consumed or produced as a result of petroleum sulfurization reactions in carbonate reservoirs. 276


INTRODUCTION
Carbon dioxide (CO 2 ) and hydrogen sulfide (H 2 S) are both gases of environmental concern. The constant increase in the concentration of atmospheric CO 2 with increasing industrial activity over the last 150 years is a major cause in today's climate change [1], and the sequestration of CO 2 through dissolution in formation waters and subsequent neutralization of aqueous carbonic acid by rock-forming minerals has been proposed as a short-term means to reduce the level of CO 2 released into the atmosphere [2]. The conversion into elemental sulfur of the hydrogen sulfide which is commonly produced along with CO 2 from sour gas-containing reservoirs is sometimes of doubtful economic interest. A possible alternative is the reinjection of CO 2 -H 2 S mixtures in depleted hydrocarbon reservoirs [3][4][5]. Such a reinjection of CO 2 -H 2 S mixtures in gas-water-rock-hydrocarbon environments will result in thermal and chemical perturbations, which will be manifested by mass transfers among the gas phase, formation waters, liquid hydrocarbons, and rockforming minerals. The transformations resulting from the injection may include, among others, a drastic decrease in the pH of the aqueous fluids, the dissolution of carbonates and sulfates, the precipitation of sulfides and elemental sulfur, and the formation of organic sulfur compounds through sulfurization of the residual oil. Following the metastable equilibrium approach pioneered by Helgeson et al. [6], we present a thermodynamic analysis of the equilibrium relations between minerals, aqueous fluids, hydrocarbons, and hydrogen sulfide in carbonate reservoirs.

THERMODYNAMIC RELATIONS
The equilibrium constant K r,T,P of the rth reaction at a given temperature T and pressure P is given by: (1) where ∆G o r is the standard molal Gibbs free energy of the rth reaction, R stands for the gas constant (1.9872 cal mol -1 K -1 ), and T and P denote the absolute temperature and total pressure expressed in Kelvin and bar, respectively. The standard molal Gibbs free energy of the rth reaction is defined by: (2) where n i,r represents the reaction coefficient of the ith species in the rth reaction, which is negative for reactants and positive for products, and ∆G o i stands for the apparent standard molal Gibbs free energy of formation of the ith species at the temperature T and pressure P of interest. Omitting the i subscript for simplicity, the latter property can be calculated from [7]: (3) where ∆G o f stands for the standard molal Gibbs free energy of formation at the reference temperature and pressure of 25°C and 1 bar, and represents the difference in the standard molal Gibbs free energy of the ith species at the temperature and pressure of interest, and that at the reference temperature and pressure (T r and P r ). In accord with [6], the standard state adopted for minerals, liquid H 2 O, and liquid hydrocarbons and organic sulfur compounds in petroleum is one of unit activity of the thermodynamic components of stoichiometric minerals and pure liquids at any temperature and pressure. The standard state for aqueous species other than H 2 O is one of unit activity of the species in a hypothetical one molal solution referenced to infinite dilution at any pressure and temperature. The standard state for gases is specified as unit fugacity of the pure hypothetical ideal gas at 1 bar and any temperature.
The parenthetical term in Equation (3) is evaluated by integrating in temperature and pressure the expression: where stands for the standard molal entropy of the species at 25°C and 1 bar, C o P r denotes the standard molal heat capacity of the species at the reference pressure of 1 bar, and V o represents the standard molal volume of the species at the temperature and pressure of interest. The temperature dependence above 298.15 K of the standard molal heat capacity at 1 bar of minerals, inorganic gases, and organic liquids can be represented by the Maier-Kelley equation [7][8][9], which is written as [10]: where a, b, and c stand for temperature-independent coefficients. Consideration of compressibility and thermal C a bT cT expansivity data indicates that the standard molal volume of minerals is insensitive to changes in temperature and pressure for the conditions encountered in sedimentary basins [7]. Although the standard molal volumes of organic liquids are much more dependent on temperature and pressure than those of minerals, experimental data indicate that the effects of simultaneously increasing temperature and pressure tend to compensate along typical sedimentary basin geotherms [11]. Consequently, the last integral in Equation (4) reduces to: for minerals and organic liquids, with representing the standard molal volume of the species at the reference temperature and pressure of 25°C and 1 bar. Adopting for gases a standard state of unit fugacity of the pure hypothetical ideal gas at 1 bar and any temperature requires that: for gases at all temperatures and pressures [6]. Finally, the partial molal equivalent of Equation (4) for aqueous species which may be written as: is evaluated by taking account of the revised Helgeson-Kirkham-Flowers equations of state for the standard partial molal heat capacity and standard partial molal volume at the temperature and pressure of interest, which are given by [12]: and: where a 1 , a 2 , a 3 , a 4 , c 1 , c 2 , and ω represent species-dependent equation of state parameters, ψ and θ designate solventdependent parameters equal to 2600 bar and 228 K, ε is the dielectric constant of H 2 O, and Q, X, and Y refer to the Born functions. The equations summarized above can be solved with the aid of the SUPCRT92 computer program [13], together with thermodynamic properties and parameters for minerals, gases, aqueous species, and liquid hydrocarbons and organic sulfur compounds [7-9, 14,15]. The thermodynamic properties at 25°C and 1 bar, heat capacity coefficients, and transition properties at 1 bar for elemental sulfur are the following [16]:

FORMATION WATER CHEMISTRY IN CARBONATE RESERVOIRS
Thermodynamic calculations indicate that most formation waters produced from carbonate reservoirs are close to equilibrium with respect to calcite and dolomite, but not anhydrite [17][18][19]. This is illustrated in Figure 1, where values of the saturation index computed in the manner described below with the EQUIL program [20] for these three minerals have been plotted as a function of reservoir temperature. The symbols correspond to formation waters produced from Jurassic reservoirs of the Paris Basin [17] and the North Sea [18], as well as Devonian rocks from the Alberta Basin [19]. Only those waters for which the electric neutrality was respected within: (11) where m i and z i stand for the molality and charge of the ith ionic species, were considered in the calculations. The saturation index Ω is defined by: where Q r denotes the ion activity product and K r represents the equilibrium constant for the rth reaction. The ion activity product is in this case defined by the product of the aqueous activities of the constitutive ions of the mineral for which the saturation test is performed according to: where a i and n i stand for the activity and stoichiometric coefficient of the ith ionic species, respectively. The activity a i of an aqueous species is defined by: Saturation index for calcite, dolomite, and anhydrite as a function of temperature. The symbols correspond to formation waters of the Alberta Basin (q), the Paris Basin (∇), and the North Sea ( ). The solid and dashed lines indicate solutionmineral equilibrium and departures of ± 0.1 log unit from this equilibirum, respectively -see text.
where γ i and m i designate the activity coefficient and molality of the ith species in the formation water. Activity coefficients of ionic species are computed by the EQUIL program using the Debye-Hückel equation modified by Helgeson [21]. According to a procedure described elsewhere [19], the pH values of the fluids were first adjusted to bring calcite to within ± 0.1 log unit from equilibrium. This pH adjustment is based on the hypothesis that pH values measured at the surface are somewhat different from the actual values at depth, as well as on the observation that calcite is usually the most abundant mineral in carbonate reservoirs. These recalculated pH values were in all cases less than a unit lower than the corresponding surface values. In addition, the pH adjustment resulted in 29 formation waters of the 34 considered in the calculations to be in equilibrium with respect to dolomite within ± 0.1 log unit (dashed lines in Fig. 1).
When sulfate and sulfide concentrations were reported separately for the formation waters [17,19], the saturation calculations for anhydrite were constrained by specifying oxygen fugacity (f O 2(g) ) values at each temperature which would correctly reproduce the sulfate and sulfide concentrations in the fluid at the adjusted pH value according to the reaction: It can be seen in Figure 1 that all formation waters are undersaturated with respect to anhydrite, in particular the higher temperature waters from the North Sea in which the sulfate concentrations are extremely low (0.1-1.1 10 -3 mol). The oxygen fugacity values constrained by the sulfate-sulfide equilibrium have been plotted as a function of temperature in Figure 2, and compared to those computed for the hematitemagnetite (HM-MT) and pyrrhotite-pyrite-magnetite (PO-PY-MT) buffers, both of which are representative of the oxidation-reduction conditions prevailing in sedimentary basins [6,22]. These mineral buffers correspond to the reactions: for the hematite-magnetite buffer, and: for the pyrrhotite-pyrite-magnetite buffer, respectively. The temperature-log f O 2(g) curves corresponding to Reactions (16) and (17) were computed with the SUPCRT92 software [13] along the liquid-vapor saturation curve for the system H 2 O. Although the oxygen fugacity values computed assuming equilibrium between sulfate and sulfide species represent a smooth distribution as a function of temperature and pressure, these values plot more than 3 log units above the hematite-magnetite assemblage. It has been demonstrated that the oxygen fugacity values in calcite-bearing reservoirs represent metastable equilibrium states between the heavier hydrocarbons in crude oil (i.e. with carbon numbers ≥ 6-15), aqueous organic (e.g. carboxylate anions) and inorganic carbon-bearing species, and calcite, and that these values fall within the range defined by the hematite-magnetite and pyrrhotite-pyrite-magnetite assemblages [6,22]. The reason for these higher oxygen fugacity values is unclear, but may be due to inconsistencies between thermodynamic data in the EQUIL and SUPCRT92 databases.
The fact that anhydrite is not at equilibrium with formation waters in diagenetic environments is well known in carbonate reservoirs associated with appreciable concentrations of hydrogen sulfide (H 2 S). As a result, elemental sulfur may form in such reservoirs [23,24] according to the reaction: CaSO 4 + 3 H 2 S (aq) + 2 H + = 4 S (c or l) + 4 H 2 O + Ca 2+ (18) A diagram showing the stability domains of elemental sulfur, anhydrite, and calcite at 50°C and 1 bar is depicted in Figure 3. The reactions for the lines corresponding to coexisting calcite and anhydrite, and coexisting calcite and elemental sulfur are: CaSO 4 + 4 CO 2(g) + 3 Ca 2+ + 4 H 2 O = 4 CaCO 3 + H 2 S (aq) + 6 H + + 2 O 2(g) (19) and: CaCO 3 + 2 H + + H 2 S (aq) + 0.5 O 2(g) = Ca 2+ + CO 2(g) + S (c or l) + 2 H 2 O (20) respectively. The invariant point in Figure 3 corresponds to the reaction: CaSO 4 + 2 H 2 S (aq) + CO 2(g) = 3 S (c or l) + CaCO 3 + 2 H 2 O + 0.5 O 2(g) (21) The equation of the three lines were obtained from equilibrium constants calculated with the SUPCRT92 software [13] and logarithmic expressions of the law of mass action for Reactions (18)- (20), which can be written as: (22) (23) and: (24) assuming a carbon dioxide fugacity f CO 2(g) = 1 bar and an oxygen fugacity f O 2(g) value buffered by Reaction (17). It can be seen in Figure 3 that all of the formation waters from the Paris Basin and Alberta Basin plot inside the stability field of calcite. However, it can also be deduced from that figure that the injection of H 2 S gas in a carbonate reservoir will tend to move the fluid composition towards the stability field of elemental sulfur. It should be noted that Reactions (18) and (20) both permit the sequestration of H 2 S under the form of elemental sulfur. Other possible controls on H 2 S partial pressures in carbonate reservoirs are the precipitation Figure 3 Activity diagram depicting the stability fields of calcite, anhydrite, and elemental sulfur at 50°C and 1 bar. The symbols correspond to formation waters of the Alberta Basin (q) and the Paris Basin (∇).  of metal sulfides and the formation of organic sulfur compounds through sulfurization of residual hydrocarbons in the depleted reservoirs. Precipitation of metal sulfides (e.g. pyrite) is a limited process in carbonate reservoirs due to the limited availability of metal ions [24,25]. Limited amounts of pyrite and marcasite have been formed in the carbonate reservoirs of the Nisku formation [24] as products of bacterial and thermochemical sulfate reduction. The formation of metal sulfides will not be further discussed since metal concentrations have not been reported for the formation waters of the Paris Basin and the North Sea considered in the present study. Petroleum sulfurization reactions leading to the formation of organic sulfur compounds are described in detail below.

HIGH H 2 S IN PETROLEUM AND NATURAL GAS RESERVOIRS
High concentrations of H 2 S gas are encountered in carbonate reservoirs in which thermochemical sulfate reduction has occurred [26][27][28][29]. This makes such reservoirs potential natural analogues for geochemical studies related to the sequestration of H 2 S in the subsurface. Partial pressures of H 2 S (p H 2 S (g) ) as high as ∼ 400 bar have been reported in Devonian gas reservoir rocks from the Alberta Basin, Canada [29]. The amount of H 2 S gas in these rocks is higher than that of CO 2 , and tends to increase with increasing temperature (or depth). To illustrate this dependence of p H 2 S (g) with respect to temperature, mole fractions of H 2 S (x H 2 S (g) ) reported for the upper Devonian Nisku reservoirs of Alberta [28] have been converted to H 2 S partial pressures (p H 2 S (g) ) according to: (25) where P is the total pressure, and plotted against temperature in Figure 4. It can be seen in this figure that the values of p H 2 S (g) start to increase exponentially with increasing presentday temperatures in the Nisku reservoirs above ∼ 110ºC. Also plotted in Figure 4 is the highest partial pressure of H 2 S (∼ 360 bar at ∼ 130°C) reported by Hutcheon [29] which is in agreement with the lower temperature data and the exponential trend represented by the dashed curve. A similar exponential relationship between H 2 S partial pressures and temperature has been proposed for sandstone reservoirs from the Norwegian Shelf [30]. The partial pressures of H 2 S in the Norwegian Shelf and the Alberta Basin are compared in Figure 5 on a log p H 2 S (g) versus temperature plot. It can be seen in this figure that the values of p H 2 S (g) in clastic reservoirs are lower by several orders of magnitude than those observed in carbonate rocks. This difference is classically interpreted as reflecting the lack of available iron in carbonate reservoirs to buffer the p H 2 S (g) values by forming iron sulfides [26,29]. In fact, it has been shown that the values of p H 2 S (g) in the clastic reservoirs of the Norwegian Shelf were most probably controlled by an iron sulfide-iron carbonate assemblage [22], for which an equilibrium relation may be written as: FeS 2 + CO 2(g) + H 2(g) + H 2 O (l) = FeCO 3 + 2 H 2 S (g) (26)  Ref. [28] Ref. [29]  Ref. [28] Ref. [29] Ref. [30] Figure 4 Partial pressure of H 2 S as a function of temperature. The symbols correspond to values reported for carbonate reservoirs from the Alberta Basin. The dashed curve has been drawn to illustrate the exponential increase of pH 2 S with increasing temperature.

Figure 5
Logarithm of the partial pressure of H 2 S as a function of temperature. The symbols correspond to values reported for carbonate reservoirs from the Alberta Basin (q and ∆) and clastic reservoirs from the North Sea ( ).
where FeS 2 and FeCO 3 represent the minerals pyrite and siderite, H 2 O (l) stands for liquid water, and CO 2(g) , H 2(g) , and H 2 S (g) denote CO 2 , H 2 , and H 2 S in the gas state, respectively. It has also been demonstrated that metastable equilibrium states between hydrocarbons, organic sulfur compounds and H 2 S gas could establish in hydrocarbon reservoirs [31]. The possibility that such metastable equilibrium states could control the partial pressures of H 2 S in carbonate reservoirs is evaluated below.

METASTABLE EQUILIBRIUM STATES AMONG HYDROCARBONS, H 2 S, NATIVE SULFUR, AND ORGANIC SULFUR COMPOUNDS
Organic sulfur compounds first form during early diagenetic processes through reactions between bacterially produced hydrogen sulfide and carbon-carbon double bonds or oxygen-bearing functional groups of the biological precursors of sedimentary organic matter [32]. These reactions result in the formation of sulfur-rich kerogens, and the subsequent generation of sulfur-rich crude oils from these kerogens. However, there is ample experimental and field evidence that H 2 S, elemental sulfur, and hydrocarbons equally react in petroleum reservoirs to produce organic sulfur compounds. Sulfurization of petroleum in carbonate reservoirs through reactions between hydrocarbons and elemental sulfur has been abundantly discussed in the Russian literature [33, and references therein]. Thiols, sulfides and disulfides have been experimentally produced by reacting low molecular weight hydrocarbons (e.g. n-heptane and cyclohexane) with elemental sulfur at temperatures as low as 50°C [33]. Hydrogen sulfide was formed as a byproduct in some of these experiments. Similarly, a mixture of C 18 n-2,5-dialkylthiophenes has been produced by reacting n-octadecane with elemental sulfur at temperatures between 200 and 250°C [34]. It has also been observed that there was an increase in aromatic sulfur compounds (e.g. benzothiophenes) in the Nisku reservoirs of Alberta with increasing H 2 S in the gas phase of these reservoirs [28]. Although elemental sulfur may accumulate in petroleum reservoirs as a net product of thermochemical sulfate reduction [25], it should perhaps be pointed out that elemental sulfur and hydrogen sulfide may appear as reactants or products depending on the hydrogen to carbon (H/C) ratios of the hydrocarbons and organic sulfur compounds involved in the multitude of sulfurization reactions that may occur in a petroleum reservoir (see below). In any event, experiments and observations of this kind suggest that reactions involving hydrocarbons, elemental sulfur, and organic sulfur compounds may control H 2 S partial pressures in carbonate reservoirs.
Recognizing that carbon atoms in organic compounds have different oxidation states depending on the neighboring atom to which they are bonded [35], one can write oxidationreduction reactions describing metastable equilibrium states between hydrocarbons, elemental sulfur, organic sulfur compounds and hydrogen sulfide. For example, such reactions can be written for liquid 2,4-dimethylbenzo[b]thiophene (C 10 H 10 S (l) ) and trans-2-methyl-5-n-pentylthiacyclopentane (C 10 H 20 S (l) ) coexisting metastably with liquid n-decane (C 10 H 22(l) ) or n-butylbenzene (C 10 H 14(l) ) as: C 10 H 22(l) + 7 S (c or l) = C 10 H 10 S (l) + 6 H 2 S (g) (27) C 10 H 22(l) + 2 S (c) = C 10 H 20 S (l) + H 2 S (g) C 10 H 14(l) + 3 S (c or l) = C 10 H 10 S (l) + 2 H 2 S (g) (29) and: C 10 H 14(l) + 3 H 2 S (g) = C 10 H 20 S (l) + 2 S (c or l) (30) where S (c or l) and H 2 S (g) stand for crystalline or liquid elemental sulfur and hydrogen sulfide gas, respectively. The two organic sulfur compounds involved in Reactions (27)- (30) have been chosen because alkylthiacyclopentanes and alkylbenzothiophenes are representative of immature and mature crude oils, respectively [32]. Their idealized structures are depicted in Figure 6 along with those of n-decane and n-butylbenzene. Figure 6 Idealized structures of the hydrocarbons and organic sulfur compounds considered in the metastable equilibrium state calculations -see text. Adopting a standard state of unit activity for elemental sulfur at all temperatures and pressures, the corresponding logarithmic expressions of the law of mass action for Reactions (27)- (30) are: (31) (32) (33) and: (34) respectively, where K (27) , K (28) , K (29) , and K (30) are the equilibrium constants for the subscripted reactions, a C 10 H 10 S (l) , a C 10 H 20 S (l) , a C 10 H 22(l) and a C 10 H 14(l) stand for the activities of the subscripted species, and f H 2 S (g) represent the fugacity of hydrogen sulfide gas. Values of the equilibrium constants for Reactions (27)- (30) have been calculated with the SUPCRT92 software [13] at temperatures and pressures representative of those in the Alberta Basin [28], and used together with Equations (31) (30) different activity ratios of the hydrocarbon and organic sulfur compound in a given reaction (see caption to Fig. 7). The partial pressures of H 2 S (p H 2 S (g) ) shown in Figures 4 and 5 [28,30] have been converted to their fugacity counterparts (fH 2 S (g) ) according to: (35) where ϕ H 2 S (g) stands for the fugacity coefficient of H 2 S gas, which was evaluated in the present study from the Peng-Robinson equation of state [36]: (36) where V stands for the molal volume of the gas mixture, b is a constant representing a correction for the repulsion between molecules and is defined by: (37) and a(T) is a temperature-dependent constant representing intermolecular attraction forces, which is equal to: where T c and P c designate the critical temperature and pressure, respectively, and κ is a constant characteristic for each gas which is defined by [36]: where ω is the acentric factor. The a(T) and b parameters in Equation (36) were calculated assuming a CO 2 -H 2 S binary mixture and the usual mixing rules [37]. The fugacity coefficient for H 2 S in the mixture is obtained from [37]: where z CO 2 (g) and z H 2 S(g) are the mole fractions of CO 2 and H 2 S in the gas mixture.
The solid curve shown in Figure 7 represents the H 2 S fugacity fixed by the pyrite-iron carbonate assemblage for the clastic reservoirs from the Norwegian shelf [22]. It can be seen in Figure 7 that all but one of the fugacities of H 2 S in the Alberta Basin carbonate reservoirs fall within the range defined by Reactions (27)- (30) and the activity ratios indicated on the different curves. Note that the standard molal thermodynamic properties of organic compounds are a nearly linear function of carbon number for homologous series of compounds [8,9]. Therefore, metastable equilibrium curves calculated for n-alkanes, n-alkylbenzenes, and n-alkylthiacyclopentanes with higher or lower carbon numbers would coincide nearly exactly with the curves shown for n-decane, n-butylbenzene, and trans-2-methyl-5n-pentylthiacyclopentane in Figure 7. Similarly, many other metastable equilibrium states involving hydrocarbons and organic sulfur compounds with different nominal oxidation states are consistent with the range of H 2 S partial pressures reported for the Nisku and other carbonate reservoirs in which thermochemical sulfate reduction may have occurred [31]. The important point is that these preliminary calculations suggest that in the absence of detrital iron, metastable equilibrium states between hydrocarbons, hydrogen sulfide, elemental sulfur and organic sulfur compounds may control the partial pressures of H 2 S in carbonate reservoirs at values which are 4 to 6 orders of magnitude higher than those encountered in sandstone reservoirs.

CONCLUSION
As part of a research project on the chemical and mineralogical consequences of injecting CO 2 -H 2 S gas mixtures in geological formations, the water-gas-rockhydrocarbon reactions involving sulfur in carbonate reservoirs have been analyzed from a thermodynamic point of view. The calculations indicate that increasing the partial pressure of H 2 S in a carbonate reservoir, thereby increasing the aqueous activity of H 2 S in the formation water, will favor the formation of elemental sulfur. This constitutes a potential sequestration reaction for H 2 S.
Considering carbonate reservoirs in which thermochemical sulfate reduction has occurred as natural analogues for the sequestration of H 2 S suggests that the partial pressures of H 2 S in these reservoirs may be controlled by metastable equilibrium states between hydrocarbons, organic sulfur compounds and elemental sulfur. Changing the fugacity of H 2 S in carbonate reservoirs could possibly affect these metastable equilibrium states. Although the kinetics of sulfurization reactions is not known, these reactions may consume or produce H 2 S depending on the H/C ratios of the hydrocarbons and organic sulfur compounds involved in the sulfurization reactions. Future research will be aimed at quantifying these reactions by performing mass transfer and Gibbs free energy minimization calculations to confirm the preliminary calculations presented in this communication.