A numerical simulation of sulfur isotopic fractionation during sulfate reduction and sulfide oxidation in organic carbon-rich sediments

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1 A numerical simulation of sulfur isotopic fractionation during sulfate reduction and sulfide oxidation in organic carbon-rich sediments Neil S. Suits 1, Michael A. Arthur 2 and Lee R. Kump 2 1 Department of Biological and Physical Sciences, Montana State University - Billings, Billings, MT Department of Geosciences, The Pennsylvania State University, University Park, PA 1682 Abstract We use a numerical model of sulfur diagenesis in marine sediments to investigate the impact of kinetic isotope effects during sulfate reduction (KIE SR ) and sulfide oxidation (KIE OX ) on 34 S values of dissolved sulfide and sedimentary pyrite formed from it. There are two versions of the model: one where rates of sulfide oxidation are limited by the molecular diffusion of oxygen from the water column, and another where sedimentary rates of oxidation are significantly enhanced due to an assumed bacterial transport of an oxidant such as nitrate into the sediment. The effective isotope discrimination at the sediment-water interface ( 34 S SWI = 34 S H2S - 34 S SO4= ) is greatest at low rates of reduction and/or high rates of sulfide oxidation. 34 S SWI cannot exceed the isotope effect associated with sulfate reduction, KIE SR, without additional isotope effects such as fractionation during sulfide oxidation, i.e. KIE OX. When sulfide oxidation rates are controlled by diffusion of oxygen, the primary control on 34 S SWI is the rate of sulfate reduction and KIE SR. Depth-profiles of sulfate reduction rates (SR) are described using a maximum rate (SR max ), usually at the SWI, and an e- folding depth (Z e-sr ), where Z e-sr is the depth where SR is equal to 1/e X SR max. For a given e-folding depth, 34 S SWI is a strong linear function of rate of reduction. At low rates of sulfate reduction, large values of KIE OX, such as those observed during disproportionation of elemental sulfur, can cause additional isotopic depletion in pore water dissolved sulfide of up to 1 at 4 cm in the sediment, but only 1-2 at the sediment-water interface (SWI) Since 34 S of pyrite is primarily controlled by the isotope ratio of dissolved sulfide at the SWI, 34 S SWI, isotope effects during disproportionation should increase depletion in 34 S of pyrite by no more than about 7. If sulfide oxidation rates are enhanced by transport of oxidants such as nitrate into the sediment, it can be much more effective at increasing depletions in 34 S values of dissolved sulfide and pyrite, both at the sediment-water interface (SWI) and at depth. Under these circumstances, KIE OX could be responsible for the depletion of 1 or more observed in sulfur in the top 5 cm of sediments from the Peru Margin and other anaerobic environments. Finally, if pyrite formation is associated with even small kinetic isotope effect (KIE PYR ~ 1 ) and is a substantial sink for H 2 S near the SWI, it can result in a significant depletion in 34 S SWI.

2 1 Introduction 34 S values of sedimentary sulfides are used to reconstruct paleoenvironments and determine rates of sedimentation and sulfate reduction (Schwarz and Burnie, 1973; Gautier, 1987; Whitaker and Kyser, 199; Kajiwara and Kaiho, 1992; Zaback and Pratt, 1992; Ohmoto et al., 1993; Kajiwara et al., 1994). They are also used as indicators of oxygen concentrations in the water column and atmosphere (Canfield and Teske, 1996; Habicht and Canfield, 1996). Furthermore, secular variations in 34 S values are used to infer evolution of the atmospheric oxygen on geologic timescales (Garrels and Perry, 1974; Veizer et al., 198; Walker, 1986; Kump, 1989; Canfield and Teske, 1996; Canfield, 24; Kah et., al., 24). However, interpretation of 34 S of sedimentary sulfides is problematic and largely based on empirical relationships, which can sometimes lead to contradictory interpretations of identical 34 S data. For example, extremely negative 34 S values are thought to be characteristic of euxinic (Anderson et al., 1987; Beier and Hayes, 1989), as well as oxic sedimentary environments (Kajiwara et al., 1994; Canfield and Teske, 1996; Habicht and Canfield, 1996). Consequently, it is important to understand what controls 34 S values of sedimentary pyrite, particularly with respect to the impact of oxygen on these values. Pyrite and other sedimentary sulfides are formed by reactions with dissolved sulfide in pore water of marine sediments. Therefore, to a first approximation, the factors that control 34 S of pyrite are the same as those that control 34 S of dissolved sulfide. Those factors include: 1) variations in the bacterial isotope effect resulting from changes in specific rates of sulfate reduction, i.e. rates per bacterium (Kaplan and Rittenberg, 1964; Rees, 1973; Chambers et al., 1975); 2) variations in bulk rates of sulfate reduction, i.e., rates per volume, resulting from changes in rates of bulk sedimentation and 2

3 availability of organic substrates (Goldhaber and Kaplan, 1974, 1975, Ronov, 1974); 3) pathways of sulfide oxidation and the isotope effects associated with each (Jørgensen, 1978, 199; Fry et al., 1984, 1988a, 1988b; Hallberg, 1984; Millero, 1986; Chanton et al., 1987b; Thode-Andersen and Jørgensen, 1989; Fossing and Jørgensen, 199; Elsgaard and Jørgensen, 1992; Canfield and Thamdrup, 1994; Canfield and Teske, 1996; Habicht et al., 1998; Habicht and Canfield, 21); 4) effects of mixing and diffusion (Fry et al., 1991; Jørgensen, 1978; Goldhaber and Kaplan, 198; Chanton et al., 1987a); and, 5) isotopic exchange between reactive species (Voge, 1939; Fossing and Jørgensen, 199; Canfield et al., 1998). The situation is further complicated by the fact that sulfur is involved in numerous reactions in sediments and the water column (Fig.1). Included among these are oxidation, reduction, disproportionation, precipitation, as well as isotopic exchange between coexisting species (Millero, 1986; Morse et al., 1987; Bak and Cypionka, 1987; Fossing and Jørgensen, 199; Zhang and Millero, 1993). The rates and relative importance of these reactions are generally uncertain. Bacteria mediate some of the reactions, while others are non-biologic (Goldhaber and Kaplan, 1974; Jørgensen, 1983; Bauld, 1986). + The puzzle for many years was the fact that laboratory cultures of sulfatereducing bacteria had a maximum fractionation of 46, whereas in sediments fractionations as great as 62 had been observed (Kaplan et al., 1963). Several arguments were presented for how this apparent increase in the isotopic fractionation might be produced in natural environments. Suggestions included: 1) fractionation due to differential diffusion of isotopically substituted species resulting from differences in concentration gradients (Jørgensen, 1978; Goldhaber and Kaplan, 198; Chanton et al., 1987a); 2) reduction of recycled sulfate, i.e. reduction of sulfate produced by oxidation of 3

4 isotopically depleted sulfide, or multiple cycles of sulfide oxidation and elemental sulfur disproportionation (Kajiwara and Kaiho, 1992; Kajiwara et al., 1994; Canfield and Thamdrup, 1994); and 3) kinetic isotope effects (KIEs) during sulfide oxidation or disproportionation of sulfoxy intermediates (Jørgensen, 199; Canfield and Thamdrup, 1994). Isotope fractionation due to diffusional effects occurs, but is unlikely to be large enough to solve the problem. Fractionation due simply to reduction of isotopically depleted recycled sulfate violates mass-isotope balance considerations, because, without alternative pathways for sulfur compounds, fractionation cannot exceed the isotope effect associated with sulfate reduction. Repeated sulfide oxidation followed by elemental sulfur disproportionation can only fractionate sulfur isotopes by the combined effects of KIE OX and KIE SR. Recycling cannot magnify net isotope fractionation unless there is a way to remove isotopically enriched sulfur from the system. Isotope fractionation during oxidation to sulfate is also problematic, because most natural biologic kinetic isotope effects are normal. With a normal KIE the product is depleted in the heavy isotope, e.g. 34 S. Inverse KIEs enrich the product in the heavy isotope and are much less common. We use the convention here that a normal KIE is negative and an inverse KIE is positive. If oxidation of sulfide to sulfate is accompanied by a normal KIE, it will enrich the remaining dissolved sulfide in 34 S, and lessen the apparent isotope fractionation ( 34 S) during sulfate reduction. This will not help our problem. However, measurements of kinetic isotope effects during biologic oxidation of sulfide are a mixed bag. Most are accompanied by small (< ±1 ) KIEs, which can be either normal (negative) or inverse (positive) (Kaplan and Rittenberg, 1964; Rees, 1973; Chambers and Trudinger, 1979; Fry et al., 1984, 1988a, 1988b). In one case, oxidation of dissolved sulfide by Thiobacillus 4

5 concretivorus produced a sulfoxy-anion, tentatively identified as polythionate, which was enriched in 34 S by +19 (Kaplan and Rittenberg, 1964; Mekhtieva and Kondrateva, 1966). Nonetheless, relatively little is known about these reactions and it is not clear that they are quantitatively important. A promising suggestion is isotope fractionation during disproportionation reactions. Disproportionation splits an intermediate sulfur species, e.g. elemental sulfur, thiosulfate, etc., into dissolved sulfate and sulfide. Most of these reactions produce sulfide that is depleted in 34 S and sulfate that is enriched in 34 S relative to the initial compound, which, based on free energy considerations alone, is their natural equilibrium state (Tudge and Thode, 195; Sakai, 1957). Bacterial disproportionation of elemental sulfur (RXN 1) produces sulfide that is depleted in 34 S relative to the elemental sulfur by -7 to -9, and sulfate that is enriched by +13 to +15 (Canfield and Thamdrup, 1994; Canfield et al., 1998; Cypionika et al., 1998; Böttcher et al., 21). Disproportionation of thiosulfate (RXN 2) created sulfide that was depleted in 34 S by 3 to 15 relative the initial thiosulfate (Habicht et al. 1998). Disproportionation of thiosulfate may also fractionate sulfur isotopes simply because the two sulfur atoms in thiosulfate are chemically and isotopically distinct (Agarwalla et al., 1965). Disproportionation of sulfite (RXN 3) created sulfide that was depleted in 34 S by 28 relative the initial sulfite (Habicht et al. 1998). 4S + 4 H 2 O 3 HS - + SO = H + RXN 1 KIE OX-S H2S = -7 ; KIE OX-S SO4 = +21 S 2 O = 3 + H 2 O HS - + SO = 4 + H + RXN 2 KIE OX-S2O3 H2S = -3 to -15 ; KIE OX-S2O3 SO4 = +3 to SO 3 = + 2 H + H 2 S + 3 SO 4 = RXN 3 KIE OX-SO3 H2S = -28 ; KIE OX-SO3 SO4 = +9 5

6 Disproportionation reactions are particularly important for sulfur isotope fractionation because they will appear as inverse KIEs. This is because the product, SO = 4, is enriched in 34 S. Due to mass and isotope balance considerations, the magnitude of the KIE, when considered as a complete oxidation of sulfide to sulfate, is larger than the isotopic difference between the initial S-substrate and the H 2 S formed from it. Consequently, disproportionation of elemental sulfur is particularly effective at fractionating pore water isotopes of H 2 S and SO = 4. Our primary goal is to examine how isotope fractionation during sulfate reduction and sulfide oxidation, affects 34 S values of pyrite. Second, we want to see if we can use 34 S profiles in marine sediments to tell us about the importance of sulfide oxidation in controlling 34 S of dissolved sulfide, and to test a hypothesis that 34 S profiles of sedimentary pyrite with isotope depletion just below the SWI, like those observed in cores we collected from the Peru Continental margin and also seen in some sediments of the Baltic Sea (Fig. 2a and b), are characteristic of sediments where sulfide oxidation quantitatively important. 34 S values of dissolved sulfide and sedimentary sulfur in these cores show a progressive depletion in 34 S in the top 25 cm of the sediment. A classic understanding of 34 S values in marine sediments (Fig. 3), which is based on analytic solutions of differential equations and considers only isotope effects accompanying sulfate reduction, produces a 34 S profile in sediments that is progressively enriched in 34 S with increasing sediment depth (Jørgensen, 1978; Goldhaber and Kaplan, 198; Sweeney and Kaplan, 198; Chanton et al., 1987b). Based on these models, profiles like those observed in Peru Margin sediments and the Baltic Sea could only be produced by changes in the environment, such as increases in sedimentation rates and/or rates of 6

7 sulfate reduction. Our question is can steady state processes that include isotope effects during oxidation of sulfide also explain these profiles? Finally, there is an important consideration when modeling sedimentary sulfide oxidation. What is the oxidant? In most marine sediments the primary oxidant is probably oxygen (Jørgensen, 1982). In upwelling zones with anoxic water columns, such as the Peru continental margin, nitrate is a significant oxidant (Fossing et al., 1995). Reactions between oxygen and sulfide can be mediated by bacteria or can occur abiotically (Millero, 1986; Zhang and Millero, 1993; Troelsen and Jorgenson, 1982). At low temperatures, oxidation of sulfide by nitrate is mediated by bacteria (Fossing et al., 1995; McHatton et al., 1996). Oxygen is passively introduced to sediments through molecular diffusion, bioturbation and bioirrigation (Berner, 198). Nitrate can also be supplied by molecular diffusion; however, in some sediments bacteria play an active role in transporting nitrate from the water column into the sediment. Chemolithoautotrophic sulfur bacteria, Thioploca spp., can concentrate nitrate intracellularly up to 3,-2, times ambient levels and are capable of migrating vertically within the sediment (Fossing et al., 1995; Hüttel et al., 1996; McHatton et al., 1996; Schulz et al., 1996). These bacteria are characteristic of shallow continental margin sediments of the Peru-Chile margin, but are also observed in other organic-carbon rich, low oxygen environments (Gallardo, 1977; Maier and Preissner, 1979; Henrichs and Farrington, 1984; Fossing et al., 1995; Schulz et al., 1996 and references therein; Ferdelmann et al., 1997). Their presence means that high rates of sulfide oxidation may be sustained within anoxic marine sediments. To answer these questions we use a numerical model to examine how kinetic isotope effects during sulfate reduction and sulfide oxidation in marine sediments 7

8 influence stable isotopic ratios of pore water sulfide and sedimentary sulfur, such as pyrite. A numerical model is an appropriate tool because the system is fundamentally nonlinear. This is because rates of sulfate reduction are a function of sulfate concentration, which is a function of sulfide oxidation rates, which are controlled by sulfide concentrations, which are in turn controlled by sulfate reduction rates. Furthermore, numerical simulations let you look at the effects of a wide range of conditions, as well as the sensitivity of 34 S values to changes in various controlling parameters and various KIEs. 2 Model Simulation The model used in this study simulates early diagenesis of sulfur in the top 1 m of recent marine sediments. It consists of 15 layers of variable thickness (.5 to 2 cm). Concentrations and stable sulfur isotopic ratios of dissolved sulfate and sulfide are calculated using reactions occurring within each sediment layer, and by accounting for molecular diffusion between adjacent layers. Primary controls are rates of sulfate reduction and sulfide oxidation, and the isotope effects accompanying each. Concentrations are reported in mmol/l. Rates are reported in mmoles/l /year. Stable isotope ratios are reported using standard delta notation 34 S sample Rsample Rstandard R standard / 1 (1) where R is the 34 S/ 32 S ratio in the sample and standard. The sulfur isotope standard is Canyon Diablo Meteorite (CDT). There are two chemical reactions considered: reduction of sulfate to form sulfide (3) and oxidation of sulfide to form sulfate (4). In order to properly compare the impact of intermediate reactions, such as 8

9 disproportionation, on net isotope fractionation it is necessary to account for the stoichiometry and isotope effects of each reaction. SO 4 = + Reduced substrate H 2 S + Oxidized product (2) H 2 S + Oxidant SO 4 = + Reduced product (3) The Reduced substrate is assumed to be organic carbon. The Oxidant is either oxygen or nitrate. Dissolved sulfide and sulfate are transported between adjacent layers by molecular diffusion. Fluxes (F D ) are proportional to the concentration gradient between the two layers, divided by the distance between their midpoints (5). The constant of proportionality is the effective diffusion coefficient (D S ). Fluxes are divided by the porosity to correct for the fact that much of the volume contains sediment. F D C Z (4) D S / Units of flux (F D ) are mmoles/cm 2 /year. C is the difference in concentrations between the layers in mmoles/l. Z is the distance between the midpoints of layers in centimeters. is the sediment porosity, and is assumed to be.85 at all depths. D SO4 is the apparent diffusion coefficient of sulfate in pore water in units of cm 2 /year and can be approximated by D D 2 SO4 SW (5) where D SW is the diffusion coefficient of sulfate in sea water at 1 C, the approximate temperature of sea water impinging on Peru shelf sediments (Li and Gregory, 1975; Lerman, 1979; Rowe and Howarth, 1985). For =.85 and D SW =.68 X 1-5 cm 2 sec -1, D SO4 is approximately 15.4 cm 2 /year (4.9 X 1-6 cm 2 /sec). The diffusion coefficient for sulfide is approximately 1.6 times that of sulfate (Goldhaber and Kaplan, 1974; 9

10 Jørgensen, 1979); therefore, in the model D H2S = 1.6 D SO4. The diffusion coefficient for dissolved O 2 is X 1-6 cm 2 /sec (Himmelblau, 1964). Concentrations and stable isotopic ratios of sulfate at the upper boundary layer are constant and equal to seawater values, i.e. approximately 28.9 mmol/l and +2 vs. CDT. Dissolved oxygen is 278 mol/l. There is no hydrogen sulfide in this layer. The upper boundary is a redox interface, presumably the sediment-water interface (SWI). Above this boundary the concentration of the oxidant is constant. The upper boundary could also represent a redox interface in the sediment separating an upper bioturbated zone from a lower interval where transport of solutes occurs only by molecular diffusion. The lower boundary at 1 m is a no flow boundary. Concentrations at the boundary are set to those of the bottom layer of the model. Reactions below this depth are assumed to be negligible and have little effect on profiles (Kaplan et al., 1963; Hartmann and Nielsen, 1969; Goldhaber et al., 1977; Jørgensen, 1977). Sulfate reduction rates are based on results of a two-g model in which rates are controlled by availability and reactivity of two oxidizable substrates (Berner, 198; Skyring, 1986). One of the substrates (G 1 ) is quite reactive; the other (G 2 ) is not. Availability of both is greatest at the sediment-water interface and declines exponentially with increasing depth, Sulfate reduction rates are first order with respect to concentrations of G 1 and G 2 and produce sulfide at depth Z according to the formula Z / Z Z / Z SRR G' e G' e (6) Z e G1 e G where G' 1 and G' 2 are corrected for the stoichiometric ratio between organic substrate (G 1 and G 2 ) oxidized and the amount of sulfate reduced. Units for SRR Z, G' 1 and G' 2 are mmoles SO = 4 /L/year. Z e-g1 and Z e-g2 are the e-folding depths for G 1 and G 2, i.e. the depth in the sediment where concentrations of G 1 and G 2 are 1/e times their respective 1

11 concentrations at the sediment-water interface (e ). It is assumed that Z e-g2 is very large, and therefore, over the depth interval of interest G 2 is constant and may be simplified as Z Z/ Z 1 ' e G 1 ' 2 SRR G e G (7) Sulfate is rarely a limiting factor in marine environments (Boudreau and Westrich, 1984); however, studies in laboratory cultures and sediments suggest that rates of reduction may be affected by concentrations of 1-4 mmol/l (Chambers and Trudinger, 1979; Postgate, 1951; Bågander, 1977; Goldhaber and Kaplan, 198). We assume that rates of reduction are independent of sulfate concentration as long as sulfate is greater than 3 mmol/l. Below this concentration, rates are first order with respect to sulfate, i.e. the calculated rate of reduction is multiplied by the sulfate concentration in the layer divided by 3 mmol/l. Z Z/ Z 1 ' e G 1 ' 2 SO4 / 3 SRR G e G m (8) Sulfate reduction rate profiles calculated on this basis display a maximum rate at the sediment water interface, then decline exponentially with increasing depth due to depletion of organic substrates Rates of sulfide oxidation are dependent on availability of dissolved sulfide and an oxidant. There are two kinds of oxidants available: those supplied by molecular diffusion and those that may be actively transported into the sediment. An example of the first is oxygen, which is only available through molecular diffusion. An example of the second is nitrate, which may be concentrated at the SWI by bacteria and then actively transported to the site of oxidation (REF). When nitrate is the oxidant, rates of sulfide oxidation are handled in a similar fashion to rates of reduction. Concentration of the 11

12 oxidant is maximum at the SWI and decreases exponentially with depth as a result of its reaction with dissolved sulfide. The expression for the potential rate of oxidation at any depth Z is Z/ Ze OX Z Max (9) HSOX HSOX e where HSOX Max and HSOX Z are the maximum potential rate of sulfide oxidation at the sediment-water interface and at depth Z, respectively. Units for HSOX Max and HSOX Z are mmoles-h 2 S/L/year. Z e-ox is the e-folding depth in centimeters for sulfide oxidation. Rates of sulfide oxidation are independent of sulfide concentrations for concentrations greater than 1 mmol/l and linearly proportional to sulfide for concentrations less than this. z / zox OX Z OX H 2S R R e m (1) While availability of sulfide must inhibit oxidation at some minimum concentration, we do not know what that minimum value is. Setting it at 1 mmol/l introduces a negative feedback necessary for model stability and does not significantly affect results. If oxygen is the oxidant, then oxidation rates at all depths are first order with respect to concentrations of both oxygen and dissolved sulfide. No further negative feedbacks are necessary. Profiles of sulfide oxidation rates generated from these equations are near zero at the sediment-water interface, climb to peak values just below this, and then decline exponentially with increasing sediment depth. The rates are limited by sulfide availability at the surface and by the oxidant availability at depth. The peak of sulfide oxidation in the sediment is physically located below the peak of sulfate reduction. Thickness of the layers in the model is variable so that resolution can be increased at depths where reaction rates are highest. In these simulations activity is concentrated 12

13 near the sediment-water interface where depth resolution is.5 cm. The deepest layers in the model are 2 cm thick. Total depth of the sediment in the simulations is 1m. In the model, reduction of sulfate and oxidation of sulfide may be accompanied by isotopic fractionation. The expressions for magnitude of the kinetic isotope effects are KIE SR (isotopic fractionation accompanying reduction of sulfate) and KIE OX (isotopic fractionation accompanying oxidation of sulfide). They are expressed as a per mil ( ) difference between the 34 S value of a reservoir and the 34 S value of the product of reduction and oxidation, respectively. The isotopic value of sulfide added to a layer as the result of sulfate reduction is expressed by equation (12). The isotopic value of sulfate added to a layer as the result of sulfide oxidation is expressed by equation (13) REDZ REDZ SO4 SR S R S (11) OX Z OX Z H 2S OX S R S (12) 34 S H2 S and 34 S SO4 are 34 S values of the reacting sulfide and sulfate reservoirs, respectively. Experiments and environmental studies indicate that SR is always a normal isotope effect with values ranging from approximately to -6 (Kaplan et al., 1963; Kaplan and Rittenberg, 1964; Chambers and Trudinger, 1979; Goldhaber and Kaplan, 198). It has been suggested that KIE SR may vary as a function of the rate of reduction (Kaplan and Rittenberg, 1964; Mekhtieva and Kondrateva, 1966). Detmers et al., (21) have made a strong argument that there is no systematic variation between the KIE SR and the rate of reduction in laboratory cultures when realistic organic substrates are used. Nonetheless, in the model SR can be treated as a constant, or varied as a function of depth and/or reaction rates. 13

14 Transport of isotopically substituted species, e.g. H 32 2 S, H 34 2 S, 32 SO = 4 and 34 SO = 4, are independent of one another and based on their individual concentration gradients. We test the idea that isotopic fractionation during molecular diffusion of isotopically substituted species significantly contributes to the total isotope fractionation of dissolved sulfide (Jørgensen, 1979; Chanton et al., 1987b), by comparing the results of this version of the model to a previous one in which diffusion was applied to bulk concentrations and delta values. The programs are written in FORTRAN and available at They are liberally adapted from models in Walker (1991) and solve for time-dependent changes in sulfur reservoirs by the reverse Euler method, using Gaussian elimination and back substitution. The time step automatically adjusts itself to compensate for possible non-linearities in the system. The maximum permissible change in the absolute value of the relative increment of each dependent variable never exceeds.1. Results are reported when a steady state has been achieved. We first look at the sensitivity of the oxygen-model to variations in sulfate reduction rates and kinetic isotope effects during oxidation. Then we see how concentrations and 34 S values of dissolve sulfide in the nitrate-model respond to variations in rates of sulfate reduction and sulfide oxidation. Next we look at the impact of variations in kinetic isotope effects during both sulfate reduction and sulfide oxidation on 34 S ratios of dissolved sulfide. We examine the impact of iron reactivity and 34 S profiles of dissolved sulfide on isotope ratios of pyrite. And finally, we compare model results to observations in nature. 14

15 3 Results and Discussion 3.1 Oxidation of Sulfide by Oxygen The Oxygen Model Increasing rates of sulfate reduction causes sulfide concentrations to rise and oxygen concentrations to decline (Fig. 4a-f). The peak rate of sulfate reduction is at the sediment surface; peak rates of sulfide oxidation are located slightly below this. Oxidation is limited by concentrations of sulfide near the SWI, and by oxygen at depth. At high rates of reduction, oxygen is depleted at shallow levels in the sediments and sulfide oxidation is limited to a thin interval just below the SWI. At slower rates of reduction, sulfide oxidation persists deeper in the sediment. At low rates of reduction, 34 S ratios of dissolved sulfide at the SWI ( 34 S SWI ) are equal to the 34 S of seawater sulfate ( 34 S SO4-SW ) plus the isotope effect accompanying sulfate reduction ( SR ), i.e., 34 S SWI = 34 S SO4-SW + KIE SR ; 2-4 = S of dissolved sulfide is relatively constant with increasing sediment depth. In contrast, at high rates of reduction, 34 S of dissolved sulfide at the SWI is highly enriched in 34 S relative to seawater sulfate, and becomes progressively more enriched with sediment depth. For values of SRR Max up to approximately 5 mmol/l/year (Z e-sr = 1 cm), there is a strong linear relationship between SRR Max and the difference between 34 S of sulfide and seawater sulfate at the sediment-water interface ( 34 S SWI ). We have recast sulfate reduction rates in a more generalized form of an integrated rate per area (SRR Int ) in order to present the relationship between rates of reduction and the apparent discrimination at the SWI, 34 S SWI (Fig. 5). This is done by dividing SRR Max by Z e-sr. The maximum possible fractionation at the SWI is equal to the KIE during sulfate reduction, i.e. 34 S SWI KIE SR. This is seen at low rates of reduction regardless of the e-folding depth of sulfate reduction (Z e-sr ). For given values of Z e-sr, there is a strong linear relationship between 15

16 the rate of reduction and 34 S SWI, which intercepts the y-axis at SR, and reaches a maximum value (minimum discrimination) of about 2 to 15. The equations for the relationships are: [Z e-sr =1 cm]: 34 S SWI = 3.97SRR Int 39.3; [Z e-sr =7.5 cm]: 34 S SWI = 1.73SRR Int 39.5; [Z e-sr =5 cm]: 34 S SWI =.5SRR Int 39.4; [Z e-sr =2.5 cm]: 34 S SWI =.6SRR Int The R 2 for all of these equations is.99 or greater. The equation for the relationship between the changes in slope m d S d SRR 34 SWI and the e-folding depth, Z e- Int SR, is an exponential with the formula: m Z e SR.54.22e ; R 2 =.97. (13) It is a function of the molecular diffusion rates of oxygen and dissolved sulfide, and sulfide-limitation on rates of oxidation. Isotope effects during sulfide oxidation with oxygen do not significantly affect 34 S SWI. On figure 5 we also plotted the values of 34 S SWI for a simulation with Z e-sr = 1 cm and KIE OX = +1. Modeled results are almost indistinguishable from results in which Z e-sr = 1 cm and OX =, but in fact a KIE OX of +1 depletes 34 S of H 2 S at the SWI by approximately 1. Although KIE OX has only a very small impact on 34 S SWI, it can have a significant influence on 34 S values at depth (Fig. 6). Positive (inverse) KIEs during sulfide oxidation cause 34 S of sulfide to become progressively depleted in 34 S with increasing sediment depth. For example, for OX = +1, 34 S of H 2 S is depleted in 34 S by 47 relative to seawater sulfate (and coexisting pore water sulfate) by 4 cm. At 1 m the depletion is greater than 55. This amounts to nearly a 15 decrease in 34 S of H 2 S in the upper 1 m of the sediment. Normal, negative KIEs during sulfide oxidation will 16

17 cause 34 S to become enriched in 34 S at depth. Nonzero values of KIE OX will only impact 34 S profiles at relatively low rates of reduction, where sulfide oxidation can be sustained deep in the sediment due the continued presence of oxygen. In this example we are using a value of SRR Max =.5 mmol/l/year. At higher rates, KIEs during sulfate reduction overwhelm the impact of KIE OX, even if KIE OX >, and 34 S of sulfide becomes progressively enriched in 34 S similar to the classic view of sedimentary sulfate reduction (Fig. 3). 3.2 Oxidation of sulfide by nitrate The Nitrate Model 3.21 Rates of sulfate reduction and sulfide oxidation. Although the model is intended to provide insight into processes controlling isotopic profiles of dissolved sulfate and sulfide in any organic-rich sediment, it is primarily designed to simulate conditions in sediments located beneath the upwelling zone of the Peruvian continental margin (Suits, 1998). Therefore, default sulfate reduction profiles used in most simulations approximate rate profiles (Fig. 7) measured in shelf sediments of the Peru margin at water depths of 1-2 m (Fossing, 199). Since rates of sulfide oxidation are unknown, sulfide-oxidation rate parameters are set so that they approximate measured concentration profiles of dissolved sulfate and sulfide (Fossing, 199; Suits, 1998). It is important to note that the sulfide oxidation rates here are at least an order of magnitude greater than calculated in the Oxygen model, i.e. when rates are limited by the diffusive flux of oxygen Impact of rate parameters on sulfide concentrations. Rate parameters (SR Max, Z e-sr, G 2, HSOX Max and Z e-ox ) were varied one at a time, while others are held constant, in order to see their impact on concentrations of dissolved sulfide and sulfate. Results for sulfide can be seen in figures 8 a-e. Sulfate 17

18 concentrations are not included because they roughly mirror those of sulfide. Because the diffusion coefficient for sulfide is approximately 1.6 times that of sulfate, sulfide diffuses out of the sediment more rapidly than it is replenished by sulfate diffusing back in. As a result, the sum of the concentrations of dissolved sulfate and sulfide is less than total dissolved sulfate in the overlying water column. The depletion in total dissolved sulfur is more pronounced at high rates of sulfate reduction. Concentrations of sulfide increase for increases in SR Max, Z e-sr and G 2. Boosting G 2 values flattens the concentration curve. Also as expected, increases in HSOX Max and Z e-ox cause sulfide concentrations to decline. In theory, high rates of sulfide oxidation deep in the sediment can consume nearly all pore water sulfide, even at high rates of reduction. While this seems peculiar, high rates of sulfate-reduction are often measured in sediments with no discernible dissolved sulfide (Fossing and Jørgensen, 199a; Ferdelmann et al., 1997) Impact of rate parameters on 34 S ratios of dissolved sulfide and sulfate. Results of simulations on sulfur isotopic profiles of dissolved sulfate and sulfide can be seen in figures 9a-j. Increases in SR Max, Z e-sr and G 2 all produce 34 S of dissolved sulfide that is enriched in 34 S both at the SWI and at depth. Increasing G 2 is particularly effective at enriching 34 S values at depth. Increasing either HSOX Max or Z e- OX causes 34 S of sulfide to be more negative, both at the SWI and at depth. In general, 34 S SWI values are more positive, and thus 34 S SWI is least, at high rates of sulfate reduction and low rates of sulfide oxidation. In contrast, 34 S SWI is greatest at low rates of sulfate reduction and high rates of sulfide oxidation. 34 S SWI cannot exceed the maximum isotope effect of bacterial reduction, unless there are processes that impart 18

19 additional isotopic fractionation. Simply recycling isotopically light sulfide will not increase 34 S SWI Impact of kinetic isotope effects on 34 S ratios of dissolved sulfide and sulfate. Increasing the magnitude of KIE SR, i.e. making it more negative, results in depletion of 34 S of sulfide at all sediment depths (Fig. 1a-d). 34 S SWI is approximately equal to KIE SR even at relatively high rates of reduction, as long as sulfide oxidation rates are also comparably great. Positive (inverse) KIEs during sulfide oxidation can produce a sharp depletion in 34 S of sulfide just below the SWI. With KIE OX = +2, the difference in 34 S of pore water sulfide and sulfate, 34 S H2S-SO4, can be greater than -55 in the top 5 cm of the sediment. KIE OX = +2 is similar to that measured during disproportionation of elemental sulfur. Thioploca spp., a Beggiatoa commonly found in Peru Margin sediments, store elemental sulfur within their cell walls; however, it is generally assumed that Thioploca oxidize elemental sulfur and not disproportionate it. Regardless of what reaction occurs, there is no evidence that Thioploca fractionate sulfur isotopes. Nonetheless, the 34 S profiles of dissolved sulfide seen in figure 1c, for values of KIE OX ~ +1 to +2, display an initial depletion 34 S profiles similar to those observed in several shallow water cores where Thioploca mats were prevalent (Suits, 1998; Suits et al., submitted). It should be noted that in order for OX to significantly impact 34 S profiles, sulfide oxidation rates (HSOX Max or Z e-ox ) must be comparable in size to rates of reduction (Fig. 11a-d). Normal, negative KIEs during oxidation produce can produce curiously spiked 34 S profiles for H 2 S, but unless oxidation rates are quite substantial, they would tend to decrease 34 S both at the SWI and at depth. 34 S SWI values are much greater for KIE OX > than they are for KIE OX < ; however, as long as the absolute value 19

20 of KIE SR is greater than the absolute value of KIE OX, then the primary affect of sulfide oxidation is to produce more negative 34 S values regardless of the sign of KIE OX. In other words, increasing HSOX Max or Z e-ox causes 34 S of sulfide to be more depleted at the SWI and at depth, even if the isotope effect is negative. The effect of soaking up sulfide enriched during sulfate reduction with a 4 KIE is more important than the effect of adding sulfate depleted in 34 S relative to the reacting sulfide. In many sediments, zones of sulfate reduction and sulfide oxidation appear to be physically inseparable (Fossing and Jørgensen, 199a; Elsgaard and Jørgensen, 1992). In the water column of the Black Sea, however, the peak in the rate of sulfide oxidation is located above the peak in the rate of reduction (Fry et al., 1991; Jørgensen et al., 1991; Muramoto et al., 1991). We look a the impact of this physical set up by simply displacing sulfate reduction 5 cm below the SWI, while leaving the zone of sulfide oxidation where it is (Fig. 12a-b). Under these circumstances, inverse KIEs during sulfide oxidation could produce highly depleted 34 S values for pyrite formed in pycnocline of the water column. Normal, negative KIEs produce unrealistically heavy 34 S values for sulfide, which can even be enriched relative to seawater sulfate. This is not meant to directly simulate 34 S of the Black Sea water column. Mixing rates, depth intervals, and reaction rates would all have to be modified appropriately. It is only meant to show that the relative positions of sulfate reduction and sulfide oxidation could significantly affect 34 S profiles, and, in this case, produces highly depleted 34 S values near the top of the chemocline. KIE SR could vary with depth due to differences in chemical reactions, reaction rates and/or bacterial populations. We look at the impact of a variable KIE SR on 34 S profiles. Figure 13 shows the 34 S profile created by an SR which ranges from about 2

21 3 near the SWI to 6 at ~3 cm. 34 S values of H 2 S show a slight depletion just below the SWI; however, the largest value of 34 S H2S-SO4 is only about 4. Even a KIE SR of 6 at depth does not produce a significant depletion in 34 S of sulfide Isotopic fractionation during diffusion Isotopic fractionation can also occur due to the effects of diffusion. These arise not because of differences in diffusion coefficients of 32 S and 34 S, which, if present, are quite small, but because of differences in concentration gradients of isotopically substituted species (Jørgensen, 1979; Chanton et al., 1987b). The flux of sulfate is always into the sediment, while the flux of sulfide is always out. The proportion of 32 S and 34 S in these fluxes depends on the relative concentration gradients of the isotopically substituted species. 34 S of sulfate always increases with depth implying that the concentration gradient of 32 SO = 4 is greater than that of 34 SO = 4. Consequently, the isotopic ratio of the sulfate flux tends to deplete sulfate near the SWI in 34 S. In contrast, 34 S of dissolved sulfide can increase or decrease with sediment depth. If it increases, then the concentration gradient of H 34 2 S is less that of H 32 2 S and 34 S will tend to be more depleted in 34 S near the sediment-water interface. If 34 S of dissolved sulfide decreases with depth, 34 S of dissolved sulfide tend to be relatively enriched in 34 S near the sediment-water interface. Therefore, the net effect of molecular diffusion on isotopic fractionation is to reinforce the patterns that are already present. We test the impact of fractionation during diffusion by comparing the results of the model in which each isotopically-substituted species is tracked individually to one where diffusion coefficients are applied to bulk concentrations (Fig. 14). KIE SR = -4 and KIE OX =. At high rates of reduction, the difference in the concentration gradients 21

22 of the isotopically substituted species contributes less 5 to the fractionation at a depth of 1 m The impact of pyrite formation and iron reactivity and 34 S of H 2 S and pyrite? Under certain circumstances, the impact of pyrite formation on isotope ratios may also need to be considered. Shelf sediments of the Peru margin have sedimentation rates between.1 cm/year and 1 cm/year (Henrichs and Farrington, 1984; Kim and Burnett, 1988). Concentration of pyritic sulfur in surface sediment is ~.5 wt.% (Suits and Arthur, 2). Assuming a porosity of 9% and a sediment density of 2.7 g/cm 3, the accumulation rate of pyrite sulfur in the upper 1 cm is between.4 and 4 mmoles/l/year. Below the upper 1 cm of sediment, pyrite concentrations increase much more slowly, indicating rates of pyrite formation that are orders of magnitude less than at the surface. 4 mmoles/l/year is a significant sink for sulfide, which is produced in this same layer at a rate of approximately 5 mmoles/l/year (Fossing, 199). This sink is concentrated at the sediment-water interface, and declines rapidly with depth. Iron competes with bacteria for dissolved sulfide and will tend to deflate rates of oxidation. However, the effect is relatively small because the system readjusts and is largely controlled by sulfide limitations on oxidation rates and the diffusion rates of oxygen. As a result, concentration profiles of sulfide and sulfate are barely affected by pyrite accumulation (results not shown). Furthermore, 34 S SWI is also largely unaffected. In a simulation where KIE OX = +2, and 9% of dissolved sulfide at the SWI goes to formation of pyrite and there is no KIE associated with precipitation (KIE PYR =.), 34 S SWI is enriched by only.1 relative to one where there is no pyrite sink. The enrichment occurs because there is no KIE during pyrite precipitation, whereas during 22

23 oxidation there is. The enrichment is so small because the sulfide oxidation rate has adjusted to the presence of an additional sink. On the other hand, what happens if there is a KIE during formation of pyrite? Laboratory studies (Price and Shieh, 1979; Wilkin and Barnes, 1996) suggest that if there is isotope fractionation during pyrite precipitation, it is quite small (±1 ). However, we show here that if pyrite is a substantial sink for dissolved sulfide, even a 1 KIE can significantly affect 34 S SWI. Figure 15b shows profiles for the impact of a 1 KIE during pyrite precipitation on 34 S SWI, i.e. pyrite is depleted in 34 S relative to dissolved sulfide. In this simulation of the Oxygen Model, pyrite is a sink for sulfide that which assumes that 9% of dissolved sulfide at the SWI is consumed by pyrite formation, a 1 value for KIE SR can cause 34 S SWI to become enriched by nearly 7 relative to one in which there is no pyrite sink. The behavior approaches a Rayleigh distillation process because the reaction rates overwhelm the ability of molecular diffusion to erase their effects. This is largely because precipitation is concentrated at the SWI where it can have the largest impact. Consequently, in sediments with high rates of pyrite formation and/or low rates of sulfate reduction, a KIE during pyrite formation could theoretically alter sulfur isotope profiles. In order to use model results to interpret 34 S values of pyrite, it is important to consider the role that iron plays in pyrite formation. 34 S values of pyrite are depthintegrated values, and are muted expressions of the variability in 34 S profiles of dissolved sulfide. Sulfur isotope ratios of pyrite are a function of 34 S of dissolved sulfide at a particular depth, the mass of pyrite formed at that depth, and the sum of the mass-isotope ratio of pyrite formed in the sediment above. Mathematically it can be expressed as: 23

24 34 S z = ( i 34 S i m i ) / m z, (14) where 34 S z is the 34 S value of the mass of pyrite (m z ) at depth z, and 34 S i is the 34 S value of the mass of pyrite (m i ) formed at depth i. Pyrite formation is controlled by availability of dissolved sulfide and reactivity of detrital iron (Berner, 197, 1984; Canfield et al., 1992). It is thought to be a paleo-environmental indicator of bottom water oxygenation (Raiswell, et al., 1988). For a given concentration of dissolved sulfide, the most important factor controlling rates of pyrite formation is reactivity of the detrital iron. One measure of iron reactivity is degree of pyritization (DOP). DOP is a measure of the fraction of detrital iron potentially available for pyrite formation that is actually converted to pyrite. DOP = Pyrite iron / (Pyrite iron + HCl-soluble iron) (15) What is important is the reactivity of the iron and the nature of the 34 S profile (Fig. 16a-d). Sediments with highly reactive iron will tend to have pyrite with 34 S values similar to 34 S SWI, and therefore reflect the discrimination at the sediment surface, 34 S SWI. In sediments where 34 S is monotonically depleted with depth (16b), 34 S of pyrite will be depleted by a few per mil relative to 34 S of sulfide at the SWI, 34 S SWI. Sediments with more reactive iron, will tend to have pyrite that is more enriched than those with more slowly reacting iron phases. In sediments where 34 S is initially depleted, and then enriched with depth (16c), 34 S of pyrite at depth will be about the same as 34 S SWI. Sediments with more reactive iron, will tend to have pyrite that is more depleted than those with more slowly reacting iron phases. In sediments where 34 S is enriched with depth (16d), 34 S of pyrite at depth will be enriched by a few per mil relative to 34 S SWI. Sediments with more reactive iron, will tend to have pyrite that is 24

25 more depleted than those with more slowly reacting iron phases. The important factor is not DOP per se, but how rapidly pyrite forms. In any case, sulfur isotope ratios of pyrite vary much less than those of H 2 S, and in the three cases shown, 34 S of pyrite is equal to 34 S SWI ±4. Furthermore, the difference between 34 S values of pyrite in sediments where oxidation is important (Fig. 15b) and one in which it is not (15d) is at most about 7. The difference is higher (~11 ), if enhanced oxidation is included (Fig.15c). 3.3 Comparison of model results and natural environments S SWI in the model and in sediments In modern sediments, 34 S SWI is inversely proportional to the log of the rate of reduction (Goldhaber and Kaplan, 1975). 34 S of dissolved sulfide at the SWI are most depleted in 34 S (~ -7 ) at very low rates of sulfate reduction (~.3 mmol/l/year). Although results from the Nitrate model simulations are consistent with this trend, the slope of the relationship can only be matched if increases in sulfate reduction rates are matched by increases in rates of sulfide oxidation (Fig. 16a). In the absence of oxidation, 34 S SWI increases much too rapidly. Of course, to some extent it is trivial to point out that sulfide oxidation rates increase with increasing rates of sulfate reduction, since any H 2 S that does not contribute to formation of sedimentary sulfur, primarily pyrite, will necessary be oxidized either in the sediment or the water column. Iron inputs usually are not sufficient to capture a significant fraction of dissolved sulfide in organic-carbon rich environments with high rates of reduction. Consequently, rates of reduction and oxidation are necessarily coupled, and oxidation will play a role in determining 34 S of pore water sulfide. We get the same general result in the Oxygen model, where increases in rates of reduction are accompanied by a decrease in 34 S SWI (Fig. 5). 25

26 In modern sediments, an increase in the percentage of sulfide oxidized--the difference between sulfide produced and pyrite accumulated--is accompanied by an increase in 34 S (Canfield and Teske, 1996). In the Nitrate model, this trend is also observed (Fig. 16b), but only when two conditions are met. First, rates of oxidation must be comparable to rates of reduction. If rates of sulfide oxidation are much less than rates of sulfate reduction, then oxidation will have little influence on 34 S. Second, it appears that an OX at least +1 to +2 is required in order to match observations in modern sediments. Of course, this assumes that default rate parameters are appropriate for the set of observations in figure 16b. Unfortunately, each sediment would have to be simulated individually to determine the appropriate value for OX. The model does, however, suggest that OX is important in controlling net sulfur isotope fractionation. One important observation is that sulfide oxidation depletes 34 S of H 2 S as long as OX SR. In other words, while an inverse isotope effect during oxidation always causes 34 S SWI to increase regardless of the rate of oxidation, a normal kinetic isotope effect during oxidation will increase 34 S SWI only if OX is less negative than SR. For example, if both OX and SR are -4, then increases in rates of oxidation will cause 34 S SWI to approach zero. We do not get the same result in the Oxygen model, where percentage of oxidation increases with rates of reduction, but 34 S SWI goes down Can 34 S profiles Baltic Sea and Peru Margin sediments be explained by OX? In KC 86 changes in 34 S of pyrite, acid-volatile sulfide (AVS) and dissolved sulfide with depth are relatively gradual and monotonic. The H 2 S profile in KC 86 can be approximated by something similar to that in figure 6, with SR ~ -35 and OX ~ +25. This is an oxygen model run, but it can still be used to simulate this core, even 26

27 though it is from sediments with a bacterial mat and overlain by an anoxic water column. That is because the main difference between the Oxygen and Nitrate models is that oxidation rates in the former are limited by the diffusional flux of oxygen. In contrast, sulfide oxidation rates in the nitrate model are largely unconstrained on the low end, and therefore can be mimic those of the oxygen model. Unfortunately this does not mean that we now know the appropriate rates and KIEs for the sediments of KC 86. What we do know is the approximate magnitude of the net isoflux, which is the balance between sulfate reduction and sulfide oxidation fluxes multiplied by their respective isotope effects. We would need more constraints on either the KIEs or the reaction rates in order to specify all values. The profile does show, however, that 1) rates of oxidation are substantial, and 2) that OX is a probably quite large. Otherwise, it would be impossible to maintain such large isotope gradients in the pore water and sediment. The 34 S profiles in 2a are more difficult to match. 34 S values of sedimentary sulfur in cores taken from the Baltic Sea and the Peru Margin range from 17 to 27 near the SWI (Fig. 2a). They become 5 to 1 more depleted over the next few centimeters. 34 S values in core 3362 from the Baltic rebound to heavier values by 1 cm, but 34 S values in most cores remain at their depleted values. There is no single simulation here (see figures 6, 11a and c, and 13) that captures that pattern exactly, though some are close. Furthermore, these are 34 S values of pyrite, not dissolved sulfide, which makes the problem even more difficult. The rapid drop in 34 S values recorded in nearly all of the profiles suggests very high rates of oxidation with a positive OX +2. Furthermore, the oxidation is concentrated in the top 5 cm of the sediment. It would be difficult to sustain such high oxidation rates with a diffusive flux of oxygen alone, but use of nitrate is generally thought to occur primarily under rather specific 27