Oxygen isotope biogeochemistry of pore water sulfate in the deep ...

4226 U.G. Wortmann et al. / Geochimica et Cosmochimica Acta 71 (2007) 4221–4232gravimetrically (Böttcher et al., 2004). Pyrite-iron contentswere calculated from TRIS contents using the ideal stoichiometryof pyrite. Iron, leachable with buffered Na-dithionitesolution (Canfield, 1989) was also measured on twosamples (1130A-7-H3 and 1130A-21X-3) yielding 0.05 and0.04 dry wt%, respectively.2.1. Reaction transport model formulationThe distribution of dissolved interstitial water species affectedby diagenetic or biologically mediated conversionprocesses can be described as a process which involvestransport by diffusion, transport by advection, and a consumptionor production function (Berner, 1964, 1980;Boudreau and Westrich, 1984; Boudreau, 1996). The standarddiagenetic equation (Berner, 1980) for a dissolved speciesdescribes the change of concentration with depth andtime as a function of diffusion, advection, porosity, andconsumption or production:oðuCÞot ¼zhoðuCÞo D B ozþ uðD i þ DÞ oCozozioðuxCÞozwhere: C is the concentration, D are diffusion coefficients todescribe diffusion due to bioturbation (D B ), diffusion due toirrigation (D i ) , and the molecular diffusion term D. Thesymbol u stands for the porosity, the advection velocity isdenoted x, time is expressed as t, and the reaction or productionfunction is termed f.In the following, we will assume that there is no bioturbation,no diffusive irrigation, and that porosity changesdowncore only as a result of compaction (for a more detaileddiscussion see, Berner, 1980; Wortmann, 2006; Chernyavskyand Wortmann, 2007). Thus we can simplify Eq.(5) and writeu oCot ¼ u oC oDoz oz þ uD o2 Coz þ D ou oC2 oz ozux oCozThese equations can now be used for inverse modelingto quantify the advection velocity, and the net volumetricSRR (f) as a function of depth (see e.g., Berg et al.,1998). The diffusion coefficient used for SO 42is computedas a function of shipboard measured temperature andporosity using the parameters given by Boudreau (1996).The reduction function describing the sulfate reduction isalmost identical to the one given by Wortmann (2006),but unlike the model used by Wortmann (2006) and Wortmannet al. (2001), here we include two major sedimentationevents in the upper 15 mbsf (Hine et al., 2002). Thesedimentation event was modeled as a depositional eventof 5.72 m of sediment within 200 years 10 ky ago, and a secondevent, depositing 9.36 m of sediment within 300 yearsabout 200 years ago. These changes increase the estimatedupwelling velocity twofold to 1.2 · 10 10 m/s, and allow usto successfully model the chemical profiles in the upper30 mbsf, which was not possible previously (see e.g., Wortmannet al., 2001; Wortmann, 2006). All modeling wasdone with REMAP (Chernyavsky and Wortmann, 2007)which was modified to include a module to calculate isotopeexchange reactions.ufufð5Þð6Þ2.2. Modeling the kinetic oxygen isotope effects in sulfateIn order to model kinetic oxygen isotope effects in sulfatewe assume that this effect is proportional to the volumetricnet reduction rate f. We thus express the isotopeeffect similar to the approach of Jørgensen (1979), and writef ðS 16 O 4 Þ¼a½S 16 O 4 Š½SO 4 Šþða 1Þ½S 16 O 4 Š f ð7Þf ðS 18 ½S 18 O 4 ŠO 4 Þ¼a½SO 4 Š ða 1Þ½S 18 O 4 Š f ð8Þwhere values in square brackets denote concentrations.Note, that S 18 O is merely a notation to describe the concentrationof 18 O in a sulfate molecule but in no way impliesthe existence of a molecule with 4 18 O isotopes (whichwould be extremely rare under natural conditions). CombiningEqs. (5) and (7), we obtainu o½S16 O 4 Šot¼u o½S16 O 4 Š oDozux o½S16 O 4 Šozoz þ ½S 16 O 4 ŠuDo2 þ D ou o½S 16 O 4 Šoz 2 oz oza½S 16 O 4 Šu½SO 4 Šþða 1Þ½S 16 O 4 Š f ð9Þand similarly for 18 O. This allows us to describe the evolutionof the d 18 O SO4 2 values as a function of depth, a and f.2.3. Modeling the oxygen isotope exchange between waterand sulfateIn the following section, we do not distinguish whetherexchange reactions occur within the cell or outside the cell.We furthermore assume that there is no kinetic oxygen isotopefractionation during microbial sulfate reduction, i.e.,that the d 18 O SO4 2 value depends only on the exchange reactionbetween water and SO 2 4.As equilibration reactions require zero net flow, we candescribe the oxygen isotope effect of the exchange reactionon the pore-water sulfate pool in terms of a closed loop.There, dissolved sulfate leaves the pore-water pool and entersa box where its oxygen isotope signature is modified bythe exchange reaction, and afterwards returns back into thepore-water sulfate pool (Fig. 6). As before, we will only describethe volumetric exchange rates. Thus, the evolution ofthe isotopic composition of the pore-water sulfate reservoircan be described in terms of the volumetric exchange flux b,the isotopic enrichment during the exchange process and afactor k describing the extent of the exchange reaction.Since we assume that dissimilatory sulfate reduction hasno effect on the d 18 O SO4 2 value, the flux of 16 O and 18 Oisproportional to the initial ratio of the given isotope to thetotal sulfate amountf ðS 16 O 4 Þ¼f ½S16 O 4 Šð10Þ½SO 4 Šand similarly for f( 18 O).We assume that there is no isotope effect on thed 18 O SO4 2 composition for the flux associated with the exchangereaction and we can write this flux as being proportionalto the initial ratio of the given isotope to the totalsulfate amount as in Eq. (10). Since the total concentration