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

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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
Oxygen isotope biogeochemistry of pore water sulfate... 4227sulfate reducing bacteriasulfate reduction {f } • δ 18 O SO4 porewaterSulfate inporewaterδ 18 O SO4 cytoplasm {δ Out }=δ 18 O SO4 porewater {δ In } • (1-k) +k•(δ H 2 O + ε)exchange flux {b} • δ 18 O SO4 porewaterexchange flux {b} • δ 18 O SO4 cytoplasmFig. 6. The principal fluxes involved in oxygen isotope exchange reactions between sulfate and water. Note that our model makes noassumption whether the exchange reactions happen cell-internal or cell-external.2of SO 4is not changed by the exchange reaction, we havethe additional constraint that the sum of the fluxes of 18 Oand 16 O cannot add any new sulfate, i.e., they must cancelbðS 16 O 4 ÞþbðS 18 O 4 Þ0ð11Þwhere b denotes the exchange velocity. Thus the isotopiccomposition of the output flux becomes simply a functionof the isotope equilibrium value and we can write it as acombination of the input and output flux asbðS 16 ½S 16 O 4 Š1O 4 Þ¼b þð12Þ½SO 4 Š 1 þðd out =1000 þ 1ÞR 0bðS 18 ½S 18 O 4 ŠO 4 Þ¼b þ ðd out=1000 þ 1ÞR 0ð13Þ½SO 4 Š 1 þðd out =1000 þ 1ÞR 0where R 0 refers to the isotopic ratio of V-SMOW, andd out ¼ d in ð1 kÞþkðd H2 O þ Þ ð14Þand d H2 O denotes the oxygen isotopic composition of thepore-water H 2 O. The reaction transport model to describethe oxygen isotope exchange for 16 O is then a combinationof Eqs. (6, 10 and 11)u o½S16 O 4 Šot¼u o½S16 O 4 Š oDozux o½S16 O 4 Šozand similarly for [S 18 O 4 ].oz þ ½S 16 O 4 ŠuDo2 oz 22.4. Modeling cell external oxidationþ D ou o½S 16 O 4 Šoz ozuf ðS 16 O 4 ÞþubðS 16 O 4 Þð15ÞCell external oxidation of H 2 S can be achieved througha solid oxidant like ferric oxihydroxide. As bioturbationwill only affect the benthic boundary layer, we can treatour oxidant as a solid, and writeoðð1uÞ½X s ŠÞot¼ oðð1 uÞx s½X s ŠÞozð1 uÞf n ð16Þwhere X s denotes a solid oxidant, f the gross flux of SO 4 2 ,x s the sedimentation rate, and n the molar ratio of the oxidationreaction.3. RESULTS AND DISCUSSIONUnder steady state conditions with no lateral changes ofboundary conditions, results of a 1-D model must equal theresults of a 2-D model. However, if lateral changes (e.g., ofsulfate concentration or biological activity) do occur, 1-Dmodels may somewhat overestimate sulfate reduction rates.At present, the hydrogeology of ODP-Site 1130 is not sufficientlyconstrained to allow for a detailed 2-D model.However, we can set up a 2-D model which is sufficientlysimilar (i.e., it uses the same spatial scales and similar fluidvelocities as observed at ODP Site 1130) to investigate thepotential error introduced by the 1-D assumptions. Tocompare the results of the two models, we plot a 1-D crosssection of the 2-D model, against the results of a 1-D modelusing the same parameters as the 2-D model. Fig. 7 showthat the main differences between the two approaches are2found in the resulting concentration of SO 4and H 2 S.(Fig. 7). This implies that the 1-D model overestimatesthe volumetric sulfate reduction rate compared to the 2-Dmodel. However, the isotopic composition remains thesame. We therefore conclude that the total fluxes computedby our model may contain a certain error, but that the ratioof the fluxes should be accurate.The d 18 O SO4 2 data from ODP Site 1130 show a distinctiveincrease up to a maximum of 28.6‰ at 27.5 mbsf, andsubsequently decrease to 11.6‰ at 300 mbsf (Fig. 8). Thereturn to values close to the seawater sulfate isotope compositionis mostly a function of the upwelling brine supplyingsulfate with a d 18 O SO4 2 11&. We will first explorewhether this d 18 O SO4 2 signal can be explained with a kineticisotope effect alone. The suggested ratio between thefractionation factors for O and S vary from 1:1.4 to 1:4
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