(2007) 256–271www.elsevier.com/locate/marchem

Marine Chemistry 106

The use of flow-through sediment reactors in biogeochemicalkinetics: Methodology and examples of applications

C. Pallud a,⁎, C. Meile b, A.M. Laverman a, J. Abell a,1, P. Van Cappellen a

a Department of Earth Sciences-Geochemistry, Utrecht University, P.O. Box 80021, 3508 TA Utrecht, The Netherlandsb Department of Marine Sciences, University of Georgia, Athens, GA 30602-3636, USA

Received 2 February 2006; received in revised form 31 October 2006; accepted 12 December 2006Available online 20 December 2006

Abstract

Flow-through reactors (FTR) provide a means to measure reaction rates on undisturbed sediment slices. Because in thisapproach the porous structure and the spatial arrangements of particle-bound constituents, including microorganisms, arepreserved, kinetic parameters are obtained whose values are representative of the initial in situ conditions. The theory andapplications of FTRs are reviewed here using data on sulfate and nitrate reduction in a number of nearshore sediments. Inparticular, we focus on the determination of maximum potential reduction rates (Rmax) and half-saturation constants (Km) of theterminal electron acceptors. Alternative methods for extracting these kinetic parameters from time-series outflow concentrationmeasurements are compared. To deal with the uncertainties associated with temporal and spatial variations in solute concentrationswithin the FTR, a novel method is presented, based on a continuous reactive transport model representation of the FTR system.Potential biases related to the loss of dissolved organic substrates via the outflow are addressed by analyzing the results of variableflow nitrate reduction experiments. For sediment intervals on which both nitrate and sulfate reduction rates have been measured,Rmax values (in units of C equivalents) are systematically higher for nitrate reduction. In addition, the relative difference in Rmax

between the two terminal electron accepting processes increases with decreasing mineralization rates.© 2007 Elsevier B.V. All rights reserved.

Keywords: Biogeochemical kinetics; Estuarine sediment; Flow-through reactor; Nitrate reduction; Reactive transport modelling; Sulfate reduction

1. Introduction

The cycling of carbon, nutrients, metals andpollutants in aquatic sediments is inherently linked tothe activity and functional capabilities of the residentmicrobial communities. A major task in sediment

⁎ Corresponding author. Present address: Department of Geologicaland Environmental Sciences, Stanford University, Stanford, CA94305-2115, USA. Tel.: +1 650 724 3220; fax: +1 650 725 2199.

E-mail address: cpallud@stanford.edu (C. Pallud).1 Present address: Department of Chemistry, Humboldt State

University, Arcata, California 95521-8299, USA.

0304-4203/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.marchem.2006.12.011

biogeochemistry therefore involves the developmentof robust kinetic expressions for microbially-drivenreaction processes to be included in early diageneticmodels (Regnier et al., 2005). Equally important is thedevelopment of experimental approaches that can beused to calibrate and validate the proposed rateequations. Laboratory experiments with simplifiedmodel systems (e.g., experiments with pure cultures,single mineral phases or otherwise well-defined com-positions) are most likely to yield results that can beinterpreted within the framework of established theoriesof chemical and biochemical kinetics and, hence, beused to derive predictive rate models (Ingvorsen and

257C. Pallud et al. / Marine Chemistry 106 (2007) 256–271

Jørgensen, 1984; Chou and Wollast, 1984; Sonne-Hansen et al., 1999; Bonneville et al., 2004; and manymore). These model systems, however, rarely capturethe complexity of natural reaction systems, andextrapolation of the rate equations and kinetic para-meters to field conditions is fraught with difficulties(Maher et al., 2006).

Process rates in sediments can also be determineddirectly. The most commonly used approaches includewhole-core incubations (Boudreau and Westrich, 1984;Jørgensen, 1977; Smith and Klug, 1981; Joye et al.,1996; Garcia-Ruiz et al., 1998), isotopic techniques(Jørgensen, 1978; Thode-Andersen and Jørgensen,1989; Li et al., 1996; Hurtgen et al., 1999; Gribsholtand Kristensen, 2003) and, more recently, microprofil-ing (Christensen et al., 1989; Stief et al., 2003; Altmannet al., 2003) and inverse modeling (Berg et al., 1998;Meile et al., 2001). With these approaches it is possibleto determine benthic fluxes, turnover rates and in situdepth distributions of reaction rates. In general, how-ever, these experimental approaches are not designed toverify or calibrate predictive rate equations.

Alternatively, one may perform kinetic experimentsdirectly with the natural sediment and its residentmicrobial community. Systematically varying theexperimental conditions and monitoring the accompa-nying changes in transformation rates should then, inprinciple, yield phenomenological rate equations for insitu geomicrobial reaction processes. A widely usedapproach is to incubate homogenized sediment slurriesand to record the response of initial reaction rates to, forinstance, changes in temperature, solid-solution ratios,and additions of substrates or inhibitors (Oremland etal., 1984; Bak and Pfennig, 1991; Koretsky et al., 2003;Roychoudhury, 2004). Sediment slurries, however,severely disrupt the physical, chemical and microbialstructure of the sediments, thereby introducing artifactsthat may significantly modify the reaction kinetics. Inparticular, slurries tend to enhance rates of microbially-mediated processes, by removing transport limitationson the supply of reactants to the cells (Marxsen andFiebig, 1993; Meile and Tuncay, 2005; Pallud and VanCappellen, 2006).

A limited number of approaches have been proposedto perform kinetic experiments on undisturbed sedi-ment, including sediment plug diffusion and flow-through reactors (Aller and Mackin, 1989; Roychoudh-ury et al., 1998). Particularly the latter approach isincreasingly being used to determine the reactionkinetics of a variety of microbial processes in intactsediments (Roychoudhury et al., 1998, 2003; Canfield,2001; Brüchert and Arnosti, 2003; Weston and Joye,

2005; Laverman et al., 2006; Pallud and VanCappellen, 2006). In a flow-through reactor (FTR)experiment, an input solution containing a knownconcentration of a soluble substrate is supplied to thereactor containing a water-saturated sediment slice. Theflow rate is kept constant and the concentrations of thesubstrate and dissolved metabolic products are mon-itored in the reactor outflow. Together with the knownflow rate, the concentration data then allow one tocalculate (quasi) steady-state reaction rates, once thecomposition of the outflow no longer changes sig-nificantly with time.

The FTR approach provides a seemingly simplemeans of determining reaction rates and obtaining rateexpressions and kinetic parameters under near in situconditions. An especially important advantage of theFTR approach is that it preserves the pore structureand the spatial distributions of particle-bound consti-tuents, including microorganisms. Given the growingutilization of FTRs in sediment biogeochemistry, it istimely to review the underlying theory of the approachand to identify possible biases in the interpretation ofreactor outflow concentration time series. The mainmotivation is to design a set of best practices forextracting meaningful kinetic information from FTRexperiments.

To illustrate the use of the FTRs, kinetic data onsulfate and nitrate reduction coupled to organic matteroxidation in nearshore sediments are presented. Therates of both processes are dependent on the concentra-tions of the respective terminal electron acceptor, sulfateor nitrate. This raises the issue of how to deal with thetemporal and spatial variations of solute concentrationsinside the FTR. The usual approximate approach basedon the assumption of linear longitudinal gradients forthe reactive solutes is therefore compared to the resultsof a continuous model explicitly coupling reaction andtransport in the FTR. With this reactive transport modelit also becomes possible to utilize the entire break-through curves of reactive solutes, including the non-steady-state outflow concentrations recorded after achange in inflow conditions.

In the FTR experiments presented here, the electrondonors are supplied internally from the organic matter ofthe sediment, in contrast to the terminal electronacceptor, which is supplied externally via the inflowsolution. Potentially, this causes a flow-dependent lossof dissolved organic compounds that serve as directelectron donor substrates. The possibility of flow-relatedbiases in the estimation of microbial reaction rates isaddressed using the results of a series of variable flownitrate reduction experiments.

258 C. Pallud et al. / Marine Chemistry 106 (2007) 256–271

2. Flow-through sediment reactors: methodology

2.1. Experimental design

The reactors used in this study consist of a sliceof sediment enclosed by a Plexiglas® ring of 1 or2 cm length (L) and 4.7 cm inside diameter, with a0.2 μm pore size nitrocellulose filter and a glassfiber backing filter covering the sediment surface ateach end (Fig. 1a). The reactor cell is closed by twoPlexiglas® caps kept in place using steel plates tight-ened with screws, while O-rings prevent leakage. Input/

Fig. 1. a) Side view of a flow-through reactor with a detailed top view of a caFTR experiments using the shuttle corer (see text for further discussion).

output channels open at the center of the caps, whileradial grooves distribute the input solution in order topromote a uniform flow through the cross section of thesediment slice.

Temperature is controlled by placing the reactorsdirectly in a thermostated water bath, or in waterjackets connected to a water bath. The results shownhere were all obtained at 21 °C. An input solution,supplied to the reactors at an imposed constant flowrate by a peristaltic pump, contains the reactivesolute (in the present case, SO4

2− or NO3−) and a flow

tracer (Br−). The reactor outflow is collected

p. b) Sequential steps in the retrieval of undisturbed sediment slices for

259C. Pallud et al. / Marine Chemistry 106 (2007) 256–271

regularly using a fraction collector. The inputsolutions used in the present study were flushedcontinuously with argon to make them anaerobic,and salinity was adjusted to that measured in thefield, using NaCl, if necessary.

A specially designed hand-pushed shuttle corer,whose liner consists of a continuous stacking of reactorcells (Fig. 1b), is used to collect undisturbed sedimentslices for the FTR experiments. Intertidal and shallowwater sediments can be cored directly, whereas fordeeper sediments box cores are subsampled with theshuttle corer. By gently inserting the corer in thesediment, the reactor cells are filled with undisturbedsediment. After core retrieval, the frontal plate isremoved, and the reactor cells are separated and sealedusing the filters and caps (Fig. 1b). Each reactor cellthen contains a sediment slice corresponding to a givendepth interval. For the FTR experiments presented here,the reactors were stored at 4 °C under anaerobicconditions for a few hours until the flow-throughexperiments were started.

2.2. Steady-state rate determinations

In a typical FTR experiment, constant inputcomposition and flow rate are maintained until thecomposition of the fluid exiting the reactor no longerchanges significantly with time. The flow rate or inputsolution composition can then be modified, forcing theoutflow composition to adjust to a new steady-state. Foreach set of steady-state conditions, the rate ofconsumption or production of a solute species inte-grated over the whole length of the FTR can becalculated as:

R ¼ ðC0−CoutÞQV

ð1Þ

where C0 is the imposed input concentration, Cout is thesteady-state concentration of the solute measured in theoutflow, Q is the volumetric flow rate and V is thevolume of the sediment slice in the reactor.

As shown by Eq. (1), for a given reactor size, ratedeterminations in FTR experiments depend on theimposed flow rate and the input concentration. Valuesof Q and C0 should be adjusted so that theconcentration difference (C0−Cout) is sufficientlylarge to be easily detected. For a reactant solute thiscan, in principle, always be achieved by decreasing C0

or Q, or both. However, if the input concentration of areactant solute is too low or the water residence time

(τ=V/Q=L/ν; where ν is the pore water velocity) toohigh, then complete consumption of the reactantoccurs. In that case the sediment volume over whichreaction is taking place is no longer constrained andonly a lower limit of the volume-normalized rate canbe obtained.

2.3. Data analysis: flow regime

Eq. (1) allows one to calculate net reaction rates in-tegrated over the entire sediment volume in the FTR. Inorder to use these net rate determinations to develop rateequations, it is necessary to make some assumptions as tohow the biogeochemical conditions are distributedspatially within the reactor. In particular, for the processesconsidered here one of the goals is to relate reaction ratesto the concentrations of the dissolved terminal electronacceptor. The operational assumption used in the deriva-tion of kinetic parameters is that the concentrations of porewater solutes are radially homogeneous in the FTR. Thisrequires that flow through the sediment slice also beradially homogeneous. The breakthrough curves of theunreactive flow tracer, Br−, are used both to check thevalidity of the one-dimensional flow assumption, and toderive the longitudinal pore water velocities and apparentdispersion coefficients.

One-dimensional unreactive solute transport througha homogeneous porous medium during steady-stateflow is described by:

ACAt

¼ DA2CAx2

� �−m

ACAx

; ð2Þ

where C is the tracer concentration in the liquid phase(mol cm−3), t is time (s), x is distance (cm), D is thedispersion coefficient (cm2 s−1) and ν is the pore watervelocity (cm s−1). Among the possible boundaryconditions for a finite sediment column, we select forthe inlet the flux continuity condition:

−DACAx

þ mC

� �x¼0

¼ mC0 ð3Þ

where C0 is the constant concentration of the tracer inthe input solution, and for the outlet (at x=L) acontinuous solute concentration:

ACAx

jx¼L ¼ 0; ð4Þ

The reader is referred to van Genuchten and Parker(1984), Schwartz et al. (1999), Peters and Smith

260 C. Pallud et al. / Marine Chemistry 106 (2007) 256–271

(2001) for the derivation and detailed discussion ofmass conservation in porous media, and the choice ofboundary conditions.

For a porous media initially free of tracer (C(x, t=0)=0), an analytical series solution to Eqs. (2), (3), and (4)exists (Brenner, 1962; van Genuchten and Parker, 1984;Schwartz et al., 1999). Computational programs forevaluating the so-called Brenner's series solution areavailable (van Genuchten and Alves, 1984). Forsufficiently high column Peclet numbers (Pe= νL/Dmol), van Genuchten and Parker (1984) suggest thefollowing equation to calculate effluent concentrations:

Cout

C0¼ 1

2erfc

L−mt2

ffiffiffiffiffiDt

p� �

þ expLmD

� �erfc

Lþ mt

2ffiffiffiffiffiDt

p� �� �

ð5Þwhere Cout is the concentration in the fluid exiting thereactor and Dmol is the molecular diffusion coefficient ofthe tracer in free solution.

The transport parameters D and ν can be obtainedthrough moment analysis, using inert tracer breakthroughcurves (here the bromide outflow concentration as a func-tion of time). The normalized moments are defined by:

Nn ¼Z l

0tnACout

Atdt=

Z l

0

ACout

Atdt ð6Þ

The first normalized moment (N1=τ) indicates themovement of the center of mass of the tracer, while thesecond (N2) measures the spreading around the center ofmass.

For a step input change, that is, when the inflowconcentration changes instantaneously from zero to afinite value C0 at t=0, the pore water velocity ν anddispersion coefficient D can be evaluated from timemoments using complementary concentrations (Ĉ=1−C/C0; Leij and Dane, 1991) or, alternatively, as (Yuet al., 1999; Leij and Dane, 2001):

m ¼ Ls¼ LR 1

0 t dCout

ð7Þ

and

D ¼ LmRl0 ðt−sÞ2 ACout

At dt

2s2¼ m3

R 10 ðt−sÞ2dCout

2Lð8Þ

2.4. Data analysis: reaction kinetics

The determination of kinetic parameters will beillustrated using FTR data on nitrate and sulfate

reduction by resident microbial communities in estuar-ine marsh sediments. The terminal electron acceptors,nitrate and sulfate, are supplied via the inflow. Oncesteady-state conditions are reached, rates of nitrate orsulfate reduction can be calculated with Eq. (1). Thesimplest way to relate the steady-state rates obtainedwith Eq. (1) to the concentration of the dissolvedterminal electron acceptor is to estimate the averageconcentration of the latter in the reactor. This requiresknowledge of the concentration gradient across theFTR. Especially when the drop in concentrationbetween the inflow and outflow solutions is not toolarge, a linear gradient may be assumed and the averagesolute concentration approximated as (Cout+C0) /2. Therates and their corresponding concentrations can then befitted to a rate equation. Here the well-knownMichaelis–Menten expression is used (derived fromMichaelis and Menten, 1913):

R ¼ REAmaxC

KEAm þ C

ð9Þ

where R is the rate of nitrate or sulfate reduction, RmaxEA is

the maximum reaction rate, KmEA is the half-saturation

concentration of the terminal electron acceptor, and C isthe estimated average (steady-state) concentration ofnitrate or sulfate inside the reactor. A number ofdifferent techniques for fitting rate data to Eq. (9) arecompared in Section 4.2.

There are a number of potential pitfalls to the aboveapproach. The first one is that the actual longitudinalgradient of the reactant may not be linear and the systemnot at steady-state. The second one is that, strictlyspeaking, the integrated rate equals the rate correspond-ing to the average solute concentration in the reactoronly for a linear dependence of the rate on the soluteconcentration. Eq. (9), for instance, does not fulfill thiscondition. As an alternative approach, the coupledtransport and consumption of the terminal electronacceptor in the reactor can be computed explicitly, usinga one-dimensional advection–dispersion-reactionmodel. If the consumption rate follows Eq. (9), thenthe corresponding mass conservation equation is

ACAt

¼ DA2CAx2

−mACAx

−REAmaxC

KEAm þ C

ð10Þ

where the concentration of the terminal electronacceptor in the reactor, C, can vary as a function oftime and longitudinal distance in the reactor.

Eq. (10), together with boundary conditions (3)and (4), is solved using a standard finite difference

261C. Pallud et al. / Marine Chemistry 106 (2007) 256–271

scheme, where the grid Peclet number (νΔx/D)dictates the use of a central versus upwind approx-imation of the spatial derivatives (Fiadeiro andVeronis, 1977; Boudreau, 1997). At high grid Pecletnumbers, other, more accurate, stable schemes mightbe necessary to avoid numerical artifacts (e.g. Ewingand Wang, 2001). The reactive transport model(RTM) can then be fitted to the breakthrough curvesof the terminal electron acceptor, using the kineticparameters, Rmax

EA and KmEA, as adjustable parameters.

With this approach there is no longer a need to makeassumptions about the internal gradient of the solute.Furthermore, it is possible to use the entire outflowconcentration data set, including the non-steady-stateportions of the breakthrough curves, to derive thekinetic parameters.

For a particular sediment slice and a given tempera-ture, the parameters Rmax

EA and KmEA in Eq. (10) are

treated as constants. That is, only changes in theterminal electron acceptor concentration are responsiblefor changes in the sulfate or nitrate reduction rate. Thisassumption can be tested by imposing a series ofdifferent inflow concentrations of nitrate or sulfate, orby changing the flow rate, and then assessing whether aunique set of Rmax

EA and KmEA values explains the entire set

of breakthrough curves.In the variable flow nitrate reduction experiments

(Sections 3.3 and 4.4), the concentrations of dissolvedorganic carbon (DOC) and dissolved inorganic carbon(DIC) were monitored in the outflow. The DOC isassumed to be produced by extracellular hydrolysis ofsedimentary organic matter, and to represent thesoluble electron donors that are utilized for microbialrespiration. The corresponding mass conservationequation for DOC thus includes rate terms forproduction and consumption. Further assuming thatthe uptake of DOC substrates by the terminal electronaccepting organisms follows Michaelis–Mentenkinetics, the concentration of DOC in the reactor isgiven by:

ACAt

¼ DA2CAx2

−mACAx

−RCmaxC

KCm þ C

þ RCProd ð11Þ

where C is the DOC concentration, RmaxC the

maximum uptake rate of DOC and KmC the correspond-

ing DOC half-saturation constant. If the rate ofproduction of DOC from sedimentary organic matter,RProdC , can be independently constrained (Section 3.3),

fitting of the RTM model to the outflow DOC datathen yields the kinetic parameters Rmax

C and KmC.

3. Applications

3.1. Sediment sampling

Intertidal marsh sediments were sampled at threelocations of contrasting salinities. Two sites are in theScheldt Estuary (Belgium and The Netherlands): Appelsis located in the upper freshwater portion of the estuary,Waarde is in the brackish section of the lower estuary.The third site, Rattekaai, is a saltmarsh in the EasternScheldt (The Netherlands). Full site descriptions can befound in Hyacinthe and Van Cappellen (2004), Palludand Van Cappellen (2006). Subtidal sediments were alsocollected in a coastal freshwater lake, the Haringvliet(The Netherlands), at a water depth of approximately10 m using a cylindrical box corer, which was imme-diately subsampled on board with the shuttle corer(Section 2.1). Information on the Haringvliet site can befound in Canavan et al. (2006). The sampling times andspecific depth intervals used in the FTR experiments arelisted in Table 1. The table also summarizes the con-ditions of the various series of experiments detailed inthe following sections.

3.2. Sulfate and nitrate reduction kinetics

The techniques for extracting kinetic parametersfrom FTR experiments are applied to sulfate reductionrate data corresponding to the 0–2 cm depth interval atRattekaai (March 2003) and the 4–6 cm depth interval atAppels (July 2003). These particular sediments wereselected because they represent contrasting levels ofpotential sulfate reducing activity: the surface saltmarshsediment at Rattekaai exhibits high rates of sulfatereduction, whereas the deeper sediment of the fresh-water Appels site exhibits much lower rates (Pallud andVan Cappellen, 2006). The outflow collection tubeswere pre-filled with 2 mL of sulfide trap solution (1%zinc acetate). Four increasing input SO4

2− concentrations(ranging from 0.25 to 2 mM) were supplied sequentiallyat a flow rate of 1.4±0.15 cm3 h−1, while Br− concen-tration was kept constant at 2 mM.

In order to compare maximum potential reactionrates of nitrate and sulfate reduction, FTR experimentswere run with the upper 0–2 cm sediments from the foursampling sites (Table 1). For the sulfate reductionexperiments, four to five increasing input SO4

2−

concentrations (ranging from 0.125 to 4 mM) weresupplied sequentially at a flow rate of 1.4±0.15 or 4.0±0.20 cm3 h−1, while Br− concentration was keptconstant at 2 mM. For the nitrate reduction experiments,parallel reactors were run with different input NO3

−

Table 1Overview of the flow-through reactor experiments used in the present study

Experiments Site Depth intervals(cm)

Samplingtime

Flow rate(ml h−1)

Input [Br−](mM)

Input [SO42−]

(mM)Input [NO3

−](mM)

Results

Flow regime Appels 0–1 August 04 0.65, 1.5, 3,6, 12

1.5, 3 – – Fig. 3

Appels 0–2, 2–4,4–6, 6–8

May 02,July 03,April 03

0.67, 1.4, 4, 8 2 – – Figs. 2, 3

Waarde 0–2, 2–4,4–6, 6–8

May 02,Feb. 03,Feb. 02

0.67, 1.4, 4, 8 2 – – Figs. 2, 3

Rattekaai 0–2, 2–4,4–6, 6–8

May 02,March 03,April 02

0.67, 1.4, 4, 8 2 – – Figs. 2, 3

Sulfate reductionkinetics

Appels 0–2 May 02 0.67 2 0.5, 1, 2.5 – Fig. 8Appels 0–2 July 03 1.4 2 0.25, 0.5, 1, 2 – Fig. 8Appels 4–6 July 03 1.4 2 0.25, 0.5, 1, 2 – Figs. 4–6Appels 0–2, 2–4,

4–6, 6–8April 03,July 03

1.4, 4 2 0.25, 0.5, 1, 2, 4 – Fig. 7

Waarde 0–2 May 02 0.67 2 0.5, 1, 2.5 – Fig. 8Waarde 0–2, 2–4,

4–6, 6–8February 02,February 03

1.4, 4 2 0.25, 0.5, 1, 2, 4 – Fig. 7

Rattekaai 0–2 March 03 1.4 2 0.25, 0.5, 1, 2 – Figs. 4–6Rattekaai 0–2, 2–4,

4–6, 6–8April 02,March 03

1.4, 4 2 0.25, 0.5, 1, 2, 4 – Fig. 7

Haringvliet 0–2 September 02 1.5 2 0.13, 0.25, 0.5,1, 2, 3.5

– Fig. 8

Nitrate reductionkinetics

Appels 0–1 May 02,August 02

4 1 – 2.5, 5, 7.5, 10 Fig. 8

Appels 0–1, 1–2 August 01 4 1 – 1 Fig. 8Waardev 0–1 May 02,

August 024 1 – 2.5, 5, 7.5, 10 Fig. 8

Haringvliet 0–1, 1–2 September 02 4 1 – 2.5 Fig. 8Rattekaai 0–1, 1–2 August 01 4 1 – 1 Fig. 8

Variable flow Appels 0–1 August 04 0.65, 1.5, 3,6, 12

1 – 2.5 Figs. 9, 10

Spatialheterogeneity

Appels 0–1 August 04 0.65, 1.5, 3,6, 12

1 – 2.5 Fig. 9

All experiments were run at 21 °C.

262 C. Pallud et al. / Marine Chemistry 106 (2007) 256–271

concentrations (ranging from 1 to 10 mM) at a flow rateof 4.0±0.20 cm3 h−1, while Br− concentration was keptconstant at 1 mM. The outflow samples were analyzedfor SO4

2− or NO3− and Br−, as described in Section 3.4.

The kinetic parameters (RmaxEA and Km

EA) were derived byfitting the RTM to the time-series outflow concentra-tions (Section 2.4). Bromide breakthrough curves (i.e.,the Br− outflow concentration as a function of time)were used to determine the pore water velocity (ν) anddispersion coefficient (D) (Section 2.3).

3.3. Effect of flow rate on nitrate reduction

For the variable flow rate experiments, eight separatesediment slices corresponding to the upper 0–1 cm depthinterval were collected at Appels, in close proximity to

one another. The FTRs were supplied with degassed(argon), de-ionized water containing 2.5 mM NO3

− and1 mM Br−. All reactors were first run at a flow rate of3 cm3 h−1 until steady-state was reached. The flow rateswere then changed to one of the following values: 0.65,1.5 (2 replicates), 3.0 (2 replicates), 6.0 (2 replicates) or12.0 cm3 h−1. The experiments were continued until theoutflow nitrate concentrations again reached steady-state. Outflow samples were analyzed for NO3

−, NO2−,

Br−, DIC, DOC and alkalinity (Section 3.4).Kinetic parameters for nitrate reduction and DOC

utilizationwere derived by fitting steady-state solutions ofthe RTM to the steady-state portions of the outflowconcentration data. For the nitrate concentrations, thevalues of Rmax

EA and KmEA in Eq. (10) were adjusted to yield

the best fit to the data for all five different flow rates. To

Fig. 2. Examples of normalized bromide breakthrough curves obtainedfor Appels 2–4 cm (circles), Waarde 0–2 cm (triangles) and Rattekaai2–4 cm (diamonds). Symbols represent experimental data points.a) The lines correspond to Brenner's series solution to the system ofEqs. (2), (3), and (4) at Pe≤5, and the analytical solution of Eq. (5) atPe>5. b) The lines correspond to the truncated semi-infinite analyticalsolution used in the original study of Roychoudhury et al. (1998).

263C. Pallud et al. / Marine Chemistry 106 (2007) 256–271

obtain the parameters RmaxC and Km

C (Eq. (11)), the rate ofDOC production in the reactor, RProd

C , was calculated bysumming the measured steady-state flux of DOC exitingthe reactor and the estimated rate of carbonmineralizationin the reactor. The latter was derived from the measuredDIC export flux, corrected for the DIC produced bycarbonate mineral dissolution, as explained below.

Sediments in the Scheldt estuary contain significantamounts of calcium carbonate (Vanwesenbeeck, 2000).At Appels, the CaCO3 content of the sediments falls inthe range 1–4 wt. % (C. Hyacinthe, Pers. Comm.).Preliminary results indicated that the contribution ofcarbonate mineral dissolution to the measured alkalinityflux was non-negligible. Based on idealized representa-tions of organic matter (CH2O) and the carbonatemineral pool (CaCO3), we assumed that per mole ofnitrate reduced and CaCO3 dissolved, one and twomolesof alkalinity were produced, respectively. Implicit inthese assumptions is that nitrate reduction proceeds atleast to N2O, and that other alkalinity producingprocesses (such as the reductive dissolution of ferriciron minerals) can be neglected. Using this approach, thecarbonate dissolution correction accounted for 39±10%of total DIC export in the FTR experiments.

3.4. Analytical methods

Concentrations of SO42− and Br− were measured by

ion chromatography (IC; Dionex DX-120). The con-centrations of NO3

− and NO2− were determined color-

imetrically with a Nutrient Autoanalyzer (Bran andLuebbe) and DOC was determined by high temperaturecombustion (Shimadzu TOC-5050A analyzer). Alkali-nity was determined by Gran titration. Samples for DICwere collected in 10 mL septum vials that had beenpreviously purged with He and sealed. These sampleswere then acidified with 30 μL of 2M phosphoric acid toconvert carbonate species to CO2 and the evolved gas inthe headspace was analyzed on a gas chromatographusing thermal conductivity detection (TRACE-GC,Interscience). Because the headspace and sample in theseptum vials had comparable volumes, a non-negligiblefraction of CO2 (up to 15%) remained in solution afterthe acid addition. The DIC values reported here werecorrected for this fraction using Henry's law.

4. Results and discussion

4.1. Transport properties

Bromide breakthrough curves measured using 1 and2 cm length reactors showed excellent agreement with

simulations using Brenner's solution for Pe<5 and theanalytical solution of Eq. (5) for Pe>5 (Fig. 2). As canbe seen on the figure, these two analytical solutionsperform better than the truncated analytical solution fora semi-infinite medium proposed in the original studyintroducing the flow-through sediment reactor method(Roychoudhury et al., 1998). Only at Pe>10 does thetruncated solution adequately reproduce the tracerbreakthrough curves. No evidence for preferential flowor channeling was found over the range of flow ratestested and for the various sediments used. These wouldhave been detected by an early (or even immediate)breakthrough of the tracer. The agreement betweenexperimental tracer breakthrough curves and calculatedbreakthrough curves assuming one-dimensional advec-tive–dispersive flow through a homogeneous porous

Fig. 4. Sulfate breakthrough curves obtained for a) Rattekaai (0–2 cm)and b) Appels (4–6 cm) sediment. Symbols represent experimentaldata points. The lines represent breakthrough curves calculated bynumerical solution of Eq. (10), using Rmax and Km values obtained viathe different approaches discussed in the text.

264 C. Pallud et al. / Marine Chemistry 106 (2007) 256–271

medium supports radially uniform flow through theFTRs.

Over the range of experimental conditions consid-ered, the dispersion coefficient,D, including mechanicaldispersion and molecular diffusion, ranged from 10−3 to5×10−1 cm2 h−1. It increased with increasing porewater velocity (Fig. 3), as expected for mechanicaldispersion in a porous medium (Pfannkuch, 1963; Bear,1972; De Smedt and Wierenga, 1984; Roychoudhury,2001). At the lowest flow rates tested, dispersion is onlydue to molecular diffusion. The values of D/Dmol dropbelow 1, because of the effect of tortuosity on bulksediment molecular diffusion coefficients (see, e.g.,Boudreau, 1997). The linear relationship between D/Dmol and Pe implies that the high porosity (φ=0.60–0.92) sediments behave as classic porous media, withdispersivities, the ratio of mechanical dispersion to porewater velocity, ranging between 0.18 and 1.58 cm.

4.2. Extraction of kinetic reaction parameters

Outflow sulfate concentrations in FTR experimentswith sediments exhibiting high (0–2 cm, Rattekaai) andlow (4–6 cm, Appels) sulfate reducing activity arecompared in Fig. 4. The mean water residence times inthe reactors were 21.8 and 16.3 h for these two sets ofdata, respectively. For the Rattekaai sediment, it tookon the order of 1.7 to 2.3 pore volume replacementsbefore the outflow sulfate concentration reached a newsteady-state after a change in the inflow concentration.For the Appels sediment, 2.8 to 3.2 pore volumes wererequired.

Fig. 3. Dispersion coefficient (D) normalized to the moleculardiffusion coefficient of bromide (Dmol) plotted versus the columnPeclet number (Pe) in flow-through reactor experiments run withdifferent depth intervals of Appels (circles), Waarde (triangles) andRattekaai (diamonds) sediments. The same range of flow rates hasbeen used to compare the three sites.

The entire outflow sulfate concentration time seriesof each FTR experiment could be reproduced by theRTM (Eq. (10)) using a single set of Rmax

EA and KmEA

values (solid lines on Fig. 4, Table 2). While the RmaxEA

values differ significantly between the salt and fresh-water marsh sediments, the sulfate half-saturation (oraffinity) constants, Km

EA, are fairly similar (0.16 and0.10 mM, respectively). Based on a larger set of FTRexperiments, Pallud and Van Cappellen (2006) con-cluded that Km

EA values for sulfate reduction bymicrobial populations in estuarine sediments show nosystematic dependence on salinity. This contradicts theview that freshwater sulfate reducing communitiesexhibit a greater affinity (lower Km

EA) for sulfate thantheir marine counterparts (Ingvorsen and Jørgensen,1984; Ingvorsen et al., 1984; Dalsgaard and Bak, 1994).

The parameters RmaxEA and Km

EA were also derivedfrom the steady-state reaction rates, calculated with Eq.(1), and the average, steady-state sulfate concentrationsestimated as (C0 +Cout) / 2, using three standardmethods: the Lineweaver–Burk linearization, the

Table 2Rmax and Km values for sulfate reduction obtained using theLineweaver–Burk linearization method, the Hanes linearizationmethod, the non-linear regression fitting method and the reactivetransport model (RTM) developed in this study

Rattekaai0–2 cm

Appels4–6 cm

Rmax (nmol cm−3 h−1) 44.64 11.24 Lineweaver–Burklinearization

33.10 11.06 Hanes linearization34.78 11.16 Non-linear regression

fitting32.00 11.20 RTM

Km (mM) 0.48 0.10 Lineweaver–Burklinearization

0.25 0.09 Hanes linearization0.26 0.09 Non-linear regression

fitting0.16 0.10 RTM

Fig. 5. a) Lineweaver–Burk and b) Hanes plots of potential steady-state sulfate reduction rates and average steady-state sulfate concen-trations in the sediment obtained in continuous flow-through reactorswith Appels 4–6 cm (circles) and Rattekaai 0–2 cm (diamonds)sediments. Symbols represent experimental data points. Concentra-tions are in mM and reaction rates in nmol cm−3 h−1.

265C. Pallud et al. / Marine Chemistry 106 (2007) 256–271

Hanes linearization, and a non-linear least-squaresregression (Table 2). The Lineweaver–Burk lineariza-tion, where the inverse of the substrate concentration(1/C) is plotted against the inverse of the measuredreaction rate (1/R), has by far been the most popularmethod used over the last fifty years by microbiolo-gists and geochemists. Already in the early 1960s,however, Dowd and Riggs (1965) drew attention to thetendency of this method to launder poor data, notingthat experimental uncertainties substantially influencethe fitted parameter values. According to Henderson(1993), Cornish-Bowden (1995), the Hanes plot (C/Rplotted versus C) should be preferred, because itminimizes distortion due to experimental uncertainties.On similar grounds, these authors also caution againstusing the Eadie–Hofstee linearization procedure (Rplotted versus R/C).

For the Appels sediment, the various parameterestimation methods yield nearly identical values of Rmax

EA

and KmEA (Table 2). For the Rattekaai sediment, however,

the Lineweaver–Burk plot predicts significantly largervalues for both Rmax

EA and KmEA compared to the other

methods. As illustrated in Fig. 5, the uneven weighing ofthe data by the Lineweaver–Burk plot may seriouslybias the estimation of the kinetic parameters (Dowd andRiggs, 1965; Henderson, 1993; Cornish-Bowden, 1995,2002). When using the Rmax

EA and KmEA values obtained

from the Lineweaver–Burk linearization, the RTMcalculations clearly do not match the observed outflowsulfate concentration time series in the FTR experimentwith Rattekaai sediment (Fig. 4). Therefore, as a generalrule, we recommend against the use of the Lineweaver–Burk linearization for estimating kinetic parameters ofmicrobial reaction processes.

The Hanes plot and the non-linear least-squaresregression method agree much better with the measuredsteady-state rates than the Lineweaver–Burk fit (Fig. 6).Nonetheless, both methods still underestimate sulfateconsumption at the lowest inflow sulfate concentrations(Fig. 4). Longitudinal sulfate concentration profilescomputed with the RTM deviate increasingly from alinear profile with decreasing sulfate concentration inthe inflow and increasing sulfate reducing activity in thereactor (results not shown). In the case of the lowactivity sediment of Appels, the average steady-statesulfate concentration approaches (C0+Cout) / 2 and,therefore, the Hanes plot and non-linear regressionmethod yield values of Rmax

EA and KmEA that are similar to

those obtained from the RTM fit (Fig. 6b and Table 2).For the higher activity sediment of Rattekaai, however,the linear approximation results in an overestimation ofthe average sulfate concentrations in the reactor by 11 to83%, especially at the lowest inflow sulfate concentra-tions (Fig. 6a).

A sensitivity analysis indicates that (C0+Cout) / 2 ap-proaches the actual average sulfate concentration to

Fig. 6. Steady-state potential sulfate reduction rates measured incontinuous flow-through reactors as a function of the average steady-state sulfate concentration in the sediment for a) Rattekaai (0–2 cm) andb) Appels (4–6 cm). Symbols represent experimental data points. Thelines correspond to the Michaelis–Menten rate expression (Eq. (9)),using the Rmax and Km values obtained with the different approachesdiscussed in the text.

Fig. 7. Relative overestimation of the average sulfate concentration inFTRs when using the linear concentration gradient approximation. Thedata shown correspond to sulfate reduction FTR experiments withsediments from three sites along an estuarine salinity gradient (Appels,Waarde and Rattekaai). The relative deviation between the estimatedand actual average sulfate concentrations drops below 5%, when lessthan 50% of the sulfate inflow is consumed in the reactor, or C0 / (C0−Cout)≥2 (see inset). This condition should thus be verified beforeusing the linear gradient approximation.

Fig. 8. Comparison of maximum reaction rates (Rmax) for sulfate andnitrate reduction, expressed in units of carbon equivalents, measuredwith FTRs on the top 0–1 or 0–2 cm depth intervals of Appels,Waarde, Rattekaai and Haringvliet sediments. See text for completediscussion.

266 C. Pallud et al. / Marine Chemistry 106 (2007) 256–271

within 5%, when the consumption of sulfate in the FTRis less than 50% of the sulfate inflow, i.e., whenC0 / (C0−Cout)≥2 (Fig. 7). The above condition should thereforebe fulfilled before deriving kinetic parameters for theconsumption of a reactive substance from steady-stateFTR rate measurements and average concentrationsestimated as (C0+Cout) / 2. Should this not be the case,consumption should be decreased by decreasing thewater residence time in the reactor, that is, by increasingthe flow rate Q.

4.3. Comparison of potential sulfate and nitratereduction rates

Maximum potential rates of sulfate and nitratereduction (Rmax

EA ) measured on sediment slices corre-sponding to the upper 0–1 or 0–2 cm depth intervals atthe four sites are presented in Fig. 8. In order to comparethe rates they are given in carbon equivalent units,assuming a 1:2 molar ratio of sulfate reduction to organic

carbon oxidation and a 5:4 ratio for nitrate reduction toorganic carbon oxidation. For the Appels (freshwatermarsh), Waarde (brackish marsh) and Haringvliet Lakesediments the rates were obtained on sediment slicesfrom replicate cores collected at the same time. ForRattekaai (saltmarsh), however, the sampling times dif-fered for the nitrate and sulfate reduction experiments.

267C. Pallud et al. / Marine Chemistry 106 (2007) 256–271

Values of RmaxEA for nitrate reduction were more than 5

times higher than the corresponding values for sulfatereduction in the freshwater and brackish sediments. Forthe Haringvliet sediments, Rmax

EA for nitrate reductionexceeded that of sulfate reduction bymore than one orderof magnitude. In general, for the freshwater and brackishsediments, the difference in the maximum potential ratesdecreased with increasing respiratory activity. Thedifference in potential rates was less pronounced at thesaltmarsh site, although the comparison is less straight-forward because the sampling times did not coincide.Overall, the findings contradict the common assumptionthat potential rates of terminal electron acceptor utiliza-tion during organic carbon oxidation mainly reflect thereactivity of the sedimentary organic matter beingdegraded (e.g., Van Cappellen and Gaillard, 1996).

The differences in RmaxEA may be related to differences

in the biomasses of the nitrate and sulfate reducingorganisms. At Appels, the densities of culturabledenitrifiers are two orders of magnitude higher thanthose of sulfate reducers (Pallud and Van Cappellen,2006; Laverman et al., 2006). Thus, at this site, sulfatereduction activity may be biomass-limited. At thebrackish site, however, the population densities ofsulfate and nitrate reducers are of the same order ofmagnitude, while in the saltmarsh sediments sulfatereducers dominate, with Most Probable Numbers(MPN) on the order of 109 cells cm−3 of sediment(Pallud and Van Cappellen, 2006). Thus, differences inbiomass alone cannot account for the systematicallyhigher Rmax

EA values of nitrate reduction.Much attention has been given to the more efficient

decomposition of organic matter by aerobic respiration,

Fig. 9. Nitrate plus nitrite breakthrough curves obtained during equal and varinflow nitrate concentration was 2.5 mM. The flow rates are indicated on th

compared to anaerobic degradation pathways (e.g.,Westrich and Berner, 1984; Canfield, 1994; Kristensenet al., 1995; Harnett et al., 1998; Meile and VanCappellen, 2005). The results presented here suggestthat nitrate reduction may also lead to inherently fasterdecomposition of organic matter than alternativeanaerobic pathways, especially sulfate reduction. Thisis in line with the high catabolic energy yield ofdissimilative nitrate reduction, which is of comparablemagnitude as that of aerobic respiration (Berner, 1980).

4.4. Effect of flow rate on nitrate reduction rates

For the five replicate FTRs with sediment fromAppels (0–1 cm depth interval) run at a flow rate of3.0 ml h−1, the outflow nitrate concentrations reachedsteady-state values after about 30 h (Fig. 9). Thecorresponding steady-state nitrate reduction rate, aver-aged for the eight reactors, was 164±27 nmol cm−3 h−1.The observed 17% variability in nitrate reduction rateamong the FTRs most likely reflected the inherentspatial heterogeneity of the sediment at the horizontalscale sampled (≈1 m2). In the variable flow portion ofthe experiments, a systematic response of the outflownitrate concentrations to the flow rate was observed(Fig. 9). As expected, with decreasing flow rate, theincreased water residence time in the reactor resulted inmore nitrate consumption and, thus lower outflownitrate concentrations.

Over the range of flow rates tested, the steady-statenitrate reduction rates varied from 102 to 180 nmolcm−3 h−1 (Fig. 10). Not only was the observedvariability in the nitrate reduction rates significantly

iable flow rate FTR experiments with Appels sediment (0–1 cm). Thee figure. See text for complete discussion.

Fig. 10. Rates of nitrate reduction and DOC export versus flow rate forthe variable flow experiments. Error bars represent the standarddeviation of replicate measurements (no replicates were performed at0.65 and 12 ml h−1). See text for complete discussion.

268 C. Pallud et al. / Marine Chemistry 106 (2007) 256–271

larger than could be accounted for by spatial hetero-geneity, but the rates also exhibited a systematic trendwith the flow rate (Fig. 10) and, thus, with the nitrateconcentrations in the reactors. This trend was consistentwith the Michaelis–Menten rate equation (Eq. (9)).Fitting of the RTM (Eq. (10)) to the entire set of steady-state rates measured under variable flow conditionsresulted in an Rmax

EA of around 200 nmol cm−3 h−1. Theaverage value of Rmax

EA was well constrained, because theinput nitrate concentration was relatively high(2.5 mM). In contrast, the data could be fitted equallywell with a relatively large range of Km

EA values (300–600 μM). A more accurate determination of Km

EA wouldrequire additional experiments with lower inflow nitrateconcentrations, in order to cover a larger range ofnitrate-limiting conditions.

The estimated steady-state carbon mineralizationrates due to respiration (93–265 nmol cm−3 h−1) weremore variable than the corresponding nitrate reductionrates. The average ratio of carbon mineralization tonitrate reduction was around 1.0 (mol/mol), which islower than the theoretical value for complete denitrifica-tion to N2 (1.25). However, the theoretical ratio assumesan oxidation state of zero for organic carbon undergoingmineralization, so some of the discrepancy in theexperimentally-derived value could be due to a loweraverage oxidation state of the in situ organic matterundergoing degradation. In addition, detection of nitritein the outflow of nitrate reduction FTR experiments withAppels sediment indicates that a fraction of denitrifica-tion may not completely convert nitrate to N2 (Laver-man et al., 2006). Incomplete denitrification would alsolower the carbon mineralization to nitrate reductionratio, relative to that for complete denitrification.

Variations in flow rate had a major impact on theDOC export rates (Fig. 10). The latter increased from 19to 112 nmol cm−3 h−1, with increasing flow rate. Thus,over the same range of flow rates the DOC export ratesincreased by a factor of 6, while the nitrate reduction ratebarely doubled. The results imply that the increasingloss of DOC from the reactors as the flow rate increaseshad only a limited effect on the activity of the residentnitrate reducing population. The values of Rmax

C and KmC

derived from the RTM fit to the DOC export rates offer apossible explanation for this observation. The para-meters Rmax

C and KmC in Eq. (11) were obtained byminimizing the difference between the model-predictedDOC export rates (i.e., the difference between RProd

C andthe DOC uptake rate) and the actual DOC export ratesderived from the measured outflow DOC concentrations(i.e., the rates plotted in Fig. 10). The fitting yieldedRmaxC values between 150 and 300 nmol cm−3 h−1, and

KmC values between 5 and 25 μM. The large uncertainty

on RmaxC reflects the combined experimental errors

associated with the estimated respiratory DIC produc-tion and DOC release rates.

The average value inferred for KmC (15 μM) was

about 4–8 times lower than the DOC concentrations inthe outflow, over the entire range of flow rates tested(data not shown). This would imply that the nitratereducers in the reactors were saturated with respect toDOC, irrespective of the flow rate. Saturation with DOCwould then explain why the nitrate reduction rate wasinsensitive to the large variations in DOC export as theflow rate was altered.

The low KmC also implies a high affinity of the nitrate

reducers for DOC produced from sediment organicmatter, which could confer the organisms with acompetitive advantage over other anaerobic hetero-trophs. Possibly, the significantly higher Rmax

EA values fornitrate reduction compared to sulfate reduction in thesediments (Fig. 8) could in part be due to significantdifferences in uptake efficiencies for DOC, and thus Km

C

values, between nitrate and sulfate reducers. Thishypothesis requires further investigation, however. Inaddition, the composition and reactivity of DOCproduced under sulfate versus nitrate reducing condi-tions should be characterized in order to gain a completepicture of the role of organic substrates in the kinetics ofthese two key respiratory pathways.

5. Conclusions and recommendations

The flow-through reactor (FTR) approach isdesigned to yield kinetic parameters and informationon reaction pathways that can be extrapolated to the

269C. Pallud et al. / Marine Chemistry 106 (2007) 256–271

natural conditions in the sediment. To this end,particular precaution should be taken to avoid disruptingthe sediment structure. We recommend sectioning thecores under an inert atmosphere, immediately after coreretrieval. Sediment slices that exhibit cracks, burrows,roots or evidence of compaction should be discarded.During transport to the laboratory or storage, the inputand output channels of the reactor should be tightlyplugged, in order for the sediment slice inside the reactorto remain water-saturated. Flow-through experimentsshould be started as soon as possible and excessivelyhigh flow rates should be avoided.

Radially homogeneous flow in the reactor is crucialfor the determination of rates from measured outflowconcentrations. Therefore, we highly recommendincluding an analysis of tracer breakthrough curveswhen carrying out FTR experiments. Tracer break-through curves not only allow one to identify non-idealflow behavior, but also to derive the longitudinal porewater velocities and dispersion coefficients. Theseparameter values are needed in order to utilize thereactive transport model (RTM) to analyze the outflowconcentration time-series of reactive solutes. Asexpected for porous media, the longitudinal dispersioncoefficients in the sediments studied here correlatepositively with the pore water velocity, yieldingdispersivities in the range 0.2–1.6 cm.

The dimensions of the reactor, the flow rates andinflow concentrations of sulfate and nitrate used in thisstudy should help guide other researchers interested inapplying the FTR approach to study reaction kinetics insediments. The reactor size and the experimentalconditions should be scaled to the expected range ofmagnitude of the rate (Section 2.2, Eq. (1)), althoughpractical considerations should also be kept in mind. Forinstance, it is convenient to select a reactor diameter thatcorresponds to a standard filter size. Also, artifactsrelated to compaction tend to become more prominentwhen the reactor diameter is decreased significantlybelow that used here. Similarly, our experience indicatesthat reducing the reactor length to less than 0.5 cm mayinterfere with the establishment of one-dimensionalflow through the sediment slice. Increasing the reactorlength, however, limits the vertical resolution at whichkinetic information can be acquired.

As with any kinetic method, it is essential to assesshow robust the rate determinations are. Comparing ratesat which reactants and products of a given reactionprocess are consumed and produced, respectively,increases confidence in the kinetic parameters, as wellas in the reaction pathway identification. Additionally,the validity of the derived reaction kinetics should be

tested under variable conditions of flow rate and inflowcomposition. We particularly recommend testing howchanging the flow rate affects the derived rates and rateparameters, as done here for coupled nitrate reduction,carbon mineralization and DOC production. Anothercheck consists in determining whether the same set ofkinetic parameters is able to explain both the steady-state and non-steady-state outflow concentrations ofreactive solutes (as shown in Fig. 4).

The RTM offers the most complete description of thecoupled flow and transformation processes in thereactor. Therefore, if feasible, we recommend that it beused for the analysis of outflow concentration timeseries. Its utilization, however, requires the measure-ment of tracer breakthrough curves for each reactor andeach flow rate used, in order to obtain the appropriatepore water velocities and longitudinal dispersioncoefficients. Fitting the RTM to the non-steady-stateportions of the outflow concentration time-series fur-ther requires a sufficiently high data density (see, forexample, Fig. 4).

Particularly when a large number of reactors pluslarge ranges of inflow composition and flow rate areconsidered, a full scale RTM data analysis may nolonger be practical. In those cases, a more traditionalanalysis of the steady-state reaction kinetics can beadopted. Nonetheless, the RTM can still be used as asensitivity tool to constrain the domain of validity of themore traditional parameter estimation techniques. Inparticular, we show here that the average concentrationof a reactive solute in the FTR can be approximated asthe midpoint between inflow and outflow concentra-tions, when the difference between the two concentra-tions is less than 50%. The experimental conditionsshould thus be adjusted to satisfy this condition. Theexample of sulfate reduction further confirms that theHanes linearization or the non-linear regression methodshould be preferred over the Lineweaver–Burk linear-ization, when deriving maximum rates and half-satura-tion constants from measured steady-state rates ofmicrobial reactions.

Acknowledgements

We thank Pieter Kleingeld for technical assistancewith the flow-through reactors. Logistical support forfield sampling was kindly provided by the NetherlandsInstitute of Ecology (NIOO-CEMO, Yerseke). Wefurther thank two anonymous reviewers for theirconstructive comments, and the Netherlands Organisa-tion for Scientific Research (NWO) for financial supportthrough a Pioneer (PVC) and Veni (AML) grant.

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