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Experimental determination of isotope enrichment factors – bias from mass removal by repetitive sampling Daniel Buchner, Biao Jin, Karin Ebert, Massimo Rolle, Martin Elsner, and Stefan B. Haderlein Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.6b03689 • Publication Date (Web): 22 Nov 2016 Downloaded from http://pubs.acs.org on December 1, 2016
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Experimental determination of isotope enrichment factors – bias from mass removal by repetitive sampling Daniel Buchner1, Biao Jin1,2, Karin Ebert1,3, Massimo Rolle1,2, Martin Elsner4, Stefan B. Haderlein1* 1
Department of Geosciences, Center for Applied Geosciences, University of Tübingen, Hölderlinstraße 12, 72074 Tübingen, Germany 2 present address: Department of Environmental Engineering, Technical University of Denmark, Miljøvej Building 113, DK-2800, Kgs. Lyngby, Denmark 3 present address: BoSS Consult GmbH, Lotterbergstraße 16, 70499 Stuttgart 4 Institute of Groundwater Ecology, Helmholtz Zentrum München, Ingolstädter Landstraße 1, 85764 Neuherberg, Germany *Corresponding author: Stefan B. Haderlein University of Tübingen Department of Geosciences Center for Applied Geosciences Hölderlinstr. 12 D-72070 Tübingen Phone +49-7071-2973148 e-mail:
[email protected] Abstract Art
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Abstract
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Application of compound-specific stable isotope approaches often involves comparisons of
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isotope enrichment factors (ε). Experimental determination of ε-values is based on the
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Rayleigh equation, which relates the change in measured isotope ratios to the decreasing
5
substrate fractions and is valid for closed systems. Even in well-controlled batch experiments,
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however, this requirement is not necessarily fulfilled, since repetitive sampling can remove a
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significant fraction of the analyte. For volatile compounds the need for appropriate corrections
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is most evident and various methods have been proposed to account for mass removal and for
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volatilization into the headspace. In this study we use both synthetic and experimental data to
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demonstrate that the determination of ε-values according to current correction methods is
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prone to considerable systematic errors even in well-designed experimental setups.
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Application of inappropriate methods may lead to incorrect and inconsistent ε-values entailing
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misinterpretations regarding the processes underlying isotope fractionation. In fact, our results
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suggest that artifacts arising from inappropriate data evaluation might contribute to the
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variability of published ε-values. In response, we present novel, adequate methods to
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eliminate systematic errors in data evaluation. A model-based sensitivity analysis serves to
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reveal the most crucial experimental parameters and can be used for future experimental
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design to obtain correct ε-values allowing mechanistic interpretations.
19 20 21
Introduction
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Compound specific isotope analysis (CSIA) is widely applied in various fields of
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environmental sciences (i) as forensic tool for contaminant source identification
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detect and quantify in situ (bio)-degradation 3–5 and (iii) for process characterization including
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identification of transformation mechanisms in (bio)-degradation studies
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applications involve isotope enrichment factors (ε), which relate quantitatively measured
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isotope ratios to substrate fractions of an analyte.
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ε-values are usually determined using laboratory batch experiments and may be lumped
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parameters, not only reflecting the underlying kinetic isotope effect of a reaction but also
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physical constraints or experimental artifacts. Thus, reported ε-values for a given process may
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span a wide range; for instance, the published εcarbon-values for reductive dehalogenation of
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trichloroethene (TCE) range from -2.5‰ to -19.6‰
7,12–14
1,2
, (ii) to
6–11
. The latter two
. Numerous experimental studies
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tried to unravel the processes and mechanisms that determine the extent of isotope
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fractionation for a given reaction, e.g., by investigating the transport of the substrate across
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the cell wall
7,8
, the efficacy of the involved enzymes
15
, the cell density
9,16
or the nutrient
13,17
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supply
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For closed systems, isotope enrichment factors can be obtained using a simplified form of the
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Rayleigh distillation equation
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between the natural logarithms of the measured substrate fraction, ln fsubstrate(t) and the
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measured isotope ratios, ln (R(t)/R(0)). While it is obvious that field sites often cannot be
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treated as closed systems and require modified forms of the Rayleigh equation
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laboratory batch reactors the applicability of the linearized form of the Rayleigh equation
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seems to be straightforward as such systems appear to fulfill all requirements of closed
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systems. These conditions are strictly met in experiments with numerous parallel replicates
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which are sacrificed sequentially for sampling
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uncertainty and variability due to different dynamics in such parallel assays.
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Alternatively, several samples can be withdrawn from the same batch reactor over time to
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monitor isotope ratios at different values of fsubstrate(t). Repetitive withdrawal of water and/or
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gas samples from batch reactors violates the closed system requirement and calls for adequate
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consideration. Unfortunately, ε-values reported in the literature often lack a clear description
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whether corrections of measured concentration data were applied. Repetitive sampling from a
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batch reactor not only leads to mass removal of the target compound(s) from the system but
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also, if water samples are withdrawn, changes the phase ratio by decreasing the water phase
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and increasing the headspace volume. Progressive change of the phase ratio, however, needs
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to be taken into account for volatile organic contaminants such as chlorinated ethenes. As
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either gas or water volume is sampled, the measured data represent the concentration in only
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one of these phases and a mass balance on the system is required using Henry’s law and the
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gas/water ratio to account for the entire amount of substrate or products
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corrections were suggested to account for the cumulative amount of substrate removed by
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repetitive sampling (CSR) 13,14,23.
. 18,19
where ε is derived from the slope of the linear correlation
4,20
, for
7,8,15
, however, at the expense of increased
21,22
. Additional
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The present study systematically investigates how such correction methods affect ε-
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values determined in batch experiments with repetitive sample removal. Using both
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experimental case studies as well as a synthetic dataset calculated for typical experimental
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conditions, we evaluate the performance of various correction methods, identify pitfalls and
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propose novel methods to eliminate systematic errors in data evaluation. A model-based
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sensitivity analysis was performed to identify which experimental parameters require the most
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stringent control and should be used to optimize the experimental design in order to obtain
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correct isotope enrichment factors that are suitable for mechanistic interpretation and thus
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indicative of the underlying isotope fractionation processes.
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Methods to determine isotope enrichment factors
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We describe current and newly proposed methods to account for mass removal by repetitive
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sampling in batch reactors considering volatile organic compounds. Based on the substrate
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fraction and stable isotope data the isotope enrichment factor (ε) can be calculated using a
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simplified Rayleigh distillation equation 18,19 :
() ≈ ∙ () (1) (0)
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R(t) and R(0) are the stable isotope ratios of the substrate at a time t and the initial time and
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fsubstrate(t) denotes the remaining substrate fraction (often approximated by the substrate
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concentration according to c(t)/c(0)) at a time t. ε-values are derived by linear regression of
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the data without forcing the regression through the origin as suggested by Scott, et al. 24.
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The substrate fractions, fsubstrate(t), at different time points come from measured concentration
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data of water samples subject to corrections accounting for volatilization into the increasing
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headspace and repetitive removal of water samples from the batch reactors. Figure 1 illustrates
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the effect of sampling and the challenges to adequately consider the effects of mass removal
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and volatilization.
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Below, we outline current (I-III) and newly proposed methods (IV and V) to calculate the
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substrate fraction:
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Figure 1 Schematic illustration of the time course of the substrate fraction, f, during biodegradation in a repetitively sampled batch reactor considering an ideal case in which neither compound’s mass nor water volume are removed from the system and a realistic case which requires correction schemes. The Figure illustrates substrate removal due to sampling by lower water levels (“slices” withdrawn) and removal due to biodegradation by concentration changes (color shades). For example, method III (Henry + CSR) adequately corrects for mass removal by sampling (nrem), but ignores that the removed mass cannot undergo further biodegradation as it would occur in an undisturbed reactor. When all amounts are summed up, this scheme therefore overestimates the remaining substance fraction fsubstrate(t) (red curve).
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(I) The substrate fraction in water phase (water) without further corrections is calculated as
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follows: () =
() ∙ () () = (2) (0) ∙ (0) (0)
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nw(t) and nw(0) correspond to the amount (moles) of the substrate in the water phase at times t
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and t=0, respectively. Measured aqueous analyte concentrations, cw(t) are multiplied by the
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water volume present at the respective time, Vw(t), to obtain nw(t) thus accounting for the
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changes of the water volume.
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(II)
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substrate in the system by accounting for both the water phase and the gas phase of the batch
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reactor. The substrate fraction, fHenry (t), is calculated as:
The correction for gas-water-partitioning (Henry) considers the total amount of
() =
() ∙ () + () ∙ () () + () = (3) (0) ∙ (0) + (0) ∙ (0) (0) + (0)
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ng(t) and ng(0) correspond to the amount of substrate in the gas phase at time t and the initial
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time. The substrate concentration in the gas phase, cg(t) is calculated from cw(t) by applying
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Henry’s law. KH is the dimensionless Henry-constant (KH=cw/cg) of the analyte at the
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appropriate temperature, calculated for 21°C according to Sander
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Vg(t) is the volume of the gas phase in the batch reactor at time t.
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and references therein.
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(III)
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(Henry+CSR) is an extension of the Henry-correction taking into account the amount of
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substrate removed by repetitive sampling of the reactor. The substrate fraction, fHenry+CSR(t), is
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calculated according to:
The correction for gas-water partitioning and cumulative sample removal
!"# () =
()
!"#
=
() ∙ () + () ∙ () + ∑*+,% ( = & − 1) ∙ ( ( = & − 1)) (0) ∙ (0) + (0) ∙ (0)
() + () + ∑*+, ( ( = & − 1) (4) (0) + (0)
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nrem(t) corresponds to the amount of the substrate removed by sampling at a given time t and is
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calculated by multiplying the concentration in the water phase (cw(t)) with the removed
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volume (Vrem(t)) at time t. The summation term denotes the cumulative amount of substrate
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removed from the system by sampling except for the last sampling. Even though this method
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adequately calculates the mass of substrate that is removed by sampling, it considers this mass
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as part of the substrate remaining fraction, as illustrated by the color shade in Figure 1. Even
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so method III accounts for the removed mass it treats this mass as being part of the system that
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is subject to further
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fraction of substrate remaining fsubstrate(t).
(bio)-transformation. Consequently, the method overestimates the
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(IV)
The stepwise correction (SW) method also accounts for gas-water partitioning and
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sample removal. Contrary to method III (Henry+CSR) this method applies an iterative
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correction scheme and avoids systematic over- or underestimation of substrate fractions which
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is conceptually inherent to methods I to III.
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First, for two consecutive sampling times individual substrate fractions, f(t-1)→t, are calculated.
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By comparing the amounts of substrate present in the system at times t and at time (t-1) after
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sample withdrawal, this fraction represents exclusively changes due to (bio)-degradation:
126 (.,)→ = (.,)→ =
() + () ( − 1) + ( − 1) − ( ( − 1)
() ∙ () + () ∙ () (5) ( − 1) ∙ ( − 1) + ( − 1) ∙ ( − 1) − ( − 1) ∙ ( ( − 1)
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Using the dimensionless Henry’s constant (KH) equation 5 can be rearranged to: (.,)→
() ∙ () 1 = ( − 1) ∙ ( − 1) ( − 1) ∙ ( − 1) + − ( − 1) ∙ ( ( − 1) 1 () ∙ () +
(.,)→
() () ∙ 2 () + 3 1 = (6) ( − 1) ( ( − 1) ∙ 2 ( − 1) + − − 1)3 ( 1
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cw(t) and cw(t-1) or Vrem(t) and Vrem(t-1) denote the measured concentrations or sample
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volumes taken at time t and the preceding time point t-1.
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Second, the overall substrate fraction at time t is calculated considering f(0)=1 (i.e., 100%
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substrate fraction) and the results of equation 6 for all preceding time steps: "5 () = (0) ∙ 6→, ∙ ,→7 ∙ … ∙ (.,)→ (7)
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As an example, for two sampling steps this method leads to the following expression: "5 (2) = (0) ∙ 6→, ∙ ,→7
(1) (2) (1) ∙ 2 1 + (1)3 (2) ∙ 2 1 + (2)3 "5 (2) = 1 ∙ ∙ (8) (0) (1) (0) ∙ 2 (0) + 1 − ( (0)3 (1) ∙ 2 (1) + 1 − ( (1)3
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As can be seen, the terms representing the substrate concentration of the intermediate time
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point t=1 cancel out and equation 8 simplifies to: (2) (1) + (1)3 (2) ∙ 2 + (2)3 2 1 1 "5 (2) = 1 ∙ ∙ (9) (0) (1) (0) ∙ 2 (0) + − ( (0)3 2 (1) + − ( (1)3 1 1
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Note that this stepwise correction method requires the phase volume ratios for each time step
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but concentration measurements only for the initial and the final time step.
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Thereby the propagation of measurement errors (e.g., detector drift) from intermediate
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sampling times are minimized
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(V)
The mass balance correction (MB) method determines the substrate fractionation,
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fMB(t), from a mass balance of reactant and products for each time point, i.e., by dividing the
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amount of the substrate at time t by the sum of the amounts of substrate and all degradation
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products at that time:
0.96 and CI
