Modelling of C/Cl isotopic behaviour during chloroethene biotic reductive dechlorination: Capabilities and limitations of simplified and comprehensive models

Predicting the fate of chloroethenes in groundwater is essential when evaluating remediation strategies. Such predictions are expected to be more accurate when incorporating isotopic parameters. Although secondary chlorine isotope effects have been observed during reductive dechlorination of chloroethenes, development of modelling frameworks and simulation has thus far been limited. We have developed a novel mathematical framework to simulate the C/Cl isotopic fractionation during reductive dechlorination of chloroethenes. This framework differs from the existing state of the art by incorporating secondary isotopic effects and considering both C and Cl isotopes simultaneously. A comprehensive general model (GM), which is expected to be the closest representation of reality thus far investigated, was implemented. A less computationally intensive simplified model (SM), with the potential for use in modelling of complex reactive transport scenarios, was subsequently validated based on its comparison to GM. The approach of GM considers all isotopocules (i.e. molecules differing in number and position of heavy and light isotopes) of each chloroethene as individual species, of which each is degraded at a different rate. Both models GM and SM simulated plausible C/Cl isotopic compositions of tetrachloroethene (PCE), trichloroethene (TCE) and cis-1,2-dichloroethene (cDCE) during sequential dechlorination when using experimentally relevant kinetic and isotopic parameters. The only major difference occurred in the case where different secondary isotopic effects occur at the different non-reacting positions when PCE is dechlorinated down to cDCE. This observed discrepancy stems from the unequal Cl isotope distribution in TCE that arises due to the occurrence of differential secondary Cl isotopic effects during transformation of PCE to TCE. Additionally, these models are shown to accurately reproduce experimental data obtained during reductive dechlorination by bacterial enrichments harbouring Sulfurospirillum spp. where secondary isotope effects are known to have occurred. These findings underscore a promising future for the development of reactive transport models that incorporate isotopic parameters.


Separate consideration of C and Cl isotopes (SM)
Here, a schematic explanation of the transitions considered between isotopologues of PCE, TCE and cDCE during PCE reductive dechlorination for the simplified model (SM) is given ( Figure   A). The matrices of isotopologue/isotopocule fractionation factors used in SM associated with each step of reductive dechlorination of PCE to cDCE are also given ( Figure B).

Figure A
Schematic explanation of the transitions considered between isotopologues of PCE, TCE and cDCE during PCE reductive dechlorination for the simplified model (SM). A more intuitive notation was used in this scheme based on the scheme suggested by Hunkeler et al.
[11]: L designates light isotopes while H designates heavy isotopes (of either C or Cl). Solid arrows correspond to transitions where bond breakage involves a light isotope of the considered element while dotted arrows correspond to transitions involving heavy isotopes. are the matrices containing the isotopologue fractionation factors relative to Cl and C associated with each transition. The corresponding matrices are given in Figure B.

Figure B
Matrices of isotopologue/isotopocule fractionation factors used in SM associated with each step of reductive dechlorination of PCE to cDCE. Unlike in GM where C and Cl are considered simultaneously, C and Cl are here treated separately. Each matrix thus represents the transition between isotopologues/isotopocules of degraded to produced compound relative to either C or Cl. Letters in bold represent the reacting position. A stands for AKIE, p for primary, s for secondary. PCE C →TCE C and PCE Cl →TCE Cl thus describe the transition of PCE to TCE relative to C and Cl, respectively, while TCE C →cDCE C and TCE Cl →cDCE Cl describe the transition of TCE to cDCE relative to C and Cl, respectively. Symmetries (PCE and cDCE) and asymmetries (TCE) are also taken into account. More particularly for C where no atom is removed during the transition, it is considered during PCE transformation to TCE that primary and secondary effects are equally distributed between the two positions. On the contrary, during TCE transformation to cDCE, it is considered that one C either undergoes a primary or a secondary isotopic effect since the reaction is regioselective and there are therefore no equal possibilities of cleaving the bond from one or the other C.

The case of Monod kinetics: equations describing PCE, TCE and cDCE isotopocules during reductive dechlorination
For PCE reductive dechlorination to cDCE, the following equations apply based on equation (10), i.e. for PCE: The first term in grey is shown (see equation (10)) but is equal to zero for PCE which is only being degraded.
For TCE : And for cDCE : The second term in grey is left here to remind of equation (10) but does not apply to cDCE which is only being produced.

Calculation of initial isotopocules (GM) and isotopologues (SM) concentrations
From hereon in, all equations are applicable to any of the simulated compounds γ (i.e. PCE, TCE or cDCE). Therefore, for the sake of readability, the γ in the superscript of the corresponding variables has been omitted. In the case of GM, the initial isotopocules concentrations can be calculated based on the initial isotopic compositions (δ 37 Cl0 and δ 13 C0 of degraded compound and the total initial concentration thereof). Initial isotopocules concentrations ℎ can be determined from the total compound concentration 0 based on the relative abundance of isotopocule h as formerly suggested by Jin et al. [13]: Where ℎ is the relative abundance of the isotopocule h containing 13C ℎ (= ∑ ℎ, ( ∈C Atoms) ) 13 C from a total of C (= 13C ℎ + 12C ℎ ) C and 37Cl ℎ (= ∑ ℎ, ( ∈Cl Atoms) ) 37 Cl from a total of Cl (= 37Cl ℎ + 35Cl ℎ ) Cl atoms.
When C and Cl are considered separately, the relative abundance of isotopologues relative to C and Cl can be determined separately by the probability mass function, as previously described by Hunkeler, van Breukelen and Elsner [11] according to: where ℎ is the relative abundance of isotopologue (or isotopocule for asymmetric molecules) h. Such simplification is possible when C and Cl are considered separately since the atoms positions relative to each other are not any more taken into consideration (isotopologues) contrary to when C and Cl are considered simultaneously as in equation (S4) (isotopocules).
For asymmetric chlorinated ethenes (e.g. TCE) the relative abundances are equally distributed between isotopocules arising due to asymmetry.
Isotopic ratios of an element E are usually given by the delta notation reported against international standards (VPDB or SMOC for C and Cl, respectively) defined as: where R and Rstd are the isotope ratios of the element E of the sample and the standard, respectively ( VPDB = 0.0111802 [31] and SMOC = 0.319766 [11]).
The relative abundance of C and Cl isotopes in isotopocules or isotopologues h is therefore calculated based on the initial isotopic compositions 13 C 0 and 37 Cl 0 as:

Final C and Cl isotopic composition
Finally, the C and Cl isotopic compositions of each compound can be computed based on the simulated isotopocule/isotopologue concentrations according to:

GM vs. SM
Tables summarising sets of isotopic parameters used to perform simulations aimed at comparing GM and SM (Table A) as well as comparison results given by the NSE and NME (Tables B and C) are summarised in this section.

Model responses
Plots representing the evolution of C and Cl isotopic compositions with time for each type of simulated isotopic effect as well as corresponding C-Cl isotope slopes are given in this section. Isotope fractionation was characterized in three to four replicate assays per experimental set.
Control experiments without addition of inoculum were also included. Aqueous samples for isotope and concentration analysis were taken to assess the remaining fractions (ranging from 100 to 5%) of initially added chlorinated ethenes. Samples were stored in glass vials sealed with PTFE-lined septa at 4 °C without headspace (for concentration analysis) or frozen upside down with headspace (for isotope analysis) after addition of NaOH 20 M to stop the dechlorination. Working PCE or TCE standards were measured every ten sample to verify the measurement stability. Samples were diluted to 100 µg⋅L -1 and analyzed five to ten times by headspace injection using a CombiPal Autosampler (CTC Analytics, Zwingen, Switzerland). The standard uncertainty is given as the standard deviation of the mean (σ/√n).

Quantification of stable isotope fractionation
The enrichment factor εE was determined for each experiment according to the Rayleigh equation as follows: ln + 1000 where is the reactant remaining fraction of the degraded compound at time t, E the considered element, δt and δ0 are the isotope ratios of one element at time t and time 0.
Unless notified otherwise, enrichment factors and dual isotope slopes were calculated by combining δ 13 C and δ 37 Cl data from all replicates and results are given with a 95% confidence interval.

Experimental determination of primary and secondary isotopic effects
According to Cretnik et al.
[17], primary and secondary isotopic effects during PCE biotic reductive dechlorination can be estimated based on the difference in Cl isotopic composition between the substrate PCE and the produced TCE and Cl -. This is based on the assumption that the products mirror the Cl isotope enrichment behaviour of the four chemically equivalent positions of PCE from which they origin. It was more specifically demonstrated that: After determining the Cl enrichment factor εPCE associated with PT by means of the Rayleigh equation, εdiff could hence be determined based on the expression above at time 0 where: The primary and secondary isotopic enrichments were consecutively determined based on the following expressions, assuming a one-step dechlorination scenario where no intermediate specie exists between PCE and TCE: where PCE prim and PCE sec correspond to the primary and secondary isotopic effects associated with PT, respectively.
PCE prim , PCE sec , and diff are given as the average between values obtained for each replicate and the uncertainties was determined by error propagation.
Since δ 37 Cl of cDCE could not be measured, no information regarding secondary and primary isotopic effects during PTD or TD could be determined.

Experimental results
Whether PCE was dechlorinated by consortium SL2-PCEb or SL2-PCEc, the lag phase lasted between 20 and 50 h while the lag phase preceding TCE dechlorination as a substrate lasted one to two orders of magnitude longer, i.e. from 200 to 1500 h depending on the replicate.
Detailed experimental results with regards to isotopic behaviour can be found in Figure C and Table E.
As reported previously [27], PCE was slightly enriched in heavy C and Cl during its dechlorination, with maximum enrichment factors of -3.6 ± 0.2‰ for C and -1.2 ± 0.1‰ for Cl associated with consortium SL2-PCEc (Table E). Conversely, both C and Cl enrichment were stronger for TCE dechlorination (only possible by consortium SL2-PCEb) where a C enrichment factor of -18.9 ± 1.3‰ and a Cl enrichment factor of -4.3 ± 0.4‰ were determined (  Figure C), yet a dual C-Cl slope determined based on the combination of data from all replicates has no significance as its associated R² is of 0.16. On the contrary, the TCE dual C-Cl slope obtained for PTD by SL2-PCEb shows a high value of R² = 0.93 (Table E and   Figure C).
Although primary and secondary Cl isotope effects could not be determined for TD by SL2-PCEb due to the lack of Cl isotope data for cDCE, such isotope effects were determined for PT and PTD according to the method suggested by Cretnik et al. and assuming a one-step scenario (Equations (S15) and (S16)) [17]. In the case of PTD, primary and secondary isotope effects were determined similarly as for PT. The apparition of cDCE in very little amounts after the apparition of TCE justifies such procedure although it should be remembered that TCE further dechlorination to cDCE might slightly affect the determined values ( Figure C, replicate C).
Primary isotopic effects of -9.0 ± 0.9 ‰ and -12.8 ± 2.1 ‰ were obtained for PT and PTD, respectively (Table E). These values are slightly to twice smaller than the previously reported value of -17.0 ± 1.6 ‰ for PT by Desulfitobacterium sp. strain Viet1 [17]. Secondary isotopic effects of 1.4 ± 0.2 ‰ and 3.1 ± 0.6 ‰ associated with PT and PTD, respectively, are on the other hand significantly different from the formerly reported value of -1.0 ± 0.5 ‰ [17], and reflect an unusual inverse secondary isotope effect. Such effect was previously reported during TCE abiotic reduction by zero valent iron at the laboratory scale [36] and twice in the field where cDCE was found to be 1 to 1.5‰ more enriched than TCE assumed to be biotically dechlorinated [37].

Experimental data simulation by model SM
The optimised parameters used for the simulations which fit the experimental data are given in this section.