ARTICLE pubs.acs.org/est
Development and Sensitivity Analysis of a Fully Kinetic Model of Sequential Reductive Dechlorination in Groundwater Flavio Malaguerra,* Julie C. Chambon, Poul L. Bjerg, Charlotte Scheutz, and Philip J. Binning Department of Environmental Engineering, Miljoevej, Building 113, Technical University of Denmark, 2800 Kgs Lyngby, Denmark
bS Supporting Information ABSTRACT: A fully kinetic biogeochemical model of sequential reductive dechlorination (SERD) occurring in conjunction with lactate and propionate fermentation, iron reduction, sulfate reduction, and methanogenesis was developed. Production and consumption of molecular hydrogen (H2) by microorganisms have been modeled using modified MichaelisMenten kinetics and has been implemented in the geochemical code PHREEQC. The model have been calibrated using a Shuffled Complex Evolution Metropolis algorithm to observations of chlorinated solvents, organic acids, and H2 concentrations in laboratory batch experiments of complete trichloroethene (TCE) degradation in natural sediments. Global sensitivity analysis was performed using the Morris method and Sobol sensitivity indices to identify the most influential model parameters. Results show that the sulfate concentration and fermentation kinetics are the most important factors influencing SERD. The sensitivity analysis also suggests that it is not possible to simplify the model description if all system behaviors are to be well described.
’ INTRODUCTION Chlorinated aliphatic hydrocarbons (CAH), such as tetrachloroethene (PCE) and trichloroethene (TCE), have been widely used in the manufacturing and cleaning industries since the 1950s and have become common pollutants in groundwater.1 Highly chlorinated ethenes PCE and TCE can be degraded under anaerobic conditions via sequential reductive dehalogenation (SERD).2 However, although many bacteria strains can transform PCE into TCE and TCE into cis-dichloroethene (cisDCE), only the specific bacteria belonging to the Dehalococcoides genus are able to perform the last two steps of the SERD, that is, from cis-DCE to vinyl chloride (VC) and from VC to ethene.3 Unfortunately, VC is a known carcinogen and is more toxic than its mother compounds; thus, incomplete degradation of chlorinated ethenes can pose a serious threat to groundwater and consequently to human health. During SERD, microorganisms use chlorinated solvents as terminal electron acceptors and H2 as electron donor. Some dehalorespiring bacteria use other compounds as electron donors, for instance, acetate, butyrate, ethanol, lactate, formate, pyruvate, and glycerol.4 In anaerobic environments, molecular H2 is produced by fermentation of organic carbon containing materials. Nevertheless, this reaction is endergonic and occurs only in sediments because H2 concentrations are kept very low by a multitude of H2-consuming microorganisms. Thus, production and consumption of H2 are closely coupled in natural systems, where H2 acts as a shortlived intermediate that is usually present at very low concentrations.5 Terminal electron-accepting processes (TEAPs) other than der 2011 American Chemical Society
chlorination can compete for H2: denitrification, iron reduction, sulfate reduction, methanogenesis, and acetogenesis are all processes that can consume molecular H2 and which can jeopardize the removal of chlorinated solvents. Hydrogen occurrence in aquifers has been mainly modeled using the concepts of (i) competitive exclusion, which states that H2 concentrations in sediments are dictated by the local predominant TEAP, and (ii) partial equilibrium, which assumes TEAPs in equilibrium with the available free energy (ΔG). Watson et al.6 showed that both concepts overly simplify the processes occurring during syntrophic degradation of organic compounds and so fail to capture the fast temporal variations of biodegradation systems. In contrast, a fully kinetic model can describe the system dynamics and the behavior of intermediate species such as H2, acetate, or other short-chained fatty acids during changes in redox processes. Previous studies have also shown that anaerobic degradation of chlorinated ethenes could not be modeled using the partial equilibrium approach due to a lack of thermodynamic control on H2 concentrations.7 Therefore, an effective way to model SERD together with subsurface redox processes is to describe microbial processes as kinetics, acting as simultaneous sources and sinks of electron donor, where the parameters account for the characteristics of the microbial strains and for environmental factors. Received: April 14, 2011 Accepted: August 30, 2011 Revised: August 26, 2011 Published: August 30, 2011 8395
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Environmental Science & Technology Several numerical models have been developed to simulate SERD. Bagley8 modeled competition for electron donors during SERD using MichaelisMentens kinetics, whereas Fennell and Gossett9 included H2 thresholds and thermodynamic limitations on donor fermentation and validated the model with H2 measurements. Later studies showed that SERD was better described by competitive inhibition kinetics,10 and models have been used to study SERD under substrate-limiting conditions11 and variable temperature.12 Reactive transport models including SERD have also been recently developed to simulate chlorinated solvent degradation in column laboratory experiments13 and in clay till fractures at field scale.14 Although the importance of nonchlorinated TEAPs on reductive dechlorination is widely recognized,15 only a few modeling studies have simultaneously considered dehalorespiration and other H2-consuming reactions,16,17 and none of them have compared the model to observations including measured H2 concentrations. In this paper we present a new model to describe SERD occurring in conjunction with fermentation, iron reduction, sulfate reduction, and methanogenesis. The model is shown to be able to reproduce the major trends of the observed H2 concentrations obtained from laboratory batch experiments. Model calibration has been performed using a Shuffled Complex Evolution Metropolis (SCEM) algorithm with observed concentrations of H2, organic acids, and chlorinated solvents. The model is used to investigate the effect of natural redox reactions on SERD, and advanced global sensitivity analysis techniques are employed to determine the most important model parameters. The paper concludes with a discussion of the possibility of model simplification.
’ MATERIALS AND METHODS Data Set Description. The data set was obtained from the laboratory batch studies of Scheutz et al.18 related to a full-scale enhanced reductive dechlorination (ERD) field demonstration The experiat a contaminated site in Denmark (Rugardsvej). ment consisted of duplicate microcosms containing 100 g of sandy sediments and 200 mL of water collected at the site. TCE and electron donor (lactate) were added to the sediments, and the microcosms were incubated at 10 °C. Water samples were regularly taken over a period of 330 days and analyzed for nitrate, sulfate, dissolved iron, organic acids (lactate, propionate, formate, and acetate), ethene, ethane, and chlorinated ethenes (TCE, DCE, and VC). PCE concentration was regularly measured to verify that no PCE was desorbing from the sediments. Methane and H2 concentrations were measured in the headspace. Details of the batch experiment design and procedures of analysis are presented in the Supporting Information (SI) of Scheutz et al.18 Water and sediment chemistry are presented in the SI (Table S1) accompanying this paper. Modeling Tool. The model has been implemented in PHREEQC,19 a biogeochemical speciation and transport code designed to perform a wide variety of aqueous geochemical calculations and which has capabilities for speciation, saturation index calculations, and reversible and irreversible reactions. PHREEQC has been extensively applied and has recently been employed to simulate SERD.17 Conceptual Model. The concept of syntrophic biodegradation assumes that degradation of organic compounds occurs in three steps, hydrolysis, fermentation, and respiration, 6 and explains the concomitant presence in sediments of intermediate
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Figure 1. Degradation pathways considered in the model.
species such as H2 or short-chained organic acids. When low molecular weight organic acids are the main electron donors, hydrolysis can be neglected and the main degradation pathway is dominated by the production and consumption of H2 and acetate. The simplified biodegradation pathway considered in this study is illustrated in Figure 1, where lactate ferments, forming acetate and propionate,20 and with propionate subsequently fermenting into acetate and H2. Hydrogen can be used by ironor sulfate-reducing bacteria, methanogens, and dechlorinating microorganisms. Acetate can be used as an electron donor for iron reduction or for transformation of TCE into cis-DCE.21 Denitrification and manganese reduction are not considered because these processes did not occur in the experiments. The list of redox reactions is presented in Table S2 of the SI. Degradation Model. Non-dechlorinating bacteria growth is modeled using the general equation ∂X ¼ μmax X IS Iinh IXmax ∂t
ð1Þ
where μmax is the temperature-dependent biomass maximum growth rate (see the SI, Figure S1), X is the biomass concentration, and ISi , Iinh, and IXmax are inhibition factors varying between 0 and 1. The inhibition due to substrate limitation is modeled using MichaelisMenten kinetics IS ¼
ED EA ED þ KED EA þ KEA
ð2Þ
where ED and EA are the electron donor and electron acceptor concentrations, respectively, and KED and KEA are the corresponding half-saturation constants. Inhibition of biomass growth by the presence of a more energetic electron acceptor is modeled through the relationship Iinh ¼
Kinh Kinh þ I
ð3Þ
where I is the concentration of the inhibitor and Kinh is an inhibition constant. Propionate-fermenting bacteria are assumed to be inhibited by acetate, and their growth is modeled using a competitive inhibition term22 IS ¼
8396
1 KS;P 1 þ ½P
½A 1 þ KI;A
!
ð4Þ
dx.doi.org/10.1021/es201270z |Environ. Sci. Technol. 2011, 45, 8395–8402
Environmental Science & Technology
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where [P] and [A] indicate propionate and acetate concentrations, KS,P is the half-saturation constant for propionate and KI,A is the inhibition constant of acetate on propionate fermentation. A threshold in biomass concentration has also been fixed in the propionate-fermenting kinetics to emulate substrate diffusion limitations when the microbial biomass becomes too large.23 Biomass colonies are assumed to slow their growth when approaching the maximum acceptable biomass concentration IXmax ¼
Xmax X Xmax
ð5Þ
where Xmax is the maximum biomass concentration present in the matrix. When propionate-fermenting bacteria concentration reaches Xmax, it is assumed that fermentation still occurs to compensate for the cell decay and is described by a zero-order rate. Bacterial decay was not implemented in the model. Dechlorinating bacteria growth is modeled through a competitive inhibition model as suggested by previous studies10,11 ∂X ED ¼ μmax X ED þ KED ∂t
S
S þ KS 1 þ
C1 C2 þ Ki1 Ki2
ð6Þ where S is the chlorinated compound acting as an electron acceptor, C1 and C2 are other chlorinated compounds (such as VC and cis-DCE for TCE degradation), and Ki1 and Ki2 are the relative inhibition constants. The exhaustive list of kinetic parameters including units is presented in Table 1. Aqueous species are related to biomass growth by24 ∂A 1 ∂X ¼ ∂t Y ∂t
ð7Þ
where A is the concentration of the aqueous component and Y is the biomass yield (moles of biomass produced per mole of aqueous component consumed or produced). Biomass. Biomass was modeled using the model compound C5H7O2N25 and was implemented in PHREEQC through reaction stoichiometries. Bacterial yields of fermenters, acetate iron reducers, and methanogens were calculated using the thermodynamic model presented by McCarty25 and account for the partitioning between catabolic and anabolic pathways. No biomass growth was considered in the stoichiometry of hydrogenotrophic sulfate and iron reducers due to the small amount of energy provided.6 Bacterial yield values for dechlorinating bacteria were comparable with the values presented in other studies.26 Two dechlorinating bacterial strains were assumed to be present in the system: bacteria that converts TCE into cisDCE using acetate as electron donor (e.g., Geobacter, Sulfurospirillium, and Dehalobacter) and Dehalococcoides bacteria, which are responsible for the subsequent dechlorination steps. Geochemistry. PHREEQC speciation calculations showed that the aqueous solution used in the experiment (SI, Table S1) was in equilibrium with calcite while being supersaturated with respect to siderite, which is common for natural groundwaters.27 Two types of ferric iron accounting for high (e.g., ferrihydrite and lepidocrocite) and low (e.g., goethite) bioavailability were included in the model as iron oxide source.28 Ferric iron was included as kinetic reactant, whereas amorphous iron sulfide (FeS [ppt]), pyrite (FeS2), and siderite (FeCO3) were included as equilibrium mineral phases. Equilibrium precipitationdissolution constants were taken from the standard PHREEQC database.
Figure 2. Results of model calibration: plots of observed (symbols) and simulated (lines) concentrations of chlorinated solvents (A), organic acids and methane (B), ferrous iron and sulfate (C), and molecular hydrogen (D). Please note the different vertical axes for plots B and C and that the concentrations in plot D are expressed in nmol/L. The error bars have been calculated from duplicate data.
Model Calibration. The model was calibrated using a combination of a trial-and-error approach and a SCEM algorithm,29 in which manual calibration was employed to find credible parameter intervals as input for the SCEM algorithm. An extensive search over the whole model space was not feasible due to the enormous computational cost and because of model failure for some parameter combinations involving overly stiff differential equations. Batch reactive models involving complex biogeochemical 8397
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Environmental Science & Technology processes are known to be very difficult to calibrate, because of the presence of numerous local minima, parameter correlation, and parameter insensitivity.30 The SCEM algorithm was preferred to other calibration techniques because of its robustness and its ability to provide a posteriori parameter probability density functions, which can be used to assess the uncertainty of each fitted parameter. Global Sensitivity Analysis. Global sensitivity analysis aims to determine the parameters that dominate the reductive dechlorination system and the parameters accounting for the majority of model uncertainty, that is, the parameters that if determined (for example, by measurements), will induce the highest reduction of model output uncertainty. Here, we applied two global sensitivity analysis (GSA) methods to provide a better model description over the full extension of the model space. The model has many parameters and the model space is very large (SI, Table S3). Thus, we chose to apply two different GSA methods to verify the coherence of sensitivity results: the Morris method31 and the Sobol sensitivity indices32 used in conjunction with a highdimensional model representation (HDMR).33 The Morris method was selected because it can produce qualitative results with a limited number of model runs. The Sobol indices were preferred to other GSA methods (e.g., FAST34 and extended FAST35) because of their ability to provide quantitative second-order indices, so that the importance of parameter interactions can be assessed. The main output of the Morris method are the values μ* and σ; a high value of μ* indicates that a parameter is important, whereas a high value of σ indicates that the μ* value is affected by the value of other parameters. The Sobol sensitivity indices provide a quantitative measure of the part of model variance (i.e., model uncertainty) attributable to each parameter. The degree of dechlorination (DOD) at the end of simulations (350 days) is employed as the sensitivity measure. More details on the GSA are presented in the SI.
’ RESULTS Experimental Data. Experimental Data show complete degradation of TCE to ethene in about 200250 days (Figure 2). A fast transformation of TCE into cis-DCE is observed at the beginning of the experiment. After that, cis-DCE is present for almost 100 days and is then transformed into VC and subsequently to ethene. Lactate is completely transformed into acetate and propionate within 10 days of the beginning of the incubation. Propionate degradation occurs up to day 40, when propionate reaches a concentration threshold of about 0.5 mmol/L. Acetate concentration decreases after complete dechlorination and is accompanied by an increase in methane, suggesting the occurrence of acetoclastic methanogenesis. Very low H2 concentrations (13 nmol/L, in agreement with field-scale levels18) are observed with intermittent peaks. High ferrous iron concentrations are observed shortly after the beginning of the experiment and decrease in conjunction with sulfate reduction from day 20. Then, between days 70 and 190, a second increase in Fe(II) is observed. Model Results and Calibration. Calibrated parameter values are presented in Table 1, and the relative 95% confidence intervals are reported in the SI (Table S4). Overall, the parameters seem to be well-defined, and the calibrated model describes the observations very well (Figure 2); however, discrepancies exist for some compounds. Calibration statistics are presented in the Supporting Information (Table S3).
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Organic Acids and Methane. The model indicates that the slowdown of propionate fermentation at day 40 is occurring when propionate-fermenting biomass reaches the concentration threshold fixed by Xmax. After this point, propionate still ferments at a very slow rate due to bacterial maintenance and to compensate for cell decay. Simulated acetate concentrations are constantly higher than observations for times after day 30. The difference may be due to other processes not considered here, such as other degradation pathways or an underestimation of the bacterial yield. Simulated methane concentrations fit very well the observed values until day 260. The model could not reproduce the observed rise in methane concentration because acetoclastic methanogenesis was not implemented in the model. However, acetoclastic methanogenesis seems to occur after dechlorination is complete (Figure 2), so the consideration of acetoclastic kinetics would not improve the description of SERD, but would add more parameters to the model and make the sensitivity analysis more tedious. Hydrogen. The model satisfactorily reproduced the occurrence and the magnitude of H2 peaks. The first H2 peak occurs at the transition from iron-reducing conditions involving the more bioavailable iron hydroxides to sulfate-reducing conditions, whereas the second rise in H2 concentration is due to the change from sulfate-reducing condition to the reduction of the less bioavailable iron. The third H2 peak is associated with the start of cis-DCE dechlorination, suggesting that iron-reducing bacteria are outcompeted by Dehalococcoides. Finally, the last rise occurs when reductive dechlorination is complete, methane concentrations increase and acetate concentrations decline. Thus, the experiments indicate that the system ends with hydrogenogenic or acetoclastic methanogenesis conditions. Sulfate and Ferrous Iron. Modeled sulfate concentrations fit the observed values: sulfate is rapidly consumed a few days after the beginning of the incubation. On the other hand, the model could not completely reproduce the ferrous iron behavior: modeled and observed concentrations fit well at the beginning and at the end of the experiment, but are in disagreement between days 25 and 150. This is due to the fact that in the model siderite is only allowed to precipitate; thus, the Fe(II) originating from siderite dissolution is missing at these times. Siderite dissolution was deliberately excluded because of the continuous changes of siderite saturation index during the experiment (Figure S2 in the SI). If dissolution were considered, Fe(II) concentrations would have been controlled mainly by the saturation index and the carbonate content. Although implementation of mineral dissolution/precipitation kinetics would have improved the model fit, no mineral kinetics were considered to avoid additional parameters and increased model complexity. Shortly after the beginning of the experiment, ferrous iron concentrations are relatively high because iron reduction is occurring and the solution is supersaturated with respect to siderite. Then, when the most bioavailable iron oxides have been depleted, iron reduction slows and gives way to sulfate reduction. Because hydrogen sulfide is released, ferrous iron precipitates as iron sulfide and subsequently to pyrite (Figure S3 in the SI). After that, bacteria using H2 or acetate reduce the less bioavailable iron, and the system again becomes supersaturated with respect to siderite and gradually reaches the saturation index of the natural groundwater. Global Sensitivity Analysis. Results of the variance-based sensitivity analysis are expressed by two sensitivity indices: the Sobol main effects Si indicate the importance of each parameter considered individually, whereas the total effects Sti account for 8398
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8399
a
H2
7.65 10
7
XMethan i
CO2
1.49 10
μMethan max
4.42 10
6
5
μVC max
5.02 1010
6.27 10
7.86 10
KMethan s
1.01 10
2/VC KH s
8
8
2/DCE KH s 3.84 108
1.09 10
8
KAcet s 6
μTCE max
VC
H2
9
8.22 10
XTCE i
5.29 108
KSulf s/ED
kSulf max 1.19 109b
3.62 108
KFe-h-lbio s/ED
7.46 108b
1.39 107
kFe-h-lbio max
7.45 109 KFe-h-bio s/ED
1.02 107b
3.72 106 kFe-h-bio max
KFe-a-lbio s/ED
6.34 107
5.77 108
μFe-a-lbio max
9
6.73 106
KFe-a-bio s/ED
9.79 10
KPs ferm
5
XFe-a-lbio i
μFe-a-bio max
6
9.59 10
KLs ferm
(mol L1)
constant ED
half-saturation
KED s
1.15 105
XFe-a-bio i
7.18 10
ferm μPmax
2.47 10
5
XDCE i
DCE
H2
5
1.13 10
XPi ferm
9.14 10
7
ferm μLmax
(s1)
(mol L1) XLi ferm
growth rate
maximum
initial biomass
Xi
μi
μDCE max 2.98 106
TCE
sulfate
Fe(III)
less biodegr
Fe(III)
readily biodegr
Fe(III)
less biodegr
Fe(III)
readily biodegr
acetate
H2
H2
H2
acetate
acetate
propionate
Not calibrated. b In mol L1 s1.
methanogenesis
dechlorination
sulfate reduction
iron reduction
fermentation
acceptor
electron donor
lactate
electron
ED
EA
Table 1. Parameter Names and Calibrated Values for the Kinetic Model
8
4.86 10
KVC s 5
KDCE s 2.86 106
8.12 10
KTCE s
1.02 104
KSulf s/EA
9.79 109
KFe-h-lbio s/EA
9.32 106
1.03 107 KFe-h-bio s/EA
KFe-a-lbio s/EA
3.76 108
KFe-a-bio s/EA
(mol L1)
constant EA
half-saturation
KEA s
TCE/DCE/VC
Fe(III)
readily biodegr
sulfate
sulfate
acetate
inhibitor
6
7
5.45 10
KVC i 6
KiDCE 1.80 107
1.36 10
KTCE i
4.39 109
KSulf i
3.99 109
KFe i
3.99 109
KFe i
9.11 10
KPi ferm
(mol L1)
inhibition constant
Kinh i Y
0.016
YMethan
0.02
YVC
YDCE 0.02
0.02
YTCE
0.15
YFe-a-lbio
0.15
YFe-a-bio
0.042
YPferm
YLferm 0.042
(molX/molED)
biomass yielda
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Environmental Science & Technology both the importance of individual parameters and interactions between parameter pairs. Both Si and Sti indicate that the initial concentration of sulfate is the most influential parameter, followed by the maximum allowable fermenting biomass. Then, the ranking sequence for the two indices changes, but both highlight parameters linked to fermentation and dechlorination kinetics (Figure 3). The Morris screening indicates that the initial concentration of sulfate is the most important parameter, followed by the half-saturation constant for hydrogenotrophic sulfatereducing bacteria and the initial concentration of lactate. The complete parameter list and graphical representations of results are available in the SI (Figure S4 and Table S5). Differences between the results of the two SA methods exist and are attributable to the huge size of the model space, but the substantial agreement of the two methods suggests that the main trends have been captured.
’ DISCUSSION Redox Processes. Hydrogen. Hydrogen peaks have been observed when the biogeochemical system switches sequentially from the utilization of one electron acceptor to another, because a redox process stops before the beginning of the next one.6 In fact, close to the equilibrium, the production and the consumption of H2 have similar rates, and so H2 concentrations are very low. When an electron acceptor is almost depleted, the associated bacterial rate decreases (eq 2) and the production of H2 exceeds the consumption. Therefore, the H2 concentration increases until the rate of the following redox process reaches the H2 production rate, and a peak in H2 concentration can be observed. In this study we observed increases in H2 concentrations in conjunction with the start of DCE degradation, suggesting that reductive dechlorination is strictly connected to syntrophic degradation of organic compounds. Moreover, the result shows that Dehalococcoides bacteria become active only when H2 production exceeds the consumption, and this occurs when the iron reduction rate slows due to electron acceptor limitations. Simulations also show that only 0.5% of the H2 produced is consumed by dehalogenating biomass and that 95% of H2 is consumed in the first 40 days by iron- and sulfate-reducing bacteria (Figure S4 in the SI), thus suggesting that the fate of H2, and consequently the success of dechlorination, is highly dependent on processes occurring shortly after the beginning of the experiment and that dominating processes may depend on the time scale considered. Iron. The increase in ferrous iron concentrations during DCE and VC dechlorination observed in the experiments suggests that iron reduction occurs in conjunction with SERD. Modeling results also show that the degree of iron bioavailability plays a major role in the dechlorination process. Dissolved H2 concentrations are known to be dependent on the degree of iron bioavailability,36 showing a higher uptake rate for readily biodegradable iron species. Here the model confirms that H2-driven dechlorination cannot occur in the presence of readily biodegradable iron, whereas Dehalococcoides can outcompete iron-reducing bacteria as the iron bioavailability decreases. Model calibration indicates an initial Fe(III) concentration of 22.8 mmol/g, a value considerably higher than the 6.2 mmol/g of Fe(III) measured on site sediments. However, measurements on sediments may be affected by spatial heterogeneities,37 and the simulated value is still reasonable for sandy Danish sediments.38 Sulfate. Sulfate has previously been shown to be a limiting factor for SERD,15 and the observed higher affinity for H2 of sulfate-reducing bacteria, and the sensitivity analysis, confirm this
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Figure 3. Graphical representation of the sensitivity analysis results. The 15 parameters with the highest Sobol total index Sti are plotted together with their Sobol main effect Si and Morris μ*. Parameters are then grouped according to the process they belong to. Please note that Sobol indices and Morris μ* are plotted on different scales and are not comparable.
result. Nevertheless, SERD has been found to be insensitive to sulfate concentrations when fermentation is fast enough to provide sufficient H2 to both Dehalococcoides and sulfate reducers;15 thus, different results may be expected when other fermenting compounds are taken into consideration. Fermentation. Different types of electron donor change the dechlorination process9 because of differences in fermentation patterns: compounds slowly delivering molecular hydrogen ensure H2 levels high enough for dechlorination to occur but do not promote methanogenesis, whereas the use of easily degraded compounds results in an overproduction of methane. The importance of the fermenting process is highlighted by the sensitivity analysis results. The growth rate of propionate fermenters and the threshold of fermenting biomass are the top-ranked parameters because they control the rate and the amount of H2 delivered to the system. Dechlorination. For the model of dechlorinating biomass kinetics described in this paper, DCE-degrading related parameters (DCE maximum growth rate, DCE and H2 half-saturation constants) are found to be the most important parameters if complete dechlorination is to be achieved, in agreement with the findings from Kouznetsova et al.17 The model is less sensitive to the parameters involved in TCE degradation because TCE degraders use acetate as electron donor: acetate is quickly and abundantly produced, and so TCE transformation into DCE is rapid and always occurring. The lesser importance of the parameters controlling VC-degrading kinetics can be explained by the temporal succession of the two processes (VC reduction starts inevitably after DCE reduction) and by the fact that DCE and VC are degraded by the same bacterial strain (higher DCE reduction rates will result in a higher biomass production and a more rapid VC reduction). To compare measured and simulated concentrations of Dehalococcoides bacteria, a bacterial mass ranging between 83 1015 and 1172 1015 g/cell39 was used. Calibration results indicate an initial concentration of 5 1010 mol of C5H7O2N/ L, which corresponds to a value between 4.8 103 and 6.3 105 cells/L. This value matches the number of Dehalococcoides VcrA genes detected in the sediments (3 1029 103 copies/L). Agreement has also been found between peak Dehalococcoides concentrations observed in groundwater during the full-scale field 8400
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Environmental Science & Technology ERD demonstration experiment18 (1 1071 108 cells/L) and maximum simulated values (5.4 1077.7 108 cells/L). Global Sensitivity Analysis. Variance-based sensitivity methods can provide quantitative information on the model in addition to the parameter ranking. The Sobol index of a parameter is equal to the output variance attributable to this parameter. For orthogonal model inputs, the sum of the Sobol indices of all orders and all parameters must be equal to 1, because the entire variability of the model is included. The sum of the firstand second-order Sobol indices of the model considered in this study is equal to 0.39, which means that only 39% of the model variance has been caught by the SA method or that only 39% of the variability of the degree of dechlorination is attributable to the single parameters or the interactions between parameter pairs. There are two possible explanations: the HDMR may have not approximated the model space correctly because not enough model runs have been performed, or higher order indices (>2) are responsible for the missing part of model variability. The first hypothesis can be rejected because results from a bootstrapped data set containing half of the model runs were similar to those obtained with the whole data set. The latter explanation implies that synergies among 3 or more parameters are essential to describe the model output. SERD in natural systems is therefore very complex and cannot be simplified to first- or second-order interactions without the loss of important system behaviors. Thus, it may be impossible to approximate interactions between SERD and redox processes with simpler models using first-order kinetics or by neglecting some degradation processes. For some parameters, the Sobol main effects Si and total effects Sti have close or equal values (Figure 3), suggesting that some parameters act on the model output independently of other factors and thus are entirely responsible for a given modeled process. For example, the parameter Lacti, the initial concentration of lactate, is independent of other parameters, because lactate is artificially introduced in the system and is quickly fermented into smaller compounds with minimal interaction with other processes. The maximum allowable fermenting biomass, Xmax, is also indicated as a parameter acting independently from the others. The amount of microbial biomass in the subsurface has been previously linked to physical factors such as sediment grain size40 or the type and age of the geological formation,41 and it is likely that the maximum fermenting biomass is also dependent on such factors. Thus, Xmax can be considered to be a lumped parameter that is largely unknown. The fate of fermenting products has already been indicated as an important component in understanding dechlorinating communities.4 A better description of fermenting processes and the influence of sediments on fermentation will help to improve the model and the understanding of its effect on SERD, especially when additional fermenting substrate is provided (e.g., during ERD). Model Complexity and Outlook. Given the complexity of the model proposed, it is necessary to comment on the significance of its parameters. The model is clearly overparameterized with a large number of parameters and cannot be well calibrated to the data used in this study. Nevertheless, the agreement between simulated and observed concentrations of H2 concentrations and chlorinated solvents, the similarity of calibrated parameters with literature data (SI, Table S6), and the relatively narrow confidence intervals obtained during the model calibration suggest that the empirical MichaelisMenten-based kinetics model presented in this study has largely captured the system complexity. The consideration of different experimental
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setups (changes of initial conditions, mineral composition, etc.) would allow better parameter determination and, consequently, produce a more general model. This work has shown that the availability of H2 measurements and their inclusion in the model improve system understanding and the description of redox processes. The hydrogen concentrations in the laboratory experiments resembled the observations in the related field-scale demonstration.18 This is promising for future use of the model concept for simulation of full-scale ERD remediations. However, the inclusion of flow and transport processes to simulate the effect of water flow42 and physicochemical heterogeneities43 on the success of SERD in sandy aquifers is required. The global sensitivity analysis tools highlight the high level of complexity required to describe the processes involved in SERD. Possible further model development involves the use of more extended data sets (e.g., with periodical measurements of biomass) to increase parameter identifiability.
’ ASSOCIATED CONTENT
bS
Supporting Information. Additional text, figures, and tables including parameter intervals used for sensitivity analysis, extended sensitivity analysis results, comparison with parameter literature values, groundwater chemical properties, temperature dependence of biomass growth rates, and siderite saturation indices. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail: fl
[email protected].
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