Environ. Sci. Technol. 2007, 41, 4980-4985
Quantifying the Degradation and Dilution Contribution to Natural Attenuation of Contaminants by Means of an Open System Rayleigh Equation BORIS M. VAN BREUKELEN* Department of Hydrology and Geo-Environmental Sciences, Faculty of Earth and Life Sciences, VU University Amsterdam, De Boelelaan 1085, NL-1081 HV Amsterdam, The Netherlands
Quantifying the share of destructive and nondestructive processes to natural attenuation (NA) of groundwater pollution plumes is of high importance to the evaluation and acceptance of NA as remediation strategy. Dilution as consequence of hydrodynamic dispersion may contribute considerably to NA, however, without reducing the mass of pollution. Unfortunately, tracers to quantify dilution are usually lacking. Degradation though of low-molecular-weight organic chemicals such as BTEX, chlorinated ethenes, and MTBE is uniquely associated with increases in isotope ratios for steady-state plumes. Compound-specific isotope analysis (CSIA) data are commonly interpreted by means of the Rayleigh equation, originally developed for closed systems, to calculate the extent of degradation under open system field conditions. For that reason, the validity of this approach has been questioned. The Rayleigh equation was accordingly modified to account for dilution, and showed that dilution contributed several to many times more to NA than biodegradation at a groundwater benzene plume. Derived equations also (i) underlined that fieldderived isotopic enrichment factors underestimate actual values operative as a consequence of dilution, and (ii) provided a check on the lower limit of isotopic fractionation, thereby resulting in more reliable predictions on the extent of degradation.
Introduction Degradation is the only natural attenuation (NA) process that truly removes organic pollutants from the environment (1). Dilution though, as result of hydrodynamic dispersion in aquifers, may have a considerable contribution to NA, reducing concentrations, but at the expense of a larger volume of groundwater becoming polluted. Because contaminants are not transformed, dilution as allowed NA process has been criticized (2-4). Quantifying the contribution of both dilution and degradation to NA is, therefore, required to evaluate NA as remediation strategy. Discriminating the degradation from the dilution effect to NA is, however, difficult at most contaminated sites, since non-degrading tracers are commonly not present, with the exception of landfill sites where leachate contains both high chloride (1, 5) and bromide (6) concentrations. Stenback et al. (7) demonstrated that bio* Corresponding author phone: +31-20-5987393; fax: +31-205989940; e-mail:
[email protected]. 4980
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degradation rates calculated from contaminant concentration data varied by a factor of 3 depending on the chosen dispersion coefficients, illustrating that the contributions of biodegradation and dilution to NA are not well constrained. Compound-specific isotope analysis (CSIA) interpreted by means of the Rayleigh equation (8, 9) allows a more accurate estimation of the extent of degradation of lowmolecular-weight organic chemicals and has recently been reviewed (10, 11). The Rayleigh equation relates the change in isotope ratio of an element in a molecule (e.g., δ13C, δ2H) to the fraction of molecule remaining, f, as a result of degradation, via the kinetic isotope fractionation factor (R) of the isotope pair and the degradation process. Increases in isotope ratio (e.g., a positive isotopic shift) nearly always indicate occurrence of degradation, since degradation is the only known NA process that may result in significant isotopic fractionation (10, 11). The isotopic shift may, in addition, be caused by isotope fractionation associated with sorption but only at the front of nonstationary pollution plumes (12). The Rayleigh equation was originally developed for closed systems, and therefore, f directly relates to the extent of degradation in laboratory batch experiments. The Rayleigh equation has, however, also been applied to estimate the extent of degradation under open system field conditions at sites contaminated with BTEX compounds (5, 13-18), chlorinated ethenes (19, 20), and MTBE (21, 22), where, besides degradation, dilution also decreased concentrations and, thereby, the fraction remaining. The validity of applying the Rayleigh equation to open system field conditions has, therefore, been questioned. It has been argued that (i) the Rayleigh equation inherently overestimates the effects of biodegradation since concentration decreases due to advection and dispersion are neglected (14), (ii) sorption and dilution restrict the use of the Rayleigh equation in quantifying the absolute amount of the biodegraded substrate fraction (15), (iii) CSIA-based quantification of biodegradation is only allowed by means of the Rayleigh equation in case of a strong correlation between contaminant concentrations and isotope ratios (17), or (iv) the Rayleigh equation can only be used to quantify in-situ biodegradation if dilution is proved to be insignificant in comparison to biodegradation (23). Two recent studies showed, however, that the Rayleigh equation can reliably be applied to open systems. Fischer et al. (24) performed a multitracer test with bromide and deuterium labeled toluene in a BTEX polluted aquifer to test whether the Rayleigh equation holds in open systems, and concluded that the Rayleigh equation is a reliable tool to quantify biodegradation in contaminated aquifers. In another recent paper Abe and Hunkeler (25) showed via modeling that the Rayleigh equation systematically, but only slightly, underestimates the extent of degradation in physical heterogeneous systems. Extreme cases of aquifer heterogeneity resulting in “flow segregation” may, however, result in larger degrees of underestimation as discussed by Kopinke et al. (12). The extent of degradation as predicted by the Rayleigh equation may consequently be considered as being conservative. The objective of this paper was to accommodate the dilution process implicitly in the Rayleigh equation to allow its application to open systems, and to better quantify the contributions of both (bio)degradation and dilution to natural attenuation. The CSIA-based method was applied to a groundwater benzene plume at a previously investigated industrial site (14). 10.1021/es062846u CCC: $37.00
2007 American Chemical Society Published on Web 06/16/2007
Derivation of Equations Derivation of an Open System Rayleigh Equation. Concentrations of organic chemicals decrease away from sources in the open system of a groundwater environment as a combined result of (bio)degradation and dilution. Other NA processes like evaporation or degassing are usually only of significance in and close to the unsaturated zone, while (equilibrium) sorption retards the spreading of pollution without changing its dissolved concentration. Whereas (bio)degradation decreases the total mass of pollution and is associated with isotopic fractionation, dilution occurs without isotopic fractionation but increases the volume of groundwater becoming polluted, thereby also lowering contaminant concentrations. The Rayleigh equation (8, 9) given below relates the change in isotope ratio to the fraction of contaminant remaining as result of degradation, fdegradation, via the kinetic isotope fractionation factor (R):
R St RS0
) f degradation(R-1) ) ( f total × F)(R-1)
(1)
where RSt is the isotope ratio of the heavy (e.g., 13C) to the light (e.g., 12C) isotope of an element (e.g., carbon) in substrate S at time is t, and RS0 is the initial isotope ratio of the source. In the original Rayleigh equation, f equals the ratio of the measured and the initial concentration as a closed system is described and only degradation is assumed to lower concentrations. In a groundwater environment however, the fraction remaining, f total, has been decreased by the combined effect of degradation and dilution. If the dilution factor, F, the number of times the source volume has become diluted at the observation location, could be determined, f as result of degradation can be calculated as f degradation ) f total × F. Note that the inverse of F is the fraction remaining due to dilution, f dilution. For example, if the source concentration is 10 times diluted, f dilution equals 0.1. Consequently, it can be derived that
fdegradation ) f total × F )
f total
fdilution or f total ) fdegradation × f dilution
(2)
The Rayleigh equation (eq 1) can be ln transformed (10) to
(
1000ln
10-3δSt + 1
10-3δS0 + 1
)
) ∆ ) ln fdegradation ) ln( ftotal × F)
(3)
where δSt and δS0 are the ratios of the heavy isotope to the light isotope of an element in substrate S at time t ) t and t ) 0, respectively, expressed in the δ notation (δsample ) ((Rsample - Rreference)/Rreference) × 1000, where Rreference is the isotope ratio of the international standard); where the lefthand term equals the isotopic shift, ∆ (‰), of a sample with respect to the source; and where , the kinetic isotopic enrichment factor, equals (R - 1) × 1000. Assuming that for a system is known, for example from laboratory closed system microcosm experiments, the dilution factor, F, can be calculated from observed concentrations and isotope ratios in the field with the following equation (eq 3 rewritten):
F ) e((∆/)-ln f total)
(4)
FIGURE 1. Hypothetical situation showing that the Rayleigh equation holds if dilution occurs independent of the stage that dilution becomes important. Shades of gray indicate the mass of substrate dissolved in a specific volume of water (circles; not to scale). Subsequently, the extent of dilution, D (%), can be calculated as
(
D (%) ) (1 - f dilution) × 100 ) 1 -
1 × 100 F
)
(5)
Next, fdegradation can be calculated from either eq 2, or directly from the Rayleigh equation (eq 1), as shown later, while the extent of (bio)degradation, B (%), follows from
B (%) ) (1 - fdegradation) × 100
(6)
Note that the accuracy of fdegradation depends on the uncertainty of the value selected, whereas the accuracy of fdilution also depends on the uncertainty of the source concentration. Figure 1 illustrates that the Rayleigh equation holds if dilution occurs. If a source concentration of 100 mg/L in 1 L becomes degraded to 10 mg/L ( f degradation ) 0.1), and subsequently 10 times diluted causing the concentration to decrease to 1 mg/L in 10 liters of water ( fdilution ) 0.1, F ) 10), the absolute amount degraded is 90 mg. Also if the source becomes first 10 times diluted to 10 mg/L in 10 liters of water, and degradation only starts thereafter, the same absolute mass is degraded (10 L × (1 - f degradation) × 10 mg/L ) 90 mg). This example shows that the Rayleigh equation not only reliably predicts the extent but also the absolute amount of substrate degraded independent of the stage that dilution becomes important, provided the isotopic enrichment factor is constant within the system. Degradation may potentially be distributed over two or more pathways having different values, in particular on the scale of a contaminant plume where degradation usually occurs under anaerobic conditions within the plume core and under more oxidized conditions at the plume fringe. Van Breukelen (26) recently developed Rayleigh-type equations that based on two-dimensional CSIA (e.g., combining two isotope pairs like δ13C and δ2H; (21, 22)) allow calculation of the effective isotopic enrichment factor that applies if degradation is distributed over two pathways. The extent of (bio)degradation and dilution are both 90% in the hypothetical situation (Figure 1) as fdegradation and fdilution are 0.1. The sum of B (%) and D (%) can thus exceed 100% and may maximally become 200%. Note however that the extent of natural attenuation, T (%), does not equal the sum of B (%) and D (%), but follows from
T(%) ) (1 - f total) × 100 ) (1 - (1 - B(%)/100) × (1 - D(%)/100)) × 100 (7) and thus cannot exceed 100%. So far, the occurrence of sorption and physical heterogeneity has been neglected. However, even if sorption is associated with isotope fractionation, sorption related isotopic shifts that may occur at the front of a plume will have disappeared once the plume has reached steady-state (12). Therefore, the derived equations also apply to steady-state VOL. 41, NO. 14, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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plumes experiencing sorption. However, the absolute mass of a contaminant degraded per aquifer volume equals (1 fdegradation) × Csource × (Kd + 1), where Kd is the dimensionless solid-water partitioning coefficient of the contaminant for the aquifer conditions. Furthermore, the Rayleigh equation always slightly, but systematically underestimates the true extent of degradation since aquifers are physical heterogeneous systems (12, 25). This implies that the extent of dilution will consequently always be slightly overestimated if the open system Rayleigh equation is applied. On Field-Derived Isotopic Enrichment Factors. To allow CSIA-based quantification of degradation an appropriate must be selected. It seems attractive to obtain directly from field observations since lab experiments are time-consuming and obviously less represent in-situ conditions. Equation 3 can be rewritten as
(
)
fdegradation ∆ ) ) ln ftotal × ftotal ln(ftotal
/
ln(fdegradation)/ln(ftotal)
) ) ln(ftotalB ) ) B* × ln(ftotal) (8)
where B*, the breakdown factor, follows from the measured concentrations and isotope ratios in the field and the assumed valid . The dilution factor, D*, equals 1 - B* and can, similar to B*, be defined as
D* )
ln fdilution ln ftotal
(9)
The ratio D*/B* indicates the relative contribution of dilution and degradation to the observed concentration decrease. If the ratio is zero, D* ) 0, and B* ) 1, the concentration decline is completely due to degradation. If for example, the ratio ) 1, D* ) B* ) 0.5, the contribution of dilution and degradation to the relative concentration decrease in logarithmic scale is equal. The following equation (eq 8 rewritten) shows that a field-derived isotopic enrichment factor, field, underestimates the true operative in the environment as a consequence of dilution (e.g., B* < 1):
field ) B* × true )
∆ ln ftotal
(10)
Results and Discussion Deriving Isotopic Enrichment Factors from Field Observations. Equation 10 shows that in open systems where concentrations are decreased by dilution (D* > 0 and B* < 1), a field derived isotopic enrichment factor, field, calculated from field concentrations and isotope ratios, will be lower (i.e., less negative) than true, since field ) true × B*. Deducing from open systems must, therefore, result in an underestimation of true. Since the extent of dilution and thereby also B* may be highly variable in the field and thus also within a monitoring network, obtained field values will vary accordingly and have a low coefficient of determination (R2). Lack of a strong correlation between contaminant concentrations and isotope ratios does not necessarily imply therefore that CSIA-based quantification of degradation by means of the Rayleigh equation is not allowed. Chen and MacQuarrie (27) found in a modeling study that the calculated “field-derived” values for part of the model domain were always much lower than specified in the model input, and that the relationships between isotope ratio and concentration of the compound were not strictly linear but exhibited variations in slope. True enrichment factors can consequently not reliably be obtained from the field if the extent of dilution is not corrected. Unfortunately, this is only possible for some types of pollution including landfill leachate having elevated chloride (1, 5) and bromide concentrations (6). 4982
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Note that degradation may become overestimated if (i) the Rayleigh equation would be applied to obtain fieldderived values, or if (ii) the Rayleigh equation would be assumed to only allow for quantification of degradation once it recalculates observed concentration gradients. The first results in underestimation of the true operative in the field since dilution always occurs (eq 10), while the second entices selection of a too low value to obtain a better fit with observed concentrations (which will be lower than predicted if dilution occurs). Both result in underestimation of true, and consequently in overestimation of the extent of (bio)degradation. Quantifying the Share of Biodegradation and Dilution to Natural Attenuation at a Field Site. The open system Rayleigh equation was applied to a previously investigated groundwater benzene plume showing CSIA-based occurrence of biodegradation (14), to further find out to what extent observed concentration decreases were besides biodegradation also due to dilution (Figure 2). The more than 160 m long benzene plume present in an anaerobic and nitratefree aquifer resulted from a spill that occurred in 1977 at an industrial site located at the shore of the Westerschelde estuary in the southern part of The Netherlands (14). Since the plume probably reached steady-state, observed positive isotopic shifts (∆13C of benzene up to +2.3‰) were unlikely caused by sorption, and must, therefore, be uniquely associated with biodegradation. Sorption-associated isotopic shifts should only manifest at the front of nonstationary plumes and moreover increase downgradient (12) which was not observed. Detailed information on the hydrogeology of the site, sampling, and analysis methods is given by Mancini et al. (14). Table 1 (calculation C1) shows that application of the open system Rayleigh equation, while selecting the same source well (W1S1) and value (-1.9‰) as Mancini et al. (14), resulted in B* values being outside the allowed range of 0-1 (see eq 8) for six out of the total of 16 well screens. The dilution factor, F, was below 1 (results of calculations not shown), while the extent of dilution was negative for these six well screens indicating that the extent of biodegradation predicted by the Rayleigh equation exceeded the observed concentration decline between the source and these six downgradient well screens. The B* values specify the two possible causes: (i) if B* exceeds 1, the predicted concentration decrease is larger than observed, while (ii) if B* is negative, downgradient concentrations are higher than the source concentration. Application of the open system Rayleigh equation thereby points out that the boundary conditions assumed by Mancini et al. (14) must be different. Mancini et al. (14) logically selected well W1S1 as source well since it had the lowest (most negative) δ13C (-28.7 ( 0.0 ‰). Although the other well DL3 present in the same source area was only slightly more enriched in δ13C (-28.6 ( 0.1 ‰), the δ13C values of both wells were statistically not different considering the uncertainty limits. This other well DL3 seems more appropriate as source well because it was present at slightly shallower depth (1-2 m below surface) while in contact with pure-phase hydrocarbons, and consequently had a much higher benzene concentration (145 mg/L versus 65.4 mg/L for W1S1). Selecting DL3 as source well however still resulted in one well (W4S4) having a B* value exceeding 1 (calculation not shown) implying that the source concentration was still higher and/or the effective at the site was larger (i.e., more negative). Calculations indicated that the source concentration must be at least 171 mg/L (results not shown), or the value must be larger than or equal to -2.4‰ for B* not to exceed 1 at well W4S4 (Table 1, calculation C2). Both possibilities seem reasonable. Griebler et al. (17) assumed that the standard deviation of a source well concentration may be 10% implying
FIGURE 2. Cross-section of the benzene plume downgradient from the source area at the industrial site previously described by Mancini et al. (14). Black vertical rectangle symbols represent the screens of the monitoring wells (coded as Sx and Wx, respectively; Table 1), shades of gray and white lines indicate interpolated benzene concentrations (mg/L), dashed black lines show the interpolated calculated extent of dilution (%), and “D: xx” and “B: xx” denote the calculated extent of dilution (%) and biodegradation (%), respectively. Results are shown for calculation C3 (E ) -3.6‰, source well is DL3; Table 1).
TABLE 1. Concentrations and Isotope Signatures of Benzene Observed within the Contaminant Plume Together with Calculated Values for B*, B (%), D (%), and D*/B* extent of biodegradation, B (%)
B*
extent of dilution, D (%)
D*/B*
well codea
benz. conc. (mg/L)
δ13C-benzene (‰)
C1b
C2c
C3d
C1
C2
C3
C1
C2
C3
C2
C3
W2S2 W2S3 W2S4 W3S2 W3S3 W3S4 W4S3 W4S4 W4S5 W5S2 W5S3 W5S4 W6S3 W6S4 W6S5 W7S4 median value:
3.57 75.0 66.3 3.4 54.5 0.85 46.7 76.0 1.51 59.7 77.2 4.29 1.26 43.6 0.38 0.79
-27.4 ( 0.1 -28.0 ( 0.1 -28.3 ( 0.1 -26.7 ( 0.4 -27.9 ( 0.1 -27.6 ( 0.1 -28.3 ( 0.2 -27.1 ( 0.1 -26.4 ( 0.4 -28.2 ( 0.0 -28.0 ( 0.0 -27.7 ( 0.2 -27.1 ( 0.3 -28.2 ( 0.1 -28.5 ( 0.0 -27.2 ( 0.0
0.24 -2.8 -16 0.37 2.38 0.14 0.64 -5.8 0.33 2.97 -2.3 0.20 0.22 0.67 0.02 0.18
0.14 0.39 0.16 0.22 0.31 0.08 0.11 1.00 0.21 0.19 0.41 0.11 0.14 0.14 0.01 0.12
0.09 0.26 0.11 0.14 0.20 0.06 0.08 0.66 0.14 0.13 0.27 0.07 0.09 0.10 0.00 0.08
51 32 19 66 35 45 19 58 71 24 32 42 58 24 10.3 56
40 23 12 56 26 35 12 47 61 16 23 32 47 16 4.2 45
29 16 8 42 18 25 8 35 47 11 16 23 35 11 2.8 33
89 -68 -26 85 -29 97.6 11 -176 92.0 -20 -72 89 95.4 13 99.4 97.3
95.9 33 48 94.7 49 99.1 63 0 97.3 51 31 95.6 98.3 64 99.7 99.0
96.5 39 50 96.0 54 99.2 65 20 98.0 54 37 96.2 98.7 66 99.7 99.2
6.2 1.6 5.1 3.6 2.3 11 7.8 0.0 3.8 4.2 1.4 8.1 6.4 6.0 138 7.7
9.8 2.8 8.1 5.9 3.9 17 12 0.5 6.3 6.8 2.7 13 10 9.5 207 12
0.21
0.15
0.10
38.5
29.0
20.4
48.6
79.5
81.1
5.5
8.8
a Samples are designated WxSy, where x refers to well number and y to screen interval. Both numbers increase with distance from the source and with depth, respectively. See Figure 2 for exact sample locations in cross-section. b Calculation C1: ) -1.9‰; source well is W1S1 ([benz.] ) 65.4 mg/L, δ13C-benz. ) -28.7 ( 0.0 ‰). c Calculation C2: ) -2.4‰; source well is DL3 ([benz.] ) 145 mg/L, δ13C-benz. ) -28.6 ( 0.1 ‰). d Calculation C3: ) -3.6‰; source well is DL3.
a concentration of 171 mg/L falls within the 95% confidence level of the measured source concentration of 145 mg/L. Mancini et al. (14) selected the only available value at that time for anaerobic benzene degradation (-1.9‰ for a methanogenic consortium (28)). Current knowledge, however, shows that may be up to -3.6‰ under sulfate-reducing conditions (28). Since both redox processes together with iron-reduction were observed to occur at the site (14), the operational at the site may vary somewhere between these outer limits depending on the actual distribution of the anaerobic redox processes coupled to benzene degradation.
The open system Rayleigh equation thus allows verification on the validity of the lower (i.e., least negative) limit of the selected value although uncertainty in the source concentration somewhat interferes. Still, it is highly likely that must be larger than originally selected because otherwise dilution would be predicted not to occur at well W4S4 present around 100 meters downgradient from the source. The calculated extents of biodegradation by means of the open system Rayleigh equation (3-47%, ) -3.6‰; 4-61%, ) -2.4‰; Table 1) were, therefore, substantially lower than those calculated by Mancini et al. (14) (10-71%, ) -1.9‰) VOL. 41, NO. 14, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Relation between -log(fbiodegradation) and -log(fdilution) for downgradient wells within the benzene plume. The dashed line shows the regression of observations indicated as dots ()D*/B*; R 2 ) 0.59) discarding the two outliers indicated as squares. Results are shown for calculation C3 (E ) -3.6‰, source well is DL3; Table 1). since larger values had to be considered. Because benzene degradation may have occurred to varying extents of methanogenic and sulfate-reducing conditions, the calculated extents of biodegradation based on the for sulfate-reducing conditions may be regarded as the lower limit (Table 1, calculation C3), while the calculations selecting an of -2.4‰ (Table 1, calculation C2) must be considered as the upper limit of the extent of biodegradation at this site. The error of CSIA analysis was small (e0.1‰, n ) 11; 0.2-0.4‰, n ) 5; Table 1) and, therefore, can be expected to only have a minor contribution to the total uncertainty of the estimates which were largely determined by uncertainty in . Furthermore, calculations demonstrate that dilution had a much stronger effect on natural attenuation than biodegradation (a factor of ()D*/B*) 6 ()median value, ) -2.4‰) to 9 times ()median value, ) -3.6‰; Table 1) stronger). The dilution factor, F, was not much affected by the selected, and ranged at the plume margins from around 20 to up to 370 at one well (W6S5; results not shown). The strong and variable impact of dilution on natural attenuation and hence on the fraction remaining resulted in a very low field ()0.14‰) together with a low coefficient of determination (R2 ) 0.18), illustrating that isotopic enrichment factors should always be selected from closed system laboratory experiments, and emphasizing that a low coefficient of determination for field observations does not imply that CSIA-based quantification of biodegradation is not allowed. Figure 2 shows that the extent of dilution increased away from the plume core and was highest at the fringe zone in agreement with dispersion theory. Interestingly, the extent of biodegradation was generally also higher at the fringe zone (Figures 2 and 3) indicating that the fringe zone favored biodegradation. Vieth et al. (16) observed enhanced biodegradation at the fringe zone of a BTEX plume as well on basis of CSIA. Higher extents of biodegradation at the fringe zone could be the consequence of both lower contaminant concentrations as well as higher oxidant availability. Biodegradation becomes enhanced if contaminant concentrations decrease below toxic levels. Moreover, since biodegradation usually follows Monod kinetics, the ratio of the degradation rate and concentration increases toward lower concentration levels as the rate order shifts from pseudo zero-order at higher concentration levels present in the plume core, to relatively faster pseudo first-order at the lower concentration levels encountered at the fringe. In addition, the high sulfate availability in the saline groundwater below the contaminant plume likely enhanced biodegradation at the lower fringe zone of the benzene plume where the sulfate concentration was around 5 mM. Sulfate was not elevated at the upper fringe zone with respect to the plume (sulfate 4984
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) 0.01-0.5 mM). Therefore, the lower limit of the extent of biodegradation (calculation C3, Table 1) applies in particular for the lower fringe zone samples were sulfate-reduction was identified to be the major redox process. Implications for Contaminant Hydrogeology. Isotopic enrichment factors derived from field observations underestimate the true values operative in the environment as shown by eq 10 since dilution occurs in open systems. Obtaining from field observations is attractive though, especially for organic chemicals for which values have not yet been determined. Note that this actually must be possible once these chemicals are present together with contaminants having well constrained values. Concentrations and isotope ratios from the latter compounds (e.g., benzene) can be used to calculate the dilution factor, F, at the observation wells, and subsequently the regression based on eq 3 allows to obtain reasonable estimates on the true in-situ for the compounds having yet unknown values. Recently, Mak et al. (23) combined conservative transport modeling and the Rayleigh equation to quantify the extents of dilution and biodegradation, respectively, in an approach to quantify the share both processes had to natural attenuation of a contaminant plume. The current study shows that combining the isotope fractionation concept with groundwater modeling and tracer studies is not necessarily required to take dilution effects into account as proposed by Richnow et al. (15). The derived open system Rayleigh equation applied to CSIA data is shown to quantify the share of degradation and dilution to natural attenuation in an uncomplicated way which is of high importance to the evaluation and acceptance of monitored natural attenuation as remediation strategy (2-4). The modified Rayleigh equation applies for steadystate plumes where possible isotope fractionation effects associated with sorption (12) have disappeared, and was developed for groundwater environments where attenuation caused by degassing or evaporation can be neglected. The Rayleigh equation has been shown to overestimate the extent of degradation, but not the extent of net removal, if nonfractionating mass-removing processes like evaporation occur before or simultaneously with degradation (29, 30). Dilution as nonfractionating process does not remove but distributes the pollutant mass over a larger area. The accuracy of the calculated extent of dilution depends on the uncertainties of both and the source concentration, and will in contrast to the calculated extent of degradation always be slightly overestimated as a consequence of physical heterogeneity (25) or flow segregation (12) in aquifer systems. The presented case study showed that the open system Rayleigh equation also provides a check on the lower (i.e., least negative) limit of the selected value and thereby results in conservative and more reliable predictions on the extent of degradation.
Acknowledgments I thank the four anonymous reviewers for their comments and suggestions that helped to improve the quality of this manuscript. The research was supported by the VU University Amsterdam via direct university funding.
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Received for review December 1, 2006. Revised manuscript received May 10, 2007. Accepted May 11, 2007. ES062846U
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