Environ. Sci. Technol. 2006, 40, 7662-7667
Kinetics of Contaminant Desorption from Soil: Comparison of Model Formulations Using the Akaike Information Criterion C H R I S T O P H E R M . S A F F R O N , †,‡ J E O N G - H U N P A R K , * ,‡ B R U C E E . D A L E , †,‡ A N D THOMAS C. VOICE‡ Department of Civil and Environmental Engineering, Michigan State University, East Lansing, Michigan 48824
Desorption of organic contaminants from soil can be modeled by dividing the desorption time-concentration profile into three distinct regimes. These are characterized by desorption that occurs faster than the experimental sampling scheme, at a rate that is captured by it, and at a rate for which the duration of the experiment and data uncertainty obscures the rate. Batch desorption curves for atrazine and naphthalene on four soils were experimentally generated to demonstrate the existence of discrete observational desorption regimes. Nine mathematical models, each containing mechanisms formulated to describe at least one of the three regimes, were fit to each contaminant-soil combination using the Gauss-Newton method for parameter estimation. Each of the nine models was ranked using the small-sample-corrected Akaike information criterion (AICc). By interpretation of the AICc values, the atrazine desorption data were best described by three regimes, while the naphthalene desorption data were best described by two regimes. Furthermore, for a given number of regimes, we could find no general basis to suggest that a particular type of rate model (chemical, physical, kinetic, or statistical) is intrinsically superior over another.
Introduction Desorption is generally assumed to be the first step in remediation of contaminated soils, and this process can limit the extent and rate of cleanup technologies including microbial bioremediation (1-4), phytoremediation (5), and pump and treat (6-8). Several researchers have suggested that contaminant desorption profiles can be modeled using distinct behavioral regimes, described by such terms as rapidly desorbing (4, 9, 10), equilibrium (11-14), slowly desorbing (4, 9, 10), nonequilibrium (11, 14, 15), diffusionlimited (16-21), very slowly desorbing (10), nondesorption (22, 23), desorption-resistant (24), and irreversible (25). To understand contaminant fate and transport in the field, or to design effective remediation strategies, we frequently need to quantify and mathematically model desorption rate * Corresponding author phone: 82-62-530-1855; fax: 82-62-5301859; e-mail:
[email protected]. Current address: Department of Environmental Engineering, Chonnam National University, Gwang-Ju, Buk-ku, South Korea 500-757. † Department of Chemical Engineering and Material Science. ‡ Department of Civil and Environmental Engineering. 7662
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processes over a range of temporal scales. Models incorporating multiple behavioral regimes are becoming increasingly common, but, at present, there is no generally accepted approach to selecting desorption rate models appropriate for an intended application. The observations made in previous research can be generalized into three classes of desorption behavior: a fast regime, where desorption occurs at rates not captured by the first few sampling points; a dynamic regime in which rates are well measured by the sampling scheme; and a slow regime where rates are slower than can be measured given the combination of data uncertainty and the duration of sampling. A number of different approaches have been used to model these observations, which differ primarily in how the dynamic regime is described. Early work by van Genuchten’s group utilized a two-fraction approach involving a compartment that is in local equilibrium with the soil solution and a dynamic compartment where release follows a masstransfer formulation (26, 27). We modified this to create a three-site chemical desorption model by adding a nondesorption compartment (22, 23). The physical models assume that pore-diffusion is the mechanism producing dynamic behavior. The one-parameter model considers only porediffusion using Fick’s law as a constitutive model, the twoparameter model builds on the one-parameter model by adding an equilibrium compartment, and we constructed the three-parameter model by adding a nondesorption compartment to the two-parameter model. Statistical models based on the gamma distribution function abstractly partition the soil into discrete mathematical domains, with each domain having a different mass transfer rate coefficient (28). The gamma model is not formulated to predict instantaneous desorption, while the hybrid gamma/two-site model adds an equilibrium domain (29). The kinetic models use a firstorder chemical reaction formulation to describe desorption from either two (three-parameter model) or three (fiveparameter model) dynamic regimes (9, 10). Contaminant desorption from soil is likely governed by a complex set of physical-chemical processes, though the available desorption models simply describe the data resulting from the integrative effect of all of these processes. Certain models may be better equipped for describing the resultant desorption data. Johnson et al. (30) compared six modeling approaches using phenanthrene desorption data from three different soils including three- and five-parameter kinetic models, the gamma-distribution model, the one- and two-parameter pore-diffusion models, and a three-parameter biphasic polymer-diffusion model. They concluded that their desorption profiles were all at least biphasic and that models composed of two regimes are good starting points for describing desorption but that the appropriate choice of a model to describe desorption rates may be system specific. The work by Johnson et al. is valuable because it provides a comparison of desorption (sub)models that can be used for fate and transport or remediation systems models. Our objective was to develop an improved approach to model selection that more formally recognizes the reported classes of desorption behavior by applying a model comparison technique that considers both model accuracy and uncertainty. Our approach incorporated several key differences. First, we are interested in describing the extent and rate of desorption that occurs over the initial desorption period where much of the contaminant is released. Our study was designed to collect sufficient experimental data to describe rates relevant over periods of hours to days, as opposed to days to months in the Johnson et al. study. Second, we used 10.1021/es0603610 CCC: $33.50
2006 American Chemical Society Published on Web 10/25/2006
Materials and Methods
TABLE 1. Selected Properties of Sorbents Used in This Study soil
% OCa
Hartsells 1.29 Capac A 3.28 Colwood A 7.80 Houghton muck 38.3
% sand 59.1 54.6 64.2 NDc
% clay
pH
CECb [cmol(+)/kg]
32.1 8.8 24.0 21.4 20.7 15.1 NDc NDc
5.3 6.8 6.0 5.1
7.1 24.4 43.0 156
% silt
The four soils used in this study and their respective properties are shown in Table 1. Soils were air-dried, ground, and passed through a 2-mm sieve. Soil samples were sterilized by γ-irradiation (1.29 Mrad/h, 5 Mrad from a 60Co source) and stored in sealed containers at room temperature. Before each experiment, 0.1 g of each soil was placed on a nutrient agar plate (32) and incubated at 30 °C for 3 days to verify sterility. No colony-forming units (CFU) were observed. Batch desorption rate studies were performed by first spiking a series of 25 mL centrifuge tubes containing 24 mL of sterile phosphate buffer (20 mM) and each sterile soil (1.5 g of Hartsells, 1.3 g of Capac, 0.3 g of Colwood, and 0.3 g of Houghton muck) with 14C-labeled atrazine or naphthalene in methanol to get an initial aqueous concentration of 2 mg/ L. The tubes were capped with Teflon-lined Mininert valves and screw-sealed with polypropylene caps. Control tubes without soil were prepared in the same manner. Tubes were tumbled at 9 rpm for 2 days in the dark, then each tube was centrifuged for 20 min at 1200g to separate soil, and the supernatant was sampled. The final concentration of contaminant in the liquid phase was determined by liquidscintillation counting (LSC), and the amount of sorbed contaminant was calculated by difference. The supernatant was then decanted to the extent possible, and the residual water determined gravimetrically. Desorption was initiated by adding fresh contaminant-free soil extract to makeup the original volume. Contaminant-free soil extract was prepared by suspending sterile soil in sterile phosphate buffer (20 mM) at the same soil/solution ratio as in the sorption experiments. The suspension was tumbled at 9 rpm for 2 days, and the supernatant was obtained after centrifugation. The tubes were tumbled again at 9 rpm and then removed periodically, and the liquid-phase was sampled for analysis by LSC.
a OC: organic carbon content. b CEC: cation exchange capacity. c ND: not determined.
two contaminants, naphthalene and atrazine. Model selection using our naphthalene desorption data provides a basis for comparison to Johnson’s approach for phenanthrene as sorption mechanisms are likely to be similar. We also studied atrazine, a widely used herbicide which is considerably less hydrophobic and adsorbs by both hydrophobic and polar mechanisms. This was done to assess whether we could find commonalities between two very different sorbates. Third, we selected four soils to cover a range of organic carbon contents from 1.3 to 38%, as this is known to be an important sorbent property for hydrophobic sorption. Fourth, we evaluated several models not evaluated by Johnson et al. including the two- and three-site chemical models, the hybrid gamma/two-site model, and the three-parameter porediffusion model. Fifth, we compared models using a tool first developed in information theory called the Akaike information criterion (AIC), which is specifically designed to compare models that describe data sets in terms of the information captured by the model (31), rather than a goodness-of-fit approach, such as the coefficient of determination, R2. To the best of our knowledge, the AIC has not been previously used for desorption model selection.
TABLE 2. Model Equations Fit to Desorption Data Sets equation number
P
dSneq ) -k(Sneq - fneqKdC) dt Snd ) fndKdCeq(sorp)
(3)
3
(5)
2
three-parameter pore diffusion
dSneq ) -k(Sneq - fneqKdC) dt ST ) Seq + Sneq + Snd
(6)
3
two-parameter pore diffusion (30)
∂Sneq ∂2Sneq 2 ∂Sneq )D + ∂t r ∂r ∂ r2 ST ) Seq + Sneq
model name chemical three-site (22, 23, 35)
chemical two-site (13-15, 26)
equation
(4)
(
)
(
)
(7) (8)
2
∂Sneq ∂2Sneq 2 ∂Sneq )D + ∂t r ∂r ∂ r2
(9)
one-parameter pore diffusion (16, 17, 19-21, 36)
∂2 S 2 ∂S ∂S )D + ∂t r ∂r ∂ r2
(10)
1
hybrid gamma/two-site (29)
dS ) dt
(11)
3
(12)
2
(13), (14), (15)
4a
gamma distribution (28) five-parameter kinetic (9, 10, 30)
three-parameter kinetic (10, 37)
(
∫
∞
0
)
kR-1 βRe-βki i d ki - ki(Si - (1 - feq)KdC) Γ(R)
kiR-1βRe-βki - ki(Si - KdC) dki 0 Γ(R) d Sr d Ss dSvs ) -krSr, ) -ksSs, ) -kvsSvs dt dt dt Sr ) frST, Ss ) fsST, Svs ) (1 - fr - fs)ST d Sr dSs ) -krSr, ) -ksSs dt dt Sr ) (1 - fs)ST, Ss ) fsST dS ) dt
∫
∞
(16), (17), (18) (19), (20)
2a
(21), (22)
a
kvs is set to zero in the five-parameter kinetic model and ks is set to zero in the three-parameter kinetic model and, therefore, are not counted as parameters.
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TABLE 3. List of Symbols. AIC AICc
C Ceq(sorp) D feq fnd fneq fr fs fvs K k Kd ki kr ks kvs n P r S SSE Seq Si Snd Sneq Sr Ss ST Svs t Γ R β
Akaike information criterion small-sample corrected Akaike information criterion contaminant concentration is the aqueous phase contaminant concentration in the aqueous phase at sorption equilibrium apparent diffusion coefficient equilibrium site fraction nondesorption site fraction nonequilibrium site fraction rapidly desorbing fraction slowly desorbing fraction very slowly desorbing fraction number of estimated parameters including the model variance first-order rate coefficient soil-water partition coefficient first-order rate coefficient for the ith soil compartment first-order rate coefficient for the rapid fraction first-order rate coefficient for the slow fraction first-order rate coefficient for the very slow fraction number of data points number of estimated parameters radial coordinate contaminant concentration in soil error sum of squares contaminant concentration in the equilibrium soil compartment contaminant concentration in the ith soil compartment contaminant concentration in the nondesorption soil compartment contaminant concentration in the nonequilibrium soil compartment contaminant concentration in the rapid compartment contaminant concentration in the slow compartment total contaminant concentration in all soil compartments contaminant concentration in the very slow compartment time gamma distribution function shape parameter scale parameter
Samples were initially taken at 1-h increments. As each experiment progressed, the sampling interval was increased. The duration of each rate experiment was 3-4 days. Each of the models shown in Table 2 was solved analytically or numerically for the purpose of parameter estimation. All of the solutions were programmed using the Matlab software package, and the output was generated using Matlab’s graphical user interface. The error sum of squares between the data and the model fits were used as objective functions for parameter estimation. These objective functions were minimized using the Gauss-Newton method assuming a tolerance of 10-3 as the convergence criterion (33). A modified version of the Gauss-Newton method was used for problems where the dependent variables were nonlinearly related to the independent variables, such as for the gamma and hybrid gamma/two-site models. Stiffness was overcome for both the gamma distribution and hybrid gamma distribution models by using reduced sensitivity coefficients. Parameter standard errors were estimated from the resultant sensitivity matrix. Convergence was problematic for the threeand five-parameter kinetic models as the slowest rate coefficients in both models tended toward zero for these data. This was addressed by setting these parameters to zero rather than having the algorithm fit them. 7664
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Model comparison and evaluation was accomplished through application of the Akaike information criterion (AIC) (31, 34). This approach uses estimates of goodness-of-fit (accuracy) and model variability (precision) to quantitatively rank different models in their abilities to describe each data set. The ranking of models based on accuracy alone, as is commonly done in a comparison of R2 values, is not sufficient because model variability is not included. Models with increasing numbers of parameters tend to have greater R2 values at the expense of greater variability in the model description of the data. The AIC technique produces numerical values that reflect both accuracy and precision, such that the lowest AIC value identifies the model that is most justified by the data. Unlike R2 values, the AIC value does not range between 0 and 1, so there is no means of comparing AIC values computed for different data sets (i.e. the AIC is only used to compare among model fits for a single data set). The AIC is computed as the sum of two penalty terms, the first for bias (inaccuracy) and the second for variability
AIC ) n ln
( )
SSE + 2K n
(1)
where the n is the number of data points, SSE is the error sum of squares, and K is the total number of estimated model parameters, which includes the number of estimated parameters (P) plus a model variance parameter (K ) P + 1). The AIC tells what inferences the data support, not what reality might be. In a sense, the AIC is a quantitative Occam’s razor (a rule that states that the simplest of competing descriptions is preferred) that can be used to select the most parsimonious model supported by the collected data. The principle of parsimony insists that the best-fit model has an optimal combination of bias and variability. Because the AIC is the sum of two penalty terms (i.e. one for bias and one for uncertainty), the smaller AIC values correspond to models that fit the data more parsimoniously. It is important to note that while the physical-chemical mechanisms used to formulate the most parsimonious model (that with the lowest AIC value) may be more justified than those in alternative models, the AIC approach alone does not allow us to validate these mechanisms. The small-sample corrected AIC (AICc) has been used in this study, due to the small sample size relative to the number of model parameters:
AICc ) AIC +
2K(K + 1) n-K-1
(2)
The nine models chosen for this inquiry were ranked for each soil-contaminant combination using the value of the AICc.
Results and Discussion Desorption rate data and the most parsimonious model prediction for each of the eight contaminant-soil combinations are shown in Figure 1. The experimental technique used in this study involves desorptive release resulting in a finite liquid-phase concentration, as opposed to the zero liquid-phase concentration achieved in “infinite-dilution” studies (9, 10). Consequently, the desorption percentage on the y-axis has been defined as the aqueous-phase concentration divided by the aqueous-phase concentration that is predicted by the measured sorption distribution coefficient, Kd. A desorption percentage of 100% corresponds to a desorption condition where the distribution of contaminant between the solid and liquid phases is the same as in the sorption experiment. It can be seen in Figure 1, that a three-regime model was always selected for atrazine, whereas two regime models were
FIGURE 1. Eight soil-contaminant combinations fit with the most parsimonious model as determined by the AICc. preferable for naphthalene. It was also noted that the atrazine profile approaches the maximum desorbed amount in a more gradual manner than does naphthalene, and models that contain a mass transfer or chemical kinetic formulation are able to better describe this type of behavior. Conversely, the naphthalene data has an abrupt transition that can be described as fast desorption followed by a plateau, and therefore modeling the intermediate dynamic regime is less important than is modeling the fast and slow regimes. The absolute values of the AICc for all models for Capac A-atrazine are presented in Figure 2. Higher absolute values (lower actual AIC values since all values were negative)
represent a more parsimonious description of the data. It can be seen that increasing the number of regimes from two to three is justified by the data for all model types. Nearly identical results were found for all other soil-atrazine combinations. For the most part, these results are consistent with what can be observed visually. In the atrazine data one can clearly infer the presence of three types of desorption behavior. The first is that which occurs initially and is characterized by the extrapolated intercept of the desorption data profile or the change in concentration from time zero to the first data point. In effect, this reflects processes that occur faster than our measurement interval is designed to VOL. 40, NO. 24, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Comparison of the AICc for the nine models. capture. While this process is not necessarily instantaneous, the rate is not measured by the data collection interval such that it cannot be distinguished from instantaneous processes. Thus, an equilibrium regime formulation is an acceptable approximation of this initial behavior. The second type of behavior is characterized by the measurable and regular increases in the amount desorbed beyond the first sampling point. This suggests a dynamic process and models with a regime governed by a rate formulation are capable of describing this behavior. The third type of behavior is the plateau, where changes in the amount desorbed cannot be measured as they are less than the variability in the measurements. While desorption may continue to occur, it is not measured by the combination of sampling and analysis techniques and the sampling interval. Models with a very slow, nondesorptive or irreversible regime are able to capture this behavior. In other words, there are desorption behaviors that are faster than the experiment measures, those that occur at rates that are measured, and an amount of contaminant either does not desorb or does so only at rates that are too slow to be measured by the selected experimental techniques. The naphthalene results, also shown in Figure 1, were somewhat different. Comparing the AICc absolute values (Figure 2) it can be seen that increasing the number of parameters was justified for the chemical and pore-diffusion models but not for the statistical and kinetic models. This was also found for Capac A and Hartsells, while for Colwood A, increasing the number of parameters was justified for the chemical, physical, and kinetic models but not for the statistical models. We believe that this results from the nature of the desorption data set. The rate of naphthalene desorption is significantly faster than was found for atrazine, and much of the dynamic behavior occurs before the first sampling point (1 h). This leaves us with few data that can be used to 7666
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estimate the equilibrium site fraction which produces a high level of model uncertainty. It can also be seen that models without equilibrium site fractions (three-parameter kinetic model, the gamma model, and the five-parameter kinetic model) produced the best AICc values (Figure 2). The soil-atrazine data clearly supports the use of a threeregime model, both visually and as reflected by the AICc values. There is little basis for choosing one three-regime model over another, however, as the differences in AICc values are not large. In contrast, the soil-naphthalene results are more ambiguous, which is due at least in part to the sparsity of data in the dynamic (or measureable rate) regime. We can infer that we could improve our description of this early behavior with more frequent sampling. Nonetheless, some desorption would likely occur before the first data point in any reasonable sampling schedule. So while we found that, in some cases, only two regimes were justified for naphthalene, this may be a result of the data available at early desorption times. We can construct a logical argument that as the initial sampling increment approaches zero, the equilibrium site fraction approaches zero. We can also hypothesize that by extending the sampling to long sampling times we should see a decreasing amount of “nondesorbable” material. This compartment may not tend toward zero, however, as some material may be truly bound to the soil. From a practical perspective, with sampling limitations on both the initial intervals and the duration of the experiment, we are left with three regimes of behavior: desorption that occurs faster than our sampling scheme, at a rate that is captured by it, and at a rate for which data uncertainty obscures the rate. We suggest that a strategy for developing an appropriate rate formulation would be to design an experimental rate study and select a sampling schedule that it is appropriate for the time scale of interest, fit the data with a three regime model, and then test (using the AIC) whether a model with fewer parameters is justified. Given a fixed number of regimes, the AIC can also be used to select one type of rate model (chemical, physical, statistical, or kinetic) over another. We would note, however, we could find no general basis to suggest that a particular type of rate model is intrinsically superior. It is important to note that the model selected depends on the data set available and the problem at hands they are not necessarily fundamental explanations of desorption phenomena. It would be reasonable to assume that the most parsimonious model is more likely to reflect physical-chemical mechanisms, but we cannot infer that a single model selection exercise such as this provides anything beyond a description of the data. However, by using a technique such as that proposed, we suggest that with multiple model selection exercises on independent data sets using different experimental techniques, mechanistic processes can eventually be inferred.
Acknowledgments This work was supported, in part, by the Department of Education Graduate Assistance in Areas of National Need Program under grant number P200A980434 and the Department of Agriculture under grant number 2001-35107-09945.
Supporting Information Available Bar charts, showing the comparison of AIC values for each soil-contaminant combination, are provided. This material is available free of charge via the Internet at http:// pubs.acs.org.
Literature Cited (1) Shuttleworth, K. L.; Cerniglia, C. E. Environmental aspects of PAH biodegradation. Appl. Biochem. Biotechnol. 1995, 54, 291302.
(2) Talley, J. W.; Ghosh, U.; Tucker, S. G.; Furey, J. S.; Luthy, R. G. Particle-scale understanding of the bioavailability of PAHs in sediment. Environ. Sci. Technol. 2002, 36, 477-483. (3) Straube, W. L.; Nestler, C. C.; Hansen, L. D.; Ringleberg, D.; Pritchard, P. H.; Jones-Meehan, J. Remediation of polyaromatic hydrocarbons (PAHs) through landfarming with biostimulation and bioaugmentation. Acta Biotechnol. 2003, 23, 179-196. (4) Cornelissen, G.; Rigterink, H.; Ferdinandy, M. M. A.; Van Noort, P. C. M. Rapidly desorbing fractions of PAHs in contaminated sediments as a predictor of the extent of bioremediation. Environ. Sci. Technol. 1998, 32, 966-970. (5) Ahn, S.; Werner, D.; Luthy, R. G. Physicochemical characterization of coke-plant soil for the assessment of polycyclic aromatic hydrocarbon availability and the feasibility of phytoremediation. Environ. Toxicol. Chem. 2005, 24, 2185-2195. (6) Zhang, Z. H.; Brusseau, M. L. Nonideal transport of reactive solutes in heterogeneous porous media 5. Simulating regionalscale behavior of a trichloroethene plume during pump-andtreat remediation. Water Resour. Res. 1999, 35, 2921-2935. (7) Piatt, J. J.; Backhus, D. A.; Capel, P. D.; Eisenreich, S. J. Temperature-dependent sorption of naphthalene, phenanthrene and pyrene to low organic carbon aquifer sediments. Environ. Sci. Technol. 1996, 30, 751-760. (8) Brubaker, G. R.; Stroo, H. F. In situ bioremediation of aquifers containing polyaromatic hydrocarbons. J. Hazard. Mater. 1992, 32, 163-177. (9) Cornelissen, G.; Van Noort, P. C. M.; Parsons, J. R.; Govers, H. A. J. Temperature dependence of slow adsorption and desorption kinetics of organic compounds in sediments. Environ. Sci. Technol. 1997, 31, 454-460. (10) Cornelissen, G.; Van Noort, P. C. M.; H. A. J., G. Mechanism of slow desorption of organic compounds from sediments: A study using model sorbents. Environ. Sci. Technol. 1998, 32, 31253131. (11) Brusseau, M. L.; Rao, P. S. C. Sorption nonideality during organic contaminant transport in porous media. Crit. Rev. Environ. Control 1989, 19, 33-99. (12) Ball, W. P.; Roberts, P. V. Long-term sorption of halogenated organic chemicals by aquifer material. 1. Equilibrium. Environ. Sci. Technol. 1991, 25, 1223-1237. (13) Cameron, D. R.; Klute, A. Convective-dispersive solute transport with a combined equilibrium and kinetic adsorption model. Water Resour. Res. 1977, 13, 183-188. (14) Selim, H. M.; Davidson, J. M.; Rao, P. S. C. Transport of reactive solutes through multilayered soils. Soil Sci. Soc. Am. J. 1977, 41, 3-10. (15) Rao, P. S. C.; Davidson, J. M.; Selim, H. M. Evaluation of conceptual models for describing nonequilibrium adsorptiondesorption of pesticides during steady-flow in soils. Soil Sci. Soc. Am. J. 1979, 43, 22-28. (16) Harmon, T. C.; Roberts, P. V. Comparison of intraparticle sorption and desorption rates for a halogenated alkene in a sandy aquifer material. Environ. Sci. Technol. 1994, 28, 16501660. (17) Werth, C. J.; Reinhard, M. Effects of temperature on trichloroethylene desorption from silica gel and natural sediments. 2. Kinetics. Environ. Sci. Technol. 1997, 31, 697-703. (18) Ball, W. P.; Roberts, P. V. Long-term sorption of halogenated organic chemicals by aquifer material. 2. Intraparticle diffusion. Environ. Sci. Technol. 1991, 25, 1237-1249. (19) Wu, S.-C.; Gschwend, P. Sorption kinetics of hydrophobic organic compounds to natural sediments and soils. Environ. Sci. Technol.
1986, 20, 717-725. (20) Farrell, J.; Reinhard, M. Desorption of halogenated organics from model solids, sediments, and soil under unsaturated conditions. 2. Kinetics. Environ. Sci. Technol. 1994, 28, 63-72. (21) Grathwohl, P.; Reinhard, M. Desorption of trichloroethylene in aquifer material: rate limitations at the grain scale. Environ. Sci. Technol. 1993, 27, 2360-2366. (22) Park, J.-H.; Zhao, X.; Voice, T. C. Biodegradation of nondesorbable naphthalene in soils. Environ. Sci. Technol. 2001, 35, 2734-2740. (23) Park, J.-H.; Zhao, X.; Voice, T. C. Development of a kinetic basis for bioavailability of sorbed naphthalene in soil slurries. Water Res. 2002, 36, 1620-1628. (24) White, J. C.; Alexander, M. Reduced biodegradability of desorption-resistant fractions of polycyclic aromatic hydrocarbons in soil and aquifer solids. Environ. Toxicol. Chem. 1996, 15, 1973-1978. (25) Kan, A. T.; Fu, G.; Hunter, M.; Chen, W.; Ward, C. H.; Tomson, M. B. Irreversible sorption of neutral hydrocarbons to sediments: experimental observations and model predictions. Environ. Sci. Technol. 1998, 32, 892-902. (26) van Genuchten, M. Th. Two-site/two-region models for pesticide transport and degradation: theoretical development and analytical solutions. Soil Sci. Soc. Am. J. 1989, 53, 1303-1310. (27) van Genuchten, M. Th.; Davidson, J. M.; Wierenga, P. J. Evaluation of kinetic and equilibrium equations for prediction of pesticide movement through porous-media. Soil Sci. Soc. Am. J. 1974, 38, 29-35. (28) Connaughton, D. F.; Stedinger, J. R.; Lion, L. W.; Shuler, M. L. Description of time-varying desorption kinetics: release of naphthalene from contaminated soils. Environ. Sci. Technol. 1993, 27, 2397-2403. (29) Ahn, I.-S.; Lion, L. W.; Shuler, M. L. Validation of a hybrid “twosite gamma” model for naphthalene desorption kinetics. Environ. Sci. Technol. 1999, 33, 3241-3248. (30) Johnson, M. D.; Keinath, T. M.; Weber, W. J., Jr. A distributed reactivity model for sorption by soils and sediments. 14. Characterization and modeling of phenanthrene desorption rates. Environ. Sci. Technol. 2001, 35, 1688-1695. (31) Burnham, K. P.; Anderson, D. R. Model Selection and Inference, 1st ed.; Springer-Verlag: New York City, 1998. (32) Methods for General and Molecular Bacteriology; Gerhardt, P., Murray, R., Wood, W., Krieg, N., Eds.; American Society for Microbiology: Washington, DC, 1994. (33) Englezos, P.; Kalogerakis, N. Applied Parameter Estimation for Chemical Engineers; Marcel Dekker: Inc.: New York, 2001. (34) Ginzburg, L. R.; Jensen, C. X. J. Rules of thumb for judging ecological theories. Trends Ecol. Evol. 2004, 19, 121-126. (35) Park, J.-H. In Department of Civil and Environmental Engineering: Michigan State University, 2000; p 155. (36) Crank, J. The Mathematics of Diffusion, 1st ed.; Oxford at the Clarendon Press: 1956. (37) Johnson, M. D.; Weber, W. J., Jr. Rapid prediction of long-term rates of contaminant desorption from soils and sediments. Environ. Sci. Technol. 2001, 35, 427-433.
Received for review February 15, 2006. Revised manuscript received August 14, 2006. Accepted August 15, 2006. ES0603610
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