sorption, nonlinear sorption, and biodegradation processes

Journal of Contaminant Hydrology 48 Ž2001. 1–21 www.elsevier.comrlocaterjconhyd

Model coupling intraparticle diffusionrsorption, nonlinear sorption, and biodegradation processes Hrissi K. Karapanagioti ) , Chris M. Gossard, Keith A. Strevett, Randall L. Kolar, David A. Sabatini School of CiÕil Engineering and EnÕironmental Science, UniÕersity of Oklahoma, Norman, OK, USA Received 25 January 2000; received in revised form 5 October 2000; accepted 5 October 2000

Abstract Diffusion, sorption and biodegradation are key processes impacting the efficiency of natural attenuation. While each process has been studied individually, limited information exists on the kinetic coupling of these processes. In this paper, a model is presented that couples nonlinear and nonequilibrium sorption Žintraparticle diffusion. with biodegradation kinetics. Initially, these processes are studied independently Ži.e., intraparticle diffusion, nonlinear sorption and biodegradation., with appropriate parameters determined from these independent studies. Then, the coupled processes are studied, with an initial data set used to determine biodegradation constants that were subsequently used to successfully predict the behavior of a second data set. The validated model is then used to conduct a sensitivity analysis, which reveals conditions where biodegradation becomes desorption rate-limited. If the chemical is not pre-equilibrated with the soil prior to the onset of biodegradation, then fast sorption will reduce aqueous concentrations and thus biodegradation rates. Another sensitivity analysis demonstrates the importance of including nonlinear sorption in a coupled diffusionrsorption and biodegradation model. While predictions based on linear sorption isotherms agree well with solution concentrations, for the conditions evaluated this approach overestimates the percentage of contaminant biodegraded by as much as 50%. This research demonstrates that nonlinear sorption should be coupled with diffusionrsorption and biodegradation models in order to accurately predict bioremediation and natural attenuation processes. To our knowledge this study is unique in studying nonlinear sorption coupled with

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Corresponding author. Present address: ICEHTrFORTH, P.O. Box 1414, Platani, Patra, Greece. Tel.: q30-61-965-218; fax: q30-61-965-223. E-mail addresses: [email protected] ŽH.K. Karapanagioti., [email protected] ŽC.M. Gossard., [email protected] ŽK.A. Strevett., [email protected] ŽR.L. Kolar., [email protected] ŽD.A. Sabatini.. 0169-7722r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 7 7 2 2 Ž 0 0 . 0 0 1 7 9 - 0

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H.K. Karapanagioti et al.r Journal of Contaminant Hydrology 48 (2001) 1–21

intraparticle diffusion and biodegradation kinetics with natural media. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Natural attenuation; Biodegradation; Sorption; Kinetics; Intraparticle diffusion; Coupled model

1. Introduction Natural attenuation is currently one of the most important topics in groundwater quality management. Diffusion, sorption and biodegradation are key processes impacting the efficiency of natural attenuation. While each process has been studied individually, limited research has coupled the kinetics of these processes. Research on the interplay of diffusionrsorption and biodegradation processes is necessary to accurately predict the magnitude of natural attenuation. Guerin and Boyd Ž1993. showed that naphthalene bioavailability is sorbent specific. The same microbial species demonstrated different biodegradation behavior for naphthalene sorbed on different soils Ži.e., low organic content vs. high organic content soils.. In phenanthrene biodegradation studies with model soils Žglass or polystyrene beads., the nature and interrelation of porosity and hydrophobicity were found to be very important ŽNam and Alexander, 1998.. Organic content, porosity, and hydrophobicity are known parameters that impact diffusion-limited and hydrophobic-motivated sorption. Another example presents aged phenanthrene to have lower biodegradation rates as compared to freshly added phenanthrene ŽHatzinger and Alexander, 1995.. Therefore, previous research has demonstrated that diffusionrsorption processes impact biodegradation processes. However, most studies have focused on an individual process Že.g., biodegradation kinetics. without studying and coupling other processes Ži.e., sorption kinetics.. Quantifying and coupling kinetics for all three processes is a challenging task. Most of the proposed models assume that sorption is linear and that desorption kinetics follow a first-order rate law ŽAngley et al., 1992; Estrella et al., 1993; Fry and Istok, 1994; Brusseau et al., 1999.. Recently, Cornelissen et al. Ž1998. proposed a first-order, two-compartment model to describe desorption. Only limited studies have incorporated intraparticle diffusion in the coupling of linear sorption and biodegradation ŽScow and Hutson, 1992; Chung et al., 1993.. None of the studies mentioned above have included nonlinear sorption in their coupled models. Recent studies have shown that sorption kinetics can be highly dependent on intraparticle diffusion ŽRugner et al., 1998; Karapanagioti et al., 2000.. ¨ Also, different samples containing varying types of organic matter can demonstrate linear Ž N s 1. or highly nonlinear Ž N as low as 0.38. sorption isotherms ŽXing and Pignatello, 1997; Huang et al., 1997; Chiou and Kile, 1998; Kleineidam et al., 1999; Xia and Ball, 1999; Karapanagioti et al., 2000; Xia and Ball, 2000; Chiou et al., 2000; Karapanagioti and Sabatini, 2000.. Nonlinearity causes effective diffusion coefficients to be concentration dependent and to increase by a factor of 10 or more during desorption ŽGrathwohl, 1998.. The hypothesis of the present study is that incorporating a nonlinear sorption term in a model coupling intraparticle diffusion, sorption and biodegradation will more accurately predict contaminant fate. The objectives of this study are as

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follows: Ž1. to study the effect of microbe addition to systems in which heterogeneous and nonlinear sorption behaviors are already well-characterized, Ž2. to develop a model that couples intraparticle diffusion, nonlinear sorption and biodegradation, Ž3. to validate the model with experimental data, and Ž4. to determine the effect of sorption nonlinearity on the overall system behavior. To our knowledge, this study is unique in studying nonlinear sorption coupled with intraparticle diffusion and biodegradation kinetics with natural media.

2. Experimental methods The Canadian River Alluvial ŽCRA. aquifer material was sampled from the closed Norman Landfill, which is a U.S.G.S Toxic Substances Research site. The sampling depth was just below the water table at about 1 m. Subsample characteristics important to sorption behavior are summarized in Table 1 Žnote that N values statistically lower than 1 were observed for the subsamples tested in the present study. and described in further detail elsewhere ŽKarapanagioti et al., 2000.. Subsample codes ŽTable 1. were based on the dominant organic matter found in organic petrology thin sections Žpalynological terms according to Tyson, 1995.. Phenanthrene was used as the model chemical in this study Žselected phenanthrene properties are presented in an earlier study; see Karapanagioti et al., 2000. and was prepared in a 100 mgrl stock solution in methanol. In all experimental vials methanol percent was always below 1%. Solutions were prepared in synthetic ground water Ždeionized water with 44 mgrl CaCl 2 P 2H 2 O, 14 mgrl CaSO4 , and 17 mgrl NaHCO 3 .. Sodium azide ŽNaN3 . was added at a concentration of 200 mgrl to minimize bacterial growth and thus biodegradation Žfor abiotic studies.. 1-Hydroxy-2-naphthoic acid Ž1H2N. has been commonly identified as one of phenanthrene’s bacterial biodegradation byproducts ŽStringfellow and Aitken, 1994; Machate et al., 1997.. 1H2N was identified in this study by analyzing the fluorescence detector spectra. Calibration solutions of 1H2N were prepared using the method described above for phenanthrene solutions. Aqueous phenanthrene and 1H2N concentrations were measured by an RF-551 Shimadzu variable wavelength fluorescence detector in cuvette mode. Excitation and emission wavelengths used were as follows: Ža. 249 and 345 for phenanthrene and Žb. 249 and 415 for 1H2N, respectively. In order to isolate microorganisms ŽMO., bulk CRA sediment samples were mixed with glass beads and deionized water, shaken for 30 min and then filtered through a 10-mm filter paper ŽKoelbel-Boelke et al., 1988.. Part of the filtrate was introduced in synthetic ground water solutions of phenanthrene. Once the phenanthrene was degraded, additional phenanthrene was added in order to increase MO biomass. MO isolation was accomplished by inoculating an agar plate containing phenanthrene with 0.1 ml of inoculum. The agar plate contained the mineral salt media present in synthetic ground water along with 15 grl agar and 1.0 ml of a 100 mgrl phenanthrene solution. The plates were then incubated for 10 days at 308C. At the end of the incubation period, two colony types were observed and the description of each was

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Sample code

Particle size Žmm.

Dominant organic matter

f oc Ž%.

Intraparticle porosity

N

K fr Žmgrkg. Žlrmg. N

log K oc at Ce s1 mgrl 95% CI

Da r a 2 Žlrs.

Coaly Organic Coatings Mixture

0.5–0.25 0.125–0.063

Coaly particles Amorphous organic matter coatings Amorphous organic matter coatings and coaly particles

1.6 0.10

0.008 0.011

0.55"0.024 0.89"0.091

33000"2500 43"15

6.3–6.4 4.6–4.7

1.1 E–10 NrA

0.18

0.003

0.68"0.013

490"27

5.4–5.5

7.2 E–08

F 0.063

f oc : organic carbon content; N: Freundlich exponent; K fr : Freundlich constant; K oc : organic carbon normalized sorption coefficient calculated at chemical equilibrium concentration Ž Ce . equal to 1 mgrl; 95% CI: 95% confidence interval; ": corresponds to "1 standard deviation; Da r a 2 : apparent diffusion rate.

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Table 1 Important sediment sample and sorption properties ŽKarapanagioti et al., 2000; palynological terms used as in Tyson, 1995.

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Table 2 Experimental variables for the different systems System

Addition of NaN3

Addition of sediments Žnumber of sediments.

Addition of MO

Day MO added

MO density

MOrNS NMOrS MOrS LMOrS

No Yes No No

No Yes Ž3. Yes Ž3. Yes Ž3.

Yes No Yes Yes

0 – 0 17

MO – MO 0.1 MO

MO: microorganisms; NS: no sediment added; NMO: no microorganisms added; S: sediment added; LMO: less microorganisms added.

recorded. Each colony type was streaked for isolation on fresh mineral salt media agar plates containing phenanthrene. A wet mount was then performed on both colonies. One set of batch experiments Žsystem. was prepared with no sediment and three different systems were prepared for each of the three sediment samples Žsee Table 2 for details on experimental variables.: Ža. MOrNS: phenanthrene solutions with MO added but no sediment ŽNS., Žb. NMOrS: sediment and phenanthrene solutions with NaN3 added to inhibit biodegradation, sorption alone was monitored, Žc. MOrS: sediment and phenanthrene solutions with MO added, and Žd. LMOrS: sediment and phenanthrene solutions that equilibrated for 17 days before MO were added at a lower density. After phenanthrene was depleted in MOrNS additional phenanthrene was added Žup to 0.1 mgrl each time., with aqueous phenanthrene and 1H2N concentrations subsequently monitored until the phenanthrene was depleted. In LMOrS, one tenth of the MO density in MOrS was introduced. All kinetic experiments were conducted in triplicate in 20 ml crimp-top Teflon-lined glass vials. The initial phenanthrene concentrations was 0.1 mgrl and the solid-to-water ratio is reported in Table 3. The vials were stored at room temperature Žaround 238C. in the dark and periodically mixed. Measurements were taken at various time intervals. Necessary controls were monitored as presented in previous studies ŽKarapanagioti et al., 2000..

Table 3 NMOrS: parameters of sorption kinetic experiment Sample code

SrW ratio Žmgr20 ml.

a Žcm.

F

Ce Žmgrl.

T 75% Žday.

Coaly Organic coatings Mixture

3.3 700 140

0.018 0.0044 0.0027

0.49 0.48 0.50

53 55 53

2100 -1 21

SrW ratio: solid-to-water ratio expressed as mg of sediment per 20 ml of solution; a: particle radius used in the numerical model; F: fractional uptake at equilibrium Žchemical mass on solid per total chemical mass.; Ce : estimated phenanthrene concentration at equilibrium; T 75%: time to reach 75% equilibrium.

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3. Model development Modeling nonlinear sorption was accomplished using a numerical solution of Fick’s 2nd law; a one-dimensional form in the radial direction is the following: ECrEt s Da Ž E 2 CrEr 2 . q Ž 2ECrrEr .

Ž 1.

where C is the chemical concentration, t is time, Da is the apparent diffusion coefficient, and r is the radial distance from the center of the particle. In the intraparticle diffusion model Da is defined as: Da s Daq ´r  Ž ´ q K d r . t f 4 s Dera

Ž 2.

where Daq is the aqueous diffusion coefficient, K d is the sorption distribution coefficient, ´ is the intraparticle porosity, r is the bulk density of the particle, t f is the tortuosity factor, De is the effective diffusion coefficient, and a is the capacity factor equal to Ž ´ q K d r . ŽGrathwohl, 1998.. The numerical model is solved using the finite difference method with Crank– Nicholson time stepping, as described by Jager ¨ Ž1997.. Model input includes the particle radius, the solid-to-water ratio, the initial water concentration, the Freundlich isotherm parameters, the solid density and the intraparticle porosity. In this study, the numerical model was used to predict sorption kinetics based on results obtained in Karapanagioti et al. Ž2000.. Ž1997. considers nonlinear sorption, but degradation is not The model of Jager ¨ incorporated into the model. Similarly, the existing model of Scow and Hutson Ž1992. and Chung et al. Ž1993. includes biodegradation in the external buffer solution, but does not allow for nonlinear sorption isotherms. Our model incorporates the best characteristics from both models by modifying Jager’s nonlinear sorption model to include ¨ biodegradation in the external solution. In addition to the assumptions mentioned by Chung et al. Ž1993., two additional assumptions were made in the development of our model: 1. Biodegradation occurs only in the external buffer solution; microorganisms are excluded from the micropores of the particles. 2. Biodegradation on the surface of the particle is negligible during the time required for the pollutant to diffuse into or out of the particles. For our model, the physical system consists of a homogeneous mixture of porous spherical particles, each with varying diameters and properties, in a homogeneous buffer solution of constant volume. Initially, the pollutant may be entirely in the external solution, entirely inside the particles, or partitioned between both. The concentrations in the inner and outer fluids can be different, but must be uniform within each. The change of internal and external chemical concentrations with time is obtained from the mass balance equations of the chemical in the particles and in the buffer solution.

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Fig. 1. Model flowchart.

Fig. 1 presents the model flowchart. The mass balance for the chemical inside the particles is written for the intraparticle concentration, C Ž r, t . as, E

Ž ´ C q rj Sj Et j jk

C jk

.s

De , j E r

2

Er

ž

r2

EC jk Er

/

Ž 3.

on the domain 0 F r F a, where the subscripts j and k indicate particles of different type and radii, respectively, and r s 0 corresponds to the center of the particle, and r s a corresponds to the particle outer boundary. Eq. Ž1. is for aqueous phase only whereas Eq. Ž3. introduces on the left side a term for the concentration in the particle Ž ´ C . and the concentration sorbed Ž r Sw C x.. De is the effective diffusion as was defined by Eq. Ž2.. The boundary conditions are EC jk Er

s0

Ž 4.

rs 0

yDe , j

EC jk Er

s k f Ž Ca y Ce .

Ž 5.

rs a

and the initial condition is C s Cp0

at

ts0

Ž 6.

Eqs. Ž4. and Ž5. are discretized using block centered differences and a weighted Euler time stepping scheme. Eq. Ž6. is discretized with a one-sided difference and explicit time stepping since it is assumed that biodegradation is negligible during the time required for diffusion. The coefficient for mass transfer from particles to the external fluid, k f , is related to the particle radii and must be empirically calibrated for a particular system. For our system, k f is at least six orders of magnitude faster than the intraparticle diffusion and, thus, does not impact the diffusion kinetics. For sorption the following three isotherms are commonly used: Ža. linear, Žb. Freundlich, and Žc. Langmuir. In the present study, the Freundlich isotherm is used: S j C jk s K fr Ž C jk .

N

Ž 7.

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where, K fr , N, are the Freundlich, sorption coefficients and depend upon the chemical and soil characteristics. The nonlinear sorption isotherms require an iterative solution for the chemical distribution within the particles. The model uses Pickard iteration ŽJager, 1997. and ¨ linearizes the sorption isotherm as Sitq1Ž m . y Sitq1Ž m y1. s

d S Citq1Ž m y1. dC

Ž Citq1Ž my1. y Citq1Ž my1. .

Ž 8.

where m is the iteration index and t is the time level. In this paper, we consider only the first-order biodegradation in the external buffer solution. The mass balance for the chemical outside the particles is written for the external concentration, CeŽ t ., as ECe Et

s yk 1Ce q n jk A jk k f Ž Ca y Ce .

Ž 9.

with the initial condition Ce s Ce0

at

ts0

Ž 10 .

where k 1 is the first-order biodegradation rate constant, n jk is the number of particles per unit volume of solution and A jk is the surface area of the particle; both differ for each particle type and size. The external buffer solution concentration is coupled with the intraparticle concentration through the boundary condition ŽEq. Ž5.. and the sink term in Eq. Ž9.. This additional process was included by replacing the equation for the edge node of the soil particle in Jager’s code with a discrete version of Eq. Ž5. as follows: ¨ yDe , j

Catq1 y Catq1 y1 Dr

s k f Ž Cat y Cet .

Ž 11 .

where the superscript refers to the time stepping. Additionally, the discrete form of Eq. Ž9. was included inside the time loop, but outside of the nonlinear sorption iteration loop and was discretized using weighted Euler time stepping.

4. Results and discussion 4.1. Sorption kinetic behaÕior Fig. 2 presents the sorption kinetic data and the model predictions for NMOrS. The model input values, as summarized in Table 1, were obtained from a previous study ŽKarapanagioti et al., 2000.. Three sediment fractions were selected because of the difference in their equilibrium and kinetic sorption behavior. In the present study, the fractional uptake at equilibrium Ž F . —the chemical mass on solid per total chemical mass—is similar for all three samples, as presented in Table 3.

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Fig. 2. NMOrS: sorption kinetic data and model predictions for all three sediment samples Žorganic matter ŽOM. originates from OC: organic coatings, CL: coaly particles..

This allows direct comparison of the sorption kinetic properties between the three samples. The experimental data in Fig. 2 agree well with model predictions Žrepresented by the lines. based on diffusion-limited intraparticle sorption. As summarized in Table 3, the sediment containing coaly particles requires more time to reach equilibrium ŽT 75% s 2100 days., whereas the sample with organic coatings reaches equilibrium much more quickly ŽT 75% - 1 day.. The sample with a mixture of coaly particles and organic coatings has a behavior in-between these two extremes ŽT 75% s 21 days.. This three orders of magnitude difference in equilibration times is due to different sorption mechanisms for varying organic matter types ŽKarapanagioti et al., 2000.. 4.2. Phenanthrene biodegradation Fig. 3 presents the biological activity in MOrNS. The biodegradation constant k 1 was calculated to be 0.043 lrh for the first phenanthrene addition Žsee Table 4.. This value is consistent with literature values for phenanthrene biodegradation ŽNam and Alexander 1998; Laor et al., 1999; Rouse et al., 1999.. Phenanthrene was added several

Fig. 3. MOrNS: biological activity with multiple phenanthrene additions and transient productionrloss of 1H2N metabolite Ž1H2N: 1-hydroxy-2-naphthoic acid; PHE: phenanthrene..

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Table 4 Lag time and first-order biodegradation rate constant System

Sediment

Lag time Žday.

k 1 Žlrh.

k 1 Žlrh. 95% CI

MOrNS MOrS

– Coaly Organic coatings Mixture

1 3.3 4 1.8

0.043"0.019 0.040"0.020 0.080"0.026 0.050"0.020

0.021–0.065 0.017–0.063 0.050–0.110 0.027–0.073

Lag time: lag time before biodegradation starts; k 1: biodegradation rate constant; ": corresponds to "1 standard deviation; CI: confidence interval.

times to the system; after each phenanthrene depletion, the biodegradation by product 1H2N was observed, supporting the occurrence of microbial degradation ŽStringfellow and Aitken, 1994; Machate et al., 1997.. The transient concentrations of 1H2N indicate that it is both being formed and depleted; thus, we were not able to perform a mass balance on 1H2N to account for phenanthrene loss. Aliquots from the initial culture, which were plated on agar containing phenanthrene, yielded two colonies. The first colony was a Gram-negative bacterium; i.e., a mucoid colony that appeared circular, entire, convex, and white. This colony did not grow as an isolate with phenanthrene-based agar. This synergistic bacterium was identified with 87% confidence as a Pseudomonas putida. The second colony was a filamentous, flat, white colony with a dark inner circle. From microscopic observations, this second colony appears to be a fungus. Further investigation using both colonial and microscopic morphology techniques, combined with dichotomous keys, revealed, with 97% confidence, that the fungus was chrysosporium. Mineral salts agar with phenanthrene was used in this experiment to isolate microorganisms capable of degrading phenanthrene because these were the organisms of interest in this study. Since 1H2N was identified, we hypothesize that the fungal colony degraded phenanthrene to an intermediate that the bacteria could use and produce 1H2N. Fig. 4 presents the data of NMOrS, MOrS, and LMOrS for each of the three sediments. Relative concentrations Ž CsrCo . less than 1.0 at early times demonstrate initial fast sorption. From Fig. 4, it is obvious that MO addition causes the phenanthrene concentration to decrease, ultimately below the detection limit. In MOrS, there is a brief lag time and then phenanthrene is depleted. In LMOrS, phenanthrene concentration follows the same path as in NMOrS until MO is added. After MO addition in LMOrS, the phenanthrene concentration decreases with a flatter slope than in MOrS, demonstrating that the lower microbial population reduces the rate of biodegradation. These trends are consistent with other studies ŽSherrill and Sayler, 1980; Scow and Alexander, 1992.. 4.3. Model Õalidation Table 4 presents the biodegradation parameters for MOrNS and MOrS as fitted by the model. Average values for k 1 , along with standard deviations, are calculated based

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Fig. 4. Experimental data of the three systems for all three sediment samples. wOrganic matter ŽOM. originates from OC: organic coatings ŽA., CL: coaly particles ŽB. or both ŽC.x. Note: Cs r Co -1.0 for short times is due to initial fast sorption.

on triplicate samples. While variations are observed, the biodegradation rate constants are statistically the same, with 95% confidence, for each case and sediment. According to Laor et al. Ž1999., attached cells might have a higher degradation rate Žup to 2.2 times higher k 1 . than suspended MO because the externally sorbed chemicals are more bioavailable, and thus the degradation rates would be higher than for cases where sorption is limited by diffusion. Park et al. Ž2000. observed the opposite effect; biodegradation rate coefficients decreased Žby a factor of 27%. for attached cells due to reduced surface area with attachment. Our results do not statistically corroborate either theory Ži.e., Laor et al., 1999 or Park et al., 2000..

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Fig. 5. LMOrS: experimental data Žaverage of triplicate. and model prediction line with one standard deviation expressed with error bars worganic matter ŽOM. originates from OC: organic coatings ŽA., CL: coaly particles ŽB. or both ŽC.x.

In the LMOrS case, the microbial population was 10 times lower ŽTable 2.. Thus the biodegradation values presented in Table 4 were divided by a factor of 10 in order to predict the biodegradation behavior for LMOrS. In order to use this method, we assume that the MO density is so low that k 1 is biomass density dependent ŽSherrill and Sayler, 1980.. Biodegradation then can be described as follows ŽSimkins and Alexander, 1984; Alexander, 1994.: ydCrdt s k 1C s k 2 BC

Ž 12 .

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where k 2 is the second-order rate constant and B is the MO cell density. Since the MO cell number is difficult to obtain for natural mixed cultures, we assume that for LMOrS Žwith one-tenth the MO addition. Eq. Ž12. can be written as: ydCrdt s k 2 w 0.1 B x C s 0.1 w k 2 B x C s 0.1 k 1 C s kX1C kX1

Ž 13 .

kX1 s 0.1

If is the biodegradation rate constant for LMOrS, then k 1. Fig. 5 presents the aqueous solution data and the model prediction lines Žwith one standard deviation.

Fig. 6. ŽA. Example of the model output as fitted to a set of data in LMOrS for the sediment with the mixture of coaly particles Žslow. and organic coatings Žfast.. Lines present the concentration in solution, sorbed and biodegraded. ŽB. MOrS: distribution of sorbed chemical in the two particle components of the mixture. ŽC. LMOrS: distribution of sorbed chemical in the two particle components of the mixture Žarrows in B and C indicate when biodegradation starts.. Note different scales in both axes of B and C.

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for LMOrS based on this assumption. The excellent agreement between the data and the model validates both the analysis approach and the model assumptions. Based on these encouraging results, we will further analyze model predictions below. The model calculates the chemical concentration distributed between three compartments: the solution, the particle, and the amount biodegraded Žall expressed as an aqueous solution concentration.. Fig. 6A presents an example of the model output for each of these three compartments. Since a lag time exists prior to the onset of biodegradation, the initial decrease in aqueous concentration is due to contaminant sorption. When biodegradation starts, the solution concentration decreases dramatically, whereas the sorbed concentration decreases smoothly Ži.e., desorption commences because of the decreasing aqueous concentration.. However, desorption occurs less slowly than biodegradation, causing aqueous concentrations to decrease. Since biodegradation is concentration dependent Žfor the assumed first-order process. the degradation rate also decreases with time Žas the aqueous concentration decreases.. The model can also predict the chemical concentration distribution for different particle components Ži.e., components with different diffusionrsorption properties.. For the same sediment, as biodegradation occurs earlier and is faster ŽMOrS., the fast component responds more readily to the onset of biodegradation and desorbs faster than the slower component Žsee Fig. 6B.. In the example presented in Fig. 6C, the particle component with fast sorption Ži.e., organic coatings. reaches a lower plateau much faster than the slower component Ži.e., coaly particles., which has a higher sorption capacity. In this case ŽLMOrS., biodegradation is slower so both of the components have time to respond to the concentration gradient caused by biodegradation and seem to desorb with the same rate Žcompare slopes after day 19.. 4.4. SensitiÕity analysis Based on the experimental validation, we used the model to explore factors causing biodegradation to be desorption rate-limited. Table 5 summarizes the parameters varied and the combinations that produced desorption rate-limited biodegradation Žnote that in this analysis the sorption distribution coefficient was not varied.. Fig. 7 compares the effect of fast and slow Ždiffusion-limited. sorption on the rate of biodegradation for varying lag times. The lines presented in Fig. 7 are the outputs for the concentration degraded when biodegradation is fast with varied pre-equilibration times Žlag times. and sorption kinetics. When there was no equilibration time between the solute and the sediment before biodegradation started Ži.e., no lag time—case A in Fig. 7., fast sorption has the greater impact on biodegradation. When sorption is fast the aqueous concentration decreases faster and the lower aqueous concentration decreases the biodegradation rate. When biodegradation is fast and sorption is slow, there is no competition for the substrate until the substrate concentration is low and biodegradation becomes desorption rate limited. When some of the solute is already sorbed before biodegradation commences Ži.e., cases B and C in Fig. 7., biodegradation is desorption rate limited when sorption is slow Ždiffusion-limited.. When sorption is fast, desorption does not limit biodegradation compared to when the sorption is slow Žcompare fast line shapes with slow ones in cases

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Table 5 Sensitivity analysis Lag Žday.

% Eq

k 1 Žlrh.

Fast sorption

Slow sorption

0 0 0 0.12 9.5 35 35 35

0r0 0r0 0r0 50rNrA 93r50 98r84 98r84 98r84

F Ž0.1. I Ž0.01. S Ž0.001. F Ž0.1. F Ž0.1. F Ž0.1. I Ž0.01. S Ž0.001.

DRL DRL DRL same as 93% – – – –

ŽDRL only for low C w . – – NrA DRL DRL DRL –

Lag: lag time before biodegradation starts; % Eq: percent of equilibrium reached before biodegradation started given for both fast sorptionrslow sorption; NrA: not analyzed; k 1 : biodegradation rate constant expressed as F: fast, I: intermediate, and S: slow. k 1 values chosen to cover a range of values given in the literature ŽNam and Alexander 1998; Laor et al., 1999; Rouse et al., 1999.; DRL: desorption rate-limited; C w : phenanthrene aqueous concentration. Fast vs. slow sorption varied by two orders of magnitude, similar to fast vs. slow biodegradation.

B and C of Fig. 7. because as the aqueous concentration is degraded, more solute desorbs. However, when sorption is slow, biodegradation is desorption rate-limited for fast biodegradation rates. For slow biodegradation rates Žsee Table 5., there is enough time for both slow and fast sorption to occur, and thus biodegradation is not desorptionrate limited. Previous researchers using other models and parameters Ži.e., higher diffusion coefficients, higher biodegradation rates, and lower sorption coefficients. ŽScow and Hutson, 1992; Chung et al., 1993; Scow et al., 1995. have seen similar trends for most of the observations presented here. According to calculations proposed by Chung et al. Ž1993., diffusion-limited sorption for variables used in the present study cannot be ignored Žespecially for the sample with organic matter dominated by coaly particles.. The use of a coupled model is recommended in order to capture the effect of sorption kinetics on biodegradation rates. Even without varying the sorption coefficient there is a pronounced effect on the biodegradation curve shape by varying the sorption kinetic properties Žsee Fig. 7.. When there are fast sorbingrdesorbing fractions in the sediment,

Fig. 7. Concentration degraded with fast biodegradation Ž k 1 s 0.1 lrh., varied pre-equilibration times Ži.e., lag periods for biodegradation. Žlag time A s 0, Bs9.5, and C s 35 days., and sorption kinetics ŽS: slow sorption; F: fast sorption..

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the use of a two-compartment first-order desorption model seems adequate to describe the initial step of fast desorption ŽCornelissen et al., 1998.. Whereas the same model is not capable of precisely describing these processes when biodegradation becomes desorption rate-limited, our model describes accurately the diffusion-limited desorption kinetics and therefore the biodegradation kinetics. 4.5. Linear Õs. nonlinear Table 6 presents another sensitivity analysis that was performed to demonstrate the effect of adding nonlinear sorption to the coupled diffusion-limited sorption and biodegradation model. The following parameters were varied during this analysis: the lag time before biodegradation, the biodegradtion rate constant, the aqueous concentration in equilibrium and thus the sorption distribution coefficient, and the diffusion rate. The sorption linearity comparison is between N s 1 and N s 0.5. One of the sediment samples evaluated in this study demonstrated an N value of 0.55 Žsee Table 1., and Kleineidam et al. Ž1999. presented samples with N values as low as 0.38. Thus, while an N value of 0.5 is highly nonlinear, it is not an extreme value. In all cases of the sensitivity analysis, the general trend was the same; an example is presented in Fig. 8. Fig. 8A presents the behavior of the aqueous solution when sorption is linear compared to nonlinear Ž N s 1 vs. 0.5, respectively.. These results require careful interpretation to avoid making wrong conclusions. Looking only at the aqueous concentration, the response appears to be similar for linear and nonlinear sorption, suggesting that it is not necessary to account for nonlinear sorption. However, Fig. 8B shows that nonlinear desorption kinetics will be much slower than would be predicted by the linear model. Concurrently, biodegradation will also be slower than the linear model would predict Žsee Fig. 8C.. Although the linear model captures the overall aqueous behavior, it overestimates both the rate of desorption and biodegradation, and thus the actual fate of the chemical. The linear model suggests that much more of the chemical is removed Ždegraded. from the system, whereas a portion of the chemical is actually still inside the particle due to its nonlinear desorption behavior. In the case of Fig. 8, the difference is 30% at the end of 10 days which is significant enough to require the use of a nonlinear-based model. How critical is it to include nonlinear sorption in the model? Table 6 presents two columns with typical error norms used to compare two model outputs; the first column presents the maximum absolute difference and the second the square root of the mean of the difference squared for the degradation curves. These two differences have also been normalized by the estimated equilibrium concentration in order to be able to compare cases where the concentrations were different. The factors that cause the highest differences are fast sorption and fast biodegradation. Also, higher sorption capacity Žor lower equilibrium concentration. increases the difference between the predictions. The greatest difference in results was 49% and the concentration-normalized square root of the mean of the difference squared was 30% between the linear and the nonlinear predictions. It should be noted that much higher sorption coefficients have been observed elsewhere ŽKarapanagioti et al., 2000., suggesting that this analysis is accurate

Lag Žday.

Eq

k1 Žlrh.

Ce Žmgrl.

K deq Žlrkg.

K fr Žfor N s 0.5. Žmgrkg. Žmgrl. N

K fr Žfor N s1. Žmgrkg. Žmgrl. N

Sorption

Linear Ž N s1.0. vs. nonlinear Ž N s 0.50. Sol. Des. Bio.

L1 )10y6 Ž100 L1 r Ce .

L2 )10y6 Ž100 L2 r Ce .

0 0 0 0 9.5 9.5 0 0 0 0 9.5 9.5 9.5

N N N N N Y N N N N N Y Y

I Ž0.01. S Ž0.001. F Ž0.1. I Ž0.01. F Ž0.1. F Ž0.1. I Ž0.01. I Ž0.01. I Ž0.01. I Ž0.01. F Ž0.1. F Ž0.1. F Ž0.1.

53 53 53 53 53 53 5.3 530 5.3 530 5.3 5.3 530

140 140 140 140 140 140 290 66 290 66 290 290 66

1000 1000 1000 1000 1000 1000 670 1500 670 1500 670 670 1500

140 140 140 140 140 140 290 66 290 66 290 290 66

Slow Slow Fast Fast Slow Fast Slow Slow Fast Fast Slow Fast Fast

S S S S S S S S S FrS S S S

2.7 Ž5.1. 3.2 Ž6.0. 13 Ž25. 9.5 Ž18. 5.3 Ž10. 13 Ž25. 0.35 Ž6.6. 18 Ž3.4. 1.6 Ž30. 34 Ž6.4. 0.76 Ž14. 2.6 Ž49. 47 Ž8.9.

1.4 Ž2.6. 1.6 Ž3.0. 9.6 Ž18. 5.5 Ž10. 2.7 Ž5.1. 6.9 Ž13. 0.19 Ž3.6. 9.2 Ž1.7. 1.0 Ž19. 16 Ž3.0. 0.41 Ž7.7. 1.6 Ž30. 19 Ž3.6.

F F F F F F F F F FF F F F

F F F F F F F F F F F F F

Lag: lag time before biodegradation starts; Eq: Y: yes or N: no, indicates if sorption equilibrium is reached before biodegradation starts; k 1 : biodegradation rate constant expressed as F: fast, I: intermediate, and S: slow. k 1 values chosen to cover a range of values given in the literature ŽNam and Alexander, 1998; Laor et al., 1999; Rouse et al., 1999.; Ce : estimated phenanthrene concentration at equilibrium; K deq : estimated sorption distribution coefficient at equilibrium; N: Freundlich exponent; K fr : Freundlich constant; Sol: solution concentration depletion; Des: desorption; Bio: biodegradation; S: slower or F: faster, indicates the solute depletion, desorption, and biodegradation rate assuming linear sorption compared to nonlinear; FrS: suggests that depletion was first faster and then slower for linear sorption; FF: suggests that both sorption and desorption were faster for linear sorption; L1 : is the absolute maximum difference between the two model prediction lines Žlinear vs. nonlinear.; L2 : is the square root of the mean of the difference squared for the two model prediction lines Žlinear vs. nonlinear..

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Table 6 Sensitivity analysis: linear vs. nonlinear sorption

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Fig. 8. Linear Ž N s1. vs. nonlinear Ž N s 0.5. sorption coupled diffusion-limited sorption and biodegradation kinetics. Prediction curves for % mass: ŽA. in solution, ŽB. sorbed, and ŽC. biodegraded.

and reasonable. Differences of that magnitude suggest that it is critical to consider nonlinear sorption as a variable in a coupling diffusionrsorption and biodegradation model.

5. Conclusions This research documents the development of a model that couples diffusionrsorption and biodegradation, validates with experimental data, and uses the model to perform sensitivity analyses. The model includes intraparticle diffusion, nonlinear sorption, and biodegradation kinetics. When biodegradation commences with chemical introduction, then fast sorption limits the biodegradation. When biodegradation starts after some lag

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period, the chemical has time to sorb before biodegradation commences and slow sorption causes biodegradation to be desorption-rate limited Žif biodegradation is relatively fast.. The uniqueness of our model is the incorporation of nonlinear sorption. While the linear sorption model captured the behavior of aqueous concentrations, differences of up to 49% were found between the linear and the nonlinear prediction for the concentration that was desorbed, and the linear model overestimated the concentration degraded. Consequently, if a linear model is used inappropriately in the field, the degradation potential and risk reduction will be overestimated. It is thus critical to consider nonlinear sorption in models estimating biodegradation, natural attenuation, and bioremediation. Nomenclature a capacity factor A jk surface area of particle Žcm2 . C chemical concentration Žmgrml. Ca concentration at the outer boundary of the particle Žmgrml. concentration outside particles Žmgrml. Ce initial outside concentration Žmgrml. Ce0 Cp0 initial inside concentration Žmgrml. apparent diffusion coefficient Žcm2rs. Da Daq aqueous diffusion coefficient Žcm2rs. effective diffusion coefficient in particle pores Žcm2rs. De ´ effective porosity of particles F fractional uptake at equilibrium Žchemical mass on solid per total chemical mass. j subscript indicating particle of different type k subscript indicating particle of different radii k1 first-order biodegradation rate Žsy1 . kf coefficient for mass transfer from particles to external fluid Žcmrs. Kd sorption distribution coefficient Žlrkg. Freundlich isotherm coefficient K fr m iteration index n number of particles per unit volume of solution Žcmy3 . N Freundlich isotherm coefficient r bulk density of the particles Žmgrml. r radial coordinate in the spherical particle Žcm. S sorbed concentration inside particle Žmgrml. t current time level tq1 future time level tortuosity factor tf

Acknowledgements This study was partially funded by the US National Science Foundation through the EPSCoR program. The authors would like to thank Prof. Dr. P. Grathwohl from the

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Universitat Germany, for providing us with the intraparticle diffusion code, ¨ Tubingen, ¨ Dr. K. Scow from U.C. Davis for providing us with her code, Tuan Van Doan from O.U. for his assistance in obtaining the experimental data, and Carrie Evenson from O.U. for her assistance in microbe isolation and identification. Samples studied in this research were taken from the Norman Landfill Research Site, which is a USGS Toxic Substances Research Site Žhttp:rrwwwok.cr.usgs.govrnorlanrsite.html.. We acknowledge the assistance of Mr. Scott Christenson in obtaining samples from the site.

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