Journal of Hydrology 369 (2009) 234–240

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Journal of Hydrology

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Activation energies of phenanthrene desorption from carbonaceous materials:Column studies

Guohui Wang 1, Peter Grathwohl*

Center for Applied Geoscience, University Tübingen, Sigwartstrasse 10, D-72076 Tübingen, Germany

a r t i c l e i n f o

Keywords:

Activation energyDesorptionPhenanthreneCoalsColumn leaching

0022-1694/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.jhydrol.2009.02.018

* Corresponding author. Tel.: +49 7071 2975429; faE-mail addresses: gwang5@buffalo.edu (G. Wang),

(P. Grathwohl).1 Present address: Department of Geology, Unive

Natural Sciences Complex, Buffalo, NY 14260, USA.

s u m m a r y

Sorption/desorption kinetics of phenanthrene from two carbonaceous samples (lignite and high-volatilebituminous coal (HC)) at different temperatures was monitored using an on-line column method. Pulver-ized samples (<30 lm) were equilibrated in the column for 2 months before desorption began. Thedesorption rates declined initially fast, followed by an extended tailing part, which could be describedvery well by a single parameter spherical diffusion model accounting for non-linear sorption. Desorptionwas carried out at stepwise increased temperatures (20–90 �C), and the apparent activation energieswere calculated based on the Arrhenius relationship for each of totally three temperature steps. Theapparent activation energies were in an order of 58–66 kJ mol�1 and 70–71 kJ mol�1 for lignite and HC,respectively and they did not increase significantly during the leaching procedure. At the end of theexperiments desorption was almost complete and only 0.2% (lignite) and 6% (HC) of the initially sorbedphenanthrene was present after the last temperature step. Fitted diffusion coefficients as well as the com-parison between the apparent activation energies and sorption/desorption enthalpies obtained for thesame samples from equilibrium isotherms imply that the diffusion occurred in organic matter of the lig-nite and in micropores of the high-volatile bituminous coal, where higher apparent activation energiesare expected.

� 2009 Elsevier B.V. All rights reserved.

Introduction

Dependency of sorption/desorption rates on temperature isdetermined by the activation energy, which essentially describeshow chemical rate constants vary with temperature. It is gener-ally accepted that two mechanisms may limit the mass-transferin sorption/desorption of hydrophobic organic compounds (HOCs)in natural organic matter: (1) molecular diffusion in an organicmatrix (Brusseau and Rao, 1989, 1991; Brusseau et al., 1991) or(2) aqueous diffusion in intraparticle pores (Rao et al., 1980;Wu and Gschwend, 1986; Ball and Roberts, 1991b). Since diffu-sion is positively temperature-dependent, both mechanisms areconsidered to be activated processes. Diffusion in an organic ma-trix is postulated to be analogous to diffusion in polymers, wherediffusion occurs through holes that are distributed discontinu-ously throughout the material (Ten Hulscher and Cornelissen,1996). Pore diffusion depends on diffusion coefficients and sorp-tion sites distributed along the pore walls, which retards the sol-

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x: +49 7071 5059.grathwohl@uni-tuebingen.de

rsity at Buffalo (SUNY), 876

ute transport. If sorption is temperature-dependent (i.e. decreaseswith increasing temperature), then this additionally affects thepore diffusion rates. Diffusion through micropores is consideredas molecule jumps from one low-energy site to the next (Kargerand Ruthven, 1992). Ten Hulscher and Cornelissen (1996) re-viewed the diffusion of organic compounds in polymers and re-port average activation energies of 60 kJ mol�1. Values higherthan 100 kJ mol�1 can be expected for glassy or highly cross-linked polymeric matrixes (Johnson and Weber, 2001). A numberof studies have been carried out to investigate the desorptionkinetics and related activation energies using different organiccompounds in different sorbents (model substances, soils andsediments; see Table 3). Cornelissen et al. (1997) studied the slowdesorption of PAHs and PCBs from laboratory-spiked and field-contaminated sediment samples and determined activation ener-gies in the range of 60–70 kJ mol�1. Castilia et al. (2000) deter-mined activation energies in column experiments on desorptionof trichloroethene from model substances and natural geosor-bents (silica gel, soil, sediment) of 47–94 kJ mol�1, which is con-sistent with the values found for diffusion in micropores.Chihara et al. (1978) found activation energies between 10 and50 kJ mol�1 for diffusion of hydrocarbons in zeolites and molecu-lar sieves. Johnson and Weber (2001) investigated desorption ofphenanthrene using heated and superheated water at different

G. Wang, P. Grathwohl / Journal of Hydrology 369 (2009) 234–240 235

temperatures (75–150 �C) and report activation energies of about40–80 kJ mol�1. Ghosh et al. (2001) measured the activation ener-gies of PAHs in a coal containing subfraction and clay/silt subfrac-tion of a harbor sediment, and found that the coal containingsubfraction has 3 times higher activation energies than the clay/silt subfraction. Kleineidam et al. (2004) carried out columndesorption experiments using aquifer materials which experi-enced more than a 1000 days long-term sorptive uptake of phen-anthrene. The desorption rates were very well fit by the retardedpore diffusion model simply by forward modeling using theparameters from the long-term sorptive uptake batch experiment.No hysteresis was observed and the desorption activation ener-gies were in the range from 45 to 59 kJ mol�1.

Several models have been developed to simulate slow soluteleaching in column tests. The desorption rate constants are ob-tained by fitting models to data from desorption experiments (suchas concentration, flux, remaining mass). The intraparticle diffusionmodel is widely used to represent desorption kinetics of contami-nants in geosorbents (Wu and Gschwend, 1986; Ball and Roberts,1991b; Grathwohl and Reinhard, 1993; Kleineidam et al., 2004).Meanwhile the two/multi-site/stage first-order models, whichneed simpler math and no geometry characterization of the geo-sorbents, are also developed to interpret the slow and very slowdesorption rates (Cornelissen et al., 1997, 1998; Ten Hulscheret al., 1999). Altfelder and Streck (2006) compared these two con-cept models and concluded that the intraparticle model performsbetter than the first-order model, especially in a long-term leach-ing process up to months or years. The two or multi-site/stagemodels need more than one rate constant as fitting parameterswhich depend on column length and flow velocity (Young and Ball,1995, 2000). In diffusion models (e.g. the spherical diffusion mod-el) usually only one rate constant to simulate desorption kinetics issufficient for a homogeneous samples (i.e. comprising one grainsize class and one type of particles) whereas for heterogeneoussamples (i.e. different grain sizes and different particles) againmulti-rate diffusion models are needed.

In this study, desorption kinetics of phenanthrene from twocarbonaceous materials was investigated in flow-through columnexperiments with stepwise increases of the temperature, and theconcentrations observed were fitted using a spherical intraparti-cle diffusion model. The main objectives of this study were (1)to determine the apparent diffusion coefficient for desorption,(2) to calculate the apparent desorption activation energies fromstepwise temperature increases using a high resolution on-linecolumn technique, (3) to find out if the apparent activation en-ergy changes with increasing desorption in order to elucidate po-tential apparent hysteresis phenomena which should lead toincreased activation energies along with the increased degree ofdesorption, and (4) to compare the measured apparent activationenergies with existing thermodynamic data on diffusion in poly-mers, micropores and water in order to elucidate potentialdesorption mechanisms.

steel column in wa

HPLCpump

Phe. solution / water

Fig. 1. On-line column setup for the s

Materials and methods

Pulverized lignite and high-volatile bituminous coal (HC) wereselected for the column experiments in this study. The grain sizeof the particles was less than 30 lm (HC) or below 10 lm (lignite)which allows for fast sorption/desorption. Phenanthrene was usedas the probe compound and was obtained as pure product (98%)from Aldrich Chemical Corp. Physicochemical properties, thermo-dynamic parameters (on sorption/desorption) and sample charac-teristics are listed in (Wang et al., 2007; Wang, 2008).

Column package and pretreatment

Stainless steel HPLC columns with 8 cm length and 1 cm innerdiameter were used. About 0.2 g pulverized sample was scatteredevenly on a clean glass wool mat, which was then rolled andpacked into the column. Two metal frits were placed at both endsof the column to prevent leaching of fine particles. Then the col-umn was filled with Millipore water from the bottom using a HPLCpump at a flow rate of 0.5 ml min�1. The total filling time was re-corded and the pore volume was calculated from mass of water inthe column. The dead volume of all the stainless steel capillaryconnection tubes was considered as well (less than 0.25% of the to-tal water-filled volume).

On–line column experiments

The sorption and subsequently desorption column experimentswere monitored on line. The column setup is shown in Fig. 1. Thepacked column was connected to a HPLC system instead of theusual separation column. A fluorescence detector with emission/extinction wavelengths of 249/345 nm was used to monitor phen-anthrene concentrations and the signals were recorded using chro-matography software every 5 s. This high resolution of themeasurement was needed in order to follow the effluent concen-trations in sufficient detail at each temperature step. Temperaturecontrol was ensured keeping the column in a water bath. Calibra-tion of the fluorescence signal was carried out for each tempera-ture step in order to account for any baseline shift in the signal.Baselines were quite stable as shown in Fig. 3. For each calibration4–6 standard solutions (2–150 lg L�1) were used and electricalsignals (mV) were converted to concentrations (lg L�1). Phenan-threne solutions were prepared using degassed Millipore waterand stock solutions in methanol; they were kept in the dark andpoisoned with sodium azide at a concentration level of 200 mg L�1

in order to inhibit bacterial growth and thus to prevent biodegra-dation of the phenanthrene. For the initial breakthrough experi-ments, the inflow phenanthrene solution was renewed every24 h. The inflow solution was directly connected to the HPLC pumpusing stainless steel capillary tubing (see Fig. 1). The phenanthrenesolution was pumped through the sample column with a constantflow rate of 1.42 or 1.45 ml min�1 under a controlled temperature

ter bath

fluorescence detector

signal recorder effluent

orption/desorption experiments.

236 G. Wang, P. Grathwohl / Journal of Hydrology 369 (2009) 234–240

(25 �C for lignite and 20 �C for HC) until complete breakthrough (orup to 85% of the input concentration) was observed. The concentra-tions of the inflow phenanthrene solutions were around 10–12% ofthe solid phenanthrene aqueous solubility at 25 �C (121 lg L�1 forlignite and 150 lg L�1 for HC, respectively). After the sorption up-take step, the sample column was detached from the HPLC system,closed tightly with stainless steel fittings and kept at 20 �C forabout 2 months. Sorption equilibrium was established for the fineparticles in the column after this two-month period (Wang et al.,2007). Thereafter, desorption experiments were carried out. Theequilibrated column was reinstalled in the HPLC system again,where another HPLC pump and new tubing (to avoid memory ef-fects) was used to purge the column with clean water at a pumpingrate of 2.96 ml min�1. The water used for purging was again deion-ized, degassed, spiked with sodium azide (200 mg L�1) and testedfor potential phenanthrene background. After the concentrationsin the effluent decreased significantly at 20 �C (about 120–250 h),the temperature was stepwise increased first to 46 �C, then to77 �C and finally to 90 �C in case of HC sample (see Fig. 3). Afterthe desorption experiments, the samples together with the glasswool were removed from the column, immediately transferred toan extraction cell and extracted with acetone and toluene in anaccelerated solvent extraction (ASE) device in order to determinethe residual phenanthrene in the sample after the column desorp-tion procedure. In order to check the reproducibility of the proce-dure, the experiment with the lignite sample was repeated underslightly different temperature steps of 30, 40, 50 and 77 �C.

Apparent activation energy (Ea,app)

If in the tailing part of a desorption experiment, the tempera-ture is stepwise increased a corresponding increase of the desorp-tion rates and thus an increase of the effluent concentrations isexpected. Then the apparent activation energy (Ea,app (kJ mol�1))of desorption for each individual temperature step (from T to T0)can be calculated according to the Arrhenius relationship in thetwo temperature point form (Silberberg, 2003):

Ea;app ¼ �RTT 0

T � T 0

� �ln

C 0

C

� �ð1Þ

where C and C0 are the transient effluent aqueous concentrations (inlg L�1 or fluorescence signal (mV)) before and after the tempera-ture step, respectively (i.e., the lowest concentration in the tailingpart before the temperature increase and the highest concentrationjust after the temperature step). R is the universal gas constant. Thisequation requires that the solid loading (Cs) stays constant duringeach temperature step. In Eq. (1), the regression of ln (C0/C) wasused to replace the classical regression using rate constants (John-son and Weber, 2001; Kleineidam et al., 2004) because at constantflow rates the concentrations are directly proportional to the ratesand concentration data were monitored directly in high resolution.The measured Ea,app represents the overall temperature effect,including both the equilibrium driving forces for desorption (i.e.,thermodynamics of phase partitioning or adsorption) and the kinet-ics of desorption (diffusion). The determined value is expected to bethe combination of the desorption enthalpy (equilibrium thermody-namics) and the temperature effects on diffusion (i.e., mobility ofthe solute and viscosity of the water) as described in

Ea;app ¼ � RTT 0

T � T 0ln

D0aq

Daq

!þ R

TT 0

T � T 0ln

C 0wCw

� � !ð2Þ

where Cw denotes the equilibrium concentrations in the pore waterand Daq is the aqueous diffusion coefficient. The first and the secondterms on the right side of Eq. (2) represent the activation energy foraqueous diffusion of the solute in water (or the organic matrix) andthe equilibrium desorption enthalpy, respectively.

Spherical intraparticle diffusion model

Solute diffusion from aqueous phase into spherical particles canbe described by Fick’s 2nd Law in radial coordinates:

@C@t¼ Da

@2C@r2 þ

2r@C@r

" #ð3Þ

where r is the radial distance from the center of a grain. Da denotesthe apparent diffusion coefficient, which depends on the aqueousdiffusion coefficient (Daq), the intraparticle porosity (e), the distribu-tion coefficient (Freundlich KFr and 1/n for non-linear sorption); thebulk density of the particle (q) and the tortuosity factor (sf).

Da ¼Daqe

ðeþ qKFrc1=n�1Þsfð4Þ

sf is estimated from the intraparticle porosity based on Archie‘s lawusing an empirical exponent m:

sf ¼ e1�m ð5Þ

A numerical code (SMART developed by Finkel et al., 1999) couplingEqs. (3)–(5) to advection was used to model the column effluentconcentrations using m, thus the pore diffusion coefficient, as theonly fitting parameter. Longitudinal dispersion could be neglectedbecause in such column experiments it is very small and becausethe model was fit to the extended tailing part of desorption curvewhere dispersion is no longer significant. Nonlinear sorption wasconsidered by implementing Freundlich sorption isotherms deter-mined for the samples at the same temperatures (Wang et al.,2007).

Results and discussion

Sorptive uptake

Breakthrough curves of phenanthrene in the columns areshown in Fig. 2. Pumping lasted 121/92 h for lignite/HC columns,and the sorbed mass as compared to the expected uptake at equi-librium (M/Meq) was 0.79 and 0.16 for lignite and HC, respectively.The sorbed mass M at time t was calculated by integration of thebreakthrough curve. The equilibrium sorptive uptake (Meq) ex-pected at the inflow concentration was calculated based on resultsfrom previous batch equilibrium sorption experiments (see Wanget al., 2007). The total mass present in the column after sorptiveuptake was 480 lg and 330 lg for lignite and HC, respectively.

Desorption

Fig. 3 shows the concentrations in the leachate of the lignite andHC columns. Desorption was initially fast, but followed by an ex-tended tailing part. The temperature was increased stepwise inthe extended tailing part where the release of phenanthrene is be-lieved to be purely limited by intraparticle diffusion. The stepwiseincrease of temperature caused immediate concentration in-creases, which reflects that desorption is thermodynamically anendothermic process.

The leaching curves were predicted with the model SMART. Themodel input parameters, fitted m values, thus the calculated appar-ent diffusion coefficients are compiled in Table 1. In case of lignite,the phenanthrene concentrations measured follow very well theintraparticle diffusion model (see Fig. 3). The observed apparentdiffusion coefficient at 20 �C was 2.58 � 10�15 cm2 s�1, where thefitted value for m was 2.56. The predicted concentrations areslightly lower than the experimental data in the beginning ofdesorption probably due to some background fluorescence becauseinitially also DOC leached from the lignite. The initial high DOC

Table 1Sample characteristic and observed apparent diffusion coefficients (20 �C) of phenanthreneis the only fitting parameter.

Sample Daqa (cm2 s�1) Da

b (cm2 s�1) logKFr; 1/n (L kg�1); (

Lignite 0.21 g 5.86E�06 2.58E�15 4.28; 0.83HC 0.17 g 5.86E�06 9.41E�14 4.55; 0.57

a Daq was calculated using Daq = 13.26 � 10�5/(g1.14 V 0.589) (Hayduk and Laudie, 1974b Da was calculated by Eqs. (4) and (5), where the averaged pore water concentrations

7.32–5.04 lg L�1during the 75–121 h period; HC: average 0.87 lg L�1, range 1.028–0.72Wang (2008).

c In m the standard deviation is extremely little probably below 1%.d Refer Wood et al. (1983).e Calculated as e = intraparticle pore volume/(mass/bulk density), where the intrapartf Calculated by Eq. (5).

0.0

0.2

0.4

0.6

0.8

1.0

Time [h]

C /C

0 HC

Lignite

0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100 120 140Time [h]

M /M

eq

HC

Lignite

0 20 40 60 80 100 120 140

a b

Fig. 2. (a) Phenanthrene breakthrough curves for the lignite and HC columns; (b) relative accumulated mass in the sorbents during the breakthrough experiment.

0

5

10

15

20

0 200 400 600 800 1000 1200Time [h]

Con

cent

ratio

n [µ

g/L]

HC

m = 1.7

20°C 46°C 77°C 90°C

0

10

20

30

40

50

60

70

0 50 100 150 200 250 300 350 400 450 500Time [h]

Con

cent

ratio

n [µ

g/L]

m = 2.56

Lignite

20°C 46°C 77°C

Fig. 3. Phenanthrene concentrations during column desorption with stepwiseincreased temperatures for the lignite and high-volatile bituminous coal (HC) samples;solid line: intraparticle pore diffusion model (‘‘m” is the fitted empirical exponentaccounting for pore geometry/tortuosity); symbols: measured concentrations.

G. Wang, P. Grathwohl / Journal of Hydrology 369 (2009) 234–240 237

concentrations (indicated by yellow colored effluent) are probablydue to generation of DOC during the 2-month equilibration of thelignite column. Yellow colored effluent water was again observedat the 77 �C step immediately after the temperature increase. TheDOC release from soil and sediment is reported as a rate-limitedprocess (Cao et al., 1999; Wehrer and Totsche, 2005). Thurman(1985) reported that the DOC content of uncolored fresh watercould be still up to 2–8 mg L�1. Therefore, a certain DOC relatedfluorescence can not be excluded for the lignite sample even ifthe column effluent was non-colored.

For the HC sample, the intraparticle diffusion model fits theeffluent concentrations again very well even in the tailing partusing just a single apparent diffusion coefficient (9.41 �10�14 cm2 s�1, the fitted value for m was 1.7). The slight initial over-estimation might be due to fast desorbing domains in the coal fol-lowed by slow diffusion from micropores (Li and Werth, 2004;Cheng and Reinhard, 2006). Ahn et al. (2005) investigated theintraparticle diffusion of phenanthrene and pyrene in polymers,coke, and activated carbon, and found that the sorption kineticsin the polymer and coke samples can be described well by theintraparticle diffusion model, whereas a branched pore model com-bining the macro- and micropore domains has to be used to simu-late the sorptive uptake in activated carbon, which is characterizedby a high micropore volume.

Mass balance

Table 2 shows the mass balance of phenanthrene sorbed anddesorbed in the column experiments based on integration of thebreakthrough curves. The ‘‘residual” indicates mass recovered bythe ASE extraction after the desorption experiment was finished.In case of lignite, the desorption seems to recover more mass thanwas sorbed during the loading of the column, which likely is due tothe background fluorescence from DOC. However, the most impor-

in the lignite and HC samples through intraparticle diffusion model (SMART), where m

–) mc (–) r (mm) qd (g cm�3) ee (%) sff (–)

2.56 0.0007 1.29 1.02 12801.7 0.01 1.32 1.50 19

).from the 20 �C tailing breakthrough were used (lignite: average 6.18 lg L�1, rangelg L�1 during the 150–280 h period); for the sorption and other parameters, see

icle volume were measured by BET method (see Wang, 2008).

Table 2Phenanthrene mass balance in lg in the column experiments; residual: extractedafter the column desorption.

Samples Sorption Residual Desorption

On-line curve integration GC/MS On-line curve integration

Lignite 480 0.8 524.3a

HC 330 19.4 340b

a Based on the stable effluent concentrations after 12 pore volumes (first 15 min);the earlier signal was affected by background fluorescence attributed to DOC.

b The fluorescence signal was baseline corrected (3 mV) by the signal measuredbefore desorption was started.

238 G. Wang, P. Grathwohl / Journal of Hydrology 369 (2009) 234–240

tant result reported in Table 2 is the residual mass in the lignitecolumn after desorption of just 0.8 lg, which accounts for only0.17% of the initially sorbed phenanthrene. In case of HC, 5.9% ofthe sorbed phenanthrene still remained in the sorbent after morethan 1000 h of leaching even at elevated temperatures.

Desorption activation energies

Fig. 4 shows the Arrhenius plots based on concentration in-creases at each temperature step. The mass desorbed during eachtemperature step was less than 5% of the total mass in the column,thus Cs was considered as reasonably constant for the calculationof Ea,app. The apparent activation energies determined are compiled

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

Lignite

LnC

[µg/

L]

20ºC46ºC

77ºC

46ºC

1/RT0.32 0.34 0.36 0.38 0.40 0.42

Fig. 4. Arrhenius plots for the determination of apparent desorption activation energies (high-volatile bituminous coal (HC) samples.

Table 3Activation energies (kJ mol�1) at the individual temperature steps, desorption enthalpies deas activation energies from literature.

Samples Temperature step 20–46 �C

HC 0.17 g Ea,app 70DHa 32

Lignite 0.21 g Ea,app 58DHa 24

Lignite 0.20 g (repeated) Temperature step 30–40 �CEa,app 60DHa 24

Literature reported activation energiesSample Compound Ea

Sediments PCBs and PAHs 60–70Silica gel/solids TCE 47–94Soil Phenanthrene 41–74Shale Phenanthrene 83–86Soil EDB 66Coal particles PAHs 115–139Silt/clay PAHs 37–41Aquifer materials Phenanthrene 45–59Elastomeric polymers Organic compounds average 60

a DH: Desorption enthalpies determined from equilibrium batch experiments (see Waoccurs in water then additionally 16.9 kJ mol�1 are expected corresponding to the activ

in Table 3. For both samples the Arrhenius plots are parallel for thedifferent temperature steps except the 77–90 �C step for HC. Inaddition, similar apparent activation energies were determinedfor the second lignite sample, which was examined at slightly dif-ferent temperature steps, indicating that the experimental tech-nique provides robust results. As an important result, no trend ofincreasing Ea,app with progressing desorption is observed. Theapparent activation energies determined are 70–71 kJ mol�1 and58–66 kJ mol�1 within the temperature range of 20–77 �C for HCand lignite, respectively. Only in the 0.21 g-lignite experiment asignificant difference in the apparent activation energies was ob-served with increasing temperature (66 kJ mol�1 at the 46–77 �Cstep compared to 58 kJ mol�1 at the 20–46 �C step). This, again,might be due to enhanced DOC leaching at 77 �C (yellowish coloredeffluent). The HC sample seems to show an elevated Ea,app at the77–90 �C step which, however, is uncertain because of the verylow signals recorded (4.6 mV and 9.3 mV after the step) close tothe baseline (3 mV) measured before the desorption .

Table 3 also reports activation energies from literature for dif-ferent materials and solutes. In general, high values for Ea havebeen associated with diffusion of HOCs in condensed organic mat-ter, coals, and shale materials. In contrast, diffusion in amorphousorganic matrices which occurs in soils show lower values for Ea.The apparent activation energies determined in this study arewithin the wide range reported in the literature. The equilibrium

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

0.32 0.34 0.36 0.38 0.40 0.42

HC

20ºC46ºC

77ºC

77ºC

90ºC

46ºC

LnC

[µg/

L]

1/RT

Ea,app) from concentration increases at each temperature step for the lignite and the

termined in equilibrium batch experiments for the two carbonaceous samples, as well

46–77 �C 77–90 �C

71 (114)36 47662840–50 �C 50–77 �C58 6125 27

Temperature20–60 �C Cornelissen et al. (1997)30–60 �C Castilia et al. (2000)75–150 �C Johnson and Weber (2001)75–150 �C Johnson and Weber (2001)40–97 �C Steinberg et al. (1987)30–400 �C Ghosh et al. (2001)30–400 �C Ghosh et al. (2001)20–70 �C Kleineidam et al. (2004)25–110 �C Ten Hulscher and Cornelissen (1996)

ng, 2008) for the respective solid loading (Cs) at each temperature step; if diffusionation energy of phenanthrene diffusion in water (see Kleineidam et al., 2004).

20

30

40

50

60

70

80

20 25 30 35 40 45 50Enthalpy [kJ/mol]

Ea

[kJ/

mol

]

Fig. 5. Comparison of equilibrium enthalpies (Wang, 2008) and apparent activationenergies for phenanthrene desorption from lignite (diamonds) and high-volatilebituminous coal (triangles); filled and open diamonds: duplicate lignite samples;dashed line: expected correlation if the activation energy of aqueous diffusion ofphenanthrene in bulk water (16.9 kJ mol�1) is added to the enthalpy.

G. Wang, P. Grathwohl / Journal of Hydrology 369 (2009) 234–240 239

desorption enthalpies determined at the same loading level (Wang,2008) can be compared to the Ea,app values compiled in Table 3, andcan give some hints on the diffusion process (see Fig. 5). If diffusionin the pore water controls the sorption/desorption kinetics, thendifferences between the activation energy of desorption and theequilibrium enthalpy of sorption/desorption should correspondto the activation energy of diffusion of phenanthrene in bulk water(16.9 kJ mol�1, Kleineidam et al., 2004). The comparison showsthat all plotted data are above the dashed line (i.e., equilibriumenthalpies plus 16.9 kJ mol�1), which means much slower diffusionrates than expected for phenanthrene diffusion in the pore water.In case of lignite, diffusion in the organic matter matrix could ex-plain this difference. For instance, a diffusion coefficient of1 � 10�10 cm2 s�1 is reported for phenanthrene diffusion at 25 �Cin fine polyoxymethylene particles (Ahn et al., 2005). This valueis more than 4 orders of magnitude lower than phenanthrene dif-fusion in water (6.7 � 10�6 cm2 s�1). For the HC sample, higheractivation energies could be expected because of diffusion inmicropores. Activation energies for diffusion are larger in microp-ores than in mesopores or macropores for liquids and gases (Werthand Reinhard, 1997).

Conclusions

This study shows that a single parameter intraparticle diffusionmodel fits the desorption of phenanthrene from carbonaceousmaterials (lignite and high-volatile bituminous coal) very well. Fit-ted apparent diffusion coefficients indicate that sorption in the or-ganic matrix (lignite) and micropores (HC) may be important. Theapparent activation energies of phenanthrene desorption do notincrease more than expected from the increase of the sorption en-thalpy at decreasing loadings (Cs), which indicates that there is nosignificantly slower desorption mechanism appearing whichwould limit desorption in the long term. Furthermore, the residualmass recoveries prove that more than 94% of the initially sorbedphenanthrene mass was released during the desorption experi-ments. The comparison between the determined apparent activa-tion energies and the enthalpies from equilibrium sorption/desorption isotherms combined with the activation energy ex-pected for the diffusion in water implies that diffusion in the coalsoccurs in the organic matter matrix of the lignite and in the porewater in micropores in the high-volatile bituminous coal.

Acknowledgements

This research was funded by Deutsche Forschungsgemeinschaft(DFG) under Project number GR 971/16-1 and ‘‘AquaTerra”, a Euro-pean Union FP6 integrated project (Project no. 505428 (GOCE)).

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