Sorption/desorption kinetics of contaminants on mobile particles: Modeling and experimental evidence

Transcription

1 WATER RESOURCES RESEARCH, VOL. 39, NO. 12, 1329, doi: /2002wr001798, 2003 Sorption/desorption kinetics of contaminants on mobile particles: Modeling and experimental evidence Steffen Bold, 1 Siegfried Kraft, Peter Grathwohl, and Rudolf Liedl Center for Applied Geoscience, University of Tübingen, Tübingen, Germany Received 24 October 2002; revised 20 May 2003; accepted 31 July 2003; published 3 December [1] In this study the impact of sorption/desorption kinetics between organic contaminants and mobile particles suspended in subsurface water is analyzed. TCE migration through a granular activated carbon column is investigated at different transport velocities with lignite and activated carbon particles as mobile carriers. The measured breakthrough characteristics of TCE can be reproduced by a reactive transport model simulating sorption/desorption kinetics applying an intraparticle diffusion approach for mobile particles and the packed bed of granular activated carbon. Model predictions are based on independently measured physicochemical parameters, i.e., no calibration of TCE sorption/desorption is required. The close matches of experimental data to predicted data validate the exclusively process-based model assumptions and indicate that this approach has large predictive capabilities. Extending these findings, a sensitivity study is presented in order to specify under which conditions sorption/desorption of contaminants in mobile particles has to be modeled as a kinetic process. It is found that sorption/ desorption kinetics are of major importance for Damköhler numbers between 0.01 and 100. INDEX TERMS: 1829 Hydrology: Groundwater hydrology; 1831 Hydrology: Groundwater quality; 1832 Hydrology: Groundwater transport; KEYWORDS: particle-facilitated transport, Damköhler number, sorption kinetics, intraparticle diffusion model, particles Citation: Bold, S., S. Kraft, P. Grathwohl, and R. Liedl, Sorption/desorption kinetics of contaminants on mobile particles: Modeling and experimental evidence, Water Resour. Res., 39(12), 1329, doi: /2002wr001798, Introduction [2] Point sources of organic contaminants in the unsaturated or saturated zone are a potential threat to groundwater quality. In groundwater risk assessment it is necessary to have valid information about contaminant migration toward the water table or along groundwater flow paths. In several experimental studies particle-facilitated transport could be observed to significantly influence solute spreading of strongly sorbing contaminants, such as hydrophobic organic compounds [e.g., Magee et al., 1991; Dohse and Lion, 1994; Sojitra et al., 1995; Kögel-Knabner and Totsche, 1998], pesticides [e.g., Seta and Karathanasis, 1997; de Jonge et al., 1998; Villholth et al., 2000], radionuclides [e.g., Saiers and Hornberger, 1996; Artinger et al., 1998; Noell et al., 1998] and inorganic contaminants [e.g., Dunnivant et al., 1992; Puls and Powell, 1992; Grolimund et al., 1996; Karathanasis, 1999]. [3] Particle-facilitated transport is especially important with regard to groundwater cleanup due to the short travel times of particles in the treatment zones (e.g., reactive walls) and the mobilization of fine-grained materials during subsurface construction. In particular, this study was motivated by the potential early breakthrough of contaminants through activated carbon reactive walls because of mobilized lignite 1 Now at Emschergenossenschaft/Lippeverband, Department of Water Resources Management, Essen, Germany. Copyright 2003 by the American Geophysical Union /03/2002WR SBH 3-1 particles from a lignite containing aquifer in Eastern Germany. For a process-based description of particle-facilitated transport in this system, three types of interactions have to be taken into account (Figure 1): (1) the interaction of particles with the soil matrix, (2) the interaction of contaminants with the soil matrix, and (3) the interaction of contaminant with mobile and immobile particles. All these processes can be kinetically limited. [4] The main focus within this study is on the processbased description of kinetically limited interactions of contaminants and mobile particles. In several publications this process has been described as an instantaneous equilibrium process [e.g., Magee et al., 1991]. Using this modeling approach, Corapcioglu and Jiang [1993] developed an analytical model, which favorably matches observed phenanthrene breakthrough curves (BTC) influenced by particle-facilitated transport. For constant colloid concentrations they modeled contaminant transport by including a modified retardation factor and dispersion coefficient. Prechtel et al. [2002] used a similar approach to simulate particle-facilitated transport for a layered soil profile in the unsaturated zone. Recent experimental studies indicate that sorption/desorption kinetics of contaminants onto/from mobile particles can significantly influence particle-facilitated transport [e.g., Saiers and Hornberger, 1996; van de Weerd and Leijnse, 1997; Noell et al., 1998; Schüssler et al., 2001]. This is supported by several modeling studies using an empirical first-order rate law to describe the contaminantparticle interactions [e.g., Corapcioglu and Jiang, 1993; Ibaraki and Sudicky, 1995, Choi and Corapcioglu, 1997;

2 SBH 3-2 BOLD ET AL.: SORPTION KINETICS ON PARTICLES [6] The objective of this paper is to experimentally identify and quantify transfer processes in mobilized particles. Specifically, the diffusion model is extended to simulate contaminant-particle interactions and verified in transport simulations. Several column tests are performed and resulting contaminant BTCs are simulated by a numerical model, accounting for intraparticle diffusion for both mobile particles and matrix. In addition, this modeling approach is used to investigate the effect of kinetic contaminant-particle interactions on particle-facilitated transport in general by means of scenario calculations. Figure 1. Relevant interactions for a process-based description of particle-facilitated transport and basic concept of the intraparticle diffusion model. 1, particle-matrix interaction; 2, contaminant-matrix interaction; 3, contaminant-particle interaction. van de Weerd and Leijnse, 1997; van de Weerd et al., 1998; Corapcioglu et al., 1999a]. This modeling approach has been recently extended to take into account twosite solute adsorption to particles [Knabner et al., 1996; Saiers and Hornberger, 1996; Schüssler et al., 2001; Saiers, 2002] Moreover, Roy and Dzombak [1998] found that a slow desorption rate of contaminants from mobile particles is probably the most important factor for enhanced solute spreading in natural systems. On the other hand, Corapcioglu et al. [1999b] could show by means of scenario calculations that kinetically controlled interactions between mobile particles and contaminant have to be taken into account only close to the contaminant and particle source or for short time periods. This is valid for lab column experiments, reactive walls, or preferential flow in soils or aquifers. [5] The use of empirical first-order rate laws to describe contaminant-particle or contaminant-matrix interactions is limited, because the reaction rates may be scale-dependent and cannot be determined a priori in independent experiments. Therefore process-based modeling approaches have been developed taking into account intraparticle diffusion in water filled intraparticle pores as the limiting factor of contaminant sorption kinetics in the soil matrix or aquifer materials [e.g., Ball and Roberts, 1991; Grathwohl and Reinhard, 1993; Farrell and Reinhard, 1994a, 1994b; Harmon and Roberts, 1994; Grathwohl, 1997; Kleineidam et al., 1999; Rügner et al., 1999; Karapanagioti et al., 2000; Liedl and Ptak, 2003]. 2. Materials and Methods [7] In order to investigate the influence of mobile particles on trichloroethylene (TCE, D aq = m 2 s 1 ) transport, column tests were performed using activated carbon (Chemviron TL830) as the column packing material. The high sorption capacity of activated carbon for organic contaminants ensures that TCE bound to mobile particles is observed in measurable concentrations at the column outlet for extended periods of time before breakthrough of the solute. Both pulverized lignite from Bitterfeld/Germany and activated carbon were used as mobile particles representing two examples of strongly sorbing artificial and naturally occurring particles. The characteristics for these materials are summarized in Table 1 and the experimental design for the column tests is outlined in Figure 2. [8] The particle density of the lignite particles was determined by a HE-pycnometer (Accupyc 1330, Micrometrics). Intraparticle porosity was measured by mercury intrusion and nitrogen adsorption (Autopore 9220 and ASAP 2010, Micrometrics Norcross). The corresponding parameters for the activated carbon material have been taken from the manufacturer (Chemviron). [9] To ensure that no particles are released within the column, particle-free water was used to prepurge the 12.5 cm column until no particles were detected in the effluent. A preequilibrated suspension consisting of 20 mg L 1 pulverized activated carbon or lignite in a 10 mg L 1 TCE solution was pumped through the column with a flow velocity of 300 m d 1. After 16 pore volumes (PVs) the flow velocity was reduced to 100 m d 1 and after an additional 16 PVs to 30 m d 1. The flow velocities are representative for groundwater treatment in permeable reactive walls. The procedure leads to a successive increase in particle filtration, i.e., lower and lower particle load in the effluent. As compared to separate experiments for each flow velocity, the stepwise procedure is preferable due to a more efficient use of experimental resources without alteration of results. Table 1. Characteristics of the Materials Used in the Column Experiments Parameter Activated Carbon Lignite Particle density, g cm Interparticle porosity, % 32 Grain size (column), mm Longitudinal dispersivity a 0.04 Intraparticle porosity, % Particle size, mm a From an independent column experiment with NaBr.

3 BOLD ET AL.: SORPTION KINETICS ON PARTICLES SBH 3-3 has been developed by Finkel et al. [1999] and is augmented in this study to take into account kinetically limited particlefacilitated transport, which is described in the following sections Particle Transport [14] Neglecting the influence of immobilized particles on the effective porosity, particle transport along a stream tube, which is parameterized with respect to travel time, is quantified by t C c;i þ t C c;i ¼ K i C c;i ð3þ Figure 2. Experimental design of the column experiment. [10] At the column inlet and outlet, particle concentration and size distribution were measured using a laser particle detector (CIS-50, Galai) allowing for the detection of particles between 0.5 mm und 150 mm in diameter. In addition, total TCE concentrations (dissolved and particlebound) were determined using a GC-MS with monochlorobenzene as internal standard. For this method, the average error is known to be on the order of 10% and the detection limit for TCE is 200 ng L 1. In addition, equilibrium sorption isotherms of TCE on activated carbon and lignite were determined. 3. Modeling Approach [11] The transport model used in this study is based on an approach of Dagan and Cvetkovic [1996], who presented a Lagrangian framework to describe reactive transport. Their approach allows an efficient separate treatment of conservative transport and reactive processes. A generic expression for the total mobile contaminant concentration at the point of interest (column outlet) is given by Ct ðþ¼ Z 1 0 gðtþ ðt; tþdt; ð1þ where t is time [T] and t represents the travel time of a conservative tracer through the column [T]. To account for variations in arrival times, e.g., due to hydraulic heterogeneities, a probability density function (PDF) of travel times g(t) is used. Several theoretical expressions for g(t) are given by Jury and Roth [1990]. The function (t, t), which has been termed reaction function by Dagan and Cvetkovic [1996], quantifies reactive processes for a continuous injection with unit input concentration. [12] In order to overcome the restriction of analytical expressions for g(t) and (t, t), the integral in equation (1) is replaced by a finite sum yielding Ct ðþ¼ Xn gðt l Þ ðt l ; tþt ð2þ l¼1 where t is the discretization of the one-dimensional stream tube model with respect to travel time t and l is the time step index. [13] On the basis of this relationship, the model SMART (Streamtube Model for Advective and Reactive Transport) where i indicates specific classes of particles differing in size and sorption properties, C c,i is the mobile particle concentration [ML 3 ], and K i is the deposition rate coefficient of particle class i [T 1 ]. The right hand side of equation (3) indicates that particle deposition is modeled according to a first-order rate law Contaminant Transport [15] Contaminants can sorb in the matrix and on mobile and immobile particles. Taking this into account, contaminant transport is described by t ( C D þ r bs matrix ðc D Þ þ X n e i ð S cm;i ðc D þ t ( ÞC c;i þ S cim;i C D C D þ X i Þr b S c;matrix;i C c;i n e ) S cm;i ðc D Þ Cc;i ¼ 0 ) where C D is the dissolved contaminant concentration [ML 3 ], r b is the bulk density of the porous medium [ML 3 ], and S c,matrix,i (C c,i ) is the mass ratio between immobile particle i and the soil matrix, which can be obtained via solving equation (3). S matrix (C D ), S cm,i (C D ), S cim,i (C D ) are the ratios of sorbed solute mass per unit mass of solid matrix, mobile and immobile particle i, respectively. The functional relationship S(C D ) depends on the mechanisms being responsible for the contaminant solid interactions. Mathematical expressions for modeling these interactions are given in the following sections. [16] If only the total mobile contaminant concentration C INP entering the modeling domain is known instead of dissolved contaminant concentration C D,INP, the corresponding boundary condition for equation (4) can be calculated by C D;INP ¼ bc INP ; ð5þ where b is the contaminant mass ratio which is not subject to particle-facilitated transport (dimensionless). Assuming that contaminant and mobile particles entering the modeling domain are preequilibrated and neglecting the volume of the intraparticle pores of the particle, C D,INP can be quantified by solving C D;INP þ X S cm;i C D;INP Cc;INP;i ¼ C INP ; ð6þ i where C c,inp,i is the concentration of mobile particle i entering the model domain [ML 3 ]. ð4þ

4 SBH 3-4 BOLD ET AL.: SORPTION KINETICS ON PARTICLES 3.3. Intraparticle Diffusion Model [17] The intraparticle diffusion model is used to simulate both the interactions of contaminant with the matrix and with mobile and immobile particles (Figure 1). Within this approach, the sorption/desorption behavior of organic chemicals is regarded as a kinetic process, limited by the diffusive transport of the solute through the tortuous pores of the matrix or particles to the sorption sites, whereas the actual process of adsorption or desorption of a molecule at the sorption site is comparatively fast and can be described as equilibrium reaction (Figure 1). [18] As the matrix grains/particles are assumed to be spherically symmetric, the underlying intraparticle diffusion equation (based on Fick s second law) can be written for a specific matrix grain/particle as ec þ 1 e t ½ ð ÞrsðÞ cš ¼ D eff 1 r 2 r with the initial and boundary conditions: and r 2 c r ð7þ cðt; r ¼ R; tþ ¼ C D ðt; tþ ð8þ c t; r ¼ 0; t r ð Þ ¼ 0 ð9þ where r is the radial coordinate [L], D eff is the effective diffusion coefficient [L 2 T 1 ], e is the intraparticle porosity (dimensionless), r is the dry solid density of matrix grains/ particles, c is the dissolved contaminant concentration in the intraparticle pores, R is the grain/particle radius and s is the mass of chemical sorbed onto surfaces of intraparticle pores per unit mass of the grains/particles. s = s(c) may represent any type of sorption isotherm, e.g., linear, Freundlich, Langmuir or others. [19] According to Grathwohl [1997], the effective diffusion coefficient D eff, accounting for the reduction of diffusion due to the tortuous pores and reduced diffusion effective area, can be empirically estimated by D eff ¼ D aq e m ð10þ where D aq is the diffusion coefficient in aqueous solution [L 2 T 1 ] and m is an empirical exponent (dimensionless). This exponent is found to be close to 2 for porous rocks [Grathwohl, 1997], and according to Sontheimer et al. [1985] around 1 for activated carbon. [20] From equation (7) the mass of the contaminant within all grains of the matrix S matrix and within the particles S cm,i and S cim,i per unit volume can be obtained, which is required for solving the reactive transport equation (4). According to Liedl and Ptak [2003], the contaminant mass is given by S matrix ðc D Þ ¼ S cm;i ðc D 1 ¼ 4p 3 R3 ð1 eþr Þ ¼ S cim;i ðc D Þ Z R 0 4pr 2 ½ec þ ð1 eþrsðþ cšdr ð11þ where the right hand side is to be evaluated for the matrix material or the particles, respectively Simplifications of Contaminant-Particle Interactions [21] If the sorption rate of the solute is significantly larger than its mass flow rate, sorption/desorption of contaminant onto/from mobile particles can be regarded as an instantaneous equilibrium reaction. This behavior may be hypothesized for small particles and will be investigated in section 4. A measure for the relative importance of kinetic to equilibrium processes is the Damköhler number, which is defined in section 3.5. [22] If the equilibrium approximation can be applied for a specific system, S cm,i (C D ) and S cim,i (C D ) in equation (4) can be obtained by S cm;i ðc D Þ ¼ S cim;i ðc D Þ ¼ s i ðc D Þ ð12þ where s i (C D ) may represent any type of sorption isotherm between dissolved contaminant and particle class i. [23] In contrast, if solute mass transfer between mobile particles and the dissolved phase is much slower than advective mass transport, particle-facilitated transport of contaminants can be regarded as fully decoupled from contaminant transport in the dissolved phase. In this case the contaminant transport equation is given by C D þ r bs matrix ðc D Þ þ ð t q t C DÞ ¼ lc D ; ð13þ and the total mobile contaminant concentration for decoupled transport can be calculated by C ¼ C D þ X i S cm;i C D;INP CC;i : ð14þ 3.5. Equilibrium Versus Decoupled Transport [24] The Damköhler number [e.g., Jennings and Kirkner, 1984] can be used to determine whether a reversible chemical reaction is fast enough to assume instantaneous equilibrium or slow enough to neglect any sorption/desorption of the particle associated contaminants. The Damköhler number is defined as the ratio between the transport and the reaction timescales. Within the Lagrangian framework it is given by D a ¼ lt ð15þ where l is the reaction rate constant [T 1 ] and t is the mean travel time of the particles, which can be calculated by t ¼ Z 1 0 tgðtþdt ð16þ [25] The reaction rate constant for the diffusion limited mass transfer between contaminants and mobile particles is proportional to the corresponding diffusion rate constant. To allow for an analytical definition of this diffusion rate constant, it is assumed that equilibrium sorption of contaminants in the intraparticle pores of mobile particles can be described by a linear isotherm. For nonlinear isotherms, a representative linear isotherm may be used as an approximation. Using this assumption and employing an analytical solution of equation (7) given by Crank [1981], the reaction rate constant can

5 BOLD ET AL.: SORPTION KINETICS ON PARTICLES SBH 3-5 Figure 3. Measured data and Freundlich sorption isotherms for TCE on activated carbon (s = mg ( ) kg 1 l C D ) and lignite (s = 54.4 mg ( ) kg 1 l C D ). be quantified as a function of t according to Grathwohl [1997] by ln 6 P 1 1 p 2 n exp n 2 p 2 t P D f app;i 2 i R 2 n¼1 i i l ¼ ð17þ t where f i is the mass fraction of mobile particle i and Dapp,i is the corresponding apparent diffusion coefficient [L 2 T 1 ], which in case of porous mobile particles can be calculated by pulverized lignite and activated carbon, respectively), only particles between 1 mm and 15 mm could be observed at the column outlet. From the measured data, size-specific particle deposition rates K i are directly calculated for the different flow velocities using the method proposed by Kretzschmar et al. [1999] neglecting longitudinal dispersion. This approximation appears to be justified because of the small dispersivity values (Table 1). [28] Observed and modeled particle and contaminant BTCs at the column outlet are shown in Figure 5. Symbols denoting particle concentrations represent sum values of histograms like those shown in Figure 4. For both lignite particles (Figure 5, top) and activated carbon particles (Figure 5, top), a decrease in flow velocity results in a decreasing particle concentration (squares and dashed lines), whereas the concentration within a specific flow velocity is constant over time. This is in accordance with the filtration theory predicting an increase in particle interception and sedimentation to the immobile matrix with decreasing flow velocity [McDowell-Boyer et al., 1986]. Because size-specific deposition rates are directly determined from the column experiments by model calibration using data from Figure 4, resulting particle BTCs favorably match the observed concentrations. It should be mentioned, that the model employed was used to simulate only steady state flow conditions with separate runs for each flow velocity. D eff ;i D app;i ¼ ð18þ e i þ k d;i ð1 e i Þr i where k d,i is the partitioning coefficient between contaminant and mobile particle i [L 3 M 1 ]. 4. Results and Discussion 4.1. Results and Modeling of Batch and Column Experiment [26] The isotherms quantifying the relationships between dissolved TCE and TCE sorbed on activated carbon and lignite particles were independently determined in batch experiments under equilibrium conditions. The measured data can be reproduced very well by the Freundlich sorption isotherm (Figure 3). The sorption of TCE on activated carbon is highly nonlinear, which is indicated by a very small value of the Freundlich exponent (0.44). The sorption capacity of activated carbon for TCE represents an upper limit for natural organic particles sorbing organic contaminants [e.g., Gounaris et al., 1993]. The sorption of TCE onto lignite is approximately three orders of magnitude less than for activated carbon. This indicates that activated carbon and lignite particles can be regarded as end-members for the sorption behavior of organic contaminants on naturally occurring particles. [27] To reduce uncertainties with particle-facilitated transport, particle-matrix interactions are calibrated first using data from the column experiments. Figure 4 shows mobile particle concentrations and size fractions at the column inlet and outlet as a function of flow velocity. Large particles are effectively filtered on their way through the column. This effect is enhanced at low flow velocities. Although particles larger than 20 mm were present in the suspension (73% and 2.3% for the experiments with Figure 4. Particle concentrations depending on particle size measured at the column inlet and outlet for different flow velocities: (top) lignite particles, (bottom) activated carbon particles.

6 SBH 3-6 BOLD ET AL.: SORPTION KINETICS ON PARTICLES Figure 5. Observed and modeled relative particle and total mobile TCE BTCs at the column outlet for (top) lignite particles and (bottom) activated carbon particles as carrier. Please note that the ordinate is linear in Figure 5 (top) and logarithmic in Figure 5 (bottom) due to the different concentration ranges. [29] Regarding the total mobile contaminant concentrations at the outlet (crosses and solid lines in Figure 5), differences in sorption capacity between lignite particles and activated carbon particles are obvious. For the experiment with lignite particles (Figure 5, top), no TCE could be measured (detection limit 200 ng L 1 ) indicating that neither dissolved TCE nor TCE bound to the lignite particles may reach the column outlet in measurable concentrations early during the experiment (finally TCE will break through). According to the measured isotherm (Figure 3) only 0.016% of TCE entering the column is bound to the lignite particles (equation (6)). On the other hand, a TCE concentration of up to 220 mg L 1 could be observed using activated carbon particles as carriers (Figure 5, bottom). These high concentrations are caused by particle-facilitated transport, resulting from an increased sorption of TCE on the mobile particles. In fact, almost 30% of TCE entering the column is bound to the activated carbon particles. [30] As TCE concentrations observed at the column outlet strongly depend on particle concentrations, it is obvious that less TCE is measured with decreasing flow velocity due to immobilization of particles. This effect is enhanced by the fact that the time for contaminant desorption from the mobile particles is increased with decreasing flow velocity. Assuming that measured TCE is only particle-bound (breakthrough of dissolved TCE would be much later) for a velocity of 300 m d 1 approximately 70%, whereas for v = 30 m d 1 almost 96% of the contaminant is desorbed from the activated carbon particles. [31] In order to assess whether contaminant-particle interactions are diffusion-limited, the observed TCE BTCs are modeled using the intraparticle-diffusion model (equations (7) (10)) to simulate not only TCE-matrix interactions but also the desorption kinetics of TCE from the mobile particles. For this purpose, model parameters characterizing TCE sorption kinetics (Freundlich sorption isotherm parameters, intraparticle porosities, particle densities, aqueous diffusion coefficient) have been determined independently. Only these sorption parameters are used in the intraparticle diffusion model, i.e., a straight forward desorption modeling is performed (Table 1). For the mobile lignite particles, both modeled total mobile TCE concentration and measured results are below the detection limit (Figure 5, top). With activated carbon particles as carriers, the modeled mobile TCE BTC favorably matches the observed TCE concentrations. This coincidence could be achieved by pure forward modeling based on data from independent experiments, i.e., no model calibration with respect to contaminant-matrix and contaminant-particle interactions was performed (Figure 5, bottom). [32] As shown in Figure 6 for the experiment with activated carbon particles, the simplified modeling approaches described in section 3.4 cannot be used to simulate the observed TCE concentrations at the column outlet. Employing the decoupled model, TCE concentrations are overestimated by a factor of 3 to 20, whereas the instantaneous equilibrium model dramatically underestimates TCE concentrations at the column outlet. These results indicate that the more general model outlined in sections has to be used in order to predict BTCs in this scenario. The applicability of the simplified approaches is investigated in the following section. Opting for a kinetic model to simulate contaminant-particle interactions in this scenario, one might argue that a first-order rate law to describe kinetically limited sorption/desorption of contaminant on mobile particles would also allow one to favorably reproduce the experimental data. This is valid but requires model calibration using rate constants as calibration parameters. Predictions based on the intraparticle diffusion model, however, are shown above to rely on independently measured parameters only and, as a result, this model is believed to provide an exclusively processbased approach with large predictive capabilities. Further, Figure 6. Observed and modeled relative total mobile TCE BTC at the column outlet for different modeling approaches. Activated carbon particles are used as carriers in the column experiment.

7 BOLD ET AL.: SORPTION KINETICS ON PARTICLES SBH 3-7 Figure 7. Simulated total mobile contaminant BTCs for several scenarios differing in terms of regarded contaminant-particle interactions. the results show that the proposed model, which will be used for sensitivity studies in the next section, is validated Influence of Kinetic Contaminant-Particle Interactions on Contaminant Spreading [33] In order to investigate the relative importance of sorption kinetics for modeling particle-facilitated transport, three different modeling approaches are used to describe contaminant-particle interactions: on the one hand the intraparticle diffusion model taking into account sorption kinetics and on the other hand the two simplified models described in section 3.4. All simulations presented in this section rely on the following assumptions: (1) mobile particles do not interact with the soil matrix (i.e., K =0), (2) mobile particles and contaminant entering the modeling domain are preequilibrated, (3) contaminant-matrix interactions can be modeled using the intraparticle diffusion model, and (4) dispersion effects can be neglected. Moreover, it is assumed for simplification that mobile particle and contaminant input concentrations are constant over time. The model approaches used for simulating contaminant-particle interactions are listed in Figure 7 ranked according to the characteristic timescale of sorption/desorption reactions. In this sense, the equilibrium model and the decoupled model can be viewed as end-members for the model approach spectrum. [34] In Figure 7 the BTCs of hydrophobic contaminants for typical scenarios are shown for the three different modeling approaches describing contaminant-particle interactions. The underlying model parameters for this scenario are summarized in Table 2. [35] Without mobile particles, contaminant transport is only influenced by contaminant-matrix interactions resulting in retarded solute spreading (crosses) which may be affected by kinetically limited sorption/desorption of contaminant on the stationary phase. In the presence of mobile particles, however, quantifying contaminant-particle interactions as instantaneous equilibrium process, this retardation is reduced (triangles). For a linear isotherm the decrease of the retardation factor can be assessed by a factor of 1/(k d,c C c ), if, in addition instantaneous equilibrium between contaminant and matrix were assumed [e.g., Magee et al., 1991]. Neglecting contaminant desorption from particles, i.e., considering decoupled transport, the BTC can be seen as a superposition of retarded transport of dissolved contaminant and unretarded transport of contaminant bound to particles (circles). Therefore contaminants can be observed already after one pore volume at concentrations, which can be estimated by equation (6). Using the intraparticle diffusion model to take into account kinetic contaminant-particle interactions, contaminant BTCs highly depend on the Damköhler number. For a high Damköhler number (D a = 500, solid curve) the BTC is very similar to the BTC assuming equilibrium reaction, whereas for a small value (D a = 0.005, dotted curve) little differences to the decoupled model can be observed. Only for a Damköhler number of 1 (dashed curve) discrepancies to both the equilibrium approach and the decoupled model are obvious. [36] To investigate how fast or how slow sorption/ desorption kinetics of the contaminant-particle interactions must be in order to justify the assumption of equilibrium reactions or decoupled transport respectively, BTCs have been simulated for several scenarios varying in terms of matrix, mobile particle and contaminant properties as well as in terms of conservative transport parameters. The intraparticle diffusion model has been used to simulate both contaminant-particle and contaminantmatrix kinetic interactions. The obtained BTCs are Table 2. Model Parameters Used for the Scenario Calculations Parameter Value Conservative transport Mean travel time, years 1.0 Contaminant parameters Total mobile input concentration, mg L Diffusion coefficient in aqueous phase, m 2 s Matrix parameters Bulk density, kg L Partitioning coefficient, L kg Grain size, mm 2.0 Intraparticle porosity, % 1.0 Mobile particle parameters Input concentration, mg L Distribution coefficient, L kg Figure 8. Influence of the Damköhler number D a on sorption/desorption kinetics.

8 SBH 3-8 BOLD ET AL.: SORPTION KINETICS ON PARTICLES compared with modeled BTCs assuming equilibrium sorption and decoupled transport of mobile particles and contaminant, respectively. In Figure 8 the relative mean square error s 2 rel between kinetic modeling results and equilibrium modeling results is shown versus the Damköhler number. Using this approach s 2 rel is given by the ratio of the mean square error between kinetic and equilibrium modeling results, and between decoupled and equilibrium modeling results. This measure is 0 if particle-contaminant interactions are an equilibrium reaction and 1 if fully decoupled transport prevails. [37] Figure 8 clearly indicates, that sorption/desorption kinetics for contaminant-particle interactions must be taken into account for Damköhler numbers between 0.01 and 100. For lower values, decoupled transport may be assumed, whereas particle-contaminant interactions can be regarded as equilibrium process for D a greater than 100. These results agree well with findings of Jennings and Kirkner [1984] and van de Weerd et al. [1998], who used a first-order-rate law to simulate sorption kinetics on the stationary phase or mobile particles, respectively. [38] In addition, this is also supported by the results of the column experiments as described above where the relative importance of the sorption process can be described by Damköhler numbers between 5 and 86 for the experiment with lignite particles and between 4 and 53 using activated carbon particles. This also explains why the measured TCE concentrations could only be simulated by a kinetic approach (Figure 6). 5. Summary and Conclusions [39] In order to investigate if contaminant-particle interactions are kinetically limited, column experiments with lignite and activated carbon particles as carrier and TCE were conducted. The results of these experiments indicate that mobile particles may enhance contaminant transport especially under nonequilibrium conditions. A reactive transport model using the intraparticle diffusion model to account for the kinetic contaminant-particle interactions could successfully be used to simulate measured TCE concentration at the column outlet. Only deposition rate coefficients of mobile particles were used for model calibration. All other parameters, which quantify TCE sorption/ desorption kinetics on particles and the column packing material, were taken from independent experiments. Model results together with experimental findings clearly indicate that intraparticle diffusion in water filled intraparticle pores can be inferred to quantify the overall mass transfer rates for hydrophobic organic contaminants and coal particles. Future research on mass transfer limitation could focus on film diffusion which may additionally limit the sorption/ desorption of organic contaminants in mobile particles. At present, it appears to be unclear how film transfer limitations potentially develop during transport of particles in porous media at the flow velocities used in the column experiments. Findings of the present study indicate that film diffusion was of no or minor importance for the setting considered. [40] By means of scenario calculations it could further be shown that kinetic limitations of contaminant-particle interactions have to be taken into account for Damköhler numbers between 0.01 and 100. For higher Damköhler numbers the sorption behavior of contaminants on mobile particles can be regarded as equilibrium process resulting in a reduction of the retardation factor, whereas for lower values contaminant-particle interactions can be neglected (decoupled transport). This study presumably applies to other types of particles and contaminants. [41] Acknowledgments. This work was funded by the German Federal Ministry of Education and Research (BMBF) under grants 02WP0198 and 02WT9936/4. References Artinger, R., B. Kienzler, W. Schüssler, and J. I. Kim, Effects of humic substances on the 241 AM migration in a sandy aquifer: Column experiments with Gorleben groundwater/sediment systems, J. Contam. Hydrol., 35, , Ball, W. P., and P. V. Roberts, Long-term sorption of halogenated organic chemicals by aquifer material. 2. Intraparticle diffusion, Environ. Sci. Technol., 25(7), , Choi, H., and M. Y. Corapcioglu, Transport of a non-volatile contaminant in unsaturated porous media in the presence of colloids, J. Contam. Hydrol., 25, , Corapcioglu, M. Y., and S. Jiang, Colloid-facilitated groundwater contaminant transport, Water Resour. Res., 29(7), , Corapcioglu, M. Y., S. Jiang, and S.-H. Kim, Transport of dissolving colloidal particles in porous media, Water Resour. Res., 35(11), , 1999a. Corapcioglu, M. Y., S. Jiang, and S.-H. Kim, Comparison of kinetic and hybrid-equilibrium models simulating colloid-facilitated contaminant transport in porous media, Transp. Porous Media, 36, , 1999b. Crank, J., Mathematics of Diffusion, 2nd ed., Oxford Univ. Press, New York, Dagan, G., and V. Cvetkovic, Reactive transport and immiscible flow in geological media, I. General theory, Proc. R. Soc. London, Ser. A, 452, , de Jonge, H., O. H. Jacobsen, L. W. de Jonge, and P. Moldrup, Colloidfacilitated transport of pesticide in undisturbed soil columns, Phys. Chem. Earth, 23(2), , Dohse, D. M., and L. W. Lion, Effect of microbial polymers on the sorption and transport of phenanthrene in a low-carbon sand, Environ. Sci. Technol., 28(4), , Dunnivant, F. M., P. M. Jardine, D. L. Taylor, and J. F. McCarthy, Cotransport of cadmium and hexachlorbiphenyl by dissolved organic carbon through columns containing aquifer material, Environ. Sci. Technol., 26(2), , Farrell, J., and M. Reinhard, Desorption of halogenated organics from model solids, sediments, and soil under unsaturated conditions. 1. Isotherms, Environ. Sci. Technol., 28(1), 53 62, 1994a. Farrell, J., and M. Reinhard, Desorption of halogenated organics from model solids, sediments, and soil under unsaturated conditions. 2. Kinetics, Environ. Sci. Technol., 28(1), 63 72, 1994b. Finkel, M., R. Liedl, and G. Teutsch, Modelling surfactant-enhanced remediation of polycyclic aromatic hydrocarbons, Environ. Modell. Software, 14, , Gounaris, V., P. R. Anderson, and T. M. Holsen, Characteristics and environmental significance of colloids in landfill leachate, Environ. Sci. Technol., 27(7), , Grathwohl, P., Diffusion in Natural Porous Media, Kluwer Acad., Norwell, Mass., Grathwohl, P., and M. Reinhard, Desorption of trichloroethylene in aquifer material: Rate limitation at the grain scale, Environ. Sci. Technol., 27(12), , Grolimund, D., M. Borkovec, K. Barmettler, and H. Sticher, Colloid-facilitated transport of strongly sorbing contaminants in natural porous media: A laboratory column study, Environ. Sci. Technol., 30(10), , Harmon, T. C., and P. V. Roberts, Comparison of intraparticle sorption and desorption rates for a halogenated alkene in a sandy aquifer material, Environ. Sci. Technol., 28(9), , Ibaraki, M., and E. A. Sudicky, Colloid-facilitated contaminant transport in discretely fractured porous media: 1. Numerical formulation and sensitivity analysis, Water Resour. Res., 31(12), , Jennings, A. A., and D. J. Kirkner, Instantaneous equilibrium approximation analysis, J. Hydraul. Eng., 110(12), , 1984.

9 BOLD ET AL.: SORPTION KINETICS ON PARTICLES SBH 3-9 Jury,W.A.,andK.Roth,Transfer Functions and Solute Movement Through Soils, Birkhäuser Boston, Cambridge, Mass., Karapanagioti, H. K., S. Kleineidam, D. A. Sabatini, P. Grathwohl, and B. Ligouis, Impacts of heterogeneous organic matter on phenanthrene sorption: Equilibrium and kinetic studies with aquifer material, Environ. Sci. Technol., 34(3), , Karathanasis, A. D., Subsurface migration of copper and zinc mediated by soil colloids, Soil Sci. Soc. Am. J., 63, , Kleineidam, S., H. Rügner, and P. Grathwohl, Impact of grain scale heterogeneity on slow sorption kinetics, Environ. Toxicol. Chem., 18(8), , Knabner, P., K. U. Totsche, and I. Kögel-Knabner, The modeling of reactive solute transport with sorption to mobile and immobile sorbents: 1. Experimental evidence and model development, Water Resour. Res., 32(6), , Kögel-Knabner, I., and K. U. Totsche, Influence of dissolved and colloidal phase humic substances on the transport of hydrophobic organic contaminants in soils, Phys. Chem. Earth, 23(2), , Kretzschmar, R., M. Borkovec, D. Grolimund, and M. Elimelech, Mobile subsurface colloids and their role in contaminant transport, Adv. Agron., 66, , Liedl, R., and T. Ptak, Modelling of diffusion-limited retardation of contaminants in hydraulically and lithologically non-uniform aquifers, J. Contam. Hydrol., 66(3 4), , Magee, B. R., L. W. Lion, and A. T. Lemley, Transport of dissolved organic macromolecules and their effect on the transport of phenanthrene in porous media, Environ. Sci. Technol., 25(2), , McDowell-Boyer, L. M., J. R. Hunt, and N. Sitar, Particle transport through porous media, Water Resour. Res., 22(13), , Noell, A. L., J. L. Thompson, M. Y. Corapcioglu, and I. R. Triay, The role of silicia colloids on facilitated cesium transport through glass bead columns and modeling, J. Contam. Hydrol., 31, 23 56, Prechtel, A., P. Knabner, E. Schneid, and K. U. Totsche, Simulation of carrier-facilitated transport of phenanthrene in a layered soil profile, J. Contam. Hydrol., 56, , Puls, R. W., and R. M. Powell, Transport of inorganic colloids through natural aquifer material: Implications for contaminant transport, Environ. Sci. Technol., 26(3), , Roy, S. B., and D. A. Dzombak, Sorption nonequilibrium effects on colloid-enhanced transport of hydrophobic organic compounds in porous media, J. Contam. Hydrol., 30, , Rügner, H., S. Kleineidam, and P. Grathwohl, Long term sorption kinetics of phenanthrene in aquifer materials, Environ. Sci. Technol., 33(10), , Saiers, J. E., Laboratory observations and mathematical modeling of colloid-facilitated contaminant transport in chemically heterogeneous systems, Water Resour. Res., 38(4), 1032, doi: /2001wr000320, Saiers, J. E., and G. M. Hornberger, The role of colloidal kaolinite in the transport of cesium through laboratory sand columns, Water Resour. Res., 32(1), 33 41, Schüssler, W., R. Artinger, J. I. Kim, N. D. Bryan, and D. Griffin, Numerical modeling of humic colloid borne Americum (III) migration in column experiments using transport/speciation code K1D and the KICAM model, J. Contam. Hydrol., 47, , Seta, A. K., and A. D. Karathanasis, Atrazine adsorption by soil colloids and co-transport through subsurface environments, Soil Sci. Soc. Am. J., 61, , Sojitra, I., K. T. Valsaraj, D. D. Reible, and L. J. Thibodeaux, Transport of hydrophobic organics by colloids through porous media. 1. Experimental results, Colloids Surf. A, 94, , Sontheimer, H., B. R. Frick, J. Fettig, G. Hörner, G. Hubele, and G. Zimmer, Adsorptionsverfahren zur Wasserreinigung (adsorption procedures for water purification), DVGW-Forschungsstelle, Karlsruhe, Germany, Villholth, K. G., N. J. Jarvis, O. H. Jacobsen, and H. dejonge, Field investigations and modeling of particle-facilitated pesticide transport in macroporous soil, J. Environ. Qual., 29, , van de Weerd, H., and A. Leijnse, Assessment of the effect of kinetics on colloid facilitated radionuclide transport in porous media, J. Contam. Hydrol., 26, , van de Weerd, H., A. Leijnse, and W. H. van Riemsdijk, Transport of reactive colloids and contaminants in groundwater: Effect of nonlinear kinetic interactions, J. Contam. Hydrol., 32, , S. Bold, Emschergenossenschaft/Lippeverband, Department of Water Resources Management, Kronprinzenstrasse 24, Essen, Germany. (steffen.boldeglv.de) P. Grathwohl, S. Kraft, and R. Liedl, Center for Applied Geoscience, University of Tübingen, Sigwartstrasse 10, Tübingen, Germany.