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Soil Science Society of America Journal 65:1622-1633 (2001)
© 2001 Soil Science Society of America

DIVISION S-1 - SOIL PHYSICS

Nonsingularity of Naphthalene Sorption in Soil

Observations and the Two-Compartment Model

Jesper Gamst*,a, Torben Olesena, Hubert De Jongeb, Per Moldrupa and Dennis E. Rolstonc

a Dep. of Environmental Engineering, Aalborg Univ., Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark
b Danish Inst. of Agricultural Sciences, Research Centre Foulum P.O. Box 50, DK-8830 Tjele, Denmark
c Soils and Biogeochemistry, Dep. of Land, Air and Water Resources, Univ. of California, Davis, CA 95616

* Corresponding author (i5jg{at}civil.auc.dk)


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 Conceptual Model Problems
 CONCLUSION
 REFERENCES
 
Realistic models for transport of organic chemicals in soil require accurate predictions of the adsorption-desorption kinetics. In this study, a physically based two-compartment one-rate (TCOR) sorption model was evaluated by comparison of model simulations to measured adsorption-desorption isotherms of naphthalene (C10H8) for five different soils on a short-term (48 h) and a longer-term (504 h) time scale. Two soils exhibited minor adsorption-desorption nonsingularity (labeled Type I soils), two soils pronounced nonsingularity (Type II soils), and the fifth soil pronounced nonsingularity only on the longer-term time scale (Type I/II soil). The TCOR sorption model fitted, measured adsorption-desorption isotherms well on both short-term and longer-term time scales. However, the TCOR sorption model parameters varied for each soil between short-term and longer-term data, especially for Type II soils. The uniqueness of the TCOR model fit was tested by varying the number of desorption data used, resulting in markedly changed parameter values. The TCOR sorption model was evaluated by using model parameters obtained from short-term data to predict longer-term sorption results. The TCOR prediction of adsorption-desorption behavior was good for Type I soils, satisfactory for the Type I/II soil, and poor for Type II soils. Model parameters obtained from short-term and longer-term experiments were used to predict independently measured adsorption kinetics, showing decreasing prediction accuracy with increasing sorption nonsingularity. The results imply that the TCOR sorption model description of the diffusion process at the grain scale is oversimplified, and that sorption nonsingularity is not well explained by kinetic factors alone.

Abbreviations: HOC, hydrophobic organic chemicals • TCOR, two-compartment one-rate • SOM, soil organic matter • RMSE, root mean square error


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 Conceptual Model Problems
 CONCLUSION
 REFERENCES
 
SORPTION OF hydrophobic organic chemicals (HOC) to soil organic matter (SOM) has a major influence on the fate and transport of contaminants in the subsurface of contaminated sites. Knowledge about the sorption processes is thus important to achieve reasonable risk assessment or for the design of appropriate remediation technologies. When modeling pollutant transport, the sorption process is often simplified by assuming a linear isotherm, instantaneous equilibrium, and reversible sorption (Yates and Jury, 1995; Jury et al., 1983; Myrand et al., 1992). Sorption tends, however, to be nonlinear for HOC sorption to soil (e.g., Kishi et al., 1990; Weber et al., 1992; Xing and Pignatello, 1996) and according to Weber et al. (1992), nonlinear sorption should be expected if a wide concentration range is considered.

Pignatello and Xing (1996) concluded that instantaneous equilibrium is inadequate to describe the sorption isotherm because of slow sorption kinetics, and they observed that measured linear adsorption coefficient, Kd, in some systems increased by up to ten-fold between short and long contact times. This indicates that the widely used relations between the organic C-water and the orctanol-water partition coefficient (Koc-Kow) relations based on short-time sorption isotherms, as proposed by Abdul et al. (1987), Karickhoff et al. (1979) or others might result in wrong predictions of the sorption isotherm. Nonsingularity and hysteresis between measured sorption and desorption isotherms has been observed for several chemicals, soils, and sediments (e.g., Kan et al., 1994; Huang and Weber, 1997; Altfelder et al., 1999; Selim et al., 1999; de Jonge et al., 2000). The rate of desorption has been shown to be significantly lower than the rate of sorption, and has been observed to decrease with increasing contact time (aging) (van Genuchten et al., 1974; Connaughton et al., 1993; Deitsch and Smith, 1999; White et al., 1999). In some cases, desorption experiments even indicate irreversible sorption or formation of a resistant fraction (Kan et al., 1997, 1998; Huang and Weber, 1997). Thus, estimates of the sorption process will be in error if sorption nonlinearity, sorption kinetics, and adsorption-desorption nonsingularity are ignored.

Slow sorption is often used to explain nonattainment of true equilibrium and adsorption-desorption nonsingularity (Pignatello and Xing, 1996; Pignatello, 2000) and is claimed to be caused by either intraorganic matter diffusion (Brusseau et al., 1991; Pignatello and Xing, 1996; Weber and Huang, 1996) or intraparticle diffusion (Wu and Gswend, 1986; Ball and Roberts, 1991; Grathwohl and Reinhard, 1993). Whether it is intraparticle diffusion or intraorganic matter diffusion that is the controlling process, modeling of the diffusion process requires knowledge about the geometry and structure of the soil particles or the SOM. This appears to be a difficult, or perhaps, even an impossible task especially because of the widely heterogeneous structure of SOM (Luthy et al., 1997). However, there seems to be some agreement that the structure of SOM can be simplified by defining a rubbery or amorphous compartment and a glassy or condensed compartment (Weber and Huang, 1996; Pignatello and Xing, 1996). Sorption to the rubbery or amorphous compartment is then considered instantaneous or fast and fully reversible, while sorption to the glassy or condensed compartment is rate limited by an intraorganic matter diffusion process that controls slow sorption and desorption nonsingularity.

Several models have been used to describe the adsorption-desorption nonlinearity. Two types of sorption models seem to be the most widely used to describe measured adsorption-desorption isotherms with success. The first group consists of the spherical diffusion models or intraparticle diffusion models that assume that slow sorption is caused by slow diffusion through water-filled pores in the soil aggregates. The diffusion is then retarded by microscale partitioning into or on SOM within the pores or into the immobile water regions (Wu and Gswend, 1986; Ball and Roberts, 1991; Grathwohl and Reinhard, 1993; Miller and Pedit, 1992). The second group is the compartment approach (Selim et al., 1976; Cameron and Klute, 1977; Hoffman and Rolston, 1980; Selim and Amacher, 1988; van Genuchten and Wagenet, 1989; Brusseau et al., 1991; Streck et al., 1995; Cornelissen et al., 2000) including the two-compartment models where the sorbent is divided into two compartments, S1 and S2, with different accessibility. The concept of the two-compartment models varies with respect to the description of sorption nonlinearity or the exchange between S1 and S2. However, the basic ideas of the models are similar. Two-compartment sorption models based on physical heterogeneity caused by mobile and immobile water were also proposed to describe sorption hysteresis (van Genuchten and Wierenga, 1976). However, they were mathematically equivalent to two-compartment sorption models based on chemical nonequilibrium (Nkedi-Kizza et al., 1984).

In this study, we evaluated the two-compartment approach and chose the TCOR sorption model proposed by Streck et al. (1995). The model is a physically based TCOR sorption model developed from the concept proposed by Brusseau et al. (1989)(1991). The TCOR model is based on the assumption that sorption is nonlinear and described by Freundlich type sorption, and that sorption to the easily accessible sites is instantaneous. Streck et al. (1995) showed that the assumption of instantaneous sorption to the easily accessible sites did not significantly weaken the model fit. The model allows for modeling of adsorption-desorption reactions and has previously been used with success to describe measured adsorption-desorption data (Streck et al., 1995; Altfelder et al., 1999; Streck and Richter, 1999) and sorption kinetic data (de Jonge et al., 2000). Altfelder et al. (2000) used model parameters estimated from data measured by one technique, to predict adsorption-desorption reactions on two soils measured by two different techniques but at similar time-scales. The evaluation of the model includes tests of the ability (i) to describe measured adsorption-desorption isotherms, and (ii) to predict adsorption-desorption behavior and sorption kinetics of naphthalene with optimized model parameters.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 Conceptual Model Problems
 CONCLUSION
 REFERENCES
 
Soils
Five soils were used in the adsorption and desorption experiments. The soils differed with respect to texture and amount and quality of SOM. Three of the soils are from typical Danish arable agricultural sites where mineral fertilizers and animal manure have been applied for several decades. Two of these, Lerbjerg 1 and Lerbjerg 5, were retrieved from the 0- to 20-cm depth at two locations along a naturally occurring texture gradient in a field near Lerbjerg, Denmark (56°22'N lat., 9°59'E long.) (Schjønning et al., 1999). One soil was retrieved from the 0- to 20-cm depth at an experimental farm near Lundgaard, Denmark (55°27'N lat.; 9°10'E long., Orthic Haplohumod). One soil was retrieved at a former manufactured gas plant site at Hjørring, Denmark. The Hjørring soil was collected in the unsaturated zone from noncontaminated clayey layer in the 3.5- to 4-m depth (ground water table ~10-m depth). Finally, one soil from the Yolo series (fine-silty, mixed, nonacid, thermic Typic Xerorthent) was collected from an agricultural field in Yolo County, California (38°32'N lat., 121°46'W long.). All soils were air dried and sieved to <2 mm. The organic C was determined by combustion in a Leco 1000 CNS analyzer (LECO Corp., St. Joseph, MI) (Tabatabai and Bremner, 1970). Some properties of the soils are shown in Table 1.


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  		Table 1. Soil properties.

 
Naphthalene Sorption
Sorption was performed with 14C-labeled naphthalene (C10H8) (Sigma Chemical Co., St. Louis, MO) with a specific activity of 1.16 x 109 Bq mmol-1 (31.3 mCi mmol-1). A stock solution containing 14C-labeled naphthalene with a specific activity of 1.17 x 109 Bq L-1 (31.5 mCi L-1) was prepared in methanol (128 mg L-1), and a stock solution containing 10 mg L-1 unlabeled naphthalene (Fluka, Buchs, Switzerland) in 0.01 M CaCl2 was prepared. Prior to each experiment, solutions of nonlabeled naphthalene were prepared with initial concentrations of 0.10 to 10 mg L-1. The naphthalene solutions were then spiked with 14C-labeled naphthalene with a specific activity of ~4.14 x 104 Bq L-1 (~1.12 µCi L-1 [~2.5 x 106 cpm L-1]). The concentration of methanol in the solutions was ~0.03 g L-1.

The influence of methanol in solution on the sorption results was tested by conducting sorption experiments at two different concentrations of nonlabeled naphthalene on the five soils, with determination of the naphthalene concentration on a gas chromatograph (Chrompack 438S, Wcot fused Silica 32 mm ID CP-sil 8CB Chrompack capillary column, Packard Instrument, AM delfts, The Netherlands). In accordance with results of others (Curtis et al., 1986; McGinley et al., 1993), no effect of the presence of methanol on adsorption could be determined. Soil and the 0.01 M CaCl2 solution were autoclaved for 2 h prior to each experiment to prevent bacterial degradation of naphthalene. Autoclaving of the soil might change the structure of the SOM and affect the sorption results (Pignatello, 2000). Thus, it was tested to see if the autoclaving affected the adsorption results after 48 h of adsorption by conducting adsorption experiments at two different concentrations with either air-dry soil or autoclaved soil. No difference in the adsorbed amount was observed.

Sorption experiments were measured at 10°C using a batch technique. Solids/solution ratios were chosen to ensure that 20 to 80% of the naphthalene mass was adsorbed. Air-dried soil (Lerbjerg 5, 5 g; Lerbjerg 1 and Lundgaard, 6 g; Yolo, 7.68 g; and Hjørring, 20 g) was weighed into 36-mL glass centrifuge tubes (48-mL centrifuge tubes for the Yolo soil), naphthalene solution was added (Yolo, 43 mL; Lerbjerg 5, Lerbjerg 1, and Lundgaard, 30 mL; and Hjørring, 25 mL), and the tubes were sealed with Teflon coated screw caps. The headspace of the tube was typically very small (<2 mL). Three replicates were made for each naphthalene concentration. The tubes were rotated vertically (50 rpm). Adsorption isotherms were measured in the concentration range 0.10 to 10 mg L-1 on a short-term (48 h) and on a longer-term (504 h) time scale. Additionally, adsorption kinetics (4 h, 24 h, 48 h, 168 h, 504 h, and 1008 h) at two different initial concentrations were measured. Soil and solution were separated by centrifuging for 10 min at 2665 x g. From each tube, two replicates were used to determine concentration of 14C-labeled naphthalene by liquid scintillation counting (Packard 1600 TR, Packard Instruments, Downers Grove, IL) using 1 mL of the supernatant mixed with 10 mL of scintillation cocktail (Packard Ultima Gold XR, Packard Bioscience, Groningen, The Netherlands). For each concentration of naphthalene, two controls without soil material, but otherwise treated similarly, were included. No sorption to tubes and Teflon caps could be observed. However, small initial loses because of evaporation (<2%) when transferring solution to tubes was observed in the blanks. This was taken into account by assuming that the amount lost due to evaporation was the same in both blanks and tubes containing soil.

Desorption isotherms were measured at two different initial concentrations at short-term adsorption and at either two or three concentrations after longer-term adsorption experiments. Six to 12 successive desorption steps were measured, all conducted on a short-term basis (48 h). Prior to each desorption step, the samples were centrifuged at 2665 x g for 10 min., and 35 mL (Yolo), 22 mL (Lundgaard, Lerbjerg 5, Lerbjerg 1), or 17 mL (Hjørring) of the supernatant was replaced by 0.01 M CaCl2. At the end of the desorption experiments, naphthalene was extracted from the soils using up to five successive hexane extraction steps to determine the mass balance. These analyses showed that 96 to 102% of the initial amount of naphthalene was recovered. Some of these analyses were conducted on a gas chromatograph to make sure that the extracted material was still naphthalene. In all samples the concentration measured on a gas chromatograph was similar to the concentration measured using 14C-labeled naphthalene.

Model
The TCOR sorption model was presented by Streck et al. (1995). The basic assumption of the model is that nonattainment of sorption equilibrium in batch experiments is caused by slow sorption. A later paper by Streck and coworkers (Altfelder et al., 1999) states that the model is based on the assumption that slow sorption is caused by intraorganic matter diffusion. However, the description of the diffusion process is simplified to a mass transfer term. The TCOR model proposed by Streck et al. (1995) represents two main changes from the sorption model presented by Brusseau et al. (1991), namely that sorption to easily accessible sites is assumed instantaneous and sorption is assumed nonlinear (Freundlich isotherm model). The basic concept is that the sorbent consists of two compartments of different accessibility. The compartment, S1, is in direct contact with the solution phase, and the compartment, S2, exchanges only with S1. The mass transfer between the compartments is driven by the concentration difference, assuming diffusion-controlled sorption rates, and it is important to note that the sorption and desorption rate between S1 and S2 are similar in the model. Sorption to S1 is considered fast compared with the time scale of the experiment, and instantaneous equilibrium can be assumed between solution and S1 by using a Freundlich isotherm,

[1]
where KF is the Freundlich coefficient (mg(1-n) Ln kg-1); n, is the Freundlich exponent; S1 and S2 are the concentration of adsorbed solute in compartment 1 and 2 (mg kg-1), respectively; and C denotes dissolved concentration (mg L-1). Sorption to Compartment 2 is rate-limited and is described by a first-order rate equation,

[2]
where f is the fraction of Compartment 1 sites (-) and {alpha} is the rate coefficient between Compartment 1 and 2 (d-1) given by,

[3]
where A* is the specific surface area (m2 kg-1) between compartment 1 and 2, while k* is a lumped mass-transfer coefficient (kg m-2 d-1). The total mass of solute is given by,

[4]
where {theta} is the volume of water (L); {rho} is the soil mass (kg) in the sorption experiment, C is the concentration of solute in water (mg L-1) and S is the total amount adsorbed (mg kg-1), given by,

[5]

At equilibrium, the relation between concentration in each compartment and solute can be written as,

[6]

Streck et al. (1995) refers to KF and n as the true equilibrium parameters. If decay and loss of chemical is assumed negligible, the mass balance within one sorption step is,

[7]

By combining Eq. [1]–[7] the TCOR sorption model can be written as,

[8]

For each sorption or desorption step, the initial condition is given by C = C0, where C0 refers to the concentration at the beginning of each step in the model. Equation [8] was then solved numerically, and the sorption parameters were estimated by fitting Eq. [8] to the measured sorption and desorption data using the Levenberg–Marquardt algorithm (Press et al., 1989). A multiplicative error model (Knopman and Voss, 1987), where all concentrations are log-transformed in the parameter estimation procedure was applied.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
Conceptual Model Problems
 CONCLUSION
 REFERENCES
 
Adsorption-Desorption Nonsingularity
Adsorption isotherms for naphthalene on the five soils were measured on both a short-term (Fig. 2) and a longer-term (Fig. 3) time scale and could be well described by a Freundlich isotherm over the investigated concentration range (0.1–10 mg L-1),

[9]
where K'F is the Freundlich coefficient related to sorption capacity (referred to as adsorption K'F in the following), and n' is the Freundlich exponent related to sorption nonlinearity. It must be noted that there will be a difference between the true equilibrium Freundlich model parameters (Eq. [1]) and adsorption Freundlich parameters (Eq. [9]). Freundlich parameters obtained from fitting Eq. [9] to the measured adsorption isotherms are presented in Table 2 and provide some information about sorption capacity and nonlinearity. Although K'F is not strictly comparable (unless C = 1 mg L-1), it does indicate that Lundgaard soil has the greatest naphthalene sorption capacity followed by Lerbjerg 5, Lerbjerg 1, Yolo, and Hjørring soil, indicating that sorption capacity increases with increasing organic C content (Table 1). However, if sorption capacities (assuming that C = 1 mg L-1) were normalized to fraction of organic C (foc), the resulting Koc values vary between 400 and 1000 L Kg-1, with Hjørring as the lowest and Yolo as the highest, implying different qualities or geometries of the SOM. Lerbjerg 1 and Lerbjerg 5, taken from the same field on a naturally occurring texture gradient, have almost identical adsorption isotherms (Figs. 2 and 3, and Table 2). This is probably becuase of similar age, quality, and accessibility to the SOM in these soils. The K'F increased by 2 to 22% between short-term and longer-term sorption isotherms (Table 2) indicating nonattainment of equilibrium in the short-term experiment and continuing slow sorption in agreement with observations made by others (Pignatello and Xing, 1996; Rügner et al., 1999; de Jonge et al., 2000). Sorption nonlinearity was very similar between measured short-term and longer-term isotherms for the four agricultural soils; Lundgaard, Lerbjerg 1, Lerbjerg 5, and Yolo. Hjørring soil changed from nonlinear sorption in short-term experiments to almost linear sorption in the longer-term experiments (Table 2), indicating that this soil shows a linear sorption isotherm when approaching equilibrium.



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  		Fig. 2. Measured and optimized short-term (48 h adsorption and 48 h desorption step) adsorption-desorption isotherms using the TCOR model (solid lines). The dotted line is the true equilibrium isotherm based on the optimized model parameters. Error bars represent standard deviation on experimental data.

 


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  		Fig. 3. Measured and optimized longer-term (504 h adsorption and 48 h desorption step) adsorption-desorption isotherms using the TCOR model (solid lines). The dotted line is the true equilibrium isotherm based on the optimized model parameters. Error bars represent standard deviation on experimental data.

 

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  		Table 2. Results of parameter estimation for short-term sorption experiment (48 h adsorption and 48 h desorption step) and longer-term sorption experiments (504 h adsorption and 48 h desorption step) and freundlich parameters fitted to the measured adsorption isotherms.

 
Adsorption-desorption isotherms were nonsingular for all soils at both short-term (Fig. 2) and longer-term (Fig. 3) time scales. Thus, the Freundlich exponents n' were lower for the desorption isotherms than for adsorption isotherms, implying pronounced nonlinearity in the desorption experiments. We characterized the nonsingularity of the adsorption-desorption isotherms by using the expression of non-singularity proposed by Ma et al. (1993),

[10]
where {omega} is a measure (in %) of nonsingularity, and n'A and n'D are the Freundlich exponents for the measured adsorption and desorption isotherms, respectively. It is important to note that this index is strictly only applicable for comparison purposes if the ratio of the replaced supernate and the time-scale are the same in all the desorption experiments. In this study, the ratios of replaced supernate are fairly similar (0.68–0.76) for the five soils and the same time scales are used in the desorption experiments. Some of the desorption isotherms were nonlinear in the log-log plot (e.g., Fig. 2d and e) implying that the Freundlich equation did not optimally describe the data. This adds additional uncertainty in calculating the nonsingularity index from Eq. [9]. In view of this, the calculated values of nonsingularity, {omega} (%), can only be considered a rough characterization of the degree of sorption hysteresis for the five soils.

Figure 1 shows {omega} for the measured adsorption-desorption isotherms (Fig. 2 and 3) of the five soils. The soils represent varying desorption behavior, and the measure of nonsingularity was used to categorize the soils into two types of sorption behavior; Type I: minor nonsingularity ({omega} < 100%) represented by Lundgaard and Lerbjerg 1, and Type II: pronounced nonsingularity ({omega} > 100%) represented by Hjørring and Yolo soil. Lerbjerg 5 shows Type I behavior in the short-term experiments (Fig. 1 and 2c) and Type II behavior in the longer-term experiment (Fig. 1 and 3c). Thus, it was characterized as a Type I/II soil.



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  		Fig. 1. Degree of sorption nonsingularity, {omega}, of the measured naphthalene adsorption-desorption isotherms as a function of the initial concentration of naphthalene in the sorption experiment. I and II represent the defined types of sorption nonsingularity. Open symbol represents short-term (48 h adsorption and 48 h desorption step) and closed symbols longer-term (504 h adsorption and 48 h desorption step) experiments.

 
There is no overall trend in the effect of the initial concentration, Ci, in the sorption experiments on {omega}. However, for Lerbjerg 1, Lundgaard, and Hjørring short-term, and Lerbjerg 1, Lerbjerg 5, and Yolo longer-term, there is a tendency that {omega} decreases when Ci increases. Seybold and Mersie (1996) and Zhu and Selim (2000) also observed that {omega} decreased if Ci increased, while Ma et al. (1993) observed no dependence on Ci. Adsorption-desorption nonsingularity has been observed in many cases and is usually explained by nonattainment of equilibrium in the sorption process and restrictions because of intraorganic matter diffusion (Streck et al., 1995; Pignatello, 2000; Luthy et al., 1997) or intraparticle diffusion (Miller and Pedit, 1992; Grathwohl et al., 1993). Kan et al. (1998), however, explained adsorption-desorption nonsingularity by proposing that sorption includes reversible and irreversible compartments. The irreversible sorption is a consequence of interaction between the HOCs and SOM, and has a fixed maximum that is filled in one or more sorption steps. In accordance, Huang and Weber (1997) proposed that entrapment of sorbing molecules in the SOM contribute significantly to the nonsingularity. Entrapment or irreversible sorption with a maximum capacity might explain the tendency that nonsingularity seems to increase with decreasing initial concentration of naphthalene (Fig. 1). This can also be explained with intraparticle diffusion, because at lower solute concentrations nonlinearity causes stronger sorption to the SOM in the pores. Thus attainment of equilibrium becomes slower because of retarded diffusion in the pores, and consequently, increased nonsingularity would be observed (Grathwohl, 1998). The more pronounced adsorption-desorption nonsingularity of Hjørring soil agrees somewhat with the observations of Huang and Weber (1997). They observed more nonsingularity in older organic materials. However, they and others observed that older organic materials showed less sorption linearity (Huang and Weber, 1997; Xing and Pignatello, 1996), which was not observed for the Hjørring soil (Table 2).

There are no clear trends in how the nonsingularity changes between short-term and longer-term experiments. Two soils (Lundgaard and Lerbjerg 1) show almost no difference, two soils (Lerbjerg 5 and Yolo) show increased nonsingularity, and one soil (Hjørring) shows less nonsingularity after longer-term sorption. The adsorption-desorption behavior of Hjørring soil could very well be explained by intraparticle diffusion. Miller and Pedit (1992) also observed less nonsingularity in a longer-term experiment, and suggested that the increased nonsingularity in the short-term experiment was caused by nonattainment of equilibrium, and thus, adsorption would continue because of diffusion into the intraparticle pores. This, however, does not explain why Yolo and Lerbjerg 5 soils show increased nonsingularity in the longer-term experiment. Instead, intraorganic matter diffusion into the glassy or condensed part of the SOM has been used to explain slower desorption from aged contaminants (White et al., 1999; Pignatello, 2000).

Model Simulation of Measured Data
The parameters in the TCOR sorption model (Eq. [1]–[8]) were optimized in a fitting procedure to describe measured adsorption and desorption isotherms for five soils on a short-term time scale (Fig. 2) and on a longer-term time scale (Fig. 3).

The TCOR sorption model describes short-term data well, whether it is a Type I or II soil (Fig. 2). Statistical analysis also showed that the root mean squared error (RMSE) values on the model fit were low (Table 2). For Type I soils (Lerbjerg 5 included), the true equilibrium KF was 12 to 25% higher than adsorption K'F (Fig. 2a–c and Table 2). Following the TCOR model, this indicates that the system had not yet reached equilibrium in the short-term experiment, and slow sorption should continue, which was also observed in the longer-term experiment (higher K'F, see Table 2). For Type II soils, true equilibrium optimized KF for the short-term experiment was more than two orders of magnitude higher than adsorption K'F for the Hjørring soil (Fig. 2d and Table 2), while it was ~130% higher for the Yolo soil (Fig. 2e and Table 2). This indicates that sorption to the Type II soils should increase dramatically with time. However, the adsorption K'F obtained for the Type II soils only increased by ~12 and 22% from short-term to longer-term adsorption for Yolo and Hjørring, respectively (Table 2). The uniqueness of the model parameters, especially on Type II soils are questionable if the high standard deviations on the optimized model parameters (Table 2) are compared with the standard deviation of the measured data (Fig. 2d and e). This indicates that the values of the optimized model parameters are very sensitive to small changes in the measured data.

Longer-term sorption experiments were also well described by the TCOR sorption model (Fig. 3 and Table 2). The general parameter uncertainty increased compared with the standard deviation on short-term data (Table 2). Even though standard deviation on the experimental results are relatively small (Fig. 3), it causes some extreme standard deviations on the fitted model parameters (e.g., KF) for Yolo soil (Table 2). Again, this shows that the TCOR model is able to give a good description of the measured data resulting in a low RMSE value, but the uniqueness of the model parameters are questionable. The smaller standard deviation on the parameters in the longer-term fit for the Hjørring soil compared with the short-term fit may actually show that the longer-term adsorption-desorption behavior of the Hjørring soil is in good agreement with the theory of the TCOR model concept. This implies that sorption is very close to equilibrium in the longer-term experiment and that desorption nonsingularity is caused alone by the fact that the next dilution occurs before the process has reached equilibrium. However, this explanation cannot be used for the short-term experiment with this soil.

The fitted model parameters indicate that the measured adsorption isotherms were almost in equilibrium after longer-term sorption, except for Lerbjerg 5 and especially Yolo (Fig. 3c and e, and Table 2). The reason why the true equilibrium KF increases between short-term and longer-term model fit for these two soils are the higher nonsingularity in the desorption isotherms in the longer-term experiments (see Fig. 1). There are several possibilities of why the model parameters become somewhat meaningless, especially for the Type II soils. The diffusion approach of the model is very simplified, since it is described by a single and constant rate. This is problematic whether it is intraorganic matter diffusion or intraparticle diffusion that is used as the explanation of sorption nonsingularity because of the complexity of the SOM and the soil particles. The assumption that the rate between S1 and S2 is similar whether it is uptake or release is problematic since different rates between adsorption and desorption has been observed several times (White et al., 1999; Connaughton et al., 1993). Irreversible sorption, as proposed by Kan et al. (1998) and Huang and Weber (1997), might also explain some of the pronounced nonsingularity. However, all these complexities cannot be included in the TCOR sorption model without introducing several new model parameters and more parameter uncertainty.

Uniqueness of the Model Parameters
In the optimization procedure, four parameter values were optimized simultaneously, and this must result in some parameter uncertainty. There were major parameter differences between short-term and longer-term model optimization especially for Type II soils (Table 2). For example, true equilibrium KF for Hjørring soil was more than two orders of magnitude smaller in the longer-term model optimization as compared with the short-term, the transfer rate, {alpha}, was 30 to 70% smaller, and the parameter, f, was more than two orders of magnitude higher. Parameter values varied if only parts of the data were used, especially if only one desorption isotherm or only parts of the desorption isotherm were used. Thus, the reliability of the model parameters is questionable. Figure 4 and Table 3 show an extreme case of parameter uncertainty in the optimization procedure. In the optimization on Fig. 4, the number of desorption steps used in the model optimizations were varied for the short-term experiment for Hjørring soil. Model simulations were continued beyond the available data to illustrate what consequence the varying model parameters have on the description of the desorption process. It is obvious that the number of desorption steps used in the model fit, markedly influences the values of the model parameters (Table 3), and that the standard deviation increases as the number of desorption steps increase. This uncertainty has major consequences on the model description of the desorption behavior (Fig. 4a–c). The model parameters in Table 3, illustrate how the nonattainment of equilibrium is used in the model to describe the nonsingularity. More nonsingularity is described by a lower fraction of easily accessible sites, f, to make sorption more kinetically limited. The exchange rate coefficient, {alpha}, between S1 and S2 becomes smaller indicating that the diffusion in the particle grains becomes more retarded. Finally, true equilibrium KF increases to secure a high initial sorption in the easily accessible sites that fits the measured adsorption isotherm. This shows that the true equilibrium parameter, KF, is meaningless, in the sense that it cannot be used as a realistic indicator of true equilibrium sorption. If the model is to be meaningful, at least this parameter should make some sense in relation to the measured data.



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  		Fig. 4. Model parameter optimization on short-term (48 h adsorption and 48 h desorption step) adsorption-desorption of naphthalene on Hjørring soil with varying numbers of desorption steps used in the optimization procedure. Open symbols represent data not used in the optimization procedure. Model simulations are continued beyond data to illustrate the consequence of varying model parameters on the description of the desorption process.

 

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  		Table 3. Results of parameter optimization on Hjørring soil if the numbers of desorption steps is changed in the short-term adsorption-desorption (48 h adsorption and 48 h desorption step) isotherm.

 
Model Prediction
The applicability of the optimized model parameters was tested using the short-term parameters (Table 2) to predict sorption results from the longer-term experiment (Fig. 5) . For Type I soil, measured data were well predicted, while for Type II soils, the measured data were poorly predicted. The change from Type I at short-term to Type II at longer-term experiments for Lerbjerg 5 causes the prediction of the longer-term experiment for this soil to be less satisfying. These results indicate that there are some conceptual problems if the model is to be used for prediction, especially for Type II soils. Since Altfelder et al. (2000) managed to predict independent adsorption-desorption isotherms measured using a different batch technique but the same time-scale, the problems are more specifically related to predictions at a different time-scale. The major problem with the TCOR model is the simplification of the diffusion process regarding diffusion into and out of the intraorganic matter domains or the intraparticle domains. This process cannot be described with just one parameter, {alpha}. Also, there are indications that some irreversible sorption may occur on the Yolo and Hjørring soil causing an overestimation of the optimized true equilibrium KF.



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  		Fig. 5. Predicting longer-term (504 h adsorption and 48 h desorption step) adsorption-desorption isotherms using model parameters optimized on short-term data (Table 2, solid lines). Dotted lines represent true equilibrium based on short-term parameters.

 
The ability of the TCOR sorption model to predict sorption kinetics was tested for Lerbjerg 1 and Hjørring soil (Fig. 6) . For the Lerbjerg 1 soil (Fig. 6a), the prediction of sorption kinetics is reasonable whether short-term or longer-term model parameters are used. However, the use of short-term parameters results in an overestimation of long-time sorption and the use of longer-term parameters results in an underestimation of short-time sorption. The TCOR model significantly overestimated long-time sorption for the Hjørring soil (Fig. 6b) if short-term parameters were used. The high true equilibrium KF for the short-term experiment obviously affects the model predictions using these parameters, illustrated by how sorption is predicted to slowly increase against a very high sorbed amount with time. However, measurements show that this is not the case, resulting in large prediction errors. Meanwhile, it is interesting that prediction based on the longer-term isotherms contains sufficient information to provide a reasonable description of short-term kinetics. The longer-term true equilibrium KF does appear to be realistic as opposed to the short-term KF. Since the adsorption-desorption behavior of the Hjørring soil is in good accordance with the observations made by Miller and Pedit (1992), intraparticle diffusion might explain the nonsingularity for this soil. If this is the case, the TCOR model is not able to describe the intraparticle diffusion process if sorption equilibrium is not yet obtained. It is important to clarify that the reasonable description of sorption kinetics using longer-term model parameters also includes the other three soils of this study, although, a general underestimation is observed as for the two soils of Fig. 6. The reasonable but underestimated predictions of sorption kinetics using longer-term model parameters are an expected result if the assumption of the TCOR model is considered. The TCOR model accounts for the small increase in the sorbed amount between short- and longer-term measurements (Table 2 and Fig. 2 and 3) by modeling sorption at smaller rates (generally lower {alpha} in the longer-term fit, except Hjørring soil), thus, resulting in an underestimation of short-time sorption kinetics. If the longer-term model parameters are used to describe short-term adsorption-desorption isotherms, it results in the same prediction problems as shown in Fig. 5. This clearly indicates that the model parameters cannot be used to predict adsorption-desorption reactions if the time scale of the predictive modeling is not similar to the time scale of the experimental data to which the model is calibrated.



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  		Fig. 6. The ability of the TCOR sorption model to predict naphthalene adsorption kinetics using either short-term or longer-term model parameters on Lerbjerg 1 (left) and Hjørring (right) soil at two different initial concentrations (0.50 mg L-1 and 5.0 mg L-1). Error bars represent standard deviation on experimental data.

 
Model Test Against a Type II Data Set From Literature
To illustrate the problems in using the TCOR model to describe Type II sorption, the model was applied to a data set of naphthalene adsorption-desorption to Lula soil measured at two different time-scales (Kan et al., 1994). Lula soil, is a sandy riverine sediment (2% clay, 6% silt, 92% sand, 0.27% foc). Short-term sorption was for 24 h of adsorption followed by two successive desorption steps of 24 h, while longer-term sorption was for 168 h of adsorption followed by two successive desorption steps of 168 h. Lula soil is characterized as a Type II soil because {omega} >> 100, although the hysteresis index of their experiment is not directly comparable with the ones presented in Fig. 1 because the time scale and the dilution ratio of each desorption step was very different. However, since {omega} >> 100, there should be no doubt that this is a Type II soil. Kan et al. (1994) reported that precautions were taken to insure that the pronounced nonsingularity observed was not caused by degradation. Model fit and optimized model parameters are presented in Fig. 7 and in Table 4. The TCOR sorption model is able to fit measured data very well on both a short-term (Fig. 7a) and longer-term (Fig. 7b) time-scale. However, the model parameters are very different when comparing the two model fits (Table 4). Thus, the prediction of adsorption-desorption behavior fails using parameters obtained from a different time-scale (Fig. 7c). The problems with the model fit for the Lula soil are very similar to the model fit for the Yolo and the Hjørring soil in that model parameters are unrealistic and varying between the short- and longer-term model fits. This clearly indicates that the TCOR model description of the diffusion process is overly simplified to give reasonable predictions and stable model parameters for a Type II soil. If irreversible sorption is the case, as reported later for the Lula soil by Kan et al. (1998), the TCOR model is also inadequate, because it contains no mechanisms to account for this.



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  		Fig. 7. Measured and optimized a (a) short-term (24 h adsorption and 24 h desorption) and (b) longer-term (168 h adsorption and 168 h desorption step) adsorption-desorption isotherms using the TCOR model (solid lines). The dotted line is the true equilibrium isotherm based on the optimized model parameters. (c) Predicting longer-term adsorption-desorption isotherms using model parameters optimized on short-term data (Table 4, solid lines). Dotted lines represent true equilibrium based on short-term parameters.

 

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  		Table 4. Results of parameter estimation for short-term (24 h adsorption and 24 h desorption step) and longer-term (168 h adsorption and 168 h desorption step) sorption data for the Lula soil taken from Kan et al. (1994) and freundlich parameters fitted to the measured adsorption isotherms.

 

   Conceptual Model Problems
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 Conceptual Model Problems
CONCLUSION
 REFERENCES
 
The present analysis of the TCOR sorption model shows that the model fits adsorption-desorption measurements well regardless of whether there is negligible or pronounced nonsingularity. However, the reliability of the model parameters is questionable because of the dependence on sorption time, the numbers of desorption data used in the model optimization, and in some cases, the unacceptably high standard deviation on model parameters. The major parameter uncertainty, especially for soils exhibiting Type II sorption, is the result of the simplified description of the adsorption-desorption process in the TCOR model. Irreversible sorption (Kan et al., 1998; Huang and Weber, 1997) and kinetically controlled desorption, where sorption is faster than desorption (Lindstrom et al., 1971; Van Genuchten et al., 1974; Connaughton et al., 1993; White et al., 1999), may be important sorption phenomena not taken into account by the TCOR model. Intraorganic matter diffusion might play a role especially in Lerbjerg 5 and Yolo soil, causing desorption to be slower and more retarded on aged contaminants as shown by White et al. (1999). Intraparticle diffusion might be an explanation of why desorption from the Hjørring soil shows less nonsingularity in the longer-term experiment as shown by Miller and Pedit (1992). Thus, the simplified description of the diffusion process using one rate constant in the TCOR model is not sufficient, especially for the Type II soils. The model concept also implies that S1 and S2 at equilibrium have the same sorption capacity (KF) and sorption nonlinearity (n). However, Cornelissen et al. (2000) and Huang et al. (1997) suggested that the different sorbate domains show varying sorption linearity and behavior and they used different isotherms to describe sorption in each compartment.

The TCOR sorption model may be improved for Type II soils if the constant rate is divided into a desorption and adsorption rate or if a third compartment in which the HOC is irreversibly sorbed is introduced. However, this would require at least one or two new model parameters, probably leading to even higher parameter uncertainty. One other problem with the TCOR model approach is that none of the parameters can be obtained independently. Thus, the introduction of new parameters is not likely to be fruitful. Development of a more conceptual and robust sorption model for soils exhibiting Type II sorption behavior is an important goal for future research.


   CONCLUSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 Conceptual Model Problems
 CONCLUSION
REFERENCES
 
The physically based TCOR sorption model proposed by Streck et al. (1995) was evaluated using measured adsorption-desorption isotherms of naphthalene on five different soils. The model fitted measured adsorption-desorption isotherms well on both a short-term and a longer-term time scale. However, the uniqueness of the model parameters was questionable because they were affected by the time scale of the experiments and the amount of desorption data used in the parameter optimization.

The ability to predict adsorption-desorption behavior from independently optimized model parameters decreased with increasing desorption nonsingularity. Hence the description of intraorganic matter or intraparticle diffusion in the TCOR sorption model appears oversimplified and does not account for processes such as slower release than uptake rates and irreversible sorption of parts of the hydrophobic organic chemical.

For soils exhibiting Type II sorption behavior, the TCOR sorption model should be used in transport or degradation experiments only when the time scale of the adsorption-desorption experiments is comparable with that of the predicted transport and degradation processes.


   ACKNOWLEDGMENTS
 
This study was supported by European Doctorate School of Technology and Science at Aalborg University and the Danish Technical Research Council, Research Talent Project entitled: ‘New methods for measuring and predicting liquid and gaseous phase transport properties in undisturbed soils’ and grant 5P42ESO4699 from the National Institute of Environmental Health Sciences, NIH, at U.C. Davis. The contents of this publication are solely the responsibility of the authors and do not necessarily represent the official view of the NIEHS, NIH, or EPA. We thank the anonymous reviewers for their constructive suggestions that helped us improve the manuscript.

Received for publication December 1, 2000.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 Conceptual Model Problems
 CONCLUSION
 REFERENCES
 




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