Published online 5 April 2007
Published in Soil Sci Soc Am J 71:674-681 (2007)
DOI: 10.2136/sssaj2006.0299
© 2007 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
SOIL PHYSICS
Modeling Cadmium Transport in Soils Using Sequential Extraction, Batch, and Miscible Displacement Experiments
Daniel C. W. Tsang*,
Weihua Zhang and
Irene M. C. Lo
Department of Civil Engineering, The Hong Kong Univ. of Science and Technology, Hong Kong, China
* Corresponding author (cedaniel{at}ust.hk).
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ABSTRACT
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Asymmetric transport behavior of Cd in soils can result from sorption nonlinearity or rate-limited sorption, of which the relative significance is difficult to be discerned by transport modeling alone. Multiple approaches incorporating batch, sequential extraction, and miscible displacement experiments were therefore used in this study. Batch isotherm was used to indicate the range of Cd concentration where sorption became nonlinear. It is noteworthy that batch kinetics illustrated a shorter apparent equilibrium time of sorption at a higher Cd concentration, which presumably correlates with the significance of rate-limited sorption. In addition, sequential extraction results indicated that the relative contribution of rate-limited specific sorption to total sorption became negligible with increasing Cd concentration. Since the rate-limited specific sorption appears to be of low capacity, it is only important for sorption at low concentration. In miscible displacement experiments, Cd transport at 10–5 M could only be simulated using a nonequilibrium model, whereas a nonlinear model was necessary for describing Cd transport at 10–3 M. Therefore, this study demonstrated that transport behavior is predominantly influenced by rate-limited sorption at sufficiently low concentration, while by sorption nonlinearity at sufficiently high concentration. Additionally, sequential extraction can be a useful tool to illustrate the significance of rate-limited specific sorption and the corresponding chemical nonequilibrium transport behavior.
Abbreviations: BTC, breakthrough curve
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INTRODUCTION
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Given the heterogeneous nature of soil sorption sites, heavy metal sorption is often nonlinear at sufficiently high concentration. Nonlinear sorption can cause asymmetrical transport behavior that accounts for the prolonged cleanup time required in many remediation projects (Berglund and Cvetkovic, 1996; Abulaban et al., 1998; Serrano, 2003). Previous modeling studies illustrated that sorption nonlinearity could be a determinant for transport behavior, where a linear transport model failed to provide an accurate simulation of the transport when the corresponding nonlinearity exponent of Freundlich isotherm was below around 0.9 (Weber et al., 1991; Brusseau, 1995). On the other hand, nonequilibrium transport behavior resulting from rate-limited sorption exhibits early breakthrough and long tailing, which also impedes effective soil remediation (Ma and Selim, 2005; Communar and Keren, 2006; Tsang and Lo, 2006a, 2006b, 2007). It is therefore desirable to evaluate the relative significance of sorption nonlinearity and rate-limited sorption.
Modeling transport data has been commonly adopted to elucidate transport behavior. From the nearly identical simulations of linear nonequilibrium and nonlinear nonequilibrium, rate-limited sorption has been concluded to be of greater importance than nonlinear sorption, although both processes influenced the shape of the breakthrough curves (Hu and Brusseau, 1998; Johnson et al., 2003). For field and laboratory data that were best described by nonlinear nonequilibrium transport (Streck et al., 1995; Fesch et al., 1998), however, an inadvertent isotherm nonlinearity may result in erroneous parameters for nonequilibrium transport (Spurlock et al., 1995). Obviously, if merely explained by modeling, the relative importance of nonlinear sorption and rate-limited sorption in determining transport behavior is ambiguous and not predictable.
Sorption would be more nonlinear with increasing concentration and the degree of nonlinearity can be reflected by batch isotherm; however, the significance of rate-limited sorption may also be influenced by concentration. First, for sorption rate limited by diffusion, which is in part controlled by the concentration gradient, the sorption kinetics would be faster at higher concentration (Divincenzo and Sparks, 1997; Hu and Brusseau, 1998). Second, the fraction of overall sorption that is rate limited may correlate with concentration because predominant sorption can occur via different mechanisms or at different sites under different contaminant loadings, in the light of free energies of sorption mechanisms. For instance, Karlsson et al. (2005) revealed that the relative contribution of high-affinity S sites to Cd sorption decreased with increasing Cd loading on organic matter because these sites were saturated while the contribution of weaker O and N sites successively increased.
In consideration of the probable dependence of rate-limited sorption on concentration, and uncertainty in modeling alone, multiple approaches are essential to improve our understanding of the transport behavior while little attention on this issue has been received thus far. The use of x-ray absorption fine-structure (XAFS) spectroscopy along with batch or miscible displacement experiments was able to verify the rate-limiting sorption mechanisms during heavy metal transport (Voegelin and Kretzschmar, 2005; Chen et al., 2006). The XAFS technique is rather complicated, however, and the equipment is not widely available. Besides, the metal concentration needed for synchrotron studies is so high (e.g., 1000–25000 mg kg–1 in the study of Karlsson et al. [2005]) that the significance of rate-limited sorption under environmental conditions may not be truly reflected. Therefore, this study intends to make use of relatively simple and fast batch experiments and sequential extraction to evaluate the relative contribution of sorption nonlinearity and rate-limited sorption, and analyze the transport behavior of Cd observed in miscible displacement experiments. The concentration range of interest (10–5–10–3 M) could result in soil contamination of 10s to 1000 mg kg–1, which is comparable to the concentration level usually encountered at contaminated sites.
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MATERIALS AND METHODS
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Sorbents and Sorbates
Three soil samples were taken from 25 to 50 cm below ground surface at The Hong Kong University of Science and Technology (UST soil), Tai Mo Shan (TMS soil), and Clearwater Bay (CWB soil) in Hong Kong. The three soils were air dried and passed through a 2-mm sieve. The particle size distribution was obtained by sieving and hydrometer methods. The soil pH was measured at a 1:2 soil/water ratio. The organic C contents of the soils were analyzed using a total organic C analyzer (TOC-5000A, Shimadzu, Kyoto, Japan) with infrared spectrometer after combustion in a furnace (total C) and acidification (total inorganic C). The BET surface area was measured by N2 gas adsorption (ASAP2010, Micromeritics Instrument Corp., Norcross, GA). The cation exchange capacity of the soils was determined by NH4–Na exchange. The clay fractions of the soils were separated by pipette and the most abundant minerals were determined by x-ray diffraction analysis. Total heavy metal contents in the soils were estimated by x-ray fluorescence spectrometry. The characteristics of the soils are reported in Table 1.
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Table 1. Characteristics of the soils from The Hong Kong University of Science and Technology (UST), Tai Mo Shan (TMS), and Clearwater Bay (CWB) in Hong Kong.
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Widespread and low-level Cd inputs come from fertilizers and atmospheric deposition of smelter dust, whereas localized and high-level Cd inputs arise from land application of sewage sludge products and discharge of industrial wastes (Sauve et al., 2000). Cadmium (10–5–10–3 M) and Br (10–4 M) solutions were prepared by dissolving Cd(NO3)2 and NaBr, respectively, in the background electrolyte of 0.03 M NaNO3. All solutions were adjusted to pH 5 with dilute HNO3, because an acidic condition is prevalent in regions with high annual rainfall and industrial sites where Cd precipitation is not likely to occur. Cadmium concentration was measured by flame atomic absorption spectrometry (Hitachi Z-8200, Hitachi Ltd., Tokyo), and Br concentration was analyzed by ion chromatography (Dionex DX-500, Dionex Corp., Sunnyvale, CA).
Batch Sorption Experiments
All batch and miscible displacement experiments were conducted at room temperature. The batch kinetics and sorption isotherm studies were performed in polypropylene centrifuge tubes at a soil/solution ratio of 1:10 (2 ± 0.005 g soil in 20 mL solution). All batch experiments were conducted in triplicate. Since the natural pH values were different for the three soils, it was necessary to equilibrate the soil to the desired pH of 5 before Cd sorption. The soils were prewashed with the background solution of 0.03 M NaNO3 (pH 5) at least three times, each during a period of 24 h, until the soil solution pH was close to 5. In batch kinetics experiments, the tubes containing the soil suspension (10–5 and 10–3 M Cd) were shaken end-over-end at 25 rpm for 14 reaction times ranging from 1 min to 7 d, and then centrifuged at 3500 rpm for 10 min. The Cd concentration in the supernatant was measured and the sorbed amount was calculated by subtraction. Batch sorption isotherms were performed with a series of 16 Cd equilibrium concentrations ranging from 10–5 to 10–3 M. The apparent equilibrium time was 24 h as determined from kinetic studies. The solution pH was measured at the end of the batch experiments. The plots of sorbed concentration against equilibrium concentration were fitted with a Freundlich isotherm, which is the most widely used nonlinear isotherm function due to sorption site heterogeneity of soils (Selim and Amacher, 1997; Hu and Brusseau, 1998).
Miscible Displacement Experiments
Eighteen columns of 3.6-cm i.d. and 10-cm length were individually packed with the three soils in small increments and compacted on the surface of the soil after each increment with a piston of slightly smaller size than the column. The bulk density was measured and the porosity was accordingly calculated, giving values of 1.508 g cm–3 and 0.433 for the UST soil columns, 1.352 g cm–3 and 0.495 for the TMS soil columns, and 1.242 g cm–3 and 0.532 for the CWB soil columns. Before the displacement experiments, soil columns were slowly saturated by feeding the background solution of 0.03 M NaNO3 (pH 5) from the bottom. After an initial equilibration period of >100 pore volumes, a stable effluent of pH 5 and 0.03 M ionic strength was maintained, and water saturation was gravimetrically checked. In addition, concentrations of Fe, Al, Ca, and dissolved organic C in the effluent were not detectable after the initial equilibration period, indicating that there was no noticeable dissolution of mineral oxides or soil organic matter during the course of the miscible displacement experiments.
The four different Cd concentrations (10–5, 5 x 10–5, 10–4, and 10–3 M) in the background solution (0.03 M NaNO3, pH 5) were injected into 12 soil columns (four for each of the three soil samples) at an average pore-water velocity of 8.58 cm h–1 for the UST soil, 7.49 cm h–1 for the TMS soil, and 6.98 cm h–1 for the CWB soil. Nonsorbing Br at 10–4 M was also injected at the same pore-water velocity to determine the physical transport parameters (i.e., Peclet number and dispersion coefficient) of the columns. The Br and Cd solutions were individually injected into the soil columns until a breakthrough plateau was observed, and then the columns were fed with background solution again. During elution, an 8-h flow interruption was performed for the soil columns fed with 10–5 and 10–3 M Cd. If nonequilibrium transport behavior arises from rate-limited sorption–desorption, there is a rise in effluent concentration during the elution front since the rate-limited solute desorption from soil would continue to proceed during the flow interruption period (Brusseau et al., 1997). Effluent samples were collected from the top of the columns and measured. The breakthrough curves (BTCs) were then constructed by plotting relative concentration (effluent concentration divided by influent concentration) vs. dimensionless time (pore volume).
Sequential Extraction
In parallel with the previous 12 columns, six soil columns (two for each of the three soil samples) were injected with Cd solutions of 10–5 and 10–3 M, respectively, until reaching a complete breakthrough plateau. At this point, the columns were dismantled and soils at three depth intervals (bottom, middle, and top) of the columns were intermingled, prewashed with deionized water for 5 min to remove entrapped Cd solution, and freeze-dried for sequential extraction. The sorption fronts of the BTCs (not shown) were nearly identical to the previous BTCs. The total sorbed Cd concentrations in these soil columns were within ±5% of the previous ones. Thus, the transport data is reproducible and can be analyzed with the aid of sequential extraction.
The sequential extraction procedures according to Lo and Yang (1998) and Li et al. (2001) were used with a minor modification (Table 2). The extractions were performed progressively on 1 ± 0.005 g of the freeze-dried Cd-contaminated soil, in 30-mL centrifuge tubes (except the final step using microwave digestion) to minimize soil loss. The samples were centrifuged at 3500 rpm for 10 min at room temperature and the concentration in the supernatant was analyzed following each extraction. The samples were then washed with 10 mL of deionized water and centrifuged between extraction steps. No visible residues were left after the last step of sequential extraction. The extraction experiments were performed in triplicate. The sum of Cd concentrations from the five steps was in excellent agreement with the total Cd content determined by total acid digestion in a microwave oven (mass recovery: 96–106% for each replicate), indicating an acceptable accuracy of this sequential extraction scheme.
Transport Modeling
The BTCs were analyzed with linear and nonlinear, equilibrium and nonequilibrium transport models. In the formulation of equilibrium transport models, one-dimensional transport of a sorbing solute through a homogeneous, saturated soil is described with the convection–dispersion equation:
 | [1] |
where x is distance (cm), t is time (h), 
is bulk density (g cm–3), 
is water content (dimensionless), D is the hydrodynamic dispersion coefficient (cm2 h–1), v is average pore-water velocity (cm h–1), C is solution concentration (mol cm–3), and S is sorbed concentration (mol g–1). When a change of Cd sorption with time (
S/t) is applied using a linear isotherm (S = KdC, where Kd is the sorption distribution coefficient [cm3 g–1]), Eq. [1] describes the linear equilibrium transport. In the case of incorporating the Freundlich isotherm (S = KfCn, where Kf is the Freundlich distribution coefficient [mol(1–n) cm3n g–1] and n is a dimensionless nonlinearity exponent), Eq. [1], which must be solved numerically, simulates nonlinear equilibrium transport.
The values of the dispersion coefficient D of the soil columns were optimized during curve fitting the Br BTCs to the equilibrium transport equation. Previous studies have confirmed that Br remains virtually nonsorbing on these soils (Tsang and Lo, 2006a, 2007). The Br transport in each soil column (not shown) exhibited a symmetrical and sharp breakthrough, which was well described by the equilibrium transport model, suggesting the absence of an immobile water region. Therefore, a chemical (two-site) nonequilibrium model should be used to evaluate the possible nonequilibrium transport of sorbing solute.
The conceptual model of chemical (two-site) nonequilibrium transport (Cameron and Klute, 1977) regards the sorption as two types, occurring either in series or parallel. One is instantaneous and at equilibrium; the other is rate-limited and described by first-order kinetics. It is noted that the two types are only kinetically defined. They could be related to heterogeneity among different soil components (e.g., clay minerals, Fe oxides, and organic matter) or heterogeneity inside a single soil component. Strict inference of only two distinct sorption sites in soil should not be drawn from the appropriateness of using a chemical (two-site) nonequilibrium model. A model incorporating more than two types of sorption would be more realistically reflective, but difficult to use in the sense of practical application. Thus, the two-site model appears to be a good balance between the degree of accuracy and field applicability. For nonlinear sorption, which is assumed for both two sorption domains, the nonequilibrium transport equation is expressed as (Simunek et al., 1998)
 | [2] |
 | [3] |
 | [4] |
where F is a fraction of instantaneous sorption and 
is a first-order rate coefficient (h–1). In the case of n = 1, Eq. [2] to [4] describe linear nonequilibrium transport. The Cd BTCs were analyzed with the linear and nonlinear, equilibrium and nonequilibrium transport equations (Eq. [1]–[4]) using the HYDRUS-1D code (Simunek et al., 1998). The value of R was calculated using the normalized first temporal moment of Cd BTCs (Maraqa et al., 1998), because R is practically regarded as an apparent (i.e., empirical) retardation factor rather than the quantity determined explicitly from batch distribution coefficient (Skaggs and Leij, 2002). For linear transport, the simulation of the equilibrium model contained zero fitting parameters, whereas that of the nonequilibrium model involved optimization of two parameters (F and ). In simulating nonlinear transport, the equilibrium model optimized one parameter (n), whereas the nonequilibrium model optimized three parameters (n, F, and ). Since a nearly linear, negative correlation between n and Kf was produced when they were simultaneously optimized in the preliminary optimization, Kf was kept constant at the value obtained from the lowest concentration (10–5 M) in the parameter estimation of nonlinear transport (Simunek et al., 1998).
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RESULTS AND DISCUSSION
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Sorption Kinetics and Isotherms
Figure 1
shows the results of sorption kinetics of Cd on the three soils at low and high (10–5 and 10–3 M) Cd concentrations. Table 3 summarizes the apparent equilibrium time and first-order rate coefficients of batch kinetics, which correlate with the significance of rate-limited sorption. A larger fraction of initial Cd (C/C0) remained with the 10–3 M solution than with the 10–5 M solution (Fig. 1a and 1b), reflecting a weaker average binding strength at a higher concentration. Following an initial instantaneous uptake, the fraction of rate-limited sorption (i.e., gradually sorbed toward apparent equilibrium) was smaller for sorption of the 10–3 M than the 10–5 M solution. It appears that, at high concentration, apparent equilibrium was reached faster and the rate coefficients were larger. Faster sorption kinetics at higher concentration is consistent with the theory of diffusion-controlled processes that are, in part, controlled by a concentration gradient (Divincenzo and Sparks, 1997; Yin et al., 1997). The extent of increase in the rate coefficient was not sufficiently large, however, to account for the reduction in equilibrium time. Therefore, how the fractionation of Cd sorption on soils changed with concentration was subsequently investigated with sequential extraction of Cd-loaded soil samples of batch kinetics and column studies.
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Fig. 1. Sorption kinetics of Cd of soils from The Hong Kong University of Science and Technology (UST), Tai Mo Shan (TMS), and Clearwater Bay (CWB) at: (a) 10–5 M; (b) 10–3 M. The pH was 5.0 ± 0.2. Each point is the average of triplicates. Error bars are standard deviations that are often smaller than the symbols.
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Figure 2
illustrates the Cd sorption isotherms of the three soils with equilibrium concentrations ranging from 0 to 10–3 M, which indicate the degree of sorption nonlinearity at the range of concentration of interest. The extent of Cd sorption on the UST soil was the largest, followed by the CWB soil, with the smallest on the TMS soil; yet the difference diminished with increasing concentration. A Freundlich isotherm was used to fit the data in two ranges (0–10–4 M and 0–10–3 M); the results are given in Table 3. It is well known that the Freundlich isotherm is linear at sufficiently low concentrations. The linear sorption range of the three soils was shown to be up to 10–4 M, where the nonlinearity exponents of the Freundlich isotherm were >0.943. When the concentration range was as high as 10–3 M, Cd sorption was obviously nonlinear, with n values lying between 0.811 and 0.886. Nonlinearity exponent n of <1 has been commonly reported for heavy metals (Selim and Amacher, 2001), demonstrating that the heterogeneity of soil sorption sites has a range of affinities for metal ions. The smaller value of n in the UST soil compared with the other two soils suggests that the average binding strength in the UST soil varied more dramatically as the sorption density changed. This probably correlates to a greater distribution change of predominant sorption sites or characteristics of the UST soil with increasing concentration, which was subsequently investigated with sequential extraction. Overall, the UST soil displayed slower sorption and more nonlinear sorption than the TMS or CWB soils.
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Fig. 2. Sorption isotherms of Cd (log scale) of soils from The Hong Kong University of Science and Technology (UST), Tai Mo Shan (TMS), and Clearwater Bay (CWB). The pH values ranged between 4.7 and 5.0. Each point is the average of triplicates and error bars represent the standard deviation (often smaller than the symbols). Freundlich isotherms yielded r2 > 0.98.
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Sequential Extraction
The change of sorbed Cd fractionation with concentration was evaluated with the aid of sequential extraction, an operational scheme extracting Cd from exchangeable to residual fractions (Table 2). Previous assessment of the sequential extraction method revealed its utility for a qualitative analysis of metals in soils, despite possible limitations of incomplete selectivity of extractants and redistribution of metals during the extraction process (Lo and Yang, 1998). The extracted fractions are operationally defined with increasing metal binding strength. Each fraction is not necessarily reflective of a single soil component or homogeneous sorption. For instance, sorption of the exchangeable fraction always involves both clay minerals and organic matter, and sorption of the organic matter fraction occurs at heterogeneous high-affinity binding sites located on different functional groups of organic matter. The five fractions of sequential extraction can be categorized in terms of binding strength; sorption as readily exchangeable ions on the first two fractions is regarded as nonspecific, while high-strength sorption of ions to specific sites of the latter three fractions is considered specific.
A preliminary study performing sequential extraction on soil samples of batch kinetics (not shown) indicates that specific sorption of Cd required a much longer reaction time (about 1 d) to reach equilibrium than nonspecific sorption (<30 min). Specific sorption of Cd has also been shown to be time dependent and the use of kinetic rather than equilibrium sorption is recommended for specific sorption (Selim and Amacher, 2001), since sorption of high binding strength is likely to be slow (Yin et al., 1997). Conversely, nonspecific sorption of Cd on these soils with little micropore volume (Table 1) tends to proceed instantaneously. Therefore, the amount of specific sorption determined from sequential extraction is correlated with the amount of rate-limited sorption that results in nonequilibrium transport behavior.
The relative distribution and sorbed amount of Cd on the three soils are summarized in 3. At 10–5 M Cd loading, the UST soil sorbed a slightly less amount of Cd in the oxide fraction but a substantially larger amount in the organic matter fraction compared with the other two soils. The sorbed amount in the oxide fraction appears to follow the corresponding Fe content of the soils (UST < TMS < CWB). The amount of Cd in the organic matter fraction (UST > TMS 
CWB) was, however, not correlated to the organic C content of the soils (CWB UST > TMS). The organic matter fraction is crucial because it contributes to slow kinetics of metal sorption–desorption (Strawn and Sparks, 2000). It seems that, in comparison with the quantitative amount of soil organic matter, the corresponding chemical characteristics such as phenolic and carboxylate content, age, and macromolecular structure (Christl et al., 2001; Otto et al., 2001; Tipping, 2002) are more influential on rate-limited Cd sorption. Since surface precipitation of Cd is unlikely in view of its large ionic radius (Voegelin et al., 2002), inner sphere complexation appears to largely contribute to specific sorption. Inner sphere complexes of Cd can be formed with S-, O-, or N-containing functional groups of soil organic matter (Otto et al., 2001; Karlsson et al., 2005) and at the edge- or corner-sharing sites of Fe oxide mineral surfaces (Collins et al., 1999; Randall et al., 1999), as verified by spectroscopic studies at pH values similar to this study. Sorption via inner sphere complexation is often found to be rate limited, which is attributed to surface diffusion toward these high-energy sites (Scheinost et al., 2001).
With increasing Cd loading from 10–5 to 10–3 M, the fractionation in the soils changed because sorption on different fractions increased to varying extents ( 3). The sorbed amount of exchangeable fraction increased substantially, whereas the amounts of other fractions, organic matter and residual fractions in particular, increased to a much lesser extent. It is indicative that exchangeable sites for nonspecific sorption are abundant but high-strength binding sites for specific sorption are of limited availability, which were mostly occupied even at 10–5 M Cd loading. As a result, the relative percentage of exchangeable fraction increased from <60% to about 90%, while the contribution of specific sorption to total sorption became insignificant (<5% for the three fractions in total). Thus, rate-limited sorption appears to be of great importance only at low concentration.
Cadmium Transport Behavior in Soils
As for the miscible displacement experiments, Fig. 3
displays the BTCs of Cd in the UST soil columns at four influent concentrations ranging from 10–5 to 10–3 M; Fig. 4
shows the Cd BTCs of 10–5 and 10–3 M in both the TMS and CWB soils. Parameter values of different transport models are listed in Table 4. The effluent pH values lay between 4.7 and 5.1. In general, Cd transport was more retarded (i.e., larger R values) at a lower input concentration, in line with previous studies (Streck et al., 1995; Hu and Brusseau, 1998). The dependence of retardation on concentration corroborated nonlinear sorption of Cd. Since sorption was more nonlinear in the UST soil than the TMS and CWB soils, as shown by batch isotherms, there was a greater reduction in retardation of Cd transport with increasing concentration.
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Fig. 3. Experimental data and optimized simulations for Cd transport in soil from The Hong Kong University of Science and Technology at four input concentrations: (a) 10–5 M; (b) 5 x 10–5 M; (c) 10–4 M; and (d) 10–3 M.
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Fig. 4. Experimental data and optimized simulations for Cd transport in Tai Mo Shan soil at input concentrations of (a) 10–5 M and (b) 10–3 M, and in Clearwater Bay soil at (c) 10–5 M and (d) 10–3 M.
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Table 4. Parameter estimates obtained during the application of the linear nonequilibrium, nonlinear equilibrium, and nonlinear nonequilibrium models to Cd miscible displacement experiments at input concentrations ranging from 10–5 to 10–3 M.
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The Cd BTCs of the UST soil were asymmetric (Fig. 3). At 10–5 M, both linear equilibrium and nonlinear equilibrium models failed to describe the early breakthrough and long tailing (Fig. 3a). Conversely, nonequilibrium transport models accounting for rate-limited sorption, either linear or nonlinear, provided a good fit to the experimental data. It is not surprising that the goodness-of-fit of simulations (r2 > 0.97) could not noticeably differentiate themselves (Table 4). It is favorable to identify the most important factor controlling the transport behavior and leave out unnecessary (i.e., less important) concerns under different conditions. The multiple approaches of this study were thus insightful and essential, where sorption was shown to be linear at the low range of concentration by batch isotherms and rate-limited specific sorption was found significant by sequential extraction. Besides, flow interruption induced an increase in effluent concentration, which is a sign of rate-limited sorption (Brusseau et al., 1997). Therefore, Cd transport at sufficiently low concentration can be described as linear and nonequilibrium.
In contrast, for the Cd BTC of 10–3 M (Fig. 3d), linear equilibrium model simulation underestimated the tailing of the elution front and linear nonequilibrium model simulation overestimated the tailing of the sorption front. Nonlinear model simulations (equilibrium or nonequilibrium) successfully described the data and coincided with each other. Similarly, comparing the goodness-of-fit of simulations (r2 > 0.98) is not conclusive (Table 4). In light of the above results, batch isotherms indicated that sorption was apparently nonlinear at the high range of concentration, and sequential extraction suggested that rate-limited sorption should be minimal. Flow interruption producing no perturbation in effluent concentration testified the unimportance of rate-limited sorption (Brusseau et al., 1997; Wang et al., 1998). As a result, additional consideration of rate-limited sorption (and thus nonequilibrium) is not necessary for transport modeling. In other words, transport behavior at sufficiently high concentration can be considered nonlinear and equilibrium. At intermediate concentrations of 5 x 10–5 and 10–4 M (Fig. 3b and 3c), both rate-limited sorption and nonlinear sorption may influence the transport behavior so that the nonlinear nonequilibrium model may be needed.
The influences of rate-limited sorption and nonlinear sorption on transport behavior were, however, less explicit in the TMS and CWB soils (Fig. 4). Nonequilibrium models (linear or nonlinear) slightly better simulated the Cd BTCs at 10–5 M (Fig. 4a and 4c) than equilibrium models, along with a small perturbation on flow interruption. The effect of rate-limited sorption appears minor. On the other hand, nonlinear models (equilibrium or nonequilibrium) fitted the Cd BTCs at 10–3 M (Fig. 4b and 4d) better than linear models. The sorption was slightly nonlinear (n > 0.88, Table 4). From the results of batch experiments and sequential extraction (Table 3), sorption on the TMS and CWB soils possessing less rate-limited specific sorption (organic matter fraction especially) was also fast and less nonlinear compared with the UST soil. The three soils taken from different origins exhibited varying degrees of rate limitation and sorption nonlinearity, probably because of their different characteristics including surface area, clay content, amount and crystallinity of mineral oxides, and quantity, age, and macromolecular structure of organic matter. In particular, soil organic matter may be responsible for rate-limited sorption, inferred from the correlation between the amount of the organic matter fraction and the extent of nonequilibrium; however, the relationship between the significance of rate-limited sorption and physicochemical properties cannot be concluded in this study. An extensive and specifically designed investigation is required in the future.
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CONCLUSIONS
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Asymmetric transport behavior can be ascribed to nonlinear sorption or rate-limited sorption on soils. This study demonstrated the capability of multiple approaches, combining batch, sequential extraction, and column experiments, to analyze the relative contribution of sorption nonlinearity and rate-limited sorption to Cd transport behavior in the three soils. Modeling the transport data alone is inconclusive because of similar goodness-of-fit of various transport models. Batch isotherms suggested the range of concentration where sorption can be regarded as linear. Batch kinetics and sequential extraction provided information about the apparent equilibrium time and the amount of specific sorption, and thus the significance of rate-limited sorption at different Cd loadings. The impact of rate-limited sorption was critical at low concentration, but insignificant at high concentration where sorption nonlinearity predominated. This may be attributed in part to a faster diffusion process but mainly to the saturation of low-capacity rate-limited specific sorption, of which the contribution to total sorption becomes unnoticeable in the case of high Cd loading. From the results of the multiple approaches, Cd transport can be regarded as linear and nonequilibrium at 10–5 M, whereas it is considered nonlinear and equilibrium at 10–3 M. In this study, sequential extraction was successfully used to give an insight into the significance of rate-limited specific sorption and the corresponding chemical nonequilibrium transport behavior across a range of Cd concentrations.
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NOTES
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All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.
Received for publication August 26, 2006.
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ABSTRACT
INTRODUCTION
