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SOIL CHEMISTRY

Theoretical Solid/Solution Ratio Effects on Adsorption and Transport: Uranium(VI) and Carbonate

^a Dep. of Civil Engineering, 238 Harbert Engineering, Center Auburn Univ., Auburn, AL 36849
^b Dep. of Geology and Geophysics, Univ. of Wisconsin, 1215 W. Dayton St., Madison, WI 53706

^* Corresponding author (barnettm{at}eng.auburn.edu).

	ABSTRACT

TOP ABSTRACT INTRODUCTION MODELING RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
The reactive transport of metal and radionuclide contaminants in the subsurface often significantly influences their long-term fate and effect in the environment. Typically, predictions of contaminant migration at a site involve the measurement of a distribution coefficient (K_D), which is used to describe the interactions between the contaminant and the subsurface. The typical implicit assumption is that the adsorption isotherm (e.g., K_D) is independent of the solid/solution ratio. Many geochemical factors, however, play a significant role in the reactive transport of contaminants in groundwater. The adsorption and transport of U(VI), for example, is strongly influenced by the presence of Fe oxyhydroxides and the carbonate system. However, these solutes or adsorbates and adsorbent interact with one another in a complex and highly nonlinear manner. Modeling of U(VI) adsorption has shown that under certain conditions, the solid/solution ratio can theoretically have a significant impact on the U(VI) adsorption isotherm. In particular, combining strongly interacting solutes [U(VI) and carbonate] and adsorbents [Fe(III) oxyhydroxides] that have monocomponent solute or adsorbate adsorption isotherms that are independent of the solid/solution ratio results in a multicomponent system where adsorption isotherms become dependent on the solid/solution ratio. The solid/solution ratio can therefore be critical when extrapolating the results of batch experiments, generally conducted at low solid/solution ratios, to column experiments and then to the field. These results have implications for modeling, scaling, and predicting the reactive transport of U(VI) and other strongly interacting solutes (e.g., metals and dissolved organic C) in subsurface environments.

	INTRODUCTION

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One of the most vexing problems in evaluating metal- and radionuclide-contaminated sites is the need to predict their reactive transport in the subsurface to accurately assess risks and guide remedial activities (Davis et al., 2004). The issue of scaling (e.g., in extending predictions of contaminant mobility from the laboratory to the field) is particularly important (Davis et al., 2004). The standard approach to predicting the subsurface transport of metals and radionuclides is the retardation factor (R_F) (Puigdomenech and Bergstrom, 1995; Jenne, 1998). Although limitations to this approach have been recognized, it is nonetheless still a commonly used approach (Bethke and Brady, 2000).

To determine R_F, representative samples of the subsurface material are taken. The partitioning of the contaminant of interest to the subsurface material is then measured in a batch experiment, where an adsorption isotherm is obtained by plotting the equilibrium adsorbed solid-phase contaminant concentration (q, mass or moles of solute per mass of adsorbent) against the equilibrium aqueous phase concentration (C, mass or moles of adsorbate per volume of solution). Commonly, a linear model is used to describe the data (Bethke and Brady, 2000), in which case, a partition coefficient (K_D, e.g., cm³ kg^–1) is related to q and C by

[1]

The K_D is then used to calculate the R_F:

[2]

where _B represents the bulk density of the solid (g cm^–3), while represents the porosity of the saturated soil (m³ m^–3). The R_F represents the rate of movement of the contaminant relative to the average groundwater velocity. The explicit assumptions used in deriving the R_F are linear adsorption (Eq. [1]) and instantaneous adsorption–desorption equilibrium.

In batch experiments, for experimental convenience (e.g., to aid in separating the aqueous phase from the solid phase, maintaining the aqueous solute concentration above the detection limit, etc.), typically a much lower solid/solution ratio is used than would be encountered in the field. The solid/solution ratio is defined here as the mass of the solid (e.g., g) divided by the volume of the liquid in contact with that solid (e.g., L). Although adsorption is most directly related to the number of moles of adsorption sites per liter of solution rather than the total grams of solid per liter of solution, these expressions are related to one another by constants (e.g., moles of Fe per kilogram of solid, moles of surface sites per mole of Fe, surface area per mole of Fe, etc.). Thus, specifying one of these parameters (e.g., the solid/solution ratio) specifies the others as well. An implicit assumption is that K_D is independent of the solid/solution ratio (USEPA, 1999). If K_D is a function of the solid/solution ratio, the K_D measured from a batch experiment solid/solution ratio could not be used to accurately predict transport at a field-relevant scale (USEPA, 1999). Assuming a typical field soil with a bulk density of 1.5 g cm^–3 and a porosity of 0.4, the solid/solution ratio is 3750 g L^–1. In contrast, a typical batch experiment may have a solid/solution ratio as low as 3.0 g L^–1.

Variations in K_D with solid/solution ratio have occasionally been reported, sometimes termed the "solids [or particle] concentration effect," typically a decrease in batch-measured K_D with an increase in the solid/solution ratio (Oscarson and Hume, 1998). There have been varying reports on the importance of the solids concentration effect on the adsorption of metals and radionuclides to solid materials, including whether it is a true phenomenon or the result of experimental artifacts. Numerous reports of a particle concentration effect were described by Honeyman and Santschi (1988). Subsequently, McKinley and Jenne (1991) reviewed the extant literature and conducted their own experiments, recognizing that the solids concentration effect, if real, "would require scaling of [adsorption] constants, defined in dilute suspensions, to the greater effective sediment concentrations encountered in the field." No solids concentration effect was observed, and other reported instances of this phenomenon were attributed to experimental errors or errors in data reduction (McKinley and Jenne, 1991).

More recent literature has also offered contradictory observations of a solids concentration effect and consequently the applicability of batch-measured adsorption isotherms to reactive transport in packed columns or in the field. Whether or not a solids concentration effect is observed, and even which direction it will take (i.e., increasing or decreasing adsorption), can depend on the relative amounts of adsorbate and adsorbent and the degree of interaction between them (Harter and Naidu, 2001). At times, generally good predictions of cation transport behavior in porous media have been obtained from independent batch adsorption data (Allen et al., 1995; Pang and Close, 1999; Papini et al., 1999; Vulava et al., 2000, 2002). Solids concentration effects are still reported frequently (Hemming et al., 1997; Porro et al., 2000), however, and have been attributed to a variety of causes, including the presence of colloids (Pham and Garnier, 1998; Sen et al., 2002), particle–particle interactions (Pabalan et al., 1998), kinetic effects (Pan and Liss, 1998), insufficient prewashing of the soil with the background electrolyte to remove preadsorbed ions (Grolimund et al., 1995), and heterogeneous media (Wise, 1993; Szecsody et al., 1998).

To the extent that the solid concentration effect is an experimental artifact, carefully designed and conducted batch experiments at low solid/solution ratio can be used to measure K_Ds and calculate R_Fs (with their explicit assumptions and attendant limitations) that can be used to accurately describe contaminant transport in the field (i.e., the model is properly scaled). To the extent that the solids concentration effect is due to real phenomena, K_Ds and R_Fs determined from batch experiments at low solid/solution ratio will not accurately describe contaminant transport in the field (i.e., the model is improperly scaled).

The purpose of this study was to examine the theoretical interactions between two reactive cosolutes, U(VI) and carbonate, and an Fe(III) oxyhydroxide adsorbent through the use of a surface complexation model to demonstrate the theoretical importance of the solid/solution ratio in controlling U(VI) adsorption in this system. Using a model, we show that this solid/solution ratio effect, far from being a simple experimental artifact, is consistent with the current paradigm of thermodynamic surface complexation models. We thus show that the standard methodology for predicting U(VI) transport (measuring a K_D and calculating a R_F) in the presence of a reactive cosolute like carbonate could lead to incorrect predictions of U(VI) transport, even if the linear, local equilibrium conditions are valid. These results may be applicable to other strongly interacting cosolutes (e.g., metals and dissolved organic C) in subsurface environments as well.

	MODELING

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Past research has suggested the U(VI) adsorption in near-surface environments is controlled primarily by interactions with Fe(III) oxyhydroxides (Payne et al., 1994; Barnett et al., 2000; Bostick et al., 2002). A variety of geochemical parameters, including pH, ionic strength, and the presence of other ions, especially carbonate, can affect the adsorption characteristics of U(VI) to Fe(III) oxyhydroxides (Villalobos et al., 2001). Uranium(VI)–Fe(III) oxyhydroxide–carbonate interactions have been extensively documented in the literature. Waite et al. (1994) developed a surface complexation model to describe the pH-dependent adsorption of U(VI) to hydrous ferric oxide (HFO) in the presence of carbonate. This model is an extension of the generalized two layer model (Dzombak and Morel, 1990), where U(VI) reacts with "strong" and "weak" surface hydroxyl groups on HFO to form bidentate surface complexes. The model has proven to successfully predict the pH-dependent partitioning of U(VI) to heterogeneous subsurface materials under the assumption that U(VI)–Fe(III)–carbonate interactions were governing the partitioning of U(VI) to these materials (Waite et al., 2000; Barnett et al., 2002; Logue et al., 2004). This model was used here to simulate the highly complex and nonlinear interactions between U(VI), carbonate, and HFO in relation to the solid/solution ratio in systems with fixed carbonate concentrations (i.e., closed systems).

The chemical reactions of the model (Table 1) were taken directly from Waite et al. (1994) as summarized in Barnett et al. (2002). The equilibrium problem was solved by using a FORTRAN version of a modified MICROQL software algorithm (Westall, 1979a, 1979b) that allowed the input of distinct mass-action and mass-balance matrices. Several theoretical adsorption isotherms at varying solid/solution ratios and carbonate concentrations were calculated (Table 2). The total (aqueous plus adsorbed) concentration of U(VI) was varied to produce theoretical isotherms with equilibrium aqueous U(VI) concentrations ranging from 0 to 5 µM. A closed system was simulated with the total carbonate concentration (aqueous plus adsorbed) held constant and thus simulating, for example, U(VI) adsorption and transport in saturated groundwater isolated from the atmosphere. The values for the Fe content came from a naturally occurring, Fe-oxide-coated sand from Oyster, VA (McIndoe, 2004) with a dithionite–citrate–bicarbonate-extractable Fe content of 115 µmol g^–1. Based on the results of previous research (Barnett et al., 2002; Logue et al., 2004), all the extractable Fe was assumed to be HFO for the purpose of modeling U(VI) adsorption. The theoretical solid/solution ratio was varied across a range of 3.33 to 333 g of Fe(III)-coated sand per liter of solution, a reasonable range of experimental values. The values of >Fe_wOH (weak surface sites) and >Fe_sOH (strong surface sites) shown in Table 2 are the respective total site concentrations used in the model for each case. The solid/solution ratio is related to the surface site concentrations, [>Fe_wOH] and [>Fe_sOH], by their respective site density. The total site density used was 0.875 mol sites mol^–1 Fe, with 0.0018 mol strong sites mol^–1 Fe and the remainder weak sites, as all parameters were taken directly from Waite et al. (1994). The solid loading corresponding to each solid/solution ratio listed in the last column of Table 2 is the product of mass of HFO per mass of soil (about 1.02 · 10^–2) and soil/solution ratio. The ionic strength of the system was held constant at 0.1 M for all simulations, as this was the ionic strength originally used to develop the adsorption model.

View this table: [in this window] [in a new window]   Table 1. Reactions included in model (temperature T = 25°C, ionic strength I = 0.1 M).

View this table: [in this window] [in a new window]   Table 2. Calculated isotherms (pH = 7, ionic strength I = 0.1 M).

	RESULTS AND DISCUSSION

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View larger version (14K): [in this window] [in a new window]   Fig. 1. Calculated adsorption isotherms in the absence of carbonate. A, B, and C correspond to the cases shown in Table 2.

View larger version (16K): [in this window] [in a new window]   Fig. 2. Calculated adsorption isotherms as a function of solid/solution ratio with total carbonate of 0.01 M. G, H, and I correspond to the cases shown in Table 2.

In the model, three direct types of U(VI)–carbonate interactions take place: (i) U(VI) and carbonate form aqueous complexes (Reactions 11–14 in Table 1); (ii) U(VI) and carbonate compete for surface sites (Reactions 19–20 and 25–26 in Table 1); and (iii) U(VI)–carbonate complexes adsorb together as ternary surface complexes (Reactions 21–22 in Table 1). In addition, carbonate can also have a fourth indirect effect on U(VI) adsorption: (iv) carbonate adsorption can lower the surface potential (Reaction 26 in Table 1), thereby decreasing the adsorption of anionic ternary U(VI)–carbonate surface complexes (Reactions 21–22 in Table 1), although this effect is reportedly minor (Wazne et al., 2003). In contrast, the surface potential does not affect the adsorption of neutral U(VI) surface complexes (Reactions 19–20 in Table 1) either way. Overall, Interactions i, ii (aqueous complexation and competition), and iv (lowering the surface potential) act to decrease U(VI) adsorption in the presence of carbonate, whereas Interaction iii (formation of ternary surface complexes) acts to increase U(VI) adsorption in the presence of carbonate.

Additional simulations were conducted to elucidate the relative importance of these interactions in producing the solid/solution ratio effect shown in Fig. 2. Figure 3 shows that at a constant solid/solution ratio, the calculated U(VI) adsorption isotherm decreases with an increase in total carbonate concentration [e.g., the adsorbed U(VI) concentration in equilibrium with a given aqueous U(VI) concentration decreases as the total carbonate concentration increases], consistent with an array of published experimental data (Barnett et al., 2002). If Interaction iii, ternary U(VI)–carbonate complexes adsorbing to the surface, controlled the theoretical interaction between U(VI) and carbonate, the plot in Fig. 3 would show the opposite effect [i.e., U(VI) adsorption isotherms would increase with an increase in total carbonate]. This rules out Interaction iii as the predominate interaction controlling U(VI) and carbonate interactions in this model. To determine which of the remaining interactions, aqueous complexation of U(VI) by carbonate (Interaction i), competition between U(VI) and carbonate for adsorption sites (Interaction ii), or lowering the surface potential (Interaction iv), controls the interaction between U(VI) and carbonate, additional adsorption isotherms were calculated in the absence of U(VI)–carbonate aqueous complexes (i.e., Interaction i) by temporarily deleting Reactions 11 to 14 from the model. As stated above, the total U(VI) concentration is <5% of the total carbonate concentration, thus "turning off" these U(VI)–carbonate aqueous complexes dramatically affects U(VI) speciation but has only minimal effects on carbonate speciation. The result is shown in the calculated U(VI) adsorption isotherms in Fig. 4 . In the absence of aqueous U(VI)–carbonate complexes (Interaction i, Reactions 11–14), the addition of 0.01 M carbonate increases the adsorption across the entire isotherm, the opposite of the overall effect observed in Fig. 3. This result thus illustrates that the formation of aqueous U(VI)–carbonate complexes (Interaction i) rather than the competition between U(VI) and carbonate for surface sites (Interaction ii) or carbonate adsorption lowering the surface potential (Interaction iv) is responsible for the decrease in U(VI) adsorption isotherms in the presence of carbonate shown in Fig. 3. Additional calculated isotherms similar to Fig. 4 at a different solid/solution ratio (3.33 g L^–1, not shown) produced similar results.

View larger version (17K): [in this window] [in a new window]   Fig. 3. Calculated adsorption isotherms with solid/solution ratio set at 3.33 g L–1 with carbonate concentration varying from 0.0 to 0.01 M. A, D, and G correspond to the cases shown in Table 2.

View larger version (19K): [in this window] [in a new window]   Fig. 4. Calculated adsorption isotherms at a solid/solution ratio of 333 g L–1. O, C, and I correspond to the cases shown in Table 2.

View larger version (14K): [in this window] [in a new window]   Fig. 5. Calculated percentage of surface sites occupied by the adsorbed species at a solid/solution ratio of 333 g L–1 and total carbonate (CTCO3) = 0.01 M, Case I in Table 2.

View larger version (15K): [in this window] [in a new window]   Fig. 6. Calculated percentage of surface sites occupied by the adsorbed species at a solid/solution ratio of 333 g L–1 and total carbonate (CTCO3) = 0.01 M in the absence of U(VI)–carbonate aqueous complexes, Case O in Table 2.

As the solid/solution ratio is increased at a fixed total carbonate concentration [e.g., to produce the U(VI) isotherms shown in Fig. 2], the aqueous carbonate concentration decreases (Fig. 7 ). Points I to IV in Fig. 7 correspond to solid/solution ratios of 3.33, 33.3, 99.9, and 333 g L^–1, respectively, at a fixed total carbonate concentration of 0.01 M. In the absence of U(VI) [or if the U(VI) concentration is too small to significantly impact carbonate adsorption as in this instance], Points I to IV of Fig. 7 still fall on the carbonate adsorption isotherm, as shown in Fig. 8 ; however, since the aqueous carbonate concentration, which strongly affects U(VI) adsorption (Fig. 3–6), is dependent on the solid/solution ratio (Fig. 7), the resulting U(VI) adsorption isotherm (Fig. 2) then itself becomes dependent on the solid/solution ratio.

View larger version (11K): [in this window] [in a new window]   Fig. 7. Calculated total aqueous carbonate vs. solid/solution ratio with a total carbonate of 0.01 M (pH = 7, ionic strength I = 0.1 M). The total aqueous carbonate is dependent on the solid/solution ratio, but all of the points (I–IV) still fall on the carbonate adsorption isotherm (Fig. 8).

View larger version (14K): [in this window] [in a new window]   Fig. 8. Calculated adsorption isotherm for carbonate at a solid/solution ratio of 333 g L–1 (Case M in Table 2). In the absence of U(VI), the carbonate isotherm is independent of the solid/solution ratio (not shown). Points I to IV correspond to the same points as in Fig. 7.

	CONCLUSIONS

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The solid/solution ratio is a potentially important parameter governing U(VI) adsorption in the presence of carbonate. Model calculations clearly show that the adsorption isotherm is theoretically dependent on the solid/solution ratio in the presence of fixed carbonate concentration, as predicted by the current surface complexation adsorption equilibrium paradigm. In particular, the adsorption of U(VI) to Fe(III)-containing materials at a fixed carbonate concentration increases with an increase in solid/solution ratio. These results are consistent with the earlier experimental results of Barnett et al. (2000), who showed that adsorption isotherms measured in batch experiments at a relatively low solid/solution ratio underpredicted the adsorption capacity of U(VI) observed in water-saturated packed columns (e.g., closed to carbonate transfer) at higher effective solid/solution ratios. A very similar effect was also recently experimentally documented by Zheng et al. (2003). We have also subsequently documented this same effect [i.e., a strong dependence of U(VI) on the solid/solution ratio at a fixed ligand concentration] experimentally in the U(VI)–Fe(III)–phosphate system (Cheng et al., 2006), which behaves in a similar manner.

Two additional points bear mentioning, however. First, the particular phenomena documented here will only be operative in systems with fixed total carbonate concentrations and not in systems with a fixed carbonate species activity (e.g., an open system where equilibrium with a constant CO₂ partial pressure is maintained). In open systems with total carbonate free to enter or exit the system as needed to maintain equilibrium with a fixed carbonate species, the total carbonate concentration will be independent of the solid/solution ratio (all other conditions being the same), eliminating the causative factor of the phenomena demonstrated here. Second, it should also be noted that, strictly speaking, adsorption isotherms are not related simply to the absolute value of the solid/solution ratio, but to the relative (i.e., to one another) concentrations of adsorbents, adsorbates, and solutes. The important point in both instances is that all of these variables must be controlled (e.g., batch adsorption experiments should be conducted at exactly the same conditions as the field) or accounted for (e.g., in a model that captures all of the molecular-scale interactions); otherwise estimates of field-scale contaminant transport based on laboratory-measured parameters may be in error.

The conclusions from our theoretical study may apply to other strongly interacting cosolutes, such as metals and dissolved organic C, as well. For example, batch-measured Freundlich adsorption constants for Cu needed to be adjusted for the solid/solution ratio to account for the variation of DOC between the batch and the field (Elzinga et al., 1999). The adsorption of Pb and Cd onto kaolonite interacted in a complex manner with organic acids (e.g., organic waste degradation products), leading to a strong dependence of K_D on the solid/solution ratio (Puls et al., 1991). Other complex multisolute reactive transport systems have also proven difficult to describe using a single adsorption isotherm obtained in batch experiments (Rennert et al., 2003). Polzer et al. (1992) also demonstrated the limitations of empirical models in capturing similar effects by deriving theoretical relationships for a binary ion exchange system.

Our results indicate that the common if implicit assumption that the adsorption of U(VI) and other metals is independent of the solid/solution ratio may not be correct in all cases. Thus, the standard methodology for predicting the transport of U(VI) (i.e., measuring an adsorption isotherm at a solid/solution ratio much lower than that present in the field) could lead to incorrect conclusions about the mobility of U(VI) in the presence of carbonate at field-scale solid/solution ratios. Hence, reactive transport models that explicitly allow the solid/solution ratio effect to be taken into account and that accurately capture the correct multicomponent, molecular-scale interactions between solutes, adsorbates, and adsorbents (e.g., surface complexation models), are required to accurately predict the transport of U(VI) in the subsurface.

	ACKNOWLEDGMENTS

 
This research was supported by grants DE-FG07-ER6321 and DE-FG02-06ER64213 from the U.S. Department of Energy, Office of Science (BER). The corresponding author appreciates the support of the Dep. of Civil Engineering at Auburn Univ. and the Dep. of Soil Quality, Wageningen Univ. and Research Centre, The Netherlands, for a sabbatical that allowed time to complete an initial draft of the manuscript.

Received for publication April 13, 2006.

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