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Published online 22 August 2006
Published in Soil Sci Soc Am J 70:1677-1687 (2006)
DOI: 10.2136/sssaj2006.0035
© 2006 Soil Science Society of America
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Soil Physics

Modeling the Transport and Retention of Arsenic (V) in Soils

Hua Zhang and H. M. Selim*

Sturgis Hall, Dep. of Agronomy and Environmental Management, Louisiana State Univ. Agric. Center, Baton Rouge, LA 70803-2110

* Corresponding author (mselim{at}agctr.lsu.edu)


   ABSTRACT
TOP
 NOTES
 ABSTRACT
INTRODUCTION
 Multireaction Transport Model
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 
Adsorption and transport of reactive solutes when nonequilibrium conditions are dominant may impact significantly their mobility in heterogeneous systems. In this study, arsenate [As(V)] sorption and transport in three soils having different properties were investigated. Kinetic batch experiments were performed to characterize arsenate [As(V)] adsorption over a wide range of concentrations. Adsorption of arsenate by all soils was strongly nonlinear and kinetic, where the rate of As(V) retention was rapid initially and was followed by gradual or somewhat slow retention behavior with increasing reaction time. Arsenic mobility in soils was investigated using the miscible displacement technique where uniformly packed soil columns under steady and water-saturated flow were used. The column transport experiments indicated strong As(V) retardation followed by slow release or extensive tailing of the breakthrough curves (BTCs). Sharp decrease in As(V) concentration during flow interruption (no flow) further verified the extensive non-equilibrium condition, which was likely due to the dominance of kinetic retention (sorption-release) processes. We evaluated several formulations of a nonlinear equilibrium-kinetic multireaction transport model (MRM) for its prediction capability of As(V) retention as well as transport in all soils. The asymmetrical and retarded BTCs for As(V) from our column experiments were well described using the MRM model. Nonlinear reversible along with a consecutive or concurrent irreversible reactions were the dominant mechanisms in the MRM model. The use of batch rate coefficients as model parameters for the predictions of As(V) BTCs underestimated the extent of retention and overestimated the extent of As(V) mobility for all soils. When utilized in an inverse mode, the MRM model provided good predictions of As(V) BTCs.

Abbreviations: BTC, breakthrough curve • MRM, multireaction transport model • MSMA, monosodium methanearsonate • RMSE, root mean square error


   INTRODUCTION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
Multireaction Transport Model
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 
ARSENIC IS A TOXIC TRACE element widely distributed in soils and aquifers from both geologic and anthropogenic sources. The elevated level of As in many soils caused by applications of As compounds such as pesticides, herbicides, wood preservatives, and livestock feed additives pose threats to surrounding surface and ground water quality. Arsenate [As(V)] is the thermodynamically stable form of As under aerobic condition and interacts strongly with solid matrix.

The movement of As in soils and aquifers is highly dependent on the adsorption–desorption reactions in the solid phase. Iron (Fe) and aluminum (Al) oxides and hydroxides in particular have high affinity to As(V) and form inner-sphere surface complex via a ligand exchange mechanism (Waychunas et al., 1993). The adsorption of As(V) on various Fe- and Al-containing minerals has been extensively investigated (e.g., Goldberg, 2002). Equilibrium models of the Freundlich and Langmuir type are commonly used to describe results of As sorption by soils (e.g., Buchter et al., 1989; Manning and Goldberg, 1997). However, the utility of results from short duration studies for predictions of As fate and transport is questionable because equilibrium conditions are rarely achieved for As transport under field conditions due to a wide variety of biological, chemical, and hydrological factors. The occurrence of non-equilibrium conditions can have significant impact on the transport of As(V) in heterogeneous soil systems. The mechanisms behind the rate-limited sorption and transport of As(V) in soils have not been fully explored. In general, rate-limited processes for reactive solutes are due to physical (transport related) and chemical (sorption related) non-equilibriums. Physical non-equilibrium includes processes such as inter- and intra-particle diffusion within soil aggregates and preferential flow through soil macropores (Brusseau, 1993). Non-equilibrium sorption of As(V) may be due to (i) heterogeneity of sorption sites on the soil matrix, (ii) rate-limited precipitation at mineral surfaces, that is, three dimensional growth of a particular As solid phase, and (iii) slow diffusion to sites within the soil matrix (Zhang and Selim, 2005).

Downward movement of As has been observed in contaminated soils. Isensee et al. (1973) investigated arsenate residual in Metapeake silt loam 14 yr after massive application of arsenical herbicides. Their results showed that a large amount of As remained in the soil profile and the concentration decreased with increasing depth, which is indicative of slow leaching processes. In Australia, McLaren et al. (1998) observed considerable downward movement of As through the soils surrounding cattle dips. They concluded that the migration of As was slow and controlled by soils properties. They showed As concentrations in the subsurface (20–40 cm) near cattle dip sites ranged from 57 to 2282 mg kg–1.

A number of studies were performed in the laboratory to investigate the transport of As in soils. For example, Hiltbold et al. (1974) studied monosodium methanearsonate (MSMA) transport in surface and subsurface soils using field profile sampling, batch experiment, and soil column experiments. Arsenic distribution in soil profile after repeated application of MSMA showed no evidence of leaching. Arsenic Kd values based on batch and column experiments showed extensive discrepancies and were attributed to the short residence time of As in the soil columns.

Other transport studies include that of Melamed et al. (1995) who studied effect of phosphate incubation on leaching of arsenate from packed columns of aggregated Oxisol. Asymmetrical BTCs were observed indicative of physical and/or chemical non-equilibrium during As movement through the columns. Darland and Inskeep (1997a, 1997b) demonstrated the effect of pore water velocity, pH, and phosphate on the transport of arsenate through packed columns of sand with Fe oxides. They found at pH 4.5 and 6.5, AsO4 transport exhibited significant retardation and tailing, while at pH 8.0, BTC of AsO4 was nearly symmetrical. Increase in added PO4 content resulted in an increase in As recovery, decrease in retardation, and symmetrical BTC. Increasing pore volume velocity from 0.2 cm h–1 to 90 cm h–1 increased As recovery from 7.24 to 74.3%. Williams et al. (2003) performed column experiments to investigate As(V) transport through a heterogeneous soil containing Fe oxide. They concluded that the effect of factors affecting As transport increased in the order pH < pore water velocity < phosphate. Attempts to model As BTCs from the soil columns showed that the use of linear or Freundlich (equilibrium) retention mechanisms describe neither the extent of retardation nor the release (desorption) during leaching.

A literature search revealed that only few studies focused on the kinetics of As(V) retention during transport in soils. Kinetic adsorption data has the advantage of accounting for the nonequilibrium sorption behavior, which may occur due to heterogeneities of sorption sites and diffusion processes in the interface between the liquid phase and the soil matrix. The objectives of this study were (i) to determine the adsorption kinetics and transport behavior of As(V) in three soils having different properties; and (ii) to test the applicability of different formulations of a multireaction (equilibrium-kinetic) transport model (MRM) in simulating kinetic sorption and transport of As(V) in soils.


   Multireaction Transport Model
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 Multireaction Transport Model
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 
The classical convection-dispersion equation (CDE) was used to describe the one-dimensional steady-state transport of reactive solute through porous media (Selim et al., 1989):

Formula 1[1]
where C is solute concentration (µg cm–3), S is amount sorbed by the soil matrix (µg g–1), x is distance (cm), t is time (h), D is hydrodynamic dispersion coefficient (cm2 h–1), {rho} is soil bulk density (g cm–3), and {theta} is volumetric water content (cm3 cm–3). In addition, v is pore water velocity (cm h–1) where v = q/{theta}, and q is Darcy's water velocity (cm h–1).

Recent approaches based on soil heterogeneity and kinetics of adsorption–desorption have been proposed for the purpose of describing the time-dependent sorption of heavy metals in the soil environment. The multireaction kinetic approach presented here considers several interactions of heavy metals with soil matrix surfaces (Amacher et al., 1988; Selim et al., 1992). Specifically, the model assumes that a fraction of the total sorption sites is kinetic in nature whereas the remaining fractions interact rapidly or instantaneously with solute in the soil solution. The model accounts for reversible as well as irreversible sorption of the concurrent and consecutive type (Fig. 1 ). The model chosen in this analysis can be presented in the following formulation:

Formula 2[2]

Formula 3[3]

Formula 4[4]

Formula 5[5]
where Se is the amount retained on equilibrium sites (mg kg–1), Sk is the amount retained on kinetic type sites (mg kg–1), Si is the amount retained irreversibly by consecutive reaction (mg kg–1), Sirr is the amount retained irreversibly by concurrent type of reaction (mg kg–1), n and m are dimensionless reaction order commonly <1, Ke is a dimensionless equilibrium constant, k1 and k2 (h–1) are the forward and backward reaction rates associated with kinetic sites, respectively, k3 (h–1) is the irreversible rate coefficient associated with the kinetic sites, and kirr (h–1) is the irreversible rate coefficient associated with solution. For the case n = m = 1, the reaction equations become linear. In the above equations we assumed n = m since there is no known method for estimating n and/or m independently (Amacher et al., 1988). The total amount of solute retention on soil is:

Formula 6[6]
The kinetic sorption data obtained from batch experiment and BTC data from column experiments were fitted to the MRM described above using Levenberg-Marquardt nonlinear least square optimization method (Press et al., 1992). Statistical criteria used for estimating the goodness-of-fit of the models to the data were the coefficients of determination r2 and the root mean square error (RMSE).

Formula 7[7]
where Cobs = observed As(V) concentration at certain time t, Cmod = simulated As(V) concentration at time t, nobs = number of measurements, and npar = number of fitted parameters.


Figure 1
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  		Fig. 1. A schematic diagram of the multireaction transport model (MRM). Here C is concentration in solution, Se, Sk, Si, and Sirr are the amounts sorbed on equilibrium, kinetic, and irreversible sites, respectively, where Ke, k1, k2, k3, and kirr are the respective rates of reactions.

 

   MATERIALS AND METHODS
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 Multireaction Transport Model
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 
Three soils from the Ap horizon (0–10 cm) of Olivier loam (fine-silty, mixed, thermic Aquic Fragiudalf), Sharkey clay (very fine, montmorillonitic, nonacid, thermic, Vertic Haplaquept), and Windsor sand (mixed, mesic Typic Dipsamment) were used in this study (Table 1). These soil samples were collected from Louisiana (Sharkey and Olivier) and New Hampshire (Windsor). The soils were air-dried and passed through a 2-mm sieve before use. They were analyzed for pH using 1:1 soil/water paste, for organic matter using the acid dichromate oxidation method, for free iron oxides by the dithionite-citrate-bicarbonate method, and for cation exchange capacity of the acid soils by exchange with 0.1 M BaCl2–0.1 M NH4Cl.


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  		Table 1. Selected physical and chemical properties of the studied soils.

 
Batch Kinetics
Kinetic retention of As(V) was studied using the batch method described by Selim et al. (1992). According to the procedure, triplicate 3-g samples of each soil were placed in polypropylene tubes and mixed with 30-mL solutions of known As(V) concentrations. Six initial As(V) concentrations (Co) were used, namely 5, 10, 20, 40, 80, and 100 mg L–1. Reagent-grade KH2AsO4 was prepared in 0.01 M KNO3 background solution to maintain somewhat constant ionic strength. The samples were shaken at 150 rpm on a reciprocal shaker and subsequently centrifuged for 10 min at 4000 rpm for each specified reaction time. A 1-mL aliquot was sampled from the supernatant at reaction times of 2, 6, 12, 24, 72, 168, 336, and 504 h. After sampling, the pH of the supernatant was measured, and samples were reweighed, the slurry was agitated using a vortex mixer and returned to the shaker. The collected samples were analyzed for total As concentration using ICP–AES (Spectro Citros CCD). The amount of arsenate adsorbed by each soil was calculated from the difference between concentrations of the supernatant and that of the initial solutions.

Column Transport
The transport of As(V) in soils was investigated using the miscible displacement technique as described by Selim et al. (1987). Acrylic columns (5-cm in length and of 6.4-cm i.d.) were uniformly packed with air-dry soil and were slowly water-saturated with a background solution of 0.01 M KNO3 at a low Darcy flux. Input solutions of 0.01 M KNO3 were applied for several pore volumes using a variable speed piston pump, and the fluxes were adjusted to the desired flow rates. Between 10 and 20 pore volumes of 0.01 M KNO3 were applied to each column before introduction of As(V) pulse solutions. One or more pulses of 100 mg L–1 As(V) solution (as KH2AsO4) in 0.01 M KNO3 as background solution, were introduced to each soil column as indicated in Table 2. For columns 101 (Olivier soil) and 103 (Windsor soil) only one As(V) pulse was introduced, whereas, for all other columns received two consecutive As(V) pulses (see Table 2). Each As(V) pulse was approximately 10 to 12 pore volume and was subsequently eluted by 0.01 M KNO3 solution. During pulse application, column flow was completely stopped for a duration of 3 to 6 d to evaluate the influence of flow interruption on As(V) transport. Flow interruption or stop-flow was accounted for in our model by simply assuming {nu} = 0 and D = Do (molecular diffusion coefficient) during flow interruption. The volume of each As(V) pulse along with soil parameters associated with each column (e.g., {nu}, {theta}, and {rho}) are given in Table 2.


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  		Table 2. Column soil physical parameters for As(V) and tritium miscible displacement experiments for single and double pulses. Values of the dispersion coefficient were estimated from tritium breakthrough results.

 
To obtain independent estimates for the dispersion coefficient (D) of Eq. [1], separate pulses of a tracer solution were applied to each soil column before As(V) pulse applications. The tracer used was tritium (3H2O) which is commonly utilized for miscible displacement experiments and the collected samples were analyzed using a Tri-Carb liquid scintillation ß counter (Packard-2100 TR) by mixing 0.5-mL aliquot with 5 mL of cocktail (Packard Ultima Gold) for 10 min on the liquid scintillation counter. The radioactivity was recorded as counts per minute (CMP). Estimates for D values are given in Table 2. Selected tritium BTCs, which represent relative concentration (C/Co) versus pore volume (V/Vo) are shown in Fig. 2 . The tritium data were described using the classical convection-dispersion equation and best-fit parameters for D and the retardation factor R (= 1 + {rho}Kd/{theta}) were obtained using nonlinear least square optimization.


Figure 2
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  		Fig. 2. Tritium breakthrough curves for soils. Solid curves depict results of curve-fitting with convection dispersion equation (CDE) for non-reactive solutes.

 

   RESULTS AND DISCUSSION
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 Multireaction Transport Model
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
SUMMARY
 REFERENCES
 
Sorption Isotherms
Adsorption isotherms describing the distribution between aqueous and sorbed phases for As(V) for different soils at sorption time of 24 h are presented in Fig. 3 . The Freundlich equation is utilized to describe such adsorption isotherms

Formula 8[8]
where S represents the (total) amount of adsorption (mg kg–1), KF is the distribution or partition coefficient (L kg–1), and b is the dimensionless reaction order commonly less than one. We utilized nonlinear least square optimization of SAS PROC NLIN (SAS Institute, 2000) to obtain best-fit parameters which provide best description of the adsorption data. Our results indicated that As(V) sorption by all soils was highly nonlinear and time dependent. The nonlinearity of As(V) isotherms is indicated by extremely small values of the Freundlich b (much <1) shown in Fig. 4 . The Parameter b did not exhibit change over reaction time, for all three soils. The only exception is the first 24 h of sorption reaction, where some changes were exhibited. As a result, we estimated average b values, after 24 h of retention, of 0.270, 0.340, and 0.284, for Oliver, Sharkey, and Windsor soil, respectively. Such small Freundlich b values for As(V) adsorption have been recorded by Buchter et al. (1989), Manning and Goldberg (1997), among others. The parameter b is a measure of the extent of heterogeneity of sorption sites having different affinities for arsenic retention by matrix surfaces. In addition, the parameter b illustrates the dependence of the sorption process on concentration where sorption by the highest energy sites takes place preferentially at the lowest solution concentration. The sorption nonlinearity also implies that As mobility in solution tends to increase as the concentration increases. Time-dependent behavior of As(V) adsorption is clearly demonstrated by the increasing values of Freundlich parameter KF with reaction time(Fig. 4).


Figure 3
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  		Fig. 3. Arsenate adsorption isotherms for Olivier, Sharkey, and Windsor soils after 24 h of reaction time. Solid curves depict results of curve-fitting with Freundlich Eq. [8].

 

Figure 4
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  		Fig. 4. Freundlich Parameters KF and b versus retention time.

 
Sorption Kinetics
Results from our kinetic batch experiments are presented in Fig. 5 which clearly illustrates the changes in the concentrations of As(V) in soil solution versus time for the different soils. For all three soils, the rate of As(V) retention was rapid initially and was followed by gradual or somewhat slow reactions. This is in agreement with the biphasic As adsorption behavior observed on minerals (Fuller et al., 1993) as well as on soils (Darland and Inskeep, 1997a; Williams et al., 2003).


Figure 5
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  		Fig. 5. Arsenate concentration in soil solution versus time during adsorption for Olivier, Sharkey, and Windsor soils. Symbols are for different initial As(V) concentrations (Co) of 20, 40, 80, 100 mg L–1. Solid curves are multireaction transport model (MRM) simulations.

 
The capability of the MRM in describing the kinetics of As(V) adsorption on three soils was investigated for the various initial (or input) concentrations (Co's) as well as for the entire data set, that is, all Co's (Overall). In our first simulation attempt, we chose a simple MRM model formulation with four parameters n, k1, k2, and k3. Results of nonlinear least-square optimization are given in Table 3 for Olivier soil. In general, for individual Co, this simple model formulation resulted in poor predictions as indicated by the large values of RMSE. The reaction order n was highly unstable as shown through the large standard errors, especially at high Co values. Similar results were obtained by Selim and Ma (2001) for Cu sorption. Selim and Ma (2001) indicated that the nonlinear reaction order n was particularly difficult to estimate from individual data sets. Based on parameter estimates from our study, we conclude that the reaction order n could not be determined from kinetic batch data of individual input concentrations.


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  		Table 3. Comparison of the goodness-of-fit of a two-phase kinetic reversible and consecutive irreversible model requires 3 parameters model formulation (M4 = k1, k2, and k3) for Olivier soil.

 
In our second attempt to describe the As(V) batch data, the entire data set (for all initial concentrations Co's) was used in nonlinear least-square optimization. This resulted in significant improvement in predictions as depicted by the small standard errors associated with all parameters (see Table 3). Since the best-fit n of 0.27 ± 0.04 for Olivier soil was not significantly different from that of the 24-h Freundlich b value of 0.284, it was decided to test whether the value of 24 h Freundlich b can be used in place of the nonlinear reaction order n. Based on r2 and RMSE values, the resulting MRM simulations were surprisingly good and not significantly different when 24-h Freundlich b was used for Windsor soil. We performed similar analyses for Windsor and Sharkey soils (results not shown) for b values of 0.284 and 0.340, respectively. Based on r2 and RMSE values, from all three soils, we conclude that the use of 24-h Freundlich b in MRM simulation of adsorption kinetics can be recommended.

To test the capability of MRM describing the retention behavior of As versus time by the three soils, several model formulations were tested. Different formulations of the MRM of Fig. 1 represent different reactions from which one can deduce retention mechanisms. Eight model formulations were derived from the general model and denoted as M1 through M8. The required model parameters are dependent on the formulation of the MRM model used. Two model formulations require only two parameters (M1 = Ke and kirr; and M2 = k1 and k2). Another two model formulations require three parameters (M3 = k1, k2, and k3; M4 = Ke, k1, and k2; and M5 = k1, k2, and kirr). Two model formulations require four parameters (M6 = Ke, k1, k2, and k3; and M7 = Ke, k1, k2, and kirr). One model formulation require five parameters (M8 = Ke, k1, k2, k3 and kirr). Model formulation M8 may be considered as the full version of the MRM model. In contrast, M1 is the simplest model formulation where As(V) retained in the Sk phase with only reversible kinetics as the governing process (see Fig. 1). In all model formulations, the nonlinear 24-h Freundlich b was used in place of n and m for each soil as discussed above, and the entire datasets (all Co's) were used in the nonlinear least-square optimization.

Estimated parameters and their goodness-of-fit for different MRM model formulations are given in Table 4. In general, three- and four-parameter model formulations provided better predictions than two-parameter formulations. However, the goodness-of-fit of the model to experimental data varied among different soils. Based on RMSE and r2, model formulations M1 and M2 consistently provided poorest predictions of As(V) retention. As a result, the use of a single fully reversible nonlinear kinetic reaction or two-phase concurrent equilibrium and irreversible processes is not recommended for describing As(V) retention in all three soils. It was observed that several other model formulations (M3-M8) were similar in their capability of describing the kinetic batch data. Similar to the findings of Selim and Ma (2001), the consecutive irreversible reaction (k3 in Fig. 1) provided improvements in description of the kinetic batch data compared to the concurrent irreversible reaction (kirr). Specifically, model formulations M3 and M5 offered similar goodness-of-fit in terms of root mean squared errors and yielded improved predictions when compared to M4 and M6. Since M3 contains only three model parameters, it may be preferred for future application. Therefore, the use of a fully kinetic model (M3) where retention is accounted for by two phases, one reversible (Sk) and one irreversible (Si) is recommended for describing As(V) kinetics.


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  		Table 4. Comparison of parameters and goodness-of-fit determined from fitting eight different MRM model formulations to kinetic adsorption data.

 
Tracer Breakthrough Curves
Selected BTCs of tritium (3H2O), which is employed as a conservative tracer in this experiment, are presented in Fig. 2 for different soils. These BTCs were fitted with classical CDE of the form

Formula 9[9]
to obtain solute dispersion coefficient (D) and retardation factor (R). For Sharkey and Windsor soils, tritium BTCs were essentially symmetrical, exhibited no tailing, and conformed to Eq. [9]. However, indicative of physical nonequilibrium, significant tailing was observed for tritium BTC of Olivier soil. Similar BTCs for aggregated soil have been observed by Selim et al. (1987) and can be explained with intraparticle diffusion through soil aggregates (Brusseau, 1993). Therefore, dispersion coefficient is further interpreted as the combination of hydrodynamic dispersion, and intraparticle diffusion Dw (cm2 h–1)

Formula 10[10]
where {alpha} (cm) is the longitudinal dispersivity. Values of {alpha} and Dw obtained from tritium BTCs were subsequently utilized in the MRM to simulate As(V) transport in soils.

Arsenate Breakthrough Curves
Breakthrough curves of As(V) are presented in Fig. 6 Go Go Go Go through 11 for all soil columns. The transport of As(V) through all the soil columns was significantly retarded relative to the transport of the conservative tracer tritium. Complete As(V) breakthrough, that is, 100% recovery of that applied, was not observed in any of the soil columns following application of approximately 10 pore volumes of As(V) pulse. The extent of retardation agrees with the relative degree of adsorption as measured from the As(V) batch isotherms (Fig. 3). Specifically, highest retardation was observed for Sharkey soil, which has highest As(V) adsorption capacity, while lowest retardation was observed for Olivier with low adsorption capacity. In fact, after two As(V) pulse application and subsequent leaching by arsenic free solution of 20 to 30 pore volumes, the percentages of As(V) mass recovery from column effluent were 82.1, 39.2, and 72.5% of that applied for column 102 (Olivier), 105 (Sharkey), and 104 (Windsor), respectively.


Figure 6
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  		Fig. 6. Comparison of multireaction transport model (MRM) formulations M1-M8 for predicting As(V) breakthrough curves for Olivier soil (top) and Windsor soil (bottom). Model parameters were those from the batch kinetic experiment (Table 4).

 

Figure 7
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  		Fig. 7. Comparison of multireaction transport model (MRM) formulations M1-M8 model for predicting As(V) breakthrough curves for Olivier soil column 101. Model parameters were obtained using nonlinear inverse modeling.

 

Figure 8
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  		Fig. 8. Comparison of multireaction transport model (MRM) formulations M1-M8 for predicting As(V) breakthrough curves for Olivier soil column 102. Model parameters were obtained using nonlinear inverse modeling.

 

Figure 9
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  		Fig. 9. Comparison of multireaction transport model (MRM) formulations M1-M8 for predicting As(V) breakthrough curves for Windsor soil column 103. Model parameters were obtained using nonlinear inverse modeling.

 

Figure 10
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  		Fig. 10. Comparison of multireaction transport model (MRM) formulations M1-M8 for predicting As(V) breakthrough curves for Windsor soil column 104. Model parameters were obtained using nonlinear inverse modeling.

 

Figure 11
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  		Fig. 11. Comparison of predictions and simulations using multireaction transport model (MRM) formulation M8 for predicting As(V) breakthrough curves for Sharkey soil column 105.

 
All measured As(V) BTCs exhibited extensive asymmetry as illustrated by the difference in the shape of the effluent side from the leaching or desorption side (see Fig. 6GoGoGoGo–11). This is not surprising if one considers the highly nonlinear and kinetic adsorption behavior observed in our batch experiments (see Fig. 3Go–5). Similar asymmetry of BTCs for As(V) has been observed by Darland and Inskeep (1997a) and Williams et al. (2003). In addition, the excessive tailing exhibited by all column BTCs demonstrated a continued slow desorption (release) of As(V) from all soils. For Sharkey soil unexpectedly high concentration of As(V) was observed during the leaching phase; the reason for this remains unclear (Fig. 11). A possible explanation is the so called colloid facilitated transport, that is, transport of As(V) associated with mobile colloidal particles in the flowing water. Puls and Powell (1992) have demonstrated that As(V) sorbed on colloidal iron oxides can be transported through aquifer material. It is possible that in situ mobilization of colloidal iron oxides increased the concentration of As(V) in the leachate from the Sharkey soil. In our study, colloidal material was visually observed in the effluent during leaching in Sharkey soil.

Flow interruption was used to check for the occurrence of nonequilibrium conditions during solute transport in soils. The purpose of stopping the flow was to provide sufficient time for the solute to diffuse into the soil matrix and/or react with sorption sites on soil matrix surfaces. This technique has been shown to provide estimation of retention parameters when nonequilibrium conditions were dominant (Brusseau et al., 1989). In our column experiments, the influence of flow-interruption on mobility of As(V) through the soil columns is clearly illustrated in the BTCs presented in Fig. 6GoGoGoGo to 11. The sharp drop in As(V) concentration as a result of flow interruptions is indicative of As(V) reactivity during stop flow. This decrease of As(V) concentration in the effluent suggests that extensive nonequilibrium condition exist during As(V) transport for all soil columns. Such behavior during flow interruption was expected because of the kinetic sorption characteristics of As(V) as exhibited by the batch experiments.

The multireaction transport model was utilized to describe the transport of As(V) through columns in two different modes, that is, a fully predictive mode and an inverse modeling mode. In the predictive mode, all necessary model parameters were provided independent of As(V) BTCs results being modeled. Specifically, model retention parameters (n, Ke, k1, k2, k3, etc.) were those given in Table 4 for our kinetic batch data, whereas the hydrodynamic dispersivity ({alpha}) and intra-particle diffusion (Dw) were obtained from tritium BTCs (Fig. 2). All other parameters such as column length (L), pore water velocity (v), bulk density ({rho}), moisture content ({theta}), and pulse duration were provided for each individual column (see Table 2). The goodness-of-fit of model prediction was evaluated based on RMSE and r2 values. Examples of model predictions using all model formulations (M1-M8) are shown in Fig. 6 for Olivier and Windsor soils. Consistent with previous studies (Ma and Selim, 1997), the use of batch model parameters overpredicted concentration maxima (peaks) and underestimated the extent of retardation (BTCs shift to the left). The steepness of the BTC fronts was overpredicted and the tailing was underpredicted by all model formulations. Therefore, the use of batch rate coefficients grossly underestimated the extent of As(V) retention in Olivier and Windsor soils. Conversely, overestimation of potential As(V) mobility was predicted by all model formulations used. We thus conclude that BTC predictions based on batch parameters did not adequately predict the breakthrough of As(V) from all soil columns studied (with RMSE ranging from 0.228 to 0.548). Results of Darland and Inskeep (1997a) based on MRM predictions of As(V) BTCs yielded similar predictions to those of our observation for the soil columns presented here.

Discrepancies between measured and MRM model predictions (using batch parameters) were observed by Barnett et al. (2000) for Uranium(VI) transport through soil columns. They suggested several fundamental differences between batch and column experiments that reduced the applicability of batch experiment data in simulating column transport experiments. In our experiments, the different retention capacities determined from batch and column experiments might result from the following reasons: difference between sorption time used for batch experiment and hydrologic retention time of column experiment; low solid/solution ratio of batch experiments; As(V) was added in one spike for batch study compare with continuous addition in column experiments; and potential buildup of reaction products in closed batch systems.

Inverse Multireaction Transport Modeling
In an inverse mode, we utilized the multireaction transport model along with nonlinear least-squares optimization scheme to test the capability of MRM for predicting As(V) BTCs without reliance on parameter estimates from the batch experiments. Therefore, one assumes that if the model is incapable of describing measured BTCs, the model is an inaccurate representation of the retention mechanisms. In general, three and four parameter model formulations provided better predictions than two parameter formulations as shown in Fig. 7GoGo to 10. However, the goodness-of-fit of model prediction to experimental data varied among individual columns. Examples using all eight model formulations are given in Table 5. The overall goodness-of-fit as evidenced by the root mean squared errors (RMSE) and r2 were best when k1, k2, and k3, (M3) or k1, k2, and kirr (M5) were used. M6, M7, and M8 provided similar goodness-of-fit in terms of RMSE and r2. Since M3 and M5 contain only three model parameters, these model formulations are perhaps preferable for future application. Based on batch as well as column transport analysis, we conclude that MRM formulations with three parameters can be recommended.


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  		Table 5. Root mean squared errors (RMSE) of predicted and optimized arsenate breakthrough curves (BTCs) across all soil columns and eight different MRM formulations (M1-M8).

 
Overall excellent fits of the model were achieved for As(V) BTCs of Olivier and Windsor columns as indicated by the small values of RMSE (<0.1) and high r2 (>0.95). In addition, the effect of flow interruption was successfully described when several model formulations along with the nonlinear optimization scheme was used. Sorption rate coefficients obtained from column BTCs were much larger than those obtained from batch experiments. This is indicative of higher As(V) sorption for soil columns than batch experiments. The MRM model failed to describe As(V) BTC of Sharkey column (Fig. 11). It is possible that other processes (e.g., colloid facilitated transport), which is not accounted in our model dominated the transport process.


   SUMMARY
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 Multireaction Transport Model
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
REFERENCES
 
In summary, we evaluated a nonlinear equilibrium-kinetic MRM for its prediction capability of As(V) retention as well as transport in three soils having different soil properties. Kinetic batch experiments were performed over a wide range of input concentrations and we concluded that As(V) adsorption was highly nonlinear with a Freundlich reaction order much less than unity for all soils investigated. Adsorption was strongly kinetic, the rate of As(V) retention was rapid initially and was followed by gradual or somewhat slow retention behavior with increasing reaction time. Based on root mean square errors, model formulations having nonlinear reversible reaction along with a consecutive or concurrent irreversible retention (M3 and M5) were considered the most favorable in describing As(V) retention over time for all three soils. These model formulations are recommended for As prediction and for future application because the fewest number of model parameters.

Column transport experiments indicated extensive As retardation followed by slow release or extensive tailing of the BTCs. The percentages of As(V) mass recovery from column effluent ranged from 82.1% for Olivier soil to as low as 39.2% for Sharkey clay. The use of batch model parameters provided poor overall predictions of all BTCs. The use of batch rate coefficients grossly underestimated the extent of As(V) retention in Windsor and Olivier soils and overestimated As(V) mobility by all model formulations used. We thus conclude that BTC predictions based on batch parameters are not recommended. However, when the multireaction transport model was utilized in an inverse mode, the model was capable of describing As(V) BTCs for Windsor and Olivier soils. Moreover, model formulations which provided best-fit of the BTCs were consistent with those based on kinetic batch data.


   NOTES
TOP
 NOTES
ABSTRACT
 INTRODUCTION
 Multireaction Transport Model
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 
Approved by the Director of the Louisiana Agricultural Experiment Station as manuscript no. 06-14-0186.

Received for publication January 23, 2006.


   REFERENCES
TOP
 NOTES
 ABSTRACT
 INTRODUCTION
 Multireaction Transport Model
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY
 REFERENCES
 




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H. Zhang and H. M. Selim
Modeling Competitive Arsenate-Phosphate Retention and Transport in Soils: A Multi-Component Multi-Reaction Approach
Soil Sci. Soc. Am. J., June 29, 2007; 71(4): 1267 - 1277.
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