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Published in J. Environ. Qual. 33:488-495 (2004).
© ASA, CSSA, SSSA
677 S. Segoe Rd., Madison, WI 53711 USA

TECHNICAL REPORT

Ground Water Quality

Mobility of Sulfate in Forest Soils

Kinetic Modeling

H. M. Selim*,a, G. R. Gobranb, X. Guanb and N. Clarkec

a Agronomy and Environmental Management Dep., Sturgis Hall, Louisiana State Univ., Baton Rouge, LA 70803
b Dep. of Ecology and Environmental Research, Swedish Univ. of Agric. Sciences, Uppsala, Sweden
c Norwegian Forest Research Inst., Høgskoleveien, Norway

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

Received for publication March 31, 2003.

   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 A GENERALIZED MULTIREACTION...
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Understanding sulfate transport and retention dynamics in forest soils is a prerequisite in predicting SO4 concentration in the soil solution and in lake and stream waters. In this study forest soil samples from the Gårdsjön catchments, Sweden, were used to study SO4 transport in soil columns from the upper three soil horizons (E, Bs, and BC). The columns were leached using a sequential leaching technique. The input solutions were CaSO4 equilibrated with forest floor material. Leaching behavior of SO4 and concentration in the effluent were measured from columns from individual horizons. Sulfate was always retained in the Bs and BC horizons, while the pattern for the E horizon varied. Attempts were also made to model SO4 breakthrough results based on miscible displacement approaches and solute convection–dispersion equation (CDE) in porous media. Several retention mechanisms were incorporated into the CDE to account for possible reversible and irreversible SO4 reactions in individual soil layers. Our modeling efforts were inadequate in describing the mobility of SO4 in the top (E) horizon. Moreover, a linear equilibrium approach was generally inadequate for describing SO4 sorption during transport in the Bs and BC horizons. In contrast, we found that the model provided good descriptions of all breakthrough results when SO4 reactivity was accounted for based on nonlinear equilibrium or first-order kinetic processes. Moreover, based on model parameter estimates, the reactivity or retention of SO4 during transport is concentration dependent. We conclude that sulfate retention during transport in this forest soil is most likely controlled by kinetic reactivity of SO4 of the reversible and irreversible mechanisms.

Abbreviations: CDE, convection–dispersion equation • MRM, multireaction model • PV, pore volume


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
A GENERALIZED MULTIREACTION...
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
DURING THE LAST three decades, two general approaches have been proposed in the literature for describing the interactions of sulfate in soils. The first approach is that of a chemical nature where thermodynamic interrelationships with speciation of cations and anions present in soil solution and the interaction with the soil surface are the major mechanisms. These models may be referred to as chemical models. Examples of such models include that of Cosby et al. (1986), Reuss and Johnson (1986), De Vries et al. (1994), among others. A common feature of these models is that both ion exchange and aluminum hydrolysis reactions are similar. They vary in their ability to quantify these processes whether the interactions are under conditions of batch or transport. In addition, transport mechanisms can be either the simple mixing-cell type or the convective–dispersive type where finite-difference or finite-element methods for solving simultaneous set of equations are included (Cosby et al., 1986). A common theme of all these chemical models is the failure to accurately describe the retention and reactions of sulfate in soils. The sorption of sulfate in all these chemical models are based on either Freundlich or Langmuir approaches. Both types are of empirical nature where they are included simultaneously with the chemical models. In addition, both approaches assume that local equilibrium is dominant. Evidence of time-dependent reaction of sulfate is numerous in the literature (see Sparks, 1989).

Another class of models focuses primarily on empirical-type approaches where lumped parameters were used to quantify the fate of sulfate in soils. Such lumped-parameters approach can be looked in terms of equilibrium, fully reversible kinetic approaches, and irreversible reactions of the kinetic type. Hodges and Johnson (1987) tested the validity of several models for describing sulfate adsorption and desorption in a Cecil soil. Their test included first-order kinetics, Elovich, and other diffusion-type equations. First-order type reactions provided only adequate descriptions of results. They also found that sulfate retained from desorption results were significantly different in comparison with results based on adsorption data. Such behavior is commonly referred to as hysteresis and may be a result of irreversible reactions as suggested by Hodges and Johnson (1987). Lack of irreversible retention of sulfate has been observed by Gobran et al. (1998b). This observation has also been noted in soils by Harrison et al. (1989) and on oxide mineral surfaces by Turner and Kramer (1992). It should also be noted that deviations between sorption and desorption could be related to kinetic retention behavior (Gobran et al., 1998a, 1998b). Irreversible sorption–desorption and the extent of kinetic reactions has also been quantified using the pressure-jump relaxation method on goethite by Zhang and Sparks (1990). They found that sulfate adsorption occurs rapidly at initial reaction stages whereas desorption is slower and may be considered as a limiting step.

Other approaches include soil acidification models, which are of the macroscopic type, that account for the process of SO4 sorption in different ways. These approaches assume equilibrium conditions and include the adsorption-isotherm approach, the solubility-product approach, and the anion-exchange approach. Prenzel (1994) discussed the various limitations of the above approaches in their ability to account for changes in pH. Recently Fumoto and Sverdrup (2000) utilized a constant-capacitance approach to describe the pH dependency of SO4 sorption isotherms in an andisol. Other modeling efforts of SO4 isotherms were reported by Gustafsson (1995) for a spodosol. Such isotherm models are of the equilibrium type and include linear and Temkin-type models.

In this paper we describe the transport of SO4 in soil columns based on a general purpose transport model of the multireaction type. The model was successfully used to predict solute retention during transport in soils (Selim, 1992; Hinz and Selim, 1994; and Selim and Amacher, 2001). Multireaction models are empirical and include linear and nonlinear equilibrium and reversible and irreversible retention reactions. A major feature of multireaction approaches is that they account for linear as well as nonlinear kinetic reactions of the consecutive as well as the concurrent type. Limitations of the multireaction models are also presented. Predictions of SO4 breakthrough results (BTCs) from a forest soil system are given here to illustrate model capability. Specifically, the multireaction model was utilized to describe SO4 BTCs from a sequential leaching experiment on forest (spodic) soil layers. Input pulse solutions of different CaSO4 concentrations were used in the sequential leaching experiment. Various versions of the multireaction model (equilibrium and kinetic) were needed to describe effluent results from the different soil layers.


   A GENERALIZED MULTIREACTION MODEL
TOP
 ABSTRACT
 INTRODUCTION
 A GENERALIZED MULTIREACTION...
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
A generalized conceptual multireaction approach, often referred to as the multi-site model, acknowledges that the soil solid phase is made up of different constituents (i.e., clay minerals, organic matter, and iron and aluminum oxides). Moreover, a solute species is likely to react with various constituents (sites) via different mechanisms (Amacher et al., 1988). As reported by Selim (1992), reactive species are assumed to react at different rates with different sites on matrix surfaces. Therefore, a multireaction kinetic approach is used to describe solute retention kinetics in soils. The multireaction model used here considers several interactions of one reactive solute species with soil matrix surfaces. Specifically, the model assumes that a fraction of the total sites reacts rapidly or instantaneously with solute in the soil solution, whereas the remaining fraction reacts more slowly with the solute. As shown in Fig. 1 , the model includes reversible as well as irreversible retention reactions that occur concurrently and consecutively. We assume a solute species is present in the soil solution phase, C (mg L–1), and in several phases representing the solute retained by the soil matrix designated as Se, S1, S2, Ss, and Sirr (mg kg–1 soil). Furthermore, we refer to ST (mg kg–1 soil) as the total amount of solute retained, i.e., the sum of all sorbed phases represented in Fig. 1, such that

[1]
We further considered the sorbed phases Se, S1, and S2 are in direct contact with the solution phase (C) and are governed by concurrent reactions. Specifically, C is assumed to react rapidly and reversibly with the equilibrium phase (Se) such that

[2]
where Ke is a distribution coefficient (L Mg–1) and n is the reaction order (dimensionless). Moreover, n represents a nonlinearity parameter, which is commonly less than unity (Amacher et al., 1988). This parameter represents the heterogeneity of sorption sites having different affinities for solute retention on matrix surfaces. The relations between C and the sorbed phases S1 and S2 were assumed to be governed by nonlinear kinetic reactions expressed as

[3]

[4]
where t is time (h), {rho} is soil bulk density (Mg m–3), and {Theta} is water content (m3 m–3). The parameters k1 and k2 are the forward and backward rate coefficients (h–1) associated with S1, and m is the reaction order, respectively. Similarly, for the reversible reaction between C and S2, k3 and k4 are the respective rate coefficients (h–1). In the above equations, we assume n = m, since there is no known method for estimating n and/or m independently.



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  		Fig. 1. A schematic of the multireaction model for solute reactivity in soils.

 
The multireaction model accounts for irreversible retention in two ways. First, as a sink term, Q, which represents a direct reaction between the solution phase C and Sirr (e.g., precipitation/dissolution or immobilization) as a first-order kinetic process, where kirr is the associated rate coefficient (h–1).


[5]
Irreversible retention was also considered to be the result of a subsequent reaction of the S2 phase into a less accessible or strongly retained phase S3 such that,

[6]

One may regard the slowly reversible phase S3 as a consequence of rearrangement of solute retained by the soil matrix. Mechanisms associated with irreversible reactions include different types of surface precipitation, which account for the formation or sorption of metal polymers on the surface, a solid solution or coprecipitate that involves co-ions dissolved from the sorbent, and a homogeneous precipitate formed on the surface composed of ions from the bulk solution or their hydrolysis products. The continuum between surface precipitation and chemisorption is controlled by several factors including: (i) the ratio of the number of sites to the number of ions in solution, (ii) the strength of the metal-oxide bond, and (iii) the degree to which the bulk solution is under saturated with respect to the metal hydroxide precipitate. Such mechanisms are consistent with one or more irreversible reactions associated with our model presented in Fig. 1.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 A GENERALIZED MULTIREACTION...
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Soil samples were collected from the Gårdsjön catchment, which is situated at 58°04' N and 12°03' E on the west coast of Sweden. The area is covered by coniferous forest with Norway spruce [Picea abies (L.) Karst], which dominate the landscape. The area is glacial till, silt loam soil that is fairly thin. The soil is classified as a spodosol–haplorthod. A detailed description of the geology, soils, vegetation, etc. of the Gårdsjön catchment is given by Olsson et al. (1985). Soil samples were taken by horizon, i.e., forest floor (FF), eluvial (E), and spodic (Bs and BC) horizons, within the control (F1) catchment. Although the uppermost mineral horizon is not well enough developed to be called either an E or A horizon, we classify it here as an E horizon. Field moist composite samples of humus (FF) were passed through a 5-mm sieve, and mineral soils through a 2-mm sieve.

To simulate leaching in a natural forest soil, and due to the importance of the interaction between inorganic and organic soil constituents, a sequential leaching experiment was designed, which is illustrated in Fig. 2 . The sequential leaching technique is thought to resemble the field situation, in that the input solution passes through each horizon in turn on its way "down" through the soil. This means that the ions and other dissolved species leached from one horizon are included in the input to the underlying horizon. The leaching columns (4.7 by 5 cm) were made of PVC and were packed with soil from each mineral horizon (E, Bs, and BC). Disturbed soils were used to minimize problems due to soil heterogeneity. The bulk density of the soil column was equivalent to that in the field. Leaching solutions were prepared by mixing the FF layer with CaSO4 solutions at two different input concentrations (Co) of 0.005 M (SI) and 0.0005 M (SII). These concentrations were chosen to examine the impact of applying the neutral salt CaSO4 to acid forest soils over a wide concentration range. The soil columns were leached with an amount of leaching solution equivalent to at least 1 yr of throughfall in Gårdsjön. The concentration of SO4–S in the SII treatment was similar to that of solution obtained by centrifuging the O horizon of Gårdsjön (Giesler et al., 1996). In the SI treatment, the total amount of S applied was approximately equivalent to the total amount of SO4–S added in the form of (NH4)2SO4 and S deposition in the (NH4)2SO4 treatment in Skogaby, southwest Sweden during 4 yr (Bergholm, 1994).



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  		Fig. 2. A schematic of the sequential leaching experiment through 5-cm soil columns from the E, Bs, and BC horizons (FF = forest floor).

 
The proportions used in mixing the solutions (SI and SII) and the FF layer varied depending on the bulk density and the pore volume (PV) of the FF layer, which were 0.6 g mL–1 and 70 mL per column, respectively. As 10 PVs were assumed to pass through the FF layer, we mixed the FF layer with the sulfate solutions in the proportion of 2 L solution to 150 g FF. After mixing, the leaching solutions were shaken for 1 h, then allowed to stand overnight, after which they were filtered. The chemical characteristics of the leaching solutions are given in Table 1.


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  		Table 1. Chemical characteristics of the (input) leaching solutions used for the soil layers SI, SII, FFSI, and FFSII (EC = electrical conductivity, DOC = dissolved organic carbon).

 
The soil columns were leached with an amount of leaching solution equivalent to at least 1 yr of throughfall at Gårdsjön. Leaching was continuous, using constant hydraulic head conditions. The soil moisture content was near water-saturation with input solutions maintained at an average flux of 33 cm d–1. This high leaching rate was used for two reasons: (i) the processes under investigation are known to be fast and (ii) to reduce any microbial activity that might occur when the time of contact between the soil and water is prolonged. The filtered leaching solutions were used to leach the soil column containing the E horizon. To obtain enough leachate sample at each collection from the first soil column (the E horizon) for analysis and for leaching the Bs horizon and then the BC horizon, we used nine, six, and two soil columns for the E, Bs and BC horizons, respectively. At each collection, all leachate samples from soil columns of the same horizon were mixed to form a composite sample. Each composite sample from the E horizon was divided into two parts; one was used for analysis and the rest was used as the equivalent input to leach the lower (Bs) horizon, and so on (see Fig. 2), so that 10 leachates were obtained from each horizon. The leachates were then filtered through a 0.45-µm membrane filter before analysis.

The input and effluent solutions were analyzed for pH using a PHM 62 Standard pH Meter with a GK2401C Combination Electrode, SO42– was determined by ion chromatography (Dionex 2000i HLPC, Sunnyvale, CA), and dissolved organic carbon (DOC) was determined using a Shimadzu total organic carbon analyzer (TOC-5000, Houston, TX ). Cations (Ca, Mg, K, Na, and Al) were analyzed using ICP-OES (Jobin-Yvon JY70 Plus, Edison, NJ) and organic matter content was expressed as the loss on ignition in oven dry samples after combustion at 450°C. The organic matter content for the E, BS, and BC layers were 5.1, 10.3, and 3.8%, respectively, and the cation exchange capacities were 36.2, 53.6, and 18.2 mmolc per kg soil, respectively. The average bulk densities were 1.23, 0.96, and 1.49 Mg m–3 and saturated moisture contents were 0.58, 0.64, and 0.46 m3 m–3, for the E, BS, and BC layers, respectively.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 A GENERALIZED MULTIREACTION...
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
SUMMARY AND CONCLUSIONS
 REFERENCES
 
We recognize that the processes governing SO4 retention in soils remain a subject of considerable debate. The magnitude of SO4 retention has often been related to a number of soil properties with the most important being: SO4 concentration in solution, aluminum (Al) and iron (Fe) sesquioxides content, solution pH, and electrolyte concentration and composition (Johnson and Henderson, 1979; Fuller et al., 1985; Inskeep, 1989; Gobran and Clegg, 1996). While the first two properties enhance SO4 retention, increasing pH and ionic strength are known to decrease SO4 retention. In our flow experiments, the effluent was collected at one pore volume interval and was analyzed for pH, DOC, etc. Changes in effluent pH vs. pore volume (V/Vo) were generally small. For the upper Bs layer, the pH range was 4.15 to 4.18 whereas the pH ranged from 4.38 to 4.47 for the lower (BC) layer. As expected, pH values in the effluent were consistently higher from the lower layer (BC) than the upper layer (Bs). Therefore, as described in the following section, we restricted our modeling efforts to SO4 only. Moreover, the applicability and model validity are performed here for the two cases considered; Case I where SO4 input concentration (Co) of 0.005 M was maintained and that for Case II where the input (Co) was 0.0005 M.

Modeling
In an effort to describe SO4 effluent results obtained from the different soil layers, we utilized various versions of the multireaction model described above. In principal, we based our efforts on the assumption of the miscible displacement approach, which describes retention reactions of solutes during transport in porous media (Selim, 1992). Several simplifying assumptions were necessary to describe the SO4 experimental data based on these models. Briefly, we tested the capability of the convection–dispersion equation (CDE) to describe the mobility of applied sulfates in individual soil layers where steady state conditions were assumed. Experimental constraints were such that the assumptions of saturated and steady flow was not completely met especially when the pulse was first introduced to each column. Our experimental conditions did not maintain water-saturated conditions initially and the applied pulse was introduced to a moist but not fully water-saturated columns. As a result, effluent adjustments in the concentration of sulfate vs. pore volume (V/Vo) for the various layers were made to reflect the late arrival of a wetting front (outflow) due to the unsaturated condition of the columns. Here, Vo is the pore volume associated with individual soil layers. Our adjustments, which were based primarily on the initial moisture conditions for individual columns, were V/Vo of 0.5, 0.25, and 0.15 for the E, Bs, and BC soil layers, respectively. All other parameters used with the CDEs were based on our experimental condition (e.g., bulk density, flux, input concentrations, etc.).

The CDE for reactive solutes in porous media may be expressed as (Selim, 1992)

[7]
where D is the hydrodynamic dispersion coefficient (m2 d–1), z is soil depth (m), and v is Darcy's water flux density (m d–1). In addition, ST is the solute concentration associated with the solid phase (mg kg–1 soil) and is given explicitly by Eq. [1]. The term ({partial}ST/{partial}t) in Eq. [7] represents all reversible processes between the solution and the solid phases, as well as irreversible (sinks or sources) rates of reactions, i.e., transformation reactions.

Equilibrium Sorption—Linear and Nonlinear
It is recognized that most Swedish forest (podsolic) soils contain a substantial amount of sulfate. In fact, as pointed out in Gobran et al. (1998b), sulfate concentration did not approach zero, even after an extended period of continued leaching. They reported that Gårdsjön catchments store a substantial quantity of sulfate (retained by Al and Fe oxide minerals). This explains the initially high sulfate concentrations (t = 0) used in our model simulations. Specifically, for the case where Co = 0.005 M, initial sulfate concentrations (C/Co) were 0.7, 0.1, and 0.1 for the E, Bs, and BC layers, respectively. For Case II, where lower input sulfate concentration was used, initial concentrations were consequently higher.

To describe effluent SO4 from the top layer shown in Fig. 3 , we assumed a simple linear sorption to account for the retention in the transport equation. Specifically, we used the following linear (equilibrium) model

[8]
to describe the reactivity of SO4 in the top soil. Equation [8] is similar to that of Eq. [1] where n = 1. Therefore, we ignored all retention reactions illustrated in Fig. 1 except for the equilibrium type reaction of the linear type. Here, Kd is a distribution coefficient and is a measure of the extent of sorption or affinity of SO4 to the soil system (L kg–1). The associated (dimensionless) retardation factor R can be expressed as

[9]
For R = 1, the solute is considered nonreactive. Due to the early arrival or breakthrough and the lack of a well-defined effluent front, our attempts to describe SO4 results for the top layer (E-I) based on linear equilibrium approach were not adequate. The simulation shown is a result of the use of R less than unity, which implies negative sorption or ion exclusion. Since a value for Kd and/or sorption isotherms for SO4 were not independently measured, we cannot support such a finding. The estimated R value that provided best-fit of the BTC for the top layer E-I (where Co = 0.005 M) was 0.59 with a standard error (SE) of 0.062 (r2 = 0.815). We should also stress here that for the top layer (E-II) where low input concentration of SO4 was applied (Co = 0.0005 M), the results indicated a concentration in the effluent no different from that of the input solution (figure not shown). As a result, no attempts were made to describe effluent results for the E-II layer.



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  		Fig. 3. Experimental and simulated breakthrough results of SO4 effluent concentrations vs. pore volume (BTCs) from the E horizon [column E-I, input SO4 (Co) of 0.005 M]. The simulation is based on best-fit of the data when a linear equilibrium sorption model was assumed.

 
Our miscible displacement modeling approach was modified to describe SO4 effluent from the BS (as well as BC) layers. We adjusted the computer code to account for a variable concentration of the input pulse rather than a constant one as is commonly accepted in most column experiments and mathematical solutions. In all our simulations presented here, for each soil column, the SO4 input concentrations from our experimental results were incorporated as inputs to the model. In addition, presentations of relative concentrations (C/Co) were based on the respective Co of the applied solution to the top layer (E).

Figure 4 shows the use of a linear equilibrium approach (Eq. [8]) for several Kd values (ranging from 0.5 to 3 L kg–1) to describe the BTC from the Bs-I column (Co = 0.005 M). It is obvious that a linear approach failed to describe the shape of the BTC results. Therefore, we attempted to use the Freundlich approach of Eq. [1] into the transport equation where the dimensionless parameter n was allowed to vary from 0.5 to 4. As shown in Fig. 5 , the use of n < 1, which is commonly observed for most solutes, did not provide a good description of the shape of the SO4 BTC (Selim, 1992). In contrast, when a larger n value (n >> 1) was used, this resulted in some improvement in the description of the effluent data. In fact, a good fit of the data was obtained when a nonlinear least-square optimization scheme was used with the CDE. As shown in Fig. 6 , the solid curve is based on the following parameter estimates that provided best-fit of the BTC; Ke = 0.802 (L kg–1) and n = 5.89 (r2 = 0.983). The use of a linear approach as shown by the dotted curve (Kd = 0.232 L kg–1 with SE = 0.11 L kg–1) gave a poor description of the effluent data (Table 2).



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  		Fig. 4. Experimental and simulated (solid and dashed curves) BTCs of SO4 effluent concentrations from the Bs horizon [column Bs-I, input SO4 (Co) of 0.005 M]. Simulations are for a range of Kd values where a linear equilibrium sorption model was assumed.

 


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  		Fig. 5. Experimental and simulated (solid and dashed curves) BTCs of SO4 effluent concentrations from the Bs horizon [column Bs-I, input SO4 (Co) of 0.005 M]. Simulations are for a range of n values where a nonlinear equilibrium model was assumed.

 


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  		Fig. 6. Experimental and simulated BTCs of SO4 effluent concentrations from the Bs horizon [column Bs-I, input SO4 (Co) of 0.005 M]. Simulations are based on best-fit of the data when a linear equilibrium model (dashed curve) and a nonlinear equilibrium (solid curve) were used.

 

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  		Table 2. Parameter estimates, standard errors (SE), root mean square errors (RMSE), and coefficient of correlation (r2) for the linear and nonlinear equilibrium models for the different columns.

 
Although the use of a large n value (>1) in Eq. [2] is unusual, recent work of Martinez et al. (1998) showed SO4 isotherms for a similar concentration range (0.005 M) as that for SI columns of our present study. Martinez et al. (1998) clearly found an SO4 isotherm of the convex type, in the presence of citric acid. Although Martinez et al. (1998) did not obtain isotherm parameters, Selim and Amacher (1997) showed that for convex isotherms n > 1 is expected. Moreover, for lower SO4 concentration ranges (up to 0.001 M), Inskeep (1989) showed linear (rather than convex) SO4 adsorption isotherms for kaolinite and amorphous iron oxide in the presence of several ligands including citric, humic, and tannic acids. In all cases mentioned, the presence of ligands effectively reduced SO4 adsorption in soils. In our case, it is possible that ligand exchange reactions as well as retention by Al and Fe oxide minerals are dominant mechanisms for SO4 adsorption in our soils.

Kinetic Sorption
Since the use of equilibrium (Freundlich) type with n > 1 is uncommon, we also attempted the kinetic reversible approach given by Eq. [2] to describe the effluent results from the Bs-I column. The use of Eq. [2] alone represents a fully reversible SO4 sorption of the nth order reaction where k1 to k2 are the associated rates coefficients (h–1). Again, a linear form of the kinetic equation is derived if m = 1. As shown in Fig. 7 , we obtained a good fit of the Bs-I effluent data for the linear kinetic curve with r2 = 0.967. The values of the reaction coefficients k1 and k2, which provided the best fit of the effluent data were 3.42 and 1.43 h–1 with SEs of 0.328 and 0.339 h–1, respectively (see Table 3). Efforts to achieve improved predictions using nonlinear (m different from 1) kinetics was not successful (figures not shown). We also attempted to incorporate irreversible (or slowly reversible) reaction as a sink term (see Eq. [5]) concurrently with first-order kinetics. A value of kirr = 0.0456 h–1 was our best estimate, which did not yield improved predictions of the effluent results as shown in Fig. 7.



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  		Fig. 7. Experimental and simulated BTCs of SO4 effluent concentrations from the Bs horizon [column Bs-I, input SO4 (Co) of 0.005 M]. Simulations are based on best-fit of the data when a kinetic model (dashed curve) and kinetic model with an irreversible reaction (solid curve) were used.

 

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  		Table 3. Parameter estimates, standard errors (SE), root mean square errors (RMSE), and coefficient of correlation (r2) for the first-order kinetic and irreversible models for the different columns.

 
Model Predictions
Thus far, the transport model, after incorporation of equilibrium or kinetic retention, was used in a calibration mode where, along with nonlinear least-square approximation, a best-fit of the model to the experimental BTC was attempted. This resulted in a set of model parameter estimates that provided the best-fit of the BTC for a specific version of the model.

To test the capability of the model, we used the model in a predictive mode where no model fitting of measured BTC was performed. Specifically, we utilized independently derived parameters from Bs-I to predict BTC effluent results from the Bs-II column. We used the linear kinetic model (with k1 = 3.42 h–1 and k2 = 1.43 h–1) based on Bs-I where the input SO4 (Co) was 0.005 M to predict Bs-II where Co of 0.0005 M was used. As illustrated by the solid curve in Fig. 8 , the predictions underestimated the SO4 concentrations vs. PV. When the model was relaxed and was used in a fitting mode to find best-fit predictions of Bs-II using the linear kinetic approach, once again adequate BTC predictions were obtained (see dashed curve in Fig. 8). Best-fit parameter estimates were, as expected, different from those derived for the Bs-I column. Specifically, best-fit k1 to k2 values, which provided the best fit of Bs-II effluent data were 1.07 and 0.89 h–1, respectively (Table 3). Such values for the rate coefficients were lower than those for the Bs-I column and are indicative of concentration-dependent reaction when the assumption of first-order kinetic sorption during transport is made. We also tested the linear equilibrium approach to model the Bs-II results and obtained less than adequate predictions as indicated by the dashed curve in Fig. 8. The estimated value for Kd was 0.138 L kg–1 and r2 of 0.963 (see Table 2). Such Kd value is smaller than the 0.232 L kg–1 value obtained for the Bs-I column illustrating the dependency of sorption on the input concentration (Co). This finding is consistent with that when kinetic rather than equilibrium sorption was assumed where increased SO4 sorption was realized for the higher Co.



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  		Fig. 8. Experimental and simulated BTCs of SO4 effluent concentrations from the Bs horizon [column Bs-II, input SO4 (Co) of 0.0005 M]. Simulations are based on best-fit of the data when a linear equilibrium model (dotted curve) and kinetic model (dashed curve) were used. The solid curve is a prediction based on the kinetic model.

 
BC Layer
Attempts to describe the SO4 effluent data from the BC layer (columns BC-I and BC-II) were performed in a similar fashion to the above E and Bs layers. Our aim was to find model versions that provide the best predictions of effluent results. Moreover, common features as well as trends of parameter estimates and retention characteristics among the different layers were sought. We described effluent data from the BC columns based on model fitting (or simulation) by use of the linear and nonlinear equilibrium approaches as well as first-order kinetics. The experimental results as well as model simulations are illustrated in Fig. 9– 11 . For both BC columns, worst simulations were obtained using the simple linear equilibrium model. Furthermore, the Kd value, which provided the best-fit of the data, was higher for the BC-I column than for BC-II column. Such a finding is consistent with that for the Bs layer and indicative of the dependency of sorption on the input concentration (Co). The associated Kd values, their standard errors, and r2 are given for the two columns in Table 2. In addition, the use of the nonlinear equilibrium model (Eq. [9]) to describe BC-I provided an extremely good model fit of the effluent data with r2 of 0.996. Moreover, similar to the column from the second layer (Bs-I), the nonlinear parameter n was greater than 1. In fact, best values were Ke = 0.873 L kg–1 and n = 2.36.



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  		Fig. 9. Experimental and simulated BTCs of SO4 effluent concentrations from the BC horizon [column BC-I, input SO4 (Co) of 0.005 M]. Simulations are based on best-fit of the data when linear equilibrium (dotted curve), nonlinear equilibrium (dashed curve), and kinetic models (solid curve) were used.

 


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  		Fig. 11. Experimental and simulated BTCs of SO4 effluent concentrations from the BC horizon [column BC-II, input SO4 (Co) of 0.0005 M]. Calculations are based on the kinetic model in a curve-fitting mode (solid curve) and prediction mode (dashed curve).

 


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  		Fig. 10. Experimental and simulated BTCs of SO4 effluent concentrations from the BC horizon [column BC-II, input SO4 (Co) of 0.0005 M]. Calculations are based on the linear equilibrium model in a curve-fitting mode (solid curve) and prediction mode (dashed curve).

 
As clearly illustrated in Fig. 9 and 11, good description of the effluent results from BC-I and BC-II were achieved when the first-order kinetic model was implemented. Furthermore, increased sorption was realized for the higher input concentration (Co = 0.005 M) of the BC-I column than for BC-II. This finding is based on the ratio of the parameters (k1/k2) that provided best-fit model fittings (see Table 3). For BC-I, the value of (k1/k2) was 2.76 compared with a value of 0.98 for BC-II. Such trends are consistent with the upper Bs layer and indicate sorption dependency on the dominant concentration within the soil column as influenced by the SO4 input (Co).

Figure 10 and 11 illustrate a comparison of simulated (curve-fitted) vs. predicted BTCs for the BC-II column. Clearly, regardless of whether a kinetic or equilibrium model was used, the predictions overestimated the extent of sorption and resulted in much delayed BTCs. These predictions were obtained with independently derived parameters from the BC-I column for the equilibrium linear model as well as the kinetic model. It is obvious that the independently measured parameters for the high concentration were inadequate in describing BTC for the low concentration. Therefore, the reactivity or retention of SO4 during transport is concentration dependent.


   SUMMARY AND CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 A GENERALIZED MULTIREACTION...
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
REFERENCES
 
In summary, SO4 transport in soil columns from the upper three soil horizons (E, Bs, and BC) of a Swedish forest (podsolic) soil was quantified. Two CaSO4 pulse input solutions (Co of 0.005 and 0.0005 M) were separately applied to the top (E) layer where sequential leaching was used for the subsequent lower (Bs and BC) layers. Sulfate breakthrough results were dependent on input-pulse concentration where lower sorption of SO4 reactivity or retention was observed for lower (Co). Efforts were made to model SO4 breakthrough results based on miscible displacement approaches and the solute CDE. Our modeling efforts were less than adequate for the top (E) horizon. For all other layers and input Co values, model simulations were described SO4 mobility in soils. We conclude that sulfate retention during transport in this forest soil is most likely controlled by nonlinear equilibrium or kinetic reactivity of SO4 of the reversible and irreversible mechanisms. Moreover, model parameter estimates indicate that the reactivity or retention of SO4 during transport were concentration dependent.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 A GENERALIZED MULTIREACTION...
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 


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This Issue in Journal of Environmental Quality

JEQ 2004 33: 413-418. [Full Text]  




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