Soil Science Society of America Journal 65:1056-1064 (2001)
© 2001 Soil Science Society of America
DIVISION S-1—SOIL PHYSICS
Solute Transport in Layered Soils
Nonlinear and Kinetic Reactivity
Liuzong Zhou and
H. M. Selim*
Agronomy Dep., Sturgis Hall, Louisiana Agric. Exp. Station, LSU Agricultural Center, Baton Rouge, LA 70803-2110
* Corresponding author (mselim{at}agctr.lsu.edu) or (xp2469{at}unix1.sncc.lsu.edu)
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ABSTRACT
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In this study, solute transport in multilayered soils where steady flow is dominant was investigated. We considered nonreactive as well as reactive solutes in layered soils with emphasis on nonlinear solute reactivity with the soil matrix. For individual soil layers, solute-retention mechanisms considered were linear, nonlinear, Langmuir, first-, second-, and nth-order kinetics, and irreversible reactions. The convective-dispersive equation (CDE) for reactive solutes was solved using the finite difference method. First-type and a combination of first- and third-type boundary conditions (BCs) for the interface between soil layers were tested. Unlike the first-type BC, the combined first- and third-type BC always achieved a good solute mass balance in multilayered soils. Physical and chemical properties of each soil layer were assumed to differ significantly from one another. For all retention mechanisms used, our simulation results indicated that solute breakthrough curves (BTCs) were similar, regardless of the layering sequence in a soil profile. This finding is consistent with an earlier finding (Selim et al., 1977), where a linear adsorption mechanism was dominant and contrary to that of Bosma and van der Zee (1992) for nonlinear adsorption. Experimental results based on miscible displacements from soil columns of a two-layer system [sand over Sharkey (very-fine, smectitic, thermic Chromic Epiaquerts) clay and Sharkey clay over sand] support our simulation results. Specifically, BTCs for pulse inputs for tritium, as well as for the Ca–Mg system, support the above conclusion. All tritium and Ca–Mg BTCs were well predicted with our multilayered model where independently derived solute physical and retention parameters were implemented.
Abbreviations: BC, boundary condition • BTC, breakthrough curve • CDE, convective-dispersive equation • CEC, cation-exchange capacity
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INTRODUCTION
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THE PHENOMENON OF SOIL stratification of the soil profile has been documented for several decades from soil survey work. The transport processes of dissolved chemicals in stratified or layered soils have been studied for several decades (Shamir and Harleman, 1967; Selim et al., 1977; Bosma and van der Zee, 1992; Wu et al., 1997). Solute transport in layered soils can be investigated through numerical methods as well as approximate analytical solutions. An early analytical method was proposed by Shamir and Harleman (1967) who used a system's analysis approach. They assumed that different layers were independent with regard to solute travel time. Each layer's response served as the BC for the downstream layer and so on. Later, Selim et al. (1977) discussed the movement of reactive solutes through layered soils using finite difference numerical methods. They considered both equilibrium and kinetic sorption models of the linear and nonlinear types. In the late 1980s, Leij and Dane (1989) developed analytical solutions for the linear sorption–type models using Laplace transforms. Their solutions were based on the assumption that each layer was semi-infinite. Bosma and van der Zee (1992) also proposed an approximate analytical solution for reactive solute transport in layered soils using an adaptation of the traveling wave solution. Recently, Wu et al. (1997) developed another analytical model for nonlinear adsorptive transport through layered soils ignoring the effects of the dispersion term. In addition, Guo et al. (1997) showed that the transfer function approach was a very powerful tool to describe the nonequilibrium transport of reactive solutes through layered soil profiles with depth-dependent adsorption.
When we study transport process of dissolved chemicals in layered soils, it is of interest to investigate whether soil layering affects solute breakthrough. When flow remains one-dimensionally vertical, which is the case when perfect horizontal stratification exists, it is of interest whether the layering order affects breakthrough results at the groundwater level (van der Zee, 1994). The early results from Shamir and Harleman (1967) showed that the order of layering did not affect breakthrough significantly. This interesting result was further elaborated upon by Barry and Parker (1987) on the basis of various analytical approaches. Results from various linear and nonlinear numerical simulation for several sorption model types also supported this conclusion (Selim et al., 1977). Furthermore, Selim et al. (1977) concluded that layering order was also unimportant for Freundlich adsorption (nonlinear, b = 0.7). Their experimental results also supported this conclusion. However, van der Zee (1994) attributed Selim and coworkers' (1977) results to the small Peclet number assumed for the nonlinear layer, which prevents nonlinearity effects to be clearly manifested. Van der Zee (1994) also used a hypothetical result to illustrate that layering sequence should have an effect. According to our understanding, BTCs are the curves of concentration versus time at the outlet. However, what van der Zee (1994) used to support his conclusion was the traveling wave, which was the curve of concentration versus depth at different times, that is, concentration profile. What van der Zee (1994) did show was that layering order would have effects on the front thickness of the traveling wave. However, we question whether a direct relationship exists between the front thickness of the traveling wave and the BTC at the outlet.
In this article, we investigated the effects of layering order or stratification sequence on the BTCs of solutes in layered soil systems and we focused on the effects of nonlinearity of solute adsorption properties on BTCs. Both simulations and transport experiments were conducted to study the transport of nonreactive and reactive solutes through water-saturated two-layered soils under steady-state flow. We assumed that each soil layer was homogeneous and isotropic with soil water and solute-sorption properties known. Linear and nonlinear equilibrium type, Langmuir-type retention, and nth-order and second-order kinetic adsorption processes were considered as the governing reaction mechanisms. The finite difference method (see Selim et al., 1990) was used to solve the CDE for solute transport in two-layered soils under steady-state flow conditions. Transport experiments were also conducted to study the movement of Mg, Ca, and 3H in water-saturated two-layered soils (Sharkey clay and acid-washed sand) under steady-state flow.
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THEORY
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A two-layered soil column of length L is shown in Fig. 1. The length of each layer is denoted by L1 and L2, respectively. To show heterogeneity, each soil layer has specific, but not necessarily the same, water content, bulk density, and solute-retention properties. Only vertical direction steady-state water flow perpendicular to the soil layers (Fig. 1) will be considered. The CDE governing solute transport in the ith layer (see Fig. 1) is given by Eq. [1] (Selim et al., 1977):
 | (1) |
where (omitting the i) C is resident concentration of solute in soil solution (µg cm-3), S is amount of solute adsorbed by the soil matrix (µg g-1), 
is soil bulk density (g cm-3), 
is volumetric soil water content (cm3 cm-3), D is solute dispersion coefficient (cm2 d-1), q is Darcy soil-water flow velocity (cm d-1), Q is a sink or source for irreversible solute interaction (µg cm-3 d-1), x is distance from the soil surface (cm), and t is time (d).
The reversible solute retention from the soil solution is represented by the term 
S/t on the left side of Eq. [1] while the irreversible solute removed from soil solution is expressed by the term Q on the right side of Eq. [1]. The initial conditions used were given by
 | (2) |
This condition signifies that each soil layer is initially solute free.
We will consider how the solute will break through the layered soils when an input pulse of solute solution having a concentration Co and for a time duration To (d) is applied at the inlet, that is, the soil surface (x = 0). In this case, both first-type BC (concentration is known) and third-type BC (flux is known) will be applicable to represent the inlet boundary. The difference between these two types of BCs was discussed by Leij et al. (1991). In this study, a third-type condition (Selim and Mansell, 1976) for the soil surface is adopted to satisfy the principle of mass conservation. Therefore, the boundary condition at the soil surface (Layer I) is
 | (3) |
 | (4) |
At the bottom of the soil column (x = L), the BC commonly adopted is
 | (5) |
Another BC needed in our analysis is the BC at the interface between layers. It should be noted that both first-type and third-type BCs are applicable at the interface. Leij et al. (1991) showed that although the principle of solute mass conservation is satisfied, a discontinuity in concentration develops when a third-type interface condition is used. On the other hand, a first-type interface condition will result in a continuous concentration profile across the boundary interface at the expense of solute mass balance. To overcome the limitations of both first- and third-type conditions, a combination of first- and third-type condition is used in this article. The first-type condition can be written as
 | (6) |
where x
L-1 and xL+1 denote that x = L1 is approached from upper and lower layer, respectively. Similarly, the third-type condition can be written as
 | (7) |
Incorporation of Eq. [6] into Eq. [7] yields
 | (8) |
The BC of Eq. [8] resembles that for a second-type BC as indicated earlier by Leij et al. (1991).
Solute-Retention Mechanisms
Six types of retention models were used to describe the reversible retention term, S/t, in Eq. [1]:
Linear
A linear adsorption relationship between S and C was assumed,
 | (9) |
where Kd is the distribution coefficient (cm3 g-1). A dimensionless retardation factor R (Lindstrom et al., 1967) can be obtained from Eq. [1] and [9]:
 | (10) |
Nonlinear (Freundlich)
A nonlinear retention was considered as follows:
 | (11) |
where b (dimensionless) is commonly less than unity for most reactive solutes and Ke (µg1-b mLb g-1) is a Freundlich partitioning coefficient (Selim and Amachar, 1997). Now a concentration-dependent retardation term can be obtained by incorporating Eq. [11] into Eq. [1]:
 | (12) |
Langmuir
We also considered Langmuir-type adsorption in the form,
 | (13) |
where Smax is the total adsorption capacity (µg g-1 soil) and k is a Langmuir affinity coefficient (cm3 g-1). The retardation factor for this model is concentration-dependent and given by
 | (14) |
First- and Nth-Order Kinetics
A reversible nth-order kinetic adsorption was considered:
 | (15) |
where Kf and Kb are the forward and backward rate coefficients (d-1), respectively; n is the nonlinear parameter and usually less than unity.
Second-Order Kinetics
Here the second-order approach of Selim and Amacher (1997) was considered:
 | (16) |
where Kf and Kb (d-1) are forward and backward rates of reaction, respectively, and 
is the amount of available or vacant sites (mg Kg-1 soil). As SSmax, the amount of available sites approaches zero (0).
Irreversible Reactions
The sink-source term Q in Eq. [1], representing decay or degradation reactions, was expressed as a first-order kinetic process:
 | (17) |
where Ks is the rate of reaction (d-1).
The governing Eq. [1] subject to conditions [2] through [6], and [8] was solved numerically using the Crank-Nicholson finite difference approximations (Selim et al., 1990). The BCs at the interface between two distinct layers were implemented in a way similar to that of Leij and Dane (1989). For all cases presented in this study where a combined first- and third-type BC at the layer interface was used, Eq. [6], as well as Eq. [8], were incorporated into the numerical scheme. In addition, a correction to the dispersion term was incorporated into the difference equations to improve numerical approximations.
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MATERIALS AND METHODS
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Sharkey clay soil having a pH of 5.9, organic matter of 1.14%, and cation-exchange capacity (CEC) of 39.06 cmolc kg-1 (sand 3%, silt 36%, clay 61%) was used in this study. In addition, an acid-washed mixture of 81% sand and 19% silt was used that had negligible CEC and organic-matter content. Acid-washed sand was chosen as a nonreactive matrix because of the absence of clay or organic matter (Ma and Selim, 1994a). The Sharkey clay soil was taken from the Ap horizon, air dried, mixed, and passed through a 2-mm screen before use. Sharkey soil and acid-washed sand were packed in small increments into plexiglass columns (6.4-cm diam.; 15-cm length). Each soil column consisted of two distinct layers: a Sharkey clay layer and a sand layer. The length of each layer varied among the different columns; these lengths are listed in Table 1. Miscible displacement methods for packed soil columns were employed to obtain solute BTCs under water-saturated and steady water flux conditions. Each layered soil column was slowly saturated from the bottom with 0.5 M CaCl2 for 3 d. After that, the soil column was saturated with 0.05 M CaCl2 at a constant flow rate until the concentration of Ca in effluent was similar to that of the input solution. At such time a pulse of 0.05 M MgCl2 was applied. This was subsequently followed by 0.05 M CaCl2 background solution to leach Mg out. The effluent was collected in 30-min intervals using a fraction collector and analyzed for cation concentrations. Once frequent checks of effluent composition indicated negligible concentration of Mg (<0.0001 M), water flow was stopped. The soil column was reversed and leached under the reverse layering order for about 3 d. Then the above transport experiment was repeated once more at the same flow rate.
Tritium breakthrough experiments were carried out in the same manner where a pulse of approximately one pore volume of 0.005 M CaCl2 solution spiked with tritium was introduced. We have two replicates identified as Columns B and C in Table 1. Analysis for Ca and Mg concentrations in the effluent were carried out using inductively coupled plasma and analysis of tritium intensity in effluent was conducted by liquid scintillation.
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RESULTS AND DISCUSSION
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Accuracy of Numerical Solution
To test the reliability of the numerical method, results from our numerical solution were compared with those from analytical solution. The data in Leij et al. (1991)(Fig. 3 [top]) were used for such a comparison. The relative concentration (C/Co) as a function of soil depth is given in Fig. 2. A first-type BC at the surface was used in order to compare our numerical solutions with the analytical solutions of Leij et al. (1991). For other cases presented in this article, a third-type BC at the surface was used. The numerical solution matches the analytical solution extremely well when the combined first- and third-type interface BC is adopted. Although some differences exist between the numerical results and the analytical solutions when the first-type interface BC was used, the magnitude of the error was considered acceptable. Possibly, the differences are due to the BCs used. Leij et al. (1991) used a semi-infinite BC at the interface and at the column exit while we use finite BC both at the interface and the lower boundary. Overall, the numerical solution for the CDE is accurate and reliable.
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Fig. 2. Relative concentration versus depth for a two-layered soil (L1 = L2 = 6 cm) based on analytical solution of Leij et al. (1991) and our numerical method, at time equals 0.4 d. The solid curve and closed circles are for a first-type boundary condition (BC) at the interface between the two layers, whereas dashed curve and open circles are for a combined first- and third-type BC.
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Linear Adsorption
Figure 3 shows a comparison of BTCs for a two-layered soil column with reverse layering orders. The parameters used for the simulation are given in Table 2. Here, R1R2 means R1 is the first (top) layer encountered and R2 is the bottom layer, where R1 and R2 refer to the retardation factor R of Eq. [10] associated with Layers 1 and 2, respectively. Conversely, R2R1 means R2 is first encountered (top layer) and R1 is the bottom layer. Here we report results for a layered soil column where one layer is nonreactive (R = 1) and the other is linearly adsorptive. In Fig. 3 (top), results are given when a first-type BC was used for the boundary interface between the two soil layers. In contrast, in Fig. 3 (bottom), a combined first- and third-type BC was used. The BTC for the case R1R2 where the nonreactive layer was first encountered (top layer) was similar to that when the layering sequence was reversed (R2R1) and the reactive layer (R2) was the top layer. This observation was true only when a combined first- and third-type BC was used. However, as illustrated in Fig. 3 (top), the BTCs from the two different columns deviated considerably from each other when the first-type BC was employed. It should be pointed out that the mass conservation principle was violated when the first-type BC was used at the interface boundary. The mass balance for the first-type BC varied from 85 to 150%. Differences in the BTCs are perhaps a result of the poor mass balance. However, for the first-type BC, we found that on the basis of several simulations, a good mass balance could be achieved and the two BTCs for differing layer sequences were similar when the transport parameters of both soil layers, especially the dispersion coefficient (D), were similar in magnitude (data not shown). On the other hand, when the combined first- and third-type BC is used, a mass balance error not exceeding ±1.5% was always achieved for all cases reported in this study. Therefore, for the linear adsorption case, we conclude that the order of soil stratification or layering sequence fails to influence solute BTCs and is consistent with those reported earlier by Shamir and Harleman (1967) and Selim et al. (1977).
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Table 2. Parameters used in simulation for linear adsorption, nonlinear adsorption, kinetic adsorption model, and sink term.
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Nonlinear Freundlich Adsorption
Simulated BTCs of solutes from a two-layered soil system with one as a nonlinear (Freundlich) adsorptive layer are given in Fig. 4. Here, R1 represents a nonreactive layer, whereas R2 stands for a nonlinear (Freundlich) adsorptive layer. The parameters used in the simulations are given in Table 3. Our simulations were carried out for a wide range of the Peclet or Brenner number (B = qL/D). Specifically, the values of B in Fig. 4 were 2, 10, and 40, respectively. We also examined the influence of the nonlinear Freundlich parameter b (see Eq. [11]) on the shape of the BTCs. Although for most solutes, the parameter b values are not commonly reported greater than unity (Selim and Amacher, 1997), we examined BTCs for b values less than as well as greater than unity (b = 0.5, 0.7, 0.9, 1.25, and 1.50). The combined first- and third-type BC was used at the interface between the layers. On the basis of our simulations, BTCs were not influenced by the layering sequences regardless of the Brenner number B when nonlinear Freundlich adsorption was considered. This result is similar to that of Selim et al. (1977). Yet van der Zee (1994) attributed their results to the small Peclet number that prevented nonlinearity effects to be clearly manifested. Dispersion is dominant for the case where the Brenner number is small whereas convection becomes the dominant process for large B values. The BTCs exhibit increasing retardation or delayed arrival, and excessive tailing of the desorption (right-hand) side of the BTCs for increasing values of nonlinear adsorption parameter b. In addition, the BTCs become less spread (i.e., a sharp front) with increasing Brenner numbers. All such cases provide similar observations, that is, the effects of nonlinearity of adsorption are clearly manifested. Nevertheless, for all combinations of b and the Brenner number B used in our simulations, the BTCs under reverse layering orders showed no significant differences. In other words, layering order is not important for solute breakthrough in layered soils with nonlinear adsorption as the dominant mechanism in one of the layers.
Langmuir-Type Adsorption
To illustrate that the above finding is universally valid, other solute adsorption processes of the nonlinear type were investigated. The Langmuir adsorption model is perhaps one of the most commonly used equilibrium formulas for describing various reactive solutes in porous media. We are not aware that such a model was tested for multilayered systems. We considered only simulated columns consisting of one nonreactive layer and one reactive layer with the Langmuir-type adsorption mechanism. The simulation results are shown in Fig. 5. The combined first- and third-type BC was used at the interface between the layers. The parameters used for simulations are given in Table 4. Consistent with the above finding, we found that for all parameters used in this study, the layering sequence has no effect on the BTCs when Langmuir-type adsorption was the dominant mechanism.
Kinetic Adsorption
In this section, first- and nth-order reversible kinetics (Eq. [15]) was considered the dominant retention mechanism. The parameters used in the simulations are given in Table 3 and the BTCs under different layering sequence are shown in Fig. 6. As previously denoted, R1 stands for the nonreactive layer whereas R2 represents a kinetic adsorptive layer. Values of the parameter n used were 0.3, 0.7, and 1.0 and the combined first- and third-type BC was employed to represent the interface condition. The BTCs under reverse layering orders showed a very good match regardless of the value of the nonlinear parameter n. For the case of first-order kinetic (n=1), a good match was also realized. Careful inspection of the results showed some deviations at the early arrival stage for both cases with n=0.3 and 0.7. One may attribute such small deviations to the extremely slow convergence that was encountered for n 
1. Considerable CPU time was required for the case with n = 0.3 and 0.7 because of extremely small time and space increments (
t and x) required in the numerical simulations.
We also carried out simulations where both layers were assumed reactive. In Fig. 7, simulations were obtained when one layer was with linear adsorption (Eq. [9]) and the second layer with first-order kinetic reaction. Simulations shown in Fig. 8 were similarly obtained except that a nonlinear (Freundlich) rather than linear was assumed for the first layer. The simulation parameters are given in Table 2. Both the first-type and combined first- and third-type BC were employed but we show only those with combined first- and third-type BC. On the basis of our simulations, layered soils with reverse layering orders showed no significant differences when a combined first- and third-type BC was used. We observed that the two BTCs deviated somewhat for the cases when one layer was nonlinear (see Fig. 8). Such small deviations were not at all obvious for the case where linear adsorption was considered (Fig. 7). However, once again, we attribute such deviations to slow convergence encountered here and similar to those encountered in simulations for nonlinear kinetics shown Fig. 6.
Irreversible (Sink) Reaction
Figure 9 shows the effect of a sink term on the shape of the BTCs for a two-layered soil where only one layer was considered reactive. Here the sink term Q for irreversible reaction was that of the first-order type given by Eq. [17]. The case considered here is that shown in Fig. 6 with nonlinear kinetic reaction (n = 0.7) with and without irreversible reaction. Therefore the BTCs shown illustrate the effect of layering when we consider multiple kinetic reactions, that is, nonlinear reversible plus a sink term. At any time, the area between the BTCs (with and without a sink) represents the amount of solute irreversibly retained by the soil. It is obvious that in the presence of a sink term, the order of soil layers did not influence the shape or the position of the BTCs. This finding is consistent with that of Selim et al. (1977) where a similar sink term was implemented. The only exception is that the reversible mechanism used here and illustrated in Fig. 9 was that of the nonlinear kinetic type.
Second-Order Adsorption
The second-order adsorption model (Eq. [16]) is a recently developed kinetic approach for describing the fate of herbicides in soils and we are not aware that this concept has been utilized for multilayered soils. For extremely large rate coefficients or at long times, the second-order model approaches the Langmuir equilibrium model (Eq. [14]). We also simulated the transport process in layered soils where one layer was assumed nonreactive whereas the second-order process was the controlling mechanism for the second layer. The BTCs shown in Fig. 10 exhibit extensive tailing, typical of second-order modeling. Moreover, the BTCs indicated similar results regardless of the order of the layers in the system.
Experimental Results
To verify our results on the basis of numerical simulations, we conducted transport experiments for both reactive as well as nonreactive solutes (see Fig. 11–13). Figure 11 shows BTCs for Mg and Ca in a soil column consisting of a Sharkey clay layer and a sand layer. These cations were selected because of earlier studies of Ca and Mg ion exchange during transport in Sharkey soil (see Gaston and Selim, 1990a,b). Specifically, one can assume an equilibrium-type adsorption or ion-exchange reaction with Sharkey soil as dominant. Moreover, for Sharkey soil, Ca exhibited a slight preference over Mg for exchange sites resulting in a nonlinear (Langmuir type) adsorption relation. The BTC results of Ca and Mg are for two types of pulses; one is the case where the input pulse first encountered the clay layer. The column was then reversed and a second pulse introduced to ensure that the new pulse first encountered the sand layer. The extent of retardation of the Mg pulse in this Ca–Mg system is manifested by the fact that some 7-pore volumes were required for C/Co to reach 0.5. Regardless of whether a sand or clay layer was first encountered, the effluent BTCs were not significantly affected by the layering sequence. Efforts were made to maintain an experimental transport condition consistent under the differing layering orders. We encountered difficulties in maintaining a constant pore volume because of the swelling of the Sharkey clay layer. Nevertheless, Ca as well as Mg results from the layered soil column indicate that the order of layers (i.e., sandclay or vice versa) did not influence the BTCs appreciably.
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Fig. 11. Experimental (symbols) and simulated (dashed and solid lines) breakthrough results for Ca and Mg in a two-layered soil column (Sharkey claysand, column A) under different layering sequences.
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Fig. 13. Experimental (symbols) and simulated (dashed and solid lines) breakthrough results for tritium in a Sharkey claysand column (column C) under different layering orders.
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Fig. 12. Experimental (symbols) and simulated (dashed and solid lines) breakthrough results for tritium in a two-layered soil column (Sharkey claysand, column B) under different layering orders.
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The BTCs from tritium pulse inputs, which were introduced as a tracer solute in two different columns (B and C) are shown in Fig. 12 and 13. One assumed that tritium is nonreactive in the Sharkey clay layer as well as in the acid-washed sand. For both soil columns, we maintained, as much as possible, a constant water flux at all times. This was particularly important when the flow direction in a column was reversed and a new tritium pulse was subsequently introduced. Moreover, we attempted to maintain a similar pulse duration (or volume) to facilitate comparison of both sides of the BTCs. The tritium BTCs are consistent with other tracer data of Selim et al. (1977) for 36Cl in a two-layered soil column and confirm the simulated BTCs presented above, which illustrates the independence of layer sequence for all solute adsorption mechanisms considered in this investigation.
Simulation of Experimental Data
We simulated the breakthroughs of Ca and Mg of Column A using our two-layered model for reactive solutes. The simulation results were also shown in Fig. 11 (solid and dashed lines for different layering arrangements). The values of Darcy water flow velocity, q, soil water content, , bulk density, , and Mg pulse duration were directly from our experimental measurements. Dispersivity values for both acid-washed sand and Sharkey clay used here were not obtained on the basis of curve-fitting; rather they were independently obtained from Ma and Selim (1994a)(b). The reaction mechanism for the Ca–Mg system was assumed to be governed by simple ion exchange for a binary system. For conditions of constant ionic strength, the cation exchange can be described by the following equation:
 | (18) |
where c is relative concentration (C/Co), K12 is the selectivity coefficient (dimensionless), and ST is the CEC. For Sharkey soil, the value of the parameter K12 used was 1.40, which was determined by Gaston and Selim (1990a) from Ca–Mg exchange isotherms. In addition, a value of 22.5 cmolc kg-1 for the CEC ST was used. Figure 11 shows that the simulation curves agree with the experimental data, especially for the adsorption front. Our simulation also show some tailing of the release curve for both Ca and Mg. Such tailing was not observed on the basis of our experimental data, however.
We also modeled the BTCs of tritium in Columns B and C. The results are shown in Fig. 12 and 13, respectively (solid and dashed lines), and indicate a good match of the experimental data. All input parameters were directly based on our experimental measurements. Dispersivity values used here for both soil layers were those obtained from Ma and Selim (1994a)(1994b). We used a retardation factor, R, of 1.1 in our calculations. A value for R of 1.08 for Sharkey clay was used by Gaston and Selim (1994a).
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SUMMARY AND CONCLUSION
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In this article, we presented simulated breakthrough results of reactive solutes in layered soil with emphasis on nonlinear reactivity with the soil matrix. Physical and chemical properties of each soil layer was assumed to differ significantly from one another. Linear and nonlinear equilibrium type, Langmuir-type retention, and nth-order and second-order kinetic adsorption processes were considered as the governing retention mechanisms. Our model is capable of predicting differences of BTCs due to layering sequence. For all parameter values used in this study, our simulation results indicated that the BTCs are similar regardless of the layering arrangement or sequence. This finding is consistent for all reversible and irreversible solute-retention mechanisms considered. Results from miscible displacement experiments for tritium as a nonreactive solute as well as competitive adsorption of Ca and Mg support the above conclusion. A two-layered system of sand over Sharkey clay and Sharkey clay over sand columns was used. On the basis of independently measured parameters, model predictions for the sand-Sharkey clay soil columns agreed well with our experimental BTCs.
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NOTES
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Approved as Manuscript no. 01-09-129.
Received for publication June 5, 2000.
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