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DIVISION S-2-SOIL CHEMISTRY

Nonequilibrium Sorption of Dimethylphthalate—Compatibility of Batch and Column Techniques

^a Federal Institute of Geosciences and Natural Resources, Stilleweg 2, 30655 Hannover, Germany
^b Department of Geoecology, Technical University Carolo-Wilhelmina, Langer Kamp 19 c, 38106 Braunschweig, Germany
^c Department of Civil Engineering, UAE University, Al-Ain, United Arab Emirates
^d Department of Civil and Environmental Engineering, Michigan State University, East Lansing, MI 48824

Corresponding author (sven.altfelder{at}bgr.de)

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
This study reconciles an apparent inconsistency between the dimethylphthalate (DMP) batch and column data reported in the literature. Some researchers found that retardation coefficients obtained by fitting a linear two-stage model to column data were about 50% smaller than those calculated from the distribution coefficient of a 14-d isotherm. In this study, sorption parameters were derived independently by fitting a linear and a nonlinear two-stage model simultaneously to the 3- and 14-d isotherms as well as to a sorption rate study reported by others. With the sorption parameters and the dispersion coefficient obtained from a tritium tracer experiment, the column data were adequately predicted. A major part of the differences in the retardation coefficients observed in other research could be related to experimental difficulties in detecting the tailing of nonequilibrium breakthrough curves.

Abbreviations: DMP, dimethylphthalate • LEA, local equilibrium assumption

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
ORGANIC CONTAMINANTS are introduced into the subsurface through diffuse sources, such as regionally applied agrochemicals, as well as point sources, including accidental spills, hazardous waste sites, or landfills. Development of remedial actions to deal with these contaminants requires understanding the physical, chemical, and biological processes affecting their mobility. Among these processes, sorption is believed to be an important mechanism that dramatically influences their environmental fate. At the laboratory scale, batch or packed column experimental techniques are commonly employed to gain insight into sorption behavior of organic compounds. Results obtained from the laboratory are then utilized to predict actual transport in the field.

The sorption behavior in batch and column studies has been found to be in agreement in many studies (e.g., Lee et al., 1988; MacIntyre et al., 1991; Gaber et al., 1992). However, results disagreed considerably in others (e.g., Bilkert and Rao, 1985; MacIntyre and Stauffer, 1988; Piatt et al., 1996). The disagreement was attributed to different causes, such as loss of sorbent from the column, variations in column flow, immobile water in the column (MacIntyre et al., 1991), mixing differences between the two methods (Schweich et al., 1983), reduction in soil particle spacing in the column compared with batch systems (Celorie et al., 1989), different soil/water ratios (Karickhoff and Morris, 1985), and the possibility of soil abrasion in batch experiments (Boesten, 1986). In contrast, an apparent disagreement may be produced by applying an equilibrium model to data although sorption equilibrium was not reached within the time scale of the batch or column experiments. Failure to reach sorption equilibrium is likely to occur since sorption of nonionic organic compounds in soil is very slow (Streck et al., 1995). If sorption equilibrium is assumed erroneously, incorrect equilibrium constants that are lower than the true equilibrium values will be estimated (Brusseau et al., 1991). A direct estimation of the equilibrium constant is difficult as equilibration may take several weeks, months, or even years (Ball and Roberts, 1991). To overcome this problem inverse modeling can be used to estimate sorption rate and equilibrium parameters from column or batch data.

In batch experiments, slow sorption rates result in continuously decreasing solute concentrations even after the typical time span of the experiment. In column experiments, slow sorption or desorption rates lead to pronounced tailing of the breakthrough curves. For the case of a pulse input, the column experiment is terminated when the quantification limit of the target compound is reached. Breakthrough curves may lack much of the tail data, although most of the solute has actually been recovered. Sorption parameters estimated by inverse modeling of batch and column data are therefore subject not only to random errors but also to errors caused by the necessity to use a truncated set of data specific to the experimental technique employed.

Most studies that found deviating sorption parameter values between batch and column experiments are limited to comparisons of parameter sets obtained from each experimental technique (MacIntyre and Stauffer, 1988; Lion et al., 1990; Piatt et al., 1996). However, as pointed out by Addiscott et al. (1995), this popular strategy (e.g., obtaining parameters by fitting to the data to be simulated) is the least desirable when attempting to identify shortcomings of either the model or the fit procedure. A more stringent model validation is the determination of all parameters independent from the data to be simulated (Addiscott et al., 1995; Brusseau, 1998).

For aquifer materials low in organic C such a strategy was applied by Larsen et al. (1992). The authors used a two-compartment model to estimate kinetic sorption parameters from batch data and found good agreement between measured and predicted transport data. For aquifer material restricted to a narrow size fraction, Young and Ball (1994)(1999) applied the same strategy using a diffusion model. While Young and Ball (1994) were able to predict transport data with good agreement, Young and Ball (1999) were less successful especially at the highest flow velocity. For soil, Ma and Selim (1994) and Streck et al. (1995) successfully predicted herbicide transport with parameters derived from batch experiments. Both studies used a two-compartment approach.

Here, we investigate data from soil column and batch experiments with DMP originally presented by Maraqa et al. (1998). These authors found that the results of batch experiments could not be explained with sorption parameters estimated from column data. Retardation coefficients determined in column studies were up to 50% smaller than those determined in batch experiments. By conducting additional experiments Maraqa et al. (1998) could exclude the causes frequently given to explain differences in results obtained in batch and column experiments. The reason for the observed discrepancy remained unclear. In our study, we challenge their results by showing that DMP transport in the soil columns can be described adequately with parameters estimated from batch experiments.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
We limit the description of the isotherm studies, the sorption rate studies and the column experiments to the main features of each experiment. More details are given in Maraqa et al. (1997)( 1998). The soils had been collected from the A and B horizons of Oakville sand (mixed mesic Typic Udipsamment) located in North Star, MI. The organic C contents of the A and B horizons were 2.25 and 0.7%, respectively. The soils were air dried and ground to pass through an 0.85-mm sieve. Experimental solutions were prepared by dissolving DMP in 0.005 M CaCl₂ containing 0.05% Na azide to avoid biodegradation. Chemical analysis of DMP was carried out using high-performance liquid chromatography with ultraviolet detection.

Batch Experiments
Batch experiments included a 14-d rate study and a 3- and 14-d sorption isotherm measured for each soil. In all experiments, the soil/solution ratio was 1:1.5 g mL^-1. The rate study was carried out at an initial concentration of 20 mg L^-1. For the isotherms, the initial concentration varied from 5 to 140 mg L^-1. The experiments were carried out in 25-mL Corex centrifuge tubes (Corning Glassworks, Corning, NY) with Teflon lined screw caps. The tubes were tumbled end over end for the desired period of time and then centrifuged at 1250 g for 30 min. Aqueous samples were collected with glass syringes and analyzed for DMP. The amount sorbed by the soil was determined by difference. Blanks were prepared to verify that sorption to the tubes and caps could be excluded.

Column Experiments
The soils used in the saturated-flow column experiments were packed into glass columns (5.45-cm i.d.) of 30.2-cm length with Teflon plates on each end. A pulse input of approximately two pore volumes of a 30 mg L^-1 DMP solution was injected into the columns with three different velocities. The columns were then eluted at the originally applied flow rates with a DMP-free 0.005 M CaCl₂–azide solution. Effluent samples were collected with glass syringes attached to the outlet of the column. No evidence of DMP sorption was detected when a miscible-displacement experiment was conducted on a column packed with glass beads.

Modeling
Model Description
Sorption of DMP in the two soils was investigated with a two-stage model. Models of this type are frequently used to describe nonequilibrium sorption of organic compounds and have often been found to work best when describing slow sorption rates (Pignatello, 1989). We assume slow sorption is diffusive uptake of solute into soil organic matter. This process is simplified by assuming that solute is transferred into two serially arranged regions within the sorbent, one of which is in direct contact with the surrounding solution. The sorbate concentrations in these two regions, S₁ and S₂ (mg kg^-1), are defined per unit sorbent mass in Region 1 and 2, respectively. The difference in concentration between the two regions is the driving force for sorption and desorption processes, with the rate assumed proportional to the respective concentration difference. In Region 1, sorption is fast relative to the duration of the experiment so that equilibrium can be assumed

(1)

In contrast, sorption in Region 2 is assumed to be rate-limited

(2)

where C is the concentration of dissolved chemical (mg L^-1), the parameters k (mg^1-m L^m kg^-1) and m denote the Freundlich equilibrium parameters, ₂ is the sorption rate coefficient (d^-1), f is the fraction of Region 1 sites, and t is time (d). The total concentration of the sorbed solute S (mg kg^-1), is given by

(3)

At equilibrium, the model predicts the same concentration in both fractions of the solid phase

(4)

S₁ and S₂ can be related to the sorbed-phase concentrations defined per unit mass of the total sorbent (e.g., Brusseau and Rao, 1989) by and . Equation [2] may then be rewritten

(5)

With , the governing equations reduce to the linear two-site model used by Maraqa et al. (1998). In this case, the coefficient k is commonly denoted k_D. The rate coefficient k₂ is related to ₂ by .

Parameter Estimation on Batch Data
The 3- and 14-d isotherms, as well as the 14-d rate study may be combined in one rate study with samples shaken for various periods of time at different concentrations. Due to the inclusion of isotherm data, the set is biased concerning information on solute partitioning after 3 and 14 d, while for sorption times before and between these times information is only available from the rate study. Assuming negligible decay, the total concentration

(6)

in a closed batch reactor remains constant . Here, is the bulk density and is the volumetric water content. The sorption rate equation can then be written as

(7)

In a rate study with a sorbent initially free of solute, Eq. [7] is subject to the initial condition , which is derived by solving

(8)

The nonlinear form of Eq. [8] was solved for C₀ using the Newton algorithm. Equation [7] was numerically solved by the Bulirsch-Stoer method (Press et al., 1989) in all cases. S₁ can then be derived using Eq. [1]. Following this S₂ can be calculated via mass balance. The model was fitted to measured data using the Levenberg-Marquardt algorithm (Press et al., 1989) and assuming a multiplicative error model (Streck et al., 1995).

Modeling of Column Data
Assuming convective–dispersive solute transport in a homogeneous soil column with constant water content and flux, negligible decay, and slow two-stage sorption the governing transport equation may be written as

(9)

where z denotes depth (positive downward), D is the dispersion coefficient (cm² d^-1), and v the average pore water velocity (cm d^-1). Equation [9] is coupled with the sorption rate (Eq. [2]) through S₂/t. The following initial and boundary conditions were assumed (pulse input)

(10)

and

(11, 11)

Equation [9] was solved numerically using a fully implicit finite difference scheme in combination with the Newton-Raphson algorithm. Transport and sorption equations were coupled by iteration. For the linear case , the numerical solution was tested against a semianalytical solution (see Streck et al. [1995] for details of this procedure) before the DMP column experiments were modeled.

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Parameter Estimation on Batch Data
Combined plots of the 3- and 14-d isotherms of DMP in Oakville A and Oakville B soils, together with the data from the rate studies, are shown in Fig. 1 . In addition, the figure shows simulation results obtained by fitting the linear and nonlinear form of the two-stage model to the data. The simulation results for Oakville A soil presented in the upper panel were estimated by fitting both models simultaneously to all data. However, for the Oakville B soil, the rate study in the lower panel of Fig. 1 is not consistent with the isotherm data. The last point of the rate study that corresponds with a sorption period of 14 d does not coincide with the 14-d isotherm, although the time-dependent partitioning should be the same at similar equilibration times. The same holds true for the rest of the rate study starting with the second data point corresponding with a sorption period of 0.5 h.

View larger version (20K): [in this window] [in a new window]   Fig. 1. Measured and simulated batch data for dimethylphthalate (DMP) on Oakville A and B soils. Simulations were carried out with the linear and nonlinear two-stage model

View larger version (17K): [in this window] [in a new window]   Fig. 2. Measured and simulated breakthrough curves of dimethylphthalate (DMP) column experiments with Oakville A soil. The simulated breakthrough curves were estimated using the parameter set given in Table 1. The local equilibrium assumption (LEA) breakthrough curves were calculated with the 14-d distribution coefficient given by Maraqa et al. (1998). The letters in each figure denote first moments E[T] calculated from the measured curve (a), fitting CXTFIT to measured data (b), the 14-d distribution coefficient (c) (all given by Maraqa et al., 1998), and the parameters of the linear two-stage model estimated from the batch data (d) (this work)

View larger version (17K): [in this window] [in a new window]   Fig. 3. Measured and simulated breakthrough curves of dimethylphthalate (DMP) column experiments with Oakville B soil. For further information see caption of Fig. 2

However, since our study aims at the apparent discrepancy between the batch- and column-derived retardation coefficient of up to 50%, we believe that despite these short-comings the accuracy of the model predictions is fairly good. One should also consider that we used a single set of three (linear model) or four (nonlinear model) parameters for modeling the complete set of data and that we used the model in a predictive mode. In contrast, Maraqa et al. (1998) (while achieving nearly perfect agreement using the same model) used a total of 10 parameters values for the description of a reduced data set with the rate study and the 3-d isotherm not included. All parameter values were obtained by fitting. Maraqa et al. (1998) did not test any model in a predictive mode. Additionally, their results were obtained by allowing to take different values (for one parameter like or k_D) for the same soil–chemical combination, a condition that is not satisfying from the modeler's perspective.

Comparing the Model Approach with that of Maraqa et al. (1998)
In the case of linear sorption the retardation coefficient R is defined as

(12)

Maraqa et al. (1998) estimated R for each column experiment using three different methods: (a) moment analysis, (b) fitting a linear two-site model using the CXTFIT program (Parker and van Genuchten, 1984) to breakthrough data, and (c) calculation using the distribution coefficient estimated from the 14-d isotherms. It can be seen from Table 2 that R increases in the same order. While the difference between R determined by moment analysis and curve fitting is small, there is a large difference between both values and that determined by means of the 14-d distribution coefficient. Although the retardation coefficients determined by fitting the linear two-stage model to batch data (this study) are even larger than those estimated by Maraqa et al. (1998) from the 14-d isotherms, our values are able to adequately predict the column data. Underestimation of R determined from the column experiments compared with R determined from batch data was nearly independent of the time scale of the column experiment. As the time scales of the rate study and the slowest column experiment are similar (14 d), the batch technique seems to be preferable for the determination of R in both soils.

(13)

where T is the dimensionless time given by , with L being the column length. The first moments E[T] are denoted by letters in Fig. 2 and 3 and were estimated from the respective retardation coefficients given in Table 2. While the first moment and the peak maximum of the corresponding breakthrough curve agree closely for Cases a, b, and c, there is a large shift of the first moment of the breakthrough curve simulated with the rate parameters (d) obtained independently from batch experiments. The breakthrough curves obtained by CXTFIT (Case b) are not shown in Fig. 2 and 3; however, they nearly coincide with the measured data. Since the first moment of a breakthrough curve is independent of kinetic limitations (Valocchi, 1985; Streck and Piehler, 1998), the simulated curve in Case d is accompanied by extensive tailing to account for the large shift between E[T] and peak maximum.

Implications of Nonequilibrium Breakthrough Curve Tailing
Tailing of breakthrough curves is a frequently observed phenomenon in column studies of organic compounds, and in addition to the fact that it can be caused by slow sorption kinetics, it has also been related to nonlinear sorption with Freundlich exponents of less than 1, to nonsingular sorption caused by differences in sorption–desorption rates, to immobile water and to transformation into a compound that can not be discriminated from the parent compound during detection (Brusseau and Rao, 1989). Nonlinearity is explicitly accounted for by the nonlinear two-stage model used in this study and also not very pronounced for DMP. Transformations are unlikely due to the use of sterilized solutions, while immobile water was not detected during the tracer transport. Additionally it was shown by Altfelder et al. (2000) that nonsingular sorption observed over an experimental time scale similar to that of Maraqa et al. (1998) is most often only apparent. It therefore seems safe to assume that the most likely cause for tailing in the experiments of Maraqa et al. (1998) was slow kinetics.

Assuming that the measured breakthrough curves of DMP in Oakville A and B soils are subject to the sorption nonequilibrium process identified in the batch study, it would be difficult to experimentally identify the extensive tailing modeled in Case d of Fig. 2 and 3. In general, such experiments have to be terminated when the quantification limit of the solute is reached, which would be well before breakthrough curve tailing of DMP stops. Table 2 shows the simulated mass recovery calculated for the experimental duration of each measured breakthrough curve. The simulated mass recovery varies between 83.7 and 99.5%, with the exception of the low velocity experiment (A3 in Table 2) where the simulated recovery is only 39.4%. The experimental recovery for the measured curves varies between 82.0 and 99.5% (Table 2). Except for Exp. A3, the simulated and experimental recoveries are reasonably close. While most of the solute has leached from the columns, low concentration tailing can continue for extended periods of time. The extrapolation of data to account for the effect of tailing (Maraqa et al., 1998) would be difficult and subject to high uncertainty. Small experimental errors in the recovered solute lead to larger errors in the calculation of the small solute mass that remains in the column and is needed for extrapolation. Any parameter estimation by moment analysis of data, for example, the independent estimation of R that is often practiced to reduce the number of fitted parameters when applying a kinetic transport model, is then impossible (Lee et al., 1991; Brusseau, 1992; Piatt and Brusseau, 1998). Maraqa et al. (1998) noted that tailing of breakthrough curves limits moment analysis of data. Furthermore, these limitations are also very likely to apply to parameter estimation by inverse modeling. It can therefore be concluded that there are severe practical limitations to estimating rate parameters using column experiments in the case of slow to very slow sorption.

To further illustrate these problems, Fig. 4 shows the effect of pore water velocity on the DMP breakthrough curves for a given set of sorption rate parameters. The figure shows simulated breakthrough curves at six different flow velocities v using the parameter set describing linear sorption on Oakville B soil (Table 1). For all simulations, we assumed a constant Peclet number of 80 and a pulse input of two pore volumes. The conditions chosen for the first three simulated curves were the same as those of the column experiments with Oakville B soil. When plotted against dimensionless time (Fig. 4), the first moments of all curves, E[T], coincide regardless of pore water velocity. At the three highest pore water velocities, the location of the peak is mainly determined by the equilibrium sorption sites. The rate-limited sites play only a minor role in the leaching of the main mass of solute. However, leaching of solute desorbed from the rate-limited sites continues for a long time at low concentrations, thus producing the deviation between peak maximum and first moment. While for the two highest velocities Fig. 4 does not resolve tailing, extreme tailing is visible for the breakthrough curve at 0.73 cm h^-1. At the intermediate pore water velocity of 0.073 cm h^-1, sorption nonequilibrium has the largest influence on breakthrough curve shape. At the lowest velocities the solute approaches local equilibrium conditions even at the nonequilibrium sites. From this it follows that the breakthrough curve at an intermediate velocity is the most sensitive to uncertainties in the rate parameter ₂. This may explain the low recovery of the simulated breakthrough curve compared with measured data in the low velocity experiment with Oakville A soil. Although both curves share the same features, tailing due to rate-limited sorption is more pronounced in the simulated curve. Unfortunately the measured breakthrough curve was terminated too early, leaving only the slight bend at the end of the curve as an indication of a similar tailing at high concentrations. It seems that the rate parameter ₂ estimated from the batch study is slightly too large so that the initial peak caused by equilibrium sites is smaller. In addition to the early termination of the experiment, this leads to the low recovery rate of the simulated compared with the measured curve in the lower panel of Fig. 2.

View larger version (22K): [in this window] [in a new window]   Fig. 4. Simulated dimethylphthalate (DMP) breakthrough curves at six different flow velocities using linear sorption rate parameters estimated for Oakville B soil. The quantification limit used to calculate recovery in Table 3 is also shown. The experimental conditions chosen for the three highest flow velocities are the same as those of the Exp. B1, B2, and B3 (figure modified after Selim et al., 1976)

View this table: [in this window] [in a new window]   Table 3. Characteristics of the simulated breakthrough curves in Fig. 4. VAR(T), , and denote variance, Damköhler number, and percentage fraction of variance due to kinetic sorption, respectively

The importance of tailing can be further evaluated by comparing the variances of the breakthrough curves. For the linear two-stage model, the variance of a breakthrough curve corresponding with a pulse input of duration can be written as (Valocchi, 1985, and Streck et al., 1995)

(14)

where

(15)

(16)

The term 1 - ß, characterizes the amount of solute bound to kinetic sites normalized to the total amount of solute in the solid and liquid phase at equilibrium. The Damköhler number represents the ratio of the residence time of a sorptive solute (minus residence time of a tracer) to reaction time. The variances and s of the simulated breakthrough curves in Fig. 4 are listed in Table 3. For the experiment with the highest pore water velocity, the variance is about 800 times larger than for the lowest flow velocity. Only in the experiment at the lowest velocity is > 100, according to Brusseau et al. (1991), LEA would be justified. However, relying on when deciding which model to use may not be sufficient. The parameter does not account for the relative significance of rate-limited sorption under various experimental conditions. A better criterion is the percentage ratio of variance due to kinetic sorption to variance to equilibrium sorption and length of pulse input (Valocchi, 1985):

(17)

The values of are listed in Table 3. Setting the critical value to 10%, only the experiment at the lowest flow velocity may be modeled with LEA. Although this agrees with the results found for a critical Damköhler number of 100, Eq. [17] shows that is not only a function of but also of the pulse length and the Peclet number P. Equation [17] can be rearranged to yield

(18)

Note that is equal to the Damköhler number for . The product is plotted as a function of pulselength and P in Fig. 5 . The figure reveals that there is no critical value of which, if exceeded, justifies the use of a LEA model. Especially at high Ps and low pulse input length, large values of are required in order to ensure that the percentage of variance due to kinetic sorption remains small.

View larger version (22K): [in this window] [in a new window]   Fig. 5. The product of the Damköhler number and the percentage fraction of variance due to kinetic sorption as a function of pulse length T0 and Peclet number P. Numbers on curves indicate values of (1 - ß)2P

Figure 6 demonstrates that the difficulties associated with estimating first and second moment of the DMP breakthrough curves at high flow velocities also apply when parameter identification is attempted by fitting a kinetic model to the data. The figure demonstrates simulated experiments at two flow velocities, 36.47 and 0.00073 cm h^-1 The experimental conditions are identical to the simulated DMP breakthrough curves at highest and lowest velocity in Fig. 4. The second parameter set given in the legend is identical to that estimated with the linear model from DMP batch data in Oakville B soil. The two other sets were produced by varying f while fk_D was kept constant. By doing so the sorption capacity of equilibrium sites remains constant, while the capacity of rate-limited sites is decreased for the first set and increased for the last set. Since the equilibrium sites dictate the shape of breakthrough curves at high flow velocities, the breakthrough curves almost coincide, despite the fact that their variances range from 306 to 2550. In contrast, at the low flow velocity, the breakthrough curves are very different due to the influence of rate-limited sites.

View larger version (24K): [in this window] [in a new window]   Fig. 6. Simulated breakthrough curves calculated for three sets of linear sorption rate parameters at two pore water velocities. Solid lines represent curves at a pore water velocity of 36.47 cm h-1, while the dotted lines represent curves at 0.00073 cm h-1. The second set of parameters is identical to that given for dimethylphthalate (DMP) sorption to Oakville B soil in Table 1. The first and last set of parameters were obtained by varying f, while keeping the product fkD constant

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
The DMP breakthrough curves in Oakville soil measured by Maraqa et al. (1998) were satisfactorily predicted with sorption parameters estimated from batch data even though apparent differences in retardation coefficients from batch and column data were reported by the authors. Although some discrepancies between measured and predicted curves remain (probably because the batch studies fail to account for short term sorption kinetics of DMP), a major part of the apparent difference in R could be related to analytical difficulties in determining the extensive tailing of measured breakthrough curves.

As demonstrated by simulations, information on tailing may be crucial when nonequilibrium sorption parameters are to be estimated by fitting a transport model to breakthrough curves of organic compounds. The lack of tail data in the DMP column experiments led to an underestimation of R by up to 60% as compared with the value obtained by fitting the two-stage model to batch data. Underestimation of R was nearly independent of the time scale of the column experiment. As the time scale of the slowest column experiment is similar to the time scale of the sorption rate experiment (14 d), the batch technique seems to be preferable in the case studied.

Although the identification of very slow sorption rates of DMP is possible with column techniques (Fig. 4), these experiments would have to be carefully designed, with flow velocities ranging over many orders of magnitude; however, this may be impracticable. At similar time scales, batch techniques were better suited for identifying slow sorption kinetics of DMP in Oakville soil. With relatively high to intermediate flow velocities, the susceptibility of sorption rate parameter estimation to tailing of DMP was not paralleled by a similar effect in the sorption rate studies.

	ACKNOWLEDGMENTS

 
Funding for this research was provided in part, by the U.S. Public Health Service through grant number ES-04911 from the National Institute of Environmental Health Sciences, USA.

Received for publication April 13, 1999.

	REFERENCES

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 

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