Rate-limited sorption of simazine in saturated soil columns

JOURNAL OF

Contaminant Hydrology ELSEVIER

Journal of ContaminantHydrology 25 (1997) 219-234

Rate-limited sorption of simazine in saturated soil columns Jos6e Fortin a, Markus Flury

b,*,

William A.

Jury b, Thilo Streck c

a Soils Department, University of Laval, Quebec G1K 7P4, Canada b Department of Soil and Environmental Sciences, University of California, Riverside, CA 92521, USA c Department of Geoecology, Technical University Carolo-Wilhelmina, Braunschweig, Germany

Received 8 February 1996; revised 18 June 1996; accepted 26 June 1996

Abstract Column flow experiments under saturated conditions were conducted to investigate the sorption behavior of simazine on a Tujunga sandy loam. The flow interruption technique was used to test whether rate-limited processes were present. The outflow results showed that the simazine sorption was not at equilibrium during the time of the experiment. This non-equilibrium was due to the sorption process, as the bromide tracer concentration did not change during flow interruption. Simazine breakthrough data could be best described by a two-stage, two-rate process, where the first rate is considerably faster than the second. The model predicts slow reaction kinetics, so that equilibrium was not reached even after 185 h of flow interruption. Outflow data of the first simazine breakthrough only could be described well with a one-stage, rate-limited sorption model; flow interruption was necessary to reveal the second sorption stage.© 1997 Elsevier Science B.V. Keywords: Dispersion;Non-equilibriummodeling;Pesticide sorption; Solution transport

1. Introduction The importance of sorption kinetics in chemical transport has long been recognized. A common procedure used to evaluate sorption of chemicals on soil is to use the batch technique, in which the chemical at different concentrations is allowed to equilibrate with a given amount of soil. The question of whether the chemical has enough time to reach equilibrium with the soil in the typical 2 4 - 4 8 h reaction time in a batch system remains a point of debate (Streck et al., 1995). When desorption is also measured, hysteresis between sorption and desorption loops is often observed. There is increasing

* Corresponding author. 0169-7722/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PI1 S0169-7722(96)00033-2

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J. Fortin et a l . / Journal of Contaminant Hydrology 25 (1997) 219-234

evidence that in many cases hysteresis is an experimental artifact caused by slow sorption kinetics (Boesten and Van der Pas, 1988; Miller and Pedit, 1992). There is considerable evidence that sorption of organic compounds has an instantaneous equilibrium component and a slower time-dependent component (Karickhoff, 1980; Karickhoff and Morris, 1985; Pignatello, 1989). For polar organic chemicals with functional groups, non-equilibrium may comprise rate-limited mass transfer and ratelimited interactions between sorbate and sorbent (Brusseau and Rao, 1989a). Three different processes involving diffusive mass transfer can cause sorption-related nonequilibrium: film diffusion, retarded intraparticle diffusion and intraorganic matter diffusion (Brusseau et al., 1991). Film diffusion has been found to be negligible compared with other mechanisms (Brusseau and Rao, 1989b). Retarded intraparticle diffusion involves diffusion of solutes through pores contained in microporous particles, with retardation occurring by instantaneous sorption to the walls. Intraorganic matter diffusion involves diffusion within the matrix of the organic-carbon components of the solid phase (Brusseau et al., 1991). Two different approaches are commonly used to model sorption non-equilibrium. In the first approach, called the radial diffusion model, sorption is described as diffusion through the spherical geometry of the sorbent, usually based on Fick's law (e.g. Miller and Weber, 1984; Crittenden et al., 1986; Wu and Gschwend, 1991). In the second approach, the sorbent is hypothesized as containing one or several sorption sites or domains. The relationship between the sorbed and mobile phases is time dependent, and the mass transfer rate between the two phases is proportional to the deviation from equilibrium (Lapidus and Amundson, 1952; Lindstrom and Boersma, 1971; Van Genuchten et al., 1974). The terms two-site and bicontinuum have been used for models where sorption is assumed to take place in two different types of sites or domains. Sorption domains may be arranged in parallel or in series, usually with one domain in equilibrium with the bulk solution. Kinetics is usually assumed to be of first order, but second-order kinetics has also been used (Selim and Amacher, 1988). The two-site or two-domain approach has been used successfully to describe non-equilibrium sorption in many studies (e.g. Selim et al., 1976; Cameron and Klute, 1977; Rao et al., 1979; Karickhoff and Morris, 1985; Brusseau et al., 1991). Streck et al. (1995) included rate-limited sorption in both domains. Multi-site models have also been proposed in the literature (Amacher et al., 1988). The purpose of the present study was to examine the sorption behavior of simazine on a Tujunga loamy sand. Column experiments including the flow interruption technique (Murali and Aylmore, 1980; Brussean et al., 1989b) were used to test different sorption mechanisms, i.e. one-stage and two-stage, equilibrium and rate-limited sorption models.

2. Materials and methods

2. l. Experimental apparatus The column apparatus used for the experiments consisted of a glass column of 7.5 cm i.d. and 15 cm length equipped with aluminum end plates. Screens at the top and bottom

J. Fortin et al. / Journal of Contaminant Hydrology 25 (1997) 219-234

221

of the column were used to support the porous material and to help spread the input solution laterally, respectively. The column was sealed with epoxy glue. The inlet end of the column was connected to a displacement pump (Accu-Flo TM pump, Beckman, Palo Alto, CA) that allows adjustable flow rates. A three-way valve was connected to the inlet of the pump for the application of the tracer and pesticide solutions. The outflow was collected using a sample collector. The tubes connecting the inlet to the pump and the outlet to the sample collector were all of Teflon TM, and the bottom end of the column was equipped with a stainless steel valve.

2.2. Soil characteristics, chemicals, and chemical analysis The experiments were performed using a Tujunga loamy sand (mixed, thermic, Typic Xeropsamment). The soil, which was collected from the top 5 cm of the field, had an average organic carbon content of 0.7% by weight. The chemicals used were bromide and the herbicide simazine (6-chloro-N2,Na-di ethyl- 1,3,5-triazine-2,4-diamine). Simazine has a water solubility of 6.2 mg 1-1 and a half-life of about 60days (Wauchope et al., 1992). Bromide was analyzed using an ion selective electrode (Fisher Scientific, Pittsburgh, PA). Simazine was analyzed by enzyme immunoassays, using an atrazine kit from Ohmicron (Newtown, PA). The detection limit of this method was 0.3 ~g 1-1. Although the method does not distinguish between different triazine compounds, it was suitable for the present experiments as only one triazine herbicide was used.

2.3. Transport studies Before the introduction of soil in the column, the bottom chamber was saturated to prevent air entrapment. The column was packed with air-dry soil in 1 cm increments, then saturated slowly from the bottom with a background solution of 0.01 M C a S Q . After saturation, the flow was inverted and at least two pore volumes of solution were leached before the beginning of the experiment. The experiments were performed under water-saturated conditions with flow in the downward direction. Bromide and simazine

Table 1 Summary of the experimental conditions Column no.

a

Flow rate Pore water velocity b Bulk density Water content Comments Jw ( c m h - l ) v (cmh - l ) Pb (gcm 3) 0 (cm3cm -3)

1 2

0.3353 0.6693

0.745 1.487

1.47 1.46

0.45 0.45

3

0.6736

1.433

1.41

0.47

4 5

0.6942 3.8282

1.543 8.507

1.47 1.47

0.45 0.45

The length of the column was in all cases L = 15cm. b Calculated as v = J w / 0 . a

Flow was stopped for 185h after 1 pore volume of input Flow was stopped for 185h after 5 pore volumes of input

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J. Fortin et al. / Journal of Contaminant Hydrology 25 (1997) 219-234

were dissolved in a 0.01M CaSO 4 solution at concentrations of 5 0 m g l ~ and 0.025 t, g1-1, respectively. Simazine was dissolved in a small amount of methanol before the addition of the C a S O 4 solution. The chemicals were applied to the column as a step input. Samples were taken periodically from the input simazine solution to evaluate changes in the chemical input concentration. Column drainage was collected using a sample collector, then refrigerated until analysis. The experimental conditions of the transport studies are summarized in Table 1. In two experiments (2 and 3) the flow was stopped for 185h and then resumed until complete breakthrough was achieved. In Experiments 2 and 3, flow was stopped after one and five pore volumes, respectively, had leached from the column.

3. Theory 3.1. Description o f sorption

Sorption of simazine was described with the linear rate-limited, two-stage model of Streck et al. (1995). In this model, sorption is assumed to occur in two regions with different accessibility. Region 1 is in contact with the bulk soil solution, whereas Region 2 is only in contact with Region 1. The sorption equations for the linear, two-stage, two-rate (2S2R) model of Streck et al. (1995) are given as dS~ f~t

= e e , ( k C - S1) - a2(S l

--

82)

(1)

dS 2 (1 - f )

dt

= c~2(S1 - $2)

(2)

where C ( M L -3) is the resident fluid concentration, S 1 and S 2 ( M M - t ) are the concentrations of sorbed chemicals in Region 1 and 2, respectively, k (L 3 M - 1) is the sorption distribution coefficient at equilibrium, c~1 and cq (T -~) are the rate coefficients of the two regions, f is the fraction of Region 1, and t (T) is time. The total amount of sorbed chemical S ( M M l ) can be expressed as S =,/S, + (1 - f ) S

2

(3)

Assuming that the first-rate process is very fast, i.e. equilibrium sorption, the equations reduce to the two-stage, one-rate (2S1R) model (Karickhoff, 1980; Streck et al., 1995) where Eq. (1) reduces to S, = k C

(4)

It should be noted that the 2S1R model in this paper is mathematically equivalent to the models of Selim et al. (1976), Cameron and Klute (1977), and Brusseau et al. (1991). If

J. Fortin et al./Journal of Contaminant Hydrology 25 (1997) 219-234

223

y one sorption domain (i.e. f = 1), Eq. (1) and Eq. (2) reduce to the ption (RLS) model (Lapidus and Amundson, 1952) --

at

= ~(kc

- s)

(5)

and Eq. (2) and Eq. (4) reduce to the local equilibrium sorption (LES) model (6)

S = kC

3.2. Description o f transport

Transport was described by the one-dimensional advection-dispersion equation (ADE), and water flow was assumed to be steady state. Combining the different sorption models with the ADE and using dimensionless variables yields the following transport equations: LES: aC* R aT

1 02C* Pe OZ 2

OC* (7)

OZ

RLS: aC *

aS *

--+(R-I)

aT

=

aT

1 02 C * - Pe aZ 2

aC * aZ

(8)

aS* (9)

aT = w ( C* - S* )

2SIR: aC* /3R aT + R ( 1 - / 3 )

aS2 aT

1 a2C * Pe aZ 2

aC* aZ

(10)

as; R(1 -/3)

a---7"-= w 2 ( C * - S2 )

(11)

2S2R: aC * -+(R/3aT (R/3-1)

R(1

-/3)

aS1* 1)

aT

aS2* +R(1 -/3)

0S]* aT = w ' ( C * - S l *

aT

1

02 C *

Pe aZ 2

)-w2(S,*-$2.)

aC *

aZ

(12)

(13)

as; aT = w2(S,* - $2" )

(14)

J. Fortin et al. ,/Journal of Contaminant Hydrology 25 (1997) 219-234

224

The initial and boundary conditions are given as C*(Z,0)=0,

S*(Z,0)=0,

C*(O,T)= 1,

S,*(Z,0)=0,

S;(Z,0)=0

lim C * ( Z , T ) = O

(15) (16)

Z--~ zc

The dimensionless variables in the equations above are defined as C C* = - Co

(17)

vt -

(18)

L Z

Z= ~

(19)

uL Pe = ~ -

(20)

S1,2 S1; 2 --

(21)

pk R = 1 + ~-

(22)

c~L o9 =

(23) U

/3=

1+

fpk ] 0 )/R

(24)

Oll,2 L

o9l,2 -

U

(R-

1)

(25)

where CO( M L -3 ) is the inlet concentration, v (L T- 1) is the pore water velocity, L (L) is the column length, z (L) is the depth coordinate, D (L2T -1) is the dispersion coefficient, p (ML 3) is the soil bulk density, Pe is the Peclet number, R is the retardation coefficient, o9 is the dimensionless rate coefficient, and /3 is proportional to the fraction of Region 1 domain. The solutions of the transport equations are obtained in Laplace space and are given in Appendix A. The Laplace-transformed solutions were inverted numerically with the FORTRAN program of the Talbot algorithm published by Jury and Roth (1990).

3.3. Parameter estimation and model discrimination Model parameters were estimated by the method of least squares, and the objective function was minimized with the Levenberg-Marquardt algorithm (Press et al., 1989). The Peclet number was determined from the bromide breakthrough curve (BTC). The

J. Fortin et al./ Journal of Contaminant Hydrology 25 (1997) 219-234

225

parameters for the sorption models were estimated from the simazine data. For the flow-interruption experiments, the objective function used was

)t/2(P) = E ( [ C ( T ) T

- C m ( Z ; p ) ] 2 q-[Cstopflow-fm,stopflow(P)] 2)

(26)

where C is the measured solute concentration, C m is the model concentration, p is the parameter vector, and Cstopnow and Cm,~topnow are the measured and modeled concentrations in the column outflow, respectively, after the time the flow was stopped. It should be noted that the second term in the objective function (Eq. (26)) is not a function of the pore volume T. The goodness of fit of the different models was compared by an extra sum of squares analysis (Bates and Watts, 1988). For nonlinear models, this analysis is only approximate; however, it can be assumed that the errors made as a result of the nonlinearity are generally small (Bates and Watts, 1988, p. 104).

4. Results

4.1. Bromide outflow Fig. 1 shows the bromide breakthrough data and the fitted ADE. All of the BTCs showed ideal behavior; there was no early breakthrough or prolonged tailing observable. Consequently, the data could be described well with the ADE. The experiment in Column 2 shows that the bromide concentration did not drop during the 185 h of flow interruption. This indicates that there was no physical non-equilibrium present. Fig. 1 shows that there was no clear dependence of the Peclet number on pore water velocity. We attribute the variation in the Peclet numbers to the differences in the packing from one column to another.

4.2. Simazine outflow The results of the simazine breakthrough experiments are presented in Fig. 2 and the parameter estimates of the different sorption models are listed in Table 2. The RLS model provided a much better fit than the LES model. Based on the parameter uncertainties, the model parameters of the RLS are well defined and the extra sum of squares analysis confirmed that the RLS model was superior to the LES model at the 1% significance level. The 2S1R model gave almost identical fits to those of the RLS model, and the two models cannot be distinguished graphically. However, the parameter uncertainties for the 2S 1R were large, and the extra sum of squares analysis showed that the 2S1R model did not improve the fit in any column at a significance level of 5%. The 2S2R model could not be fitted to the data because of high parameter correlations. From this information alone we would logically conclude that the sorption process for simazine was rate-limited with a single sorption stage and one rate-process.

226

J. Fortin et al. / Journal of Contaminant Hydrology 25 (1997) 219-234 1,0-

Column 1

0.80.6-0.40.20.0

t-O

o co 0 .~_

rr

Column2

,-Io

/ ~

Pe = 66.9/°

_

,,v

0.6.

0.4-

j

0.2-

IFIowinterrul:)tionl

t"

I

I

0.5

I

1.0

Pe=4~

1.0-

0.80.6-" 0.4" 0.2-0,0

1,0-

0.8-

0.0 tO

~,,m9--°°'e'oe~

o

Column 3

I

1.5

2.0 _At,

~ v

0.0

O9~O910~

'

0.5

0.0

I

Column 4

1.0-

'

1.0

I

1.5 ~

'

I

2.0

e ,~o

0.8-

0.60.4-" 0.2~-0"~00"~

0.0 1.0-

0.8 S 0.6-" 0.40.2-" 0.0 0.0

,

0.5

I

1.0

I

'

1.5

i: 0.5

t

2.0

I

I

1.0

1.5

0.0

- ~

0.0

I

0.5

'

I

1.0

I

1.5

I

2.0

Pore Volume

oO

Column 5

~-7

'

I

2.0

Pore Volume

Fig. 1. Bromide breakthrough data (O), fitted ADE model (continuous lines), and values of estimated Peclet numbers (Pe).

Fig. 3 shows the simazine breakthrough in Column 3 for the flow interruption experiment. The flow was interrupted when nearly complete breakthrough of simazine was achieved. After 185 h of flow interruption, the simazine concentration in the outflow dropped considerably. This reduction in relative concentration in the outflow cannot be attributed to degradation. First, no reduction in the concentration of the input solution was observed for the entire period of the experiment, and second, estimated simazine degradation assuming first-order degradation kinetics and a half-life of 60days (Wauchope et al., 1992) would only explain a concentration decrease of about 8%. Moreover, the method of analysis used in the present study does not distinguish between different triazine compounds, including degradation by-products. The flow interruption experiment in Column 3 was then used to reexamine the simazine sorption process. The first part of the simazine breakthrough together with the drop in concentration after the flow interruption were used to estimate the parameters of the RLS, 2S 1R, and 2S2R models. To calculate the outflow concentration after resuming flow, the resident concentrations in the column had to be calculated before and after the

227

J. Fortin et al. / Journal of Contaminant Hydrology 25 (1997) 219-234

1.0-

1.0- Column3 o~o,-°'o~°"%0.8-

0.8t-

.9_ tO

0 tO

0.6-

o.8-

0.4-

0.4-

0.2-

o.;

0.0 0

0 0

.>_ n"

1.0-

' 7 ' 1 ' 1 ' 1 ' 1 ' 1

1

2

3

Column 4 / / 7

4

0.0

5

?1 r...~[

6

0.6-

0.6-

0.4-

0.40.2- J

0.20.0

0

1

,

2

3

, I , I , I

4

5

'

i 2

a 3

1.0~ • Column5

jem'-~-

0.8-

ii

, 1

0.8-

J ,/

~/,o1~

6

'

i 4

i 5

'

i 6

~ 6

P/ 1

Data LES RLS,2S1R

~ ......

0.0 i---..--~Vl , I '

0

'

2

I '

3

I '

4

I '

5

I

6

Pore Volume Fig. 2. Simazine breakthrough data (©) and fitted sorption models (continuous and dashed lines).

flow interruption. This was done by solving the equations for a no-flow system for every depth interval. Diffusion in the vertical direction was neglected, as there were only minor concentration gradients along the column axis. The parameters were then determined based on Eq. (26). The estimated parameter values are given in Table 3 and the fitted breakthrough is shown in Fig. 4 (continuous line). The RLS and the 2S1R models were not able to reproduce the breakthrough and the drop of concentration after the flow was stopped (Fig. 4). However, the 2S2R model yielded an excellent fit. The extra sum of squares analysis confirmed that the 2S2R model was superior to the other two models at a significance level of 1%. Fig. 5 shows the aqueous and the total sorbed concentrations within the column expressed relative to the expected equilibrium concentration at a given depth obtained with the optimized parameter set. The equilibrium concentration in Fig. 5 refers to the no-flow system. It should be noted that this is different from the equilibrium concentration in the flow system. The RLS and the 2S1R models gave similar results. In these two models, the concentrations before the flow interruption were close to equilibrium, and they reached equilibrium after the flow interruption. The 2S2R model calculates concentrations that were not in equilibrium. Even after the flow interruption, the aqueous concentration was still considerably larger than at equilibrium, whereas the total sorbed concentration was smaller than at equilibrium. The concentration profiles within the column after flow interruption were then used as initial conditions for the transport models to predict the second breakthrough of simazine. The transport equations were in this case solved numerically with a fully implicit finite-difference code. The results of these calculations are shown in Fig. 4

228

J. Fortin et al. / Journal of Contaminant Hydrology 25 (1997) 219 234

Table 2 Estimated parameters of the sorption models C o l u m n no.

S u m o f squares

Parameter

Estimate

A p p r o x i m a t e standard error

t ratio

Local equilibrium sorption (LES) 1 3 4 5

7.727E-2 2.029E- 1 1.589E 1 7.197E- 2

R R R R

2.251 2.440 2.199 2.206

0.023 0.053 0.027 0.034

101.2 46. l 81.9 65.1

R to R to R to R to

2.265 14.51 2.495 4.680 2.219 7.377 2.222 6.622

0.020 3.201 0.025 0.485 0.014 0.708 0.013 0.576

113.7 4.5 100.8 9.6 156.0 10.4 169.7 11.5

R /3 w2 R /3 to 2 R /3 to e R /3 o92

2.262 2.5E- 6 65.08 2.523 0.631 2.531 2.208 1.1E 9 31.25 2.224 0.502 6.606

Rate-limited sorption (RLS) 1

4.656E - 2

3

2.287E

2

4

2.571E

2

5

7.101E-3

Two-stage one-rate sorption (2S1R)

1

4 . 6 5 6 E -- 2

3

2.011E-2

4

2.408E - 2

5

7.080E - 3

0.024 4.001 523 0.028 0.067 1.005 0.017 0.927 58.5 0.016 0.182 4.956

96.3 6.3E - 7 0.12 89.0 9.4 2.5 126.8 1.2E-9 0.5 138.8 2.8 1.3

Two-stage two-rate sorption (2S2R) 1 , 3 , 4 , 5 - - N o fit possible

(dashed lines). The RLS and 2S 1R models could not reproduce the experimental results. On the other hand, the 2S2R model predicted the data very well. We therefore conclude that the sorption process is much better represented by a two-stage, two-rate process CQ

e.- 1 . 0 -

0.8-

o

GO

oo

~e--0 . 6 8

0

mOoo~oOmo

T

o o

0.4-

l Flow interruption -

0

I

o

._

N

0 o

ooo~ oOo~O

~oo~ o

.0

0.2-

o o

~0.0 0

I 2

'

I 6

'

I

8

10

'

I

12

Pore Volume Fig. 3. Simazine b r e a k t h r o u g h in C o l u m n 3 before and after 185 h of flow interruption.

J. Fortin et aL /Journal of Contaminant Hydrology 25 (1997) 219-234

229

Table 3 Parameters of stop flow experiment in Column 3 Model

Sum of squares

Parameter

Estimate

Approximate standard error

t ratio

RLS

3.806E- 1

2S1R

9.534E-2

2S2R

2.256E- 2

R to R /3 o9~ R /3 ogl o9z

2.886 1.219 3.086 0.720 0.195 7.481 0.326 8.234 0.035

0.879 1.551 1.008 0.242 0.736 1.3E + 3 55.1 41.1 0.713

3.3 0.79 3.1 3.0 0.27 5.9E - 3 5.9E- 3 0.2 0.05

~

.

_,,,,-~,, f ___ ,joo_oo~&o~o

1.0-

o

_~,F

0.60.40.2C

0.0

.m0

....

0

.,-.

,(U

1.0~

E::

0.6-

j

i

i

i

i

2

4

6

8

10 oo

~_~

12 o

.~o%O'°~°%

o

f'-')

0.4-

.___~

0.2-

c~

o.o

-'~

....

---"

IT'

'

0

2

/

1.0-

-

'

4

'

'

I

8

~

'

I

10 oo

%~-o~

~

0.8-.

I

6

12 o

0.60.4-

J

o

/

"

-

0.0

o

Data

-

Fit Prediction

- .......

0.2:~:~,

0

I 2

t 4

I 6

I 8

'

I 10

'

I 12

Pore Volume Fig. 4. Simazine data and model simulations for the stop flow experiment in Column 3. O, Data points used to estimate the parameters for the various models. The continuous line is the fitted model; the dashed line is the prediction based on the simulated parameter values.

230

J. Fortin et al. / Journal of Contaminant Hydrology 25 (1997) 219-234

C/Ceq 0.0

1.0

S/Seq

2.0

3.0

it

0.0

(a)

E

5-

10-

O.. £3

15

15

0.0 0

1.0

'

,

2.0 I

3.0 ,

I

0.0

0.2 0.4 0.6 0.8 1.0 , I , I , I i t i

0

(b)

(b)

5-

5-

10-

10-

15

0.8 1.0 ] I t

(a)

10 t

~ e-

0.2 0.4 0.6 , I , I , I

0

t l l

15

-

RLS

. . . . . . . . . . . . . . 2S1R ....... 2S2R

Fig. 5. Calculated resident concentrations profile in the column at the beginning (a) and at the end (b) of the flow interruption. Concentrations in the liquid and solid phases are expressed in relation to the respective equilibrium concentration. For the 2S1R and 2S2R models, the total sorbed concentration is given as S = f S I + ( l - f ) S 2.

than by a two-stage, one-rate, or a single-stage, rate-limited model. In this two-rate process, the first rate was much faster than the second. The second-rate process was so slow that even after 185 h the concentrations had not yet reached equilibrium. There is a large uncertainty for the estimated parameters of the 2S2R model, particularly for the parameters R and /3 (Table 3). This uncertainty is associated with a high correlation between these two parameters. We therefore cannot interpret the parameter values of the 2S2R model. However, we can still state that the data are best described with the two-rate model, and cannot be explained with the single-rate model.

5. Discussion The drop in simazine concentration during flow interruption implies that the sorption process is rate-limited (Brusseau et al., 1989a). Intraorganic matter diffusion is a possible mechanism responsible for this slow sorption, although the contribution of mineral surfaces to sorption cannot be ruled out as the organic carbon content of this soil was small (Brusseau and Rao, 1989b). There is evidence in the literature that sorption of organic chemicals can be explained with a two-domain concept (e.g. Brusseau and Rao, 1989b). For simazine, Gamerdinger et al. (1991) and Kookana et al. (1993) obtained a good description of BTCs with a two-site one-rate model. According to these results, the early breakthrough and tailing

J. Fortin et al. / Journal of Contaminant Hydrology 25 (1997) 219-234

231

observed in the experiments were due to rate-limited processes, such as intraorganic matter diffusion of simazine and chemical reaction non-equilibrium. Kookana et al. (1993) found that in their study the two-site one-rate model was superior to the RLS model. Our results show that the first simazine breakthrough in all columns could be described well with the RLS and the 2S1R model. However, neither the RLS nor the 2S 1R models were able to explain the drop of concentration during the flow interruption period. As shown in Fig. 4, all stages of the flow interruption experiment can be represented with the 2S2R model. Streck et al. (1995) found that only a nonlinear approach could describe the simazine data in a combined batch and field experiment when parameters were independently estimated from laboratory batch studies. The nonlinear 2S1R and 2S2R models gave the best results (Streck et al., 1995). In our study, we did not use nonlinear sorption models, because these models could not be fitted to the experimental data. We cannot rule out a nonlinear sorption process, but the presented data do not provide evidence that nonlinearity is needed. 6. Conclusions Column experiments with flow interruption showed that the simazine sorption process was not at equilibrium. Bromide data indicate that the non-equilibrium was due to the sorption process, because the concentration of nonsorbing bromide did not change during the flow interruption. In this study, simazine sorption could be best described by a two-stage two-rate model, where the first rate is considerably faster than the second. The model predicts slow reaction kinetics, so that equilibrium was not reached even after 185 h. Two main conclusions can be drawn from the model simulations: 1. Even though the data of the first simazine breakthrough were described very well using the RLS model, flow interruption was necessary to reveal a second sorption stage for simazine in this soil. 2. Our study confirms and emphasizes the results of Brusseau et al. (1989b), who pointed out that the identification of sorption processes from non-interrupted BTCs may be ambiguous when non-equilibrium is present. Measuring the outflow concentration from non-interrupted BTCs only may not be sufficient to evaluate the processes involved, as many different models can adequately describe outflow BTC, and the process assumptions involved may be very different.

Appendix A A. 1. Solution of transport equations The solution of the transport equations (Eqs. (7)-(16)) in Laplace space for the breakthrough stage of the experiment is given as 1 [ PeZ ] C* ( Z ; s ) = - e x p | ~ - - ( 1 - ~')] (gl) s

[ z

J. Fortin et al. / Journal of Contaminant Hydrology 25 (1997) 219-234

232

and ~ ' : = ¢ l+4g(s~)Pe

(A2)

where s denotes the Laplace variable. The function g(s) represents the different sorption models and is given as LES:

g( s) = Rs

RLS:

g(s)=s

(A3) I+(R-1 [

2S1R:

g(s)=sR~

2S2R:

g(S)

~ S

(A4)

(1-/3)°)2] 1+ s/3R(1 /3)+/30)2

(A5) (A6)

1 ~- 0) 1

where a:=/3R- 1 +

R(1 -/3)0)2

R(1 - / 3 ) s + 0)2

b := (/3R - 1)s + 0)1 +

0)2 - -

R(1 - / 3 ) s + 0 ) 2

(A7)

(AS)

The solutions for the flow interruption stage are identical to the batch solutions given by Streck et al. (1995).

A.2. Notation C C*

d* f k L P

Pe R S

S S* S 1, S 2

s? ,s2"

concentration in aqueous phase (ML 3) relative concentration in aqueous phase Laplace transform of relative concentration in aqueous phase fraction of Region 1 domains in 2S1R and 2S2R models sorption distribution coefficient (L 3 M -1) length of soil column (L) parameter vector in least-square procedure Peclet number retardation factor Laplace variable total concentration of adsorbed chemicals (MM i) relative total concentration of adsorbed chemicals concentration of adsorbed chemicals in Regions 1 and 2, respectively (MM 1) relative concentration of adsorbed chemicals in Regions 1 and 2, respectively time (T)

J. Fortin et aL / Journal of Contaminant Hydrology 25 (1997) 219-234

T z Z OL

a 1 0/2

233

dimensionless time depth (L) dimensionless depth rate c o e f f i c i e n t in R L S m o d e l ( T -1 ) rate c o e f f i c i e n t o f R e g i o n 1 in 2 S 2 R m o d e l ( T

1)

rate c o e f f i c i e n t o f R e g i o n 2 in 2 S 1 R and 2 S 2 R m o d e l s ( T -1 ) dimensionless fraction of Region 1 domains

X2

sum of squared deviations d ~0, (.01~ 0) 2 i m e n s i o n l e s s rate c o e f f i c i e n t s

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