Application of Two-Site/Two-Region Models for Studying Simultaneous Nonequilibrium
Transport and Degradation of Pesticides
A. P. Gamerdinger, R. J. Wagenet,* and M. Th. van Genuchten
ABSTRACTIn these models, water is commonly divided into mobile and immobile regions. Brusseau and Rao (1989b)
discussed intra-organic-matter diffusion as a third process that may contribute to the tailing of hydrophobicorganic compounds.
The desire to distinguish physical and chemical processes that result in asymmetric breakthrough curves
has led experimentalists to use several
solutes in soilcolumn studies. Tritiated water (3H2O) is often used
to determine if immobile water is present in the system(Rao et al., 1980; Nkedi-Kizza et al., 1983). This tracer
is probably the most suited for measuring the macroscopic average pore-water velocity, v, and the dispersion coefficient, D. The Cl ion is also often used asa tracer, the advantage being that this tracer is safer
to handle than radioactive tritium. However, the useof Cl is only effective in so far as this tracer truly
behaves as a noninteracting solute, thereby mimicking
the flow of water. If this is true, then it may be possible
to define a retardation factor, R, of unity. Unfortunately, Cl often undergoes anion exclusion, especiallyin relatively fine-textured soils (Biggar and Nielsen,
1962; Corey et al., 1963; Jacobs, 1964), resulting in R
< 1.
Organic-chemical transport is simultaneously influenced by both sorption and degradation. Miscible-displacement techniques may be better suited to simultaneous study of sorption and degradation than are
traditional batch techniques, as flowing conditions,even in the laboratory, may better represent dynamic,transient field conditions. Unfortunately, nonequilibrium sorption confounds the measurement of degradation in miscible-displacement studies. Likewise,
chemically or biologically mediated transformations
may complicate the measurement of sorption, particularly when sorption is time dependent. A survey ofthe literature reveals that, in most previous soil-column experiments, great efforts were taken to eliminate
degradation during studies of sorption kinetics accomplished with pesticide-displacement experiments.
Detailed study of asymmetric breakthrough curves
may be accomplished through a combination of analytical solutions of candidate transport models andproperly designed experiments. The theoretical development of the two-site sorption (equilibrium andkinetic) and two-region (mobile-immobile water)transport models under conditions in which the solute
is being transformed has been presented by van Genuchten and Wagenet (1989). We presented a genericanalytical solution that allows implementation of different hypotheses about the relative rates of degradation in the liquid and solid phases of a soil. Here,
we show how the generic model can be used to advantage in the analysis of observed column effluent
data for Cl, 3H2O, and atrazine, and for 2,4,5-T effluent
data of van Genuchten (1974). We emphasize that the
purpose of our study is not to provide a comprehensive analysis of atrazine movement, but rather to il-

Quantitative laboratory study of pesticide sorption and degradation during transport can provide insight into the basic processes
affecting pesticide fate in field soils. Accordingly, we demonstrate
the application of analytical solutions of two-site/two-region transport models useful in studying simultaneous pesticide sorption anddegradation. Soil-column displacement experiments involving 3H2O,
Cl, and atrazine (2-chloro-4-ethylamino-6-isopropylamino-s-triazine) were conducted during steady-state water flow at two pore-watervelocities and two pesticide concentrations. The soil used is a Valois
silry loam (coarse-loamy, mixed, mesic Typic Dystrochrept). Effluent
data from these experiments were used to demonstrate the application of these analytical solutions, as well as a parameter-estimation
computer program based on these solutions. The ability to use laboratory-derived estimates of equilibrium sorption parameters to describe sorption under flowing conditions was evaluated at each flow
velocity. Significant correlation between soil sorption partitioning
and degradation prevents the simultaneous determination of bothprocesses using these solutions. However, estimates of degradation
obtained from mass balances of the column data were useful in identifying the equilibrium sorption parameters. Data collected elsewherefor 2,4,5-T (2,4,5-trichlorophenoxyacetic acid) herbicide transport
were used as an additional example of the application of the modelwith degradation. Strengths and weaknesses of the models, and suggestions for further study, are presented.

Aleached through porous media have been observed for a variety of chemicals in a broad range of

SYMMETRIC BREAKTHROUGH CURVES for SOlutCS

soils. Much of these data were obtained in laboratoryscale experiments and are reviewed elsewhere (Rao etal., 1979; van Genuchten and Wagenet, 1989; Brusseau and Rao, 1989a). Recently, Winters and Lee(1987) reported tailing of three trace organics during
in situ experiments under field conditions. Similar observations have also been made for organic contaminant transport in groundwater systems (Goltz andRoberts, 1986). These results indicate a need for understanding the processes behind the tailing phenomenon as contaminant-transport models are being implemented in research and management.
Several models have been proposed to describe
asymmetric breakthrough curves where tailing is attributed to either chemical or physical nonequilibrium
processes. One-site or two-site chemical-processmodels assume that sorption is not at equilibrium andhas a time-dependent or kinetic component. On theother hand, physical-process two-region models assume that sorption is always at equilibrium, but thattransfer to some sorption sites is diffusion controlled.
A.P. Gamerdinger, Dep. of Soil Science, Univ. of Florida, Gainesville, FL 32611; R.J. Wagenet, Dep. of Soil, Crop, and Atmospheric
Sciences, Cornell Univ., Ithaca, NY 14853; and M.Th. van Genuchten, USDA-ARS, U.S. Salinity Lab., 4500 Glenwood Drive, Riverside, CA 92501. Joint contribution from the Dep. of 891!, Crop,and Atmospheric Sciences, Cornell Univ., and the U.S. Salinity Lab.
Received 29 June 1988. *Corresponding author.
Published in Soil Sci. Soc. Am. J. 54:957-963 (1990).

957

958

SOIL SCI. SOC. AM. J, VOL. 54, JULY-AUGUST 1990

lustrate typical applications of the general two-site/
two-region model to both degradable and nondegradable chemicals.
MATERIALS AND METHODS
Batch sorption studies and column displacement experiments were performed using a Valois silty loam soil. All soil
was collected from the 5- to 30-cm depth of a field site previously used for alfalfa production. The soil was air dried
and passed through a 2-mm sieve prior to use. The soil usedin one displacement and in one sorption isotherm experiment was sterilized by gamma irradiation from a Co source.
Selected physical and chemical properties are listed in Table
1. Aqueous stock solutions were prepared with analyticalgrade atrazine (99.9% pure; USEPA Pesticides and Industrial
Chemical Repository, Research Triangle Park, NC), 3H2O
(Amersham, Arlington Heights, IL), and Cl as KC1 in 0.01
M CaSO4. A Hewlett-Packard HP1090A liquid chromatograph, Beckman LS 9800 liquid scintillation counter, and a
Buchler-Cotlove chloridometer were used to analyze for atrazine, 3H2O, and Cl, respectively.
Sorption Isotherms
Equilibrium sorption isotherms were generated using standard sorption-isotherm batch techniques (Rao and Davidson, 1979). Duplicate samples of 5 g of soil and 10 mL ofatrazine in solution at each of eight concentrations (0.06-21
jig/mL) were shaken for 48 h in screw-cap test tubes. The
samples were allowed to stand for an additional 15 to 30
min to separate the soil-water mixture from the supernatantsolution. The supernatant was filtered through a 0.45-^mnylon membrane. The resulting samples, and also those used
for estimating the initial and input concentrations, were analyzed by direct injection into the HPLC.
Column Displacement Experiments
Six soil-column experiments were conducted, designatedI through VI (Table 2). The method described by Zhong etal. (1986) was followed with some modifications.
A pulse of
aqueous solution containing either 3H2O and Cl (Exp. I andII) or atrazine and Cl (Exp. Ill-VI) was applied to 21.3-cmlength glass soil columns under steady-state water flow at
two different velocities. The experiments are further distinguished as Exp. la and Ha for 3H2O (Table 3); Exp. Ilia, IVa,

Table 3. Values of the retardation coefficient (/?), the pore-watervelocity (v) and the apparent diffusion coefficient (D) estimatedfrom the soil-column displacement experiments involving Cl andtritium.
Experiment

Tracer

la
Ib
Ha

3

lib

Cl
Cl

H2O

Cl

3

H2O

Illb

IVb
Vb

Cl

Cl
Cl

Vlb

R

D

V

(dimensionless)l.OOOf0.910 ± 0.008
l.OOOf
0.916 ± 0.008
0.9 If
0.9 If
0.9 If
0.91f(cmVh)(cm/h)
1.01 ± 0.20
6.07 ± 0.07
0.841 ± 0.193
6.07f
0.907 ± 0.013 0.251 ± 0.046
0.214 ± 0.031
0.907f0.864 ± 0.002 0.104 ± 0.004
0.933 ± 0.063 1.66 ± 0.63
0.877 ± 0.014 0.533 ± 0.078
6.27 ±0.13 13.80 ± 1.62

f Parameter held constant during fitting procedure; fitted values include the0.05 confidence interval.

Va, and Via for atrazine (Table 4); and Exp. Ib to Vlb for
Cl, which was applied in all six cases (Table 3). Atrazine wasapplied at an input concentration, c0, equal to approximately
1 Mg/mL in Exp. Ilia and IVa, and 10 Mg/mL in Exp. Va
and Via. Column-effluent data were collected and analyzed
for each species.
In addition, on completion of each atrazine experiment,
soil from the columns was extruded and then extracted withmethanol to determine the total amount of atrazine remaining in the system. Mass balance was determined anddegradation rates were estimated by applying a first-orderkinetic-rate equation to the data. When the efficiency of theextraction procedure (92%) was considered, recovery of atrazine by this process was 100 ± 4% in experiments with nodegradation. Use of identical techniques in experiments withdegradation, and considering only cases in which the massbalance difference was >; 10%, provide estimates of pesticidedegradation that could be compared with those obtained
from the breakthrough curves of the same columns, but derived from use of the parameter-optimization program
CXT4 as described below.
Soil-column effluent data were evaluated using a modified
version of the parameter-optimization code CXTFIT of Parker and van Genuchten (1984). The code was modified topermit the optimization of the degradation parameters in
the general two-site/two-region models as discussed in van
Genuchten and Wagenet (1989). A series of numerical experiments with hypothetical data sets (not further discussedhere) were conducted with the resulting code (called CXT4)
for verification of the correct inversion on the two-site/two-

Table 1. Chemical and physical properties of Valois soil.
pH(1:1 H2O extract)
5.9

Cation-exchange
capacity

Particle-size fraction
Organic C

Exchangeable acidity

Sand

Silt

Clay

mmol/100 g

%

15.0

1.64

mmol/100 g
11.0

30.1

55.2

14.7

Table 2. Experimental conditions used in the six soil-column studies of tritium, Cl and atrazine displacement.
Experimental
parameters

Experiment no.

—I

Solutes included
Input concentration, c0

1

Approximate pore-water velocity (cm h' )Bulk density, p (g cnr3)
Volumetric water content, 9 (cm3 cm"3)
Percent saturation
T(°C)
t Sterilized soil; all other cases used nonsterile soil.

II

nit

IV

V

VI

0.985
(Mg/mL)
1
1.348
0.454
89

Cl ——————
9.443(Mg/mL)
1
1.356
0.448
92

9.969
(Mg/mL)
6
1.291
0.490
96

25

25

25

3

- H2O, Cl ———————
462.5, 100(Bq/mL, Mg/mL)
1
6
1.334
1.295
0.471
0.450
92
90
22
24.5

_t____

0.968(Mg/mL)
1

1.318
0.443
88
25

. __

GAMERDINGER ET AL.: SIMULTANEOUS TRANSPORT AND DEGRADATION OF PESTICIDES
Table 4. Estimated and measured parameters of atrazine breakthrough curves in experiments Ilia to Via. ND indicates that theloss of atrazine during the time period of this experiment was 2.5%
and was within the limits of experimental error Parameters k, a,
and /are defined in Eq. [1] and [2], and 8 and n are defined in
Eq. [5e].
MeasFitted 4/ ured i£ Actual n

Exp.

no.

*t

a

f

Two-Region Model——-mm——- a(cm - cim) -

——

2.46
2.46
Va 1.82
IVa 2.46
Via 1.82

Ilia
IVa

f Determined from the equilibrium sorption isotherm.
$ Fitted with the two-site model.
§ Corrected for noneluted atrazine.
H Determined independently in another experiment and fixed.

region model with degradation. These experiments also illustrated the sensitivity of the optimization to small changes
in the parameters describing sorption, mobile-immobile
water, and degradation in the solution and sorbed phases.
Program CXT4 is available from the authors on request.
In previous displacement experiments conducted in ourlaboratory, Zhong et al. (1986) used Cl as a tracer for measuring v and D in similar column-displacement experiments
using aldicarb [2-methyl-2(methylthio) propionaldehyde0(methylcarbamoyl)oxime], a weakly sorbing pesticide, forthe sandy soils used in their experiments. The
experiments
in our study were conducted using either 3H2O and Cl, or
Cl in combination with atrazine for the purpose of distinguishing between physicalprocesses associated with mobileimmobile water flow (3H2O), and chemical processes of anion exclusion (Cl) and nonequilibrium sorption (atrazine).
Due to restrictions (specific to our laboratory and university
policies) on the use of radioactive3 materials, experimentsthat combined both atrazine and H2O as a tracer in thesame soil column could not be conducted.
Theoretical Model
Appropriate analytic solutions of the transport models describing both two-site sorption and two-region transport are
discussed in detail in van Genuchten and Wagenet (1989).
In short, the two models assume that pesticide transport
under steady-state water flow can be represented as follows.
Two-Site Model£Z£ ££ = £ > £2 I £ _ V £ £ _ ^

e )dt

dx

dx

e

[(I - f)kc - s2] -we-

[1]

[4]
where all terms are as previously defined, except that thesubscripts m and im now refer to mobile and immobile regions of soil water, q = ffmvm, and a, /and k are redefined
to describe diffusion-type interactions between the two liquid
regions of the soil, rather than chemical-kinetic processes.
Equations [1] and [2] show that, at least in theory, it ispossible to have three different degradation coefficients if thetwo-site model is assumed to be applicable: fi, for degradationin the liquid phase, /*sl for degradation from the type-1 (equilibrium) sorbed phase, and ns2 for degradation from the type2 (kinetically) sorbed phase. Similarly, Eq. [3] and [4] indicate four possible degradation-rate
coefficients if the tworegion model holds: nlm and Mum for degradation in the mobile
and immobile liquid phases, respectively, and Msm and jusim
for degradation from the mobile and immobile sorbed
phases, respectively. As shown by van Genuchten and Wagenet (1989), at most, two degradation coefficients in both thetwo-site and two-region models can be considered macroscopically as truly independent model parameters, thus illustrating the complexity of the measurement and parameter-estimation problem. Experimentally, we are only able
to distinguish a single, "lumped" degradation-rate coefficient. Two options are available in the CXT4 code as it iscurrently written: degradation in the liquid phase only, or asingle degradation rate that applies over the entire soil-water
system. Chemical hydrolysis of atrazine is catalyzed by contact with soil and a more rapid rate constant for the soilwater system has been reported (Armstrong et al., 1967;
Armstrong and Chesters, 1968; Gamble and Khan, 1985).
Although two distinct rate coefficients for the solution andsorbed phases have not been measured, there is evidence
that degradation occurs in the sorbed phase. Therefore, we
assume that all degradation coefficients are the same, regardless of whether the chemical is dissolved in the liquid
phase or adsorbed onto the solid matrix, or whether thechemical is in= the mobile
or stagnant regions of the soil.
==
Therefore,
MI
MSI
M
2
M for the two-site model, andS
Mim = Mum = Msm = ^sim = M for the two-region model.
Given the above simplifications, the two-site and two-region models can be expressed in the same dimensionlessform with five independent parameters. For the two-site
model, these parameters are

P = vL/D

R = 1 + pk/6

[5a,b]= e + fpk

<a =[5c,d]

6 + pk-= a[(l - f)kc

- S2] - fis2

[5e]

[2]

where/is the fraction of equilibrium-type sorption sites; kis the distribution coefficient for linear solute partitioning
between the solution (c) and sorbed (s) phases; a is a kinetic
rate coefficient; n represents the degradation rate constant
as applied to equilibrium sites (/nsl) of the solid phase, tononequilibrium sites (ns2) of the sorbed phase, and to theliquid phase (MI). Other symbols not yet denned are the volumetric water content (6), the soil bulk density (p), distance(x), and time (t).

ll]«i» + (1 - flpk]

h-1

h_0.0266§ 0.00056
0.0144$ ± 0.0018 0.36$ ± 0.02
0.0144H
0.3611
0.0413 0.0456§ 0.0005_
0.0121 0.0005
0.0132$ ± 0.0008 0.35$ ± 0.01
0.01 321!
0.35H
0.0441 0.0456§ 0.0005
0.0132H
0.0584
ND
ND
0.35H

959

where L is the length of transport, and for the two-region
two-remodel

P = vmL/D

R = 1 + pk/6

6 + pk$ =— =[6a,b][6c,d][6e]

960

SOIL SCI. SOC. AM. J., VOL. 54, JULY-AUGUST 1990

P is commonly called the Peclet number and ^ is a dimensionless degradation parameter. The parameter /3 is a di-mensionless partitioning coefficient, and o> is a dimensionlessrate coefficient for either kinetic sorption or mobile-immo-

bile exchange. The above parameters are discussed in detailby van Genuchten and Wagenet (1989).

RESULTS AND DISCUSSION
Sorption Isotherms
The equilibrium sorption isotherm for atrazine on
Harford soil was described with both the linear (s =kc) and nonlinear (s = k/;") forms of the Freundlich
equation (Fig. 1). Application of the linear form predicted, for the linear range ofthe curve (first sevendata points), k = 1.98 with r2 = 0.99, while the non-2
linear form predicted kf = 2.46 and n = 0.87 with r= 0.99 for the entire isotherm. Although the isotherm
appears linear over the range of concentrations usedin displacement experiments (1-10 Mg/mL), sorption
nonlinearity affected analysis of miscible-displacement data and was, therefore, considered during thesubsequent analysis of the breakthrough curves(BTCs) discussed below. Isotherms for sterilized andunsterilized soil were indistinguishable.
Column Displacement Experiments
A representative column effluent curve for the simultaneous application of Cl and 3H2O on Harford
soil is shown in Fig. 1 for the relatively fast flow experiment (v = approximately 6 cm/h). Clearly, the two
tracers are eluted symmetrically (without tailing), indicating that, at this v, there were not significant effectsofimmobile water on transport. Since other Cl and3
H2O curves measured at other velocities exhibited
identical behavior, we decided to use only the two-site
formulation in subsequent analysis of the atrazine displacement in Harford soil. Note that the Cl tracer always eluted first, thus providing evidence for anion
exclusion, as expected. We assume that tritium is not
subject to any sorption, ion-exchange, or anion-exclusion processes. The distribution coefficient k is thenzero and R (Eq. [5b]) becomes unity. The assumptionof having R = 1 for tritiated water enabled us to estimate v directly from the effluent curve (Parker andvan Genuchten, 1984), which was in agreement withdirect measurements of v.

Given that R = 1, the program CXT4 was used toestimate the parameters v and D (Table 3) for the twotritiated-water experiments (Exp. la, Ha). Using v as
estimated from the 3H2O effluent data, we next fitted
D and R to the Cl data, while keeping v fixed. Resultsin Table 3 (Exp. Ib, lib), show that R generally was-0.91.
In the experiments conducted with atrazine at two
velocities and two concentrations (Exp. Ill- VI) the
BTCs were asymmetrical and tailed, as others havereported (Rao and Davidson, 1979; Goltz and Roberts, 1986). Breakthrough curves measured here for Cl
were symmetrical, similar to that reported in Fig. 2.
The Cl data were used with R = 0.91 to determine v
and D. The atrazine data were then simulated for fivecases; the results are summarized in Table 4 and discussed below.
Miscible-displacement experiments were more sensitive to isotherm nonlinearity than was the batchisotherm method, and isotherm nonlinearity was considered in simulations of the BTCs measured in thesoil-column experiments. The two-site model formulation assumes a linear isotherm (Eq. [5b]); therefore,
linearized values of k were calculated for each initialconcentration applied in the miscible-displacement
experiments. Rao and Davidson (1980) demonstrated
how the ratio of the nonlinear and linear forms (Eq.
[7]) of the Freundlich equation can be used to determine a linearized value of k for a particular concentration when the isotherm is, in fact, nonlinear:[7]k =For low-concentration experiments (c0 = 0.968 and
0.985 Mg/mL), k = 2.46 mL/g and, for high concentration experiments (c0 = 9.443 and 9.969 jug/mL), k= 1.82 mL/g. Retardation factors for miscible-displacement experiments were based on these linearized
estimates of k and were held constant in all simulations of atrazine BTCs.
Effluent data from atrazine Experiments Ilia (v =0.86, c0 = 0.968 Mg/mL) and IVa (v = 0.93, c0 = 0.985
Mg/mL) simulated with the two-site model are shownin Fig. 3. In 1Exp. Ilia (Fig. 3a), a degradation rate (M= 0.00056 rr ) was estimated from the atrazine massbalance determination using the effluent data, theoO

ATRAZINE ADSORPTION ISOTHERM
VALOISLOAM

01

H20 (Exp. la)—— fitted

R = 1.0

bJ
O

O

o

0.8

1.2

1.6

2.0

2.4

2.8

PORE VOLUMES (V/VO)

5

10

15

SOLUTION CONCENTRATION, C

Fig. 1. Adsorption isotherms for atrazine on Valois silty loam soil.

Fig. 2. Representative breakthrough curve for 3H2O and Cl in tracer

experiments on Valois soil. Pore-water velocity, v = 6.07 cm/h,
R is a retardation factor.

961

GAMERDINGER ET AL.: SIMULTANEOUS TRANSPORT AND DEGRADATION OF PESTICIDES

amount remaining in the column at the end of the experiment, and the applied mass. This value of n wasthen used to calculate \l/ = 0.0266. Then, using CXT4
and this value of ^, the sorption parameters estimatedwith the two-site model were a = 0.0144 and/= 0.36
(Table 4). It is important to note that the value of a isconsistent with that predicted with the regression equation relating a and k recently presented by Brusseau
and Rao (1989a). For Exp. IVa (Fig. 3b), the parameters« and/were fixed at the values estimated in the above
simulation of Exp. Ilia. A one-parameter optimization
was used to estimate ^ = 0.0413, which approximatesthe experimentally estimated value of 0.0456. The firstsimulation (Fig. 3a) demonstrates how nonequilibrium
sorption can be estimated when degradation is quantified independently. The second simulation (Fig. 3b)illustrates how a degradation rate can be predicted when
the sorption parameters are known. The two processes
can be studied simultaneously by way of the two-site
model but, given the significant correlation between R
and \{/, both equilibrium sorption and degradation cannot be determined through curve-fitting the data froma single experiment.
In the low velocity (v = 0.9 cm/h), low concentration (c0 = 1 Mg/mL) experiments (Exp. Ilia, IVa), 16
to 18% of the applied atrazine was not eluted from thesoil column and was recovered by extraction of thesoil at the completion of the experiment. Degradation
appears as a sink term in the model formulation, and\l/ had to be corrected to include noneluted as well asdegraded atrazine in these two cases. The loss of theparent compound to processes other than degradation
0.40

3o.

0.30-•

Irradiated Valois soila observed— fitted

o
U

3b.

o

o

0.20

R - 8.51

f . 0.44B'
u- 1.150'

R = 8.32/J = 0.442°
u = 1.645°

k- 1.82
f = 0.35

a-0.0132v = O.B77 cm/hr
C0= 9443 n/\a = 0.0144
v = 0.864 cm/hr

0.10--

0.00-0.0120i> = 0.0266

k = 2.46
f = 0.36

0.20 - •UJ(such as volatilization) would also confound prediction of $ and M, and must be considered in attempts
to predict the degradation of unstable compounds. In
the high velocity(v = 6 cm/h) and high concentration(c0 = 10 Mg/mL) experiments (Exp. V, VI) the percentage of noneluted atrazine was less than 5% of theapplied atrazine, within the limits of experimental error, and did not affect estimates of \l/.
Breakthrough curves and model simulations forExp. Va, IVa, and Via are shown in Fig. 4a, 4b, and4c, respectively. Data from Exp. Va (v = 0.88 cm/h,
c0 = 9.443 Mg/mL) were simulated with degradation
fixed
to the mass-balance-determined value of 0.0005
Ir1, while the sorption parameters a and/were estimated with the two-site model. The parameters (a =0.0132 a n d / = 0.35) approximated those estimatedin Exp. Ilia (a = 0.0144 and/= 0.36). The agreementof the predicted values for these data with different
initial concentrations and the ability to simulate thedata in both cases demonstrates that linearized valuesof A; can be calculated and used with this model underconditions of isotherm nonlinearity.
The sorption parameters from Exp. Va were thenused in simulations of data from Exp. IVa (v = 0.93
cm/h, c0 = 0.985 jug/mL; Fig. 4b) and Via (v = 6.3
cm/h, c0 = 9.969 Mg/mL; Fig. 4c). An accurate prediction of the experimental BTC was obtained when
predicting the low-concentration data (IVa) from theparameters estimated with high-concentration data.
The predicted value of \[/ also agrees with the measured
value. The simulated curve of the high-velocity data(Via) was shifted to right of the observed values, sug-•o0.15--

Untreated Valois soil
n observed—— fitted

R = 8.30

P = 0.437
u = 1.536

It = 0.0413°
v = 0.933 cm/hr

UJ

0.10-•
0.05 • •

0.00

10

12

14

PORE VOLUME (V/VO)

Fig. 3. Breakthrough curves in which (3a) sorption parameters were
estimated with the two-site model and degradation (^) was determined independently with mass-balance data, and (3b) the sorption parameters were fixed to the values estimated in (3a) anddegradation was estimated with the two-site model. Parameters
k , f , a, and v are defined in Eq. [1] and [2], and R, ft, and u> aredefined in Eq. [5].

PORE VOLUMES (V/Vo)

Fig. 4. Breakthrough curves in which (4a) sorption parameters were
estimated with the two-site model and degradation (ifr) was determined independently with mass-balance data, and (4b, 4c) the
sorption parameters were fixed to the values estimated in (4a),and degradation was estimated with the two-site model. Parameters k , f , a, and v are defined in Eq. [1] and [2], and R, ft, and o>
are defined in Eq. [5].

962

SOIL SCI. SOC. AM. J., VOL. 54, JULY-AUGUST 1990
1.00

o
O

o

I

5
o
o

o

0.00
PORE VOLUME (VAo)

Fig. 5. Measured (van Genuchten et al., 1974) and simulated breakthrough curves for the pesticide 2,4,5-T (pore-water velocity, v =8.73 cm/A) developed with the two-region model for the two casesof no degradation (n = 0) and degradation (n > 0). Values of theretardation coefficient (R), Peclet number (P) and sorption rate
coefficient(o>) were determined independently with batch and3
H2O data. Parameters <f>, ft, and M are defined in Eq. [5].

gesting that nonequilibrium may be greater than thatwhich is accounted for with the estimated values of/and a.
Data from van Genuchten (1974) were used as anadditional case to evaluate the application of the tworegion formulation of the model to describe degradation during transport when the nonequilibrium condition results from the presence of immobile water
rather than two-site sorption. A BTC for 2,4,5-T herbicide on Glendale silt loam (fine-silty, mixed [calcareous], thermic Typic Torrifluvent) is shown in Fig.
5. The parameters R = 2.14, P = 56, and w = 0.722
were determined in batch and 3H2O studies and fixedin simulations of the 2,4,5-T BTC. In Case 1 of Fig.
5, the curve was simulated with degradation fixed tozero. The fitted curve overestimates the mass present
in the system and, therefore, the concentration in thecentral region of the curve. In Case 2, the curve wassimulated with ^ > 0, resulting in a better descriptionof the observed data, particularly in the1 central regionof the curve. A value of M = 0.022 d" was predicted
and corresponds to a half-life of 32 d. Independent
estimates of degradation were not available for these
data. However, O'Connor and Wierenga (1973) evaluated the persistence of 2,4,5-T on Glendale silt loam
in lysimeter studies and monitored dissipation of theherbicide over a period of several months. They foundthat the time required for complete degradation of
2,4,5-T varied between 43 and 85 d (O'Connor and
Wierenga, 1973), slightly faster than the degradation
rate predicted with the two-region model. O'Connor
and Wierenga found that degradation was more rapid
when the soil had been previously treated with 2,4,5T; they, in fact, reported data for second and third
applications. The lack of soil-column pretreatment
with 2,4,5-T may explain the longer half-life predicted
here with laboratory miscible-displacement data.
CONCLUSIONS
Potential applications of the two-site/two-region
model for predicting pesticide degradation rates underconditions of chemical and physical nonequilibrium
were demonstrated. The inclusion of the degradation
parameter in the familiar two-site/two-region model
improved the description of effluent data (van Genuchten, 1974) in a case where degradation was considered a confounding process in the original interpretation of experimental results. These techniques areapplicable to other nonpesticidal organic-chemical
contaminants.
This study demonstrates that proper execution andanalysis of organic-chemical displacement experiments is not easy due to the many simultaneous processes and parameters involved. Of course, parsimonyof parameters is a serious consideration when thesetypes of models are applied to field conditions. However, we still need to know the relevant processes affecting organic-contaminant transport and transformation. Thus, carefully designed and executedlaboratory experiments remain important. Appropriate models of the type used in this study, together withlaboratory displacement studies, offer an opportunity
to differentiate between various processes and properties. This study only illustrated potential applications of the model. A more comprehensive analysis oforganic-chemical transport with degradation also requires a series of batch-type degradation experiments
in which, hopefully, some of the degradation parameters can be estimated independently.
ACKNOWLEDGMENTS
The authors wish to thank Dr. L.W. Lion of Cornell University for the use of his laboratory for the tritium studies,and Dr. P.S.C. Rao of the University of Florida for his in-sight and suggestions regarding the manuscript.

BENJAMIN ET AL.: WATER AND HEAT TRANSPORT IN RIDGED SOILS

963