Inverse Analyses of Transport of Chlorinated Hydrocarbons Subject
to Sequential Transformation Reactions
Francis X. M. Casey* and Jiřı́ Šimůnek
ABSTRACT

to include nonequilibrium transport and transient waterflow within the numerical model, HYDRUS-1D (Šimůnek et al., 1998a). Inverse methods (van Genuchten, 1981;
Kool et al., 1985) have become the standard in soil
science to identify solute transport parameters, and havebeen shown to be very successful. Nonetheless, there
still has been little inverse application of transport models to solutes that undergo transformation and to theirdegradation daughter products. Inverse application ofthese transformation transport models can lead to better
identification of transport processes, which can increase
our understanding and lead to better prediction.
Ground water contamination by chlorinated aliphatichydrocarbons (CAHs) is an area that reflects the importance of having methods that can lead to deeper understanding of solutes undergoing transport and transformation. The prevalent use of CAHs as industrial solventsand in dry cleaning operations has caused widespreadground water contamination. The National Academy of
Sciences identified TCE, a CAH, as the most common
contaminant at nearly 300 000 to 400 000 hazardous waste
sites in the USA (National Academy of Science, 1994).
Ground water remediation of CAHs by zero-valent metals shows promise because of its relatively low costs andthe virtual elimination of the CAHs and their degradation daughter products (Focht et al., 1996; Appleton,
1996). It is theorized that CAHs in the presence of zerovalent metals, such as iron filings, undergo a reduction
process where electrons are exchanged between the pollutant molecule and an electron donor (i.e., zero-valent
metal). In the reduction of TCE (C2HCl3 ), there is sequential removal of chloride ions, which produces dichloroethylene isomers (C2H2Cl2 ) that are further reduced to vinyl chloride (C2H3Cl), then ethylene (C2H4 ),and finally ethane (C2H6 ).
Numerous degradation experiments of TCE in thepresence of zero-valent metals have shown that the process is first order and can be 5 to 15 orders of magnitude
greater than natural abiotic rates (e.g., Focht et al., 1996;
Gavaskar et al., 1998; Gillham et al., 1997; Gillham andO’Hannesin, 1994; Orth, 1992; Orth and Gillham, 1996).
Other batch sorption studies have reported evidence
for nonequilibrium sorption (Burris et al., 1995, 1998) thatcan result in more complex degradation processes andchemical nonequilibrium transport. Casey et al. (2000b)
used effluent miscible-displacement experiments to study
the fate and transport processes of dissolved concentrations of TCE flowing through water-saturated zerovalent metal filings. They reported breakthrough curvesof TCE and its degradation daughter product, ethylene,
and described the breakthrough curves by means ofequilibrium and nonequilibrium convective–dispersive

Chemical and biological transformations can significantly affectcontaminant transport in the subsurface. To better understand suchtransformation reactions, an equilibrium–nonequilibrium sorption
transport model, HYDRUS-1D, was modified by including inverse
solutions for multiple breakthrough curves resulting from the transport of solutes undergoing sequential transformations. The inverse
solutions were applied to miscible-displacement experiments involving dissolved concentrations of trichloroethylene (TCE) undergoing
reduction and/or transformations in the presence of zero-valent metal
porous media (i.e., iron or copper-coated iron filings) to produce
ethylene. The inverse model solutions provided a reasonable description of the transport and transformation processes. Simultaneous fitting of multiple breakthrough curves of TCE and ethylene placed
additional constraints on the inverse solution and improved the reliability of parameter estimates. Confidence intervals of optimized parameters were reduced significantly in comparison with those obtainedby fitting TCE breakthrough curves independently. Further evidence
for accurate parameter estimates was given when the parameter values
agreed with previously reported values from independent batch anddegradation experiments. Optimized values of the normalized degradation rates for the equilibrium (1.4 ⫻ 10⫺4 to 7.2 ⫻ 10⫺5 L h⫺1 m⫺2 )and nonequilibrium (1.2 ⫻ 10⫺4 to 5.5 ⫻ 10⫺5 L h⫺1 m⫺2 ) models
compared well with values (0.03 to 6.5 ⫻ 10⫺5 L h⫺1 m⫺2 ) obtained
from previous studies. The estimated TCE–iron sorption coefficients(0.52 to 2.85 L kg⫺1 ) were also consistent with a previously reported
value (1.47 L kg⫺1 ).

T

ransformation processes, such as biotransformation and radioactive decay, are very common andhave major influence on the movement of contaminantsin porous media. Examples of solutes undergoing various transformation reactions and migration in the soil
include radionuclides (Evans et al., 1997; Viswanathan
et al., 1998), nitrogen species (Mishra and Misra, 1991;
Misra et al., 1974), organic phosphates (Castro and Rolston, 1977), and organic hydrocarbons (Burt, 1999; Schaerlaekens et al., 1999). These reactions are frequently identified and modeled as linear, instantaneous processes;
however, they can often be much more complex. Solutes
involved in transformation reactions in addition to nonideal transport greatly confound the study, modeling,
and prediction of solute transport. There is a need formodeling techniques that can help identify these processes by unraveling the complexity.
Several models exist, such as CHAIN (van Genuchten
et al., 1985), which can describe the transport of solutes
undergoing ideal first-order transformation reactions.
CHAIN, an analytical equilibrium, one-dimensional convection–dispersion transport model, has been expanded
F.X.M. Casey, Dep. of Soil Science, North Dakota State Univ., Fargo,
ND 58105. J. Šimůnek, George E. Brown Jr. Salinity Lab., USDAARS, Riverside, CA 92507. Received 23 Oct. 2000. *Corresponding
author (Francis_Casey@NDSU.NoDak.edu).
Published in J. Environ. Qual. 30:1354–1360 (2001).

Abbreviations: L, length; M, mass; T, time; TCE, trichloroethylene.

1354

1355

CASEY & ŠIMŮNEK: ANALYSES OF TRANSPORT OF CHLORINATED HYDROCARBONS

models. Casey et al. (2000b) did not find other degradation products in their effluent breakthrough curves. Furthermore, in their study they applied the model inversion only to the transport of TCE and then used the
optimized transformation coefficients to obtain a reasonable prediction of the ethylene breakthrough curves.
The objective of this study was to modify the equilibrium–nonequilibrium transport model HYDRUS-1D by
including an inverse solution that allows simultaneous
fit of multiple breakthrough curves resulting from transformation reactions. This modification can improve theinterpretation of various transformation reactions, especially when complex transport processes occur. It has
been shown previously (e.g., Eching and Hopmans,
1993; Inoue et al., 2000) that simultaneous fit of related
information (e.g., pressure heads and outflow during
outflow experiments, or pressure heads and concentrations during infiltration experiments) can result in significant reduction of confidence intervals of optimized parameters and thus more reliable determination of
governing processes. The HYDRUS-1D model was
modified to solve equilibrium and nonequilibrium transport models inversely for multiple solutes subject tosequential transformation reactions. The zero-valent
metal miscible-displacement experiments from the
Casey et al. (2000b) study were used to demonstrate
the inverse application of the modified HYDRUS-1Dmodel. The columns that Casey et al. (2000b) used forthe miscible displacement study were packed with iron(Fe) or iron coated in copper (Cu–Fe). It will be shownthat the confidence intervals of the optimized parameters improve when information about both TCE andethylene breakthrough curves is used as opposed to only
using information from the TCE breakthrough curve.

The following set of coupled differential equations governs
the one-dimensional, convective–dispersive, linear-equilibriumtransport of a sequence of solutes consecutively undergoingdegradation and transformation (van Genuchten, 1985):

⳵C1
␳K
⳵C
⳵2C
⫽ D 21 ⫺ v 1 ⫺ ␥1 b d,1C1
⳵t
⳵x
⳵x
␪
⳵Ci
␳bKd,i
⳵Ci
⳵2Ci
Ri⫽D 2 ⫺v
⫺ ␥i
Ci
⳵t
⳵x
⳵x
␪
␳K
⫹ ␥i⫺1 b d,iCi⫺1 (i ⱖ 2)
␪

[1a]

[1b]

where Ci is the solution concentration (M L⫺3 ), D is the hydrodynamic dispersion (L2 T⫺1 ), v is velocity (L T⫺1 ), x is distance(L), t is time (T), ␥i is the first-order degradation rate constant(T⫺1 ), Kd,i is the distribution coefficient (L3 M⫺1 ), ␳b is thebulk density (M L⫺3 ), ␪ is the volumetric water content (L3L⫺3 ), and the retardation factor Ri (unitless) is given by:

Ri ⫽ 1 ⫹␳bKd,i␪冢1 ⫹ ␳ fK␪ 冣⳵C⳵t ⫽ D⳵⳵xC ⫺ v⳵C⳵x ⫺ ␣␪␳ [(1 ⫺ f)K C ⫺ S ]
b

d,1

1

2

1
2

1

1 b

d,1

1

S2,1

f␳ K
⫺ ␥S1,1 b d,1C1[3a]
␪
␳ fK ⳵C⳵C ␣ ␳
⳵2C
1 ⫹ b d,i i ⫽ D 2 i ⫺ v i ⫺ i b[(1 ⫺ f)Kd,iCi ⫺ SS2,i]
␪ ⳵t
⳵x
⳵x
␪
f␳bKd,if␳ K⫺ ␥S1,iCi ⫹ ␥S1,i⫺1 b d,i⫺1Ci⫺1␪␪␳⫹ b␥S2,i⫺1SS2,i⫺1 (i ⱖ 2)
[3b]
␪

冢

冣

where f is the fraction of exchange sites assumed to be at equilibrium (unitless), ␥S1,i represents solid phase degradation rate
constants associated with the equilibrium sorption sites (T⫺1 ),␥S2,i represents solid phase degradation rate constants associated with the nonequilibrium sorption sites (T⫺1 ), and ␣iis the first-order kinetic rate sorption constant (T⫺1 ). In thisstudy we assumed that the transformation rates were the sameon both equilibrium and kinetic sorption sites (␥S1,i ⫽ ␥S2,i )and that degradation only occurred in the sorbed phase. Massconservation equations for the nonequilibrium sites (SS2,i,
M M⫺1 soil) are given by (van Genuchten and Wagenet, 1989):

⳵SS2,i⫽ ␣i[(1 ⫺ f)Kd,iCi ⫺ SS2,i] ⫺ ␥S2,iSS2,i⳵t

MATERIALS AND METHODSMathematical Models and Inverse Solution

R11995). Hence, it was assumed in Eq. [1] that degradation occurs
only in the sorbed phase.
Equations [1a,b] and [2] can be extended to include theconcept of nonequilibrium two-site adsorption–desorption reactions (Selim et al., 1977; van Genuchten and Wagenet, 1989;
Gamerdinger et al., 1990). Sorption on labile exchange sites
or Type-1 sites (signified by subscript S1) is assumed to beinstantaneous, while on remaining resistant exchange sites orType-2 sites (signified by subscript S2), sorption is kinetic.
The following expressions govern nonequilibrium mass transport for a homogeneous system during steady-state water flow:[2]

where the subscript i denotes the ith chain member in thetransformation reaction. For the purposes of this study, degradation was considered to be a surface process (Burris et al.,[4]

HYDRUS-1D Version 2.0 (Šimůnek et al., 1998a) numerically solves either the equilibrium model (Eq. [1a,b] and[2]) or the nonequilibrium model (Eq. [3a,b] and [4]) using
Galerkin-type linear finite element schemes. Additionally,
HYDRUS-1D may be applied inversely so that the model
solution can be fit to the measured data. However, Version
2.0 of HYDRUS-1D could inversely solve the equilibrium or
nonequilibrium transport models only for the first solute in
the chain of transformation reactions (i.e., C1 in Eq. [1a] or[3a]). Thus modifications were needed to allow HYDRUS-1D
to simultaneously fit breakthrough curves of several solutes
undergoing sequential first-order transformation reactions.
Šimůnek et al. (1998a) described the method of parameter
optimization used in HYDRUS-1D, where the numericalmodel solution is fit to measured data. This is done by iteratively changing model parameters and thus improving model
fits to the measured data until a desired degree of precision
is obtained. The simulated results that are optimized are used
together with the measured data to create an objective function, U (Šimůnek et al., 1998b):
m

nk

k⫽1

j⫽1

冤

U(b,q) ⫽ 兺 yk 兺 wj,k q*k (x,tj) ⫺ qk(x,tj,b)

冥

2

[5]

where the right-hand side represents deviations between themeasured and calculated space–time variables (e.g., concentrations at different times in the flow domain). In Eq. [5], m

1356

J. ENVIRON. QUAL., VOL. 30, JULY–AUGUST 2001

Table 1. Physical properties of 40-mesh zero-valent metal packing material for two columns.
Packing material
Property

Iron

Bulk density, g cm⫺3
Particle density, g cm⫺3
Specific surface area, m2 g⫺1†
Pore volume, mL
Surface area concentration, m2 L⫺1‡
Volumetric water content, cm3 cm⫺3

Copper-coated iron

2.42
7.10
5.76
29.40
21 147
0.66

3.09
6.36
3.73
22.90
0.51

† Measured using the BET method (Brunauer et al., 1938).
‡ Calculated after Johnson et al. (1996).

is the number of different sets of measurements, nk is the number of measurements in a particular measurement set, q*k (x,tj )represents specific measurements at time tj for the kth measurement set at location x, qk(x,tjb) is the corresponding model
prediction for the vector of optimized parameters b (e.g., Kd,
D, ␣, and ␥), and yk and wj,k are weights associated with a particular measurement set or point, respectively. Minimizationof U is done by the Levenberg–Marquardt nonlinear minimization algorithm (Marquardt, 1963). HYDRUS-1D was modified to include simultaneous parameter optimization for multiple solute breakthrough curves resulting from transformation
reactions. To do this, the code was amended to include parameters from the secondary breakthrough curves (i.e., i ⬎ 1 in
Eq. [1b, 2, 3b, and 4]) into the U (Eq. [5]). The objectivefunction, which includes parameters from multiple breakthrough curves, can then be minimized using the Levenberg–
Marquardt algorithm so that the model solution is fit simultaneously to the measured data of TCE and its degradation
daughter products. The breakthrough curves of TCE and its
degradation products were considered as different measurement sets. Weights yk were selected such that contributionsof residuals of each breakthrough curve were about equal,
while weights wj,k were set equal to one.
HYDRUS-1D also specifies the upper and lower boundsof the 95% confidence level around each fitted parameter b.
It is desirable that the real value of the target parameter always
be located in a narrow interval around the estimated mean
as obtained with the optimization program. Large confidence
limits indicate that the results are not very sensitive to thevalue of a particular parameter (Šimůnek et al., 1998a).
To compare optimized ␥ values with previously reported
values, it was important to consider the specific surface area
(as, L2 M⫺1 ) of the zero-valent metal. Johnson et al. (1996)
was able to compare observed degradation rates (␥obs, T⫺1 )from several studies by normalizing the ␥obs values according
to the surface area of the zero-valent metals. The following
relation was presented by Johnson et al. (1996):

␥obs ⫽ ␥normas␳m[6]where ␥norm is the normalized degradation rate (L3 T⫺1 L⫺2 )and ␳m is the mass concentration of zero-valent metal (M L⫺3of solution). The terms as and ␳m multiplied together equal
the surface area concentration of the zero-valent metal (L2 L⫺3of solution; Table 1).

Experimental Procedure
Casey et al. (2000b) described in details the experimental
procedures. Two columns (21.4-mm diameter and 124-mm
length), packed with 40-mesh iron filings (Fe; Fisher Scientific,
Pittsburgh, PA1 ) or 40-mesh Fisher iron filings plated with
1
Names of all products or brands are provided solely for the reader’sinformation and do not imply endorsement of individual brands, nor
criticism of similar suitable products.

1.78% copper (Cu–Fe), were saturated and used for all miscible-displacement experiments. Table 1 shows the physical properties of the packing material for the two columns. Threeexperiments were run on each column where a pulse of one
pore volume of 42 mg L⫺1 TCE was passed through the columns at pore water velocities of 12.4 (denoted as fast), 6.2(intermediate), or 3.1 (slow) mm min⫺1. These pore watervelocities resulted in one pore volume being displaced every
10, 20, or 40 min, and the order in which the experiments
were run was fast, intermediate, and slow. Column effluent
was sampled every 5 min for each experiment and diverted
to an online high performance liquid chromatography (HPLC)
system. The experimental displacement system is described in
depth by Casey et al. (2000a). The on-line HPLC was equippedwith a Beckman (Fullerton, CA) 128 diode-array flow throughphoto detector capable of separating out TCE and its daughter
products (1,1-dichloroethylene; 1,2-cis-dichloroethylene; 1,2trans-dichloroethylene; vinyl chloride; and ethylene) and determining their concentrations in the effluent. The detection
limit of TCE and its degradation daughter products was approximately 0.01 mg L⫺1. Casey et al. (2000b) described theanalytical procedures in detail.

RESULTS AND DISCUSSION
Figures 1 and 2 present the breakthrough curves of
TCE and ethylene from the Casey et al. (2000b) study
and the corresponding inverse solutions to the equilibrium and nonequilibrium models from the current study.
Trichloroethylene and ethylene were the only products
detected in the column effluent. Excellent descriptionsof the TCE and ethylene breakthrough curves wereobtained when both curves were fitted simultaneously.
This is reflected by the relatively high coefficients ofdetermination (r 2; ranging from 0.94 to 1.00 for theequilibrium model and 0.96 to 1.00 for the nonequilibrium model; Table 2). These correlations for the combined fit of the TCE and ethylene breakthrough curves
were much better than those reported by Casey et al.
(2000b) (r 2 ⫽ 0.69 to 0.99 for the equilibrium model,
0.91 to 0.99 for the nonequilibrium model). Casey et al.
(2000b) were only able to inversely fit the TCE breakthrough curves and predict, not fit, the ethylene breakthrough curves. Significant improvement in descriptionof the ethylene breakthrough curves in comparison with
the Casey et al. (2000b) study was registered, especiallyfor slow water flow rates.
Table 2 presents the optimized parameters from theinverse solutions to the equilibrium and nonequilibrium
models that were simultaneously fitted to the TCE andethylene breakthrough curves. For the equilibrium model,
␥TCE, ␥ethylene, Kd,TCE, and Kd,ethylene values were simultaneously optimized to their corresponding breakthroughcurves (indicated by the subscripts TCE or ethylene).
The source for the ethylene production came directlyfrom the degradation of TCE. Dispersivity (␭ ⫽ D/v)
values were assumed to be identical for the TCE andethylene breakthrough curves, and hence estimatedfrom both curves simultaneously. For the nonequilibrium model, ␥TCE, ␥ethylene, Kd,TCE, Kd,ethylene, ␣TCE, and ␣ethylene
were simultaneously optimized to their corresponding
breakthrough curves. Note that we assume that thetransformation rates ␥ for both TCE and ethylene areCASEY & ŠIMŮNEK: ANALYSES OF TRANSPORT OF CHLORINATED HYDROCARBONS

1357

Fig. 1. Breakthrough curves from the column filled with iron filings(Fe column) for the fast, intermediate, and slow flow rates. Inverse
model solutions to the equilibrium (Eq. [1a,b and 2]) and nonequilibrium (Eq. [2a,b and 3]) models are also plotted.

Fig. 2. Breakthrough curves from the column filled with iron fillings
coated with copper (Cu–Fe column) for the fast, intermediate, andslow flow rates. Inverse model solutions to the equilibrium (Eq.
[1a,b and 2]) and nonequilibrium (Eq. [2a,b and 3]) models arealso plotted.

the same on both equilibrium and kinetic sorption sites
and only take place in the sorbed phase. We also assumed similar f values for the TCE and ethylene breakthrough curves. Assuming similar ␭ and f values forthe concurrent TCE and ethylene breakthrough curves
seems reasonable because both solutes passed throughthe exact same column filled with the exact same medium (Bear, 1972).
Optimized dispersivities (␭) were about an order ofmagnitude larger for the equilibrium model than for thenonequilibrium model (Table 2). This is a typical resultof fitting breakthrough curves and not taking into account all underlying processes, which may cause themodel code to move the effects of the unaccounted processes into another process. In our case, the kinetic
sorption was not accounted for in the equilibrium

model, which may have moved the kinetic sorption effect into the dispersion term. Values of both ␥ and Kd
parameters for both soil columns are about the samefor the equilibrium and nonequilibrium models.
Simultaneous inversion places additional constraint
on the inverse solution, which improved the stability
and reliability of the parameter estimates by reducing
the confidence intervals (Šimůnek et al., 1998b). Casey
et al. (2000b) obtained significant cross-correlations between optimized parameters and their correspondingly
large confidence intervals when they optimized nonequilibrium model solute transport parameters (␭, f, Kd,
␥, and ␣) to the TCE breakthrough curves only. The
95% confidence intervals of optimized parameters fromthe Casey et al. (2000b) study often spanned physicallynonrealistic values, such as negative values of Kd and1358

J. ENVIRON. QUAL., VOL. 30, JULY–AUGUST 2001

Table 2. Values of the equilibrium (Eq. [1a,b, and 2]) and nonequilibrium (Eq. [3a,b and 4]) transport model parameters† with 95%
confidence intervals (in parentheses) for the simultaneous inverse fit of the trichloroethylene (TCE) and ethylene breakthrough curves.‡
Experiment

Iron column
FastIntermediate
Slow
Copper-coated ironcolumnFastIntermediate
Slow

␭

f

Kd,TCE

Parameter
␣TCE

␥TCE

Kd,ethylenemin⫺1
L kg⫺1Equilibrium transport model

␥ethylene␣ethylene

r2

cm

L kg⫺1min⫺10.34 (0.05)
0.24 (0.05)
1.58 (0.15)

0.62 (0.01)
0.46 (0.02)
2.06 (0.14)

0.048 (0.002)
0.051 (0.001)
0.052 (0.001)

1.08 (0.06)
0.85 (0.04)
1.57 (0.04)

0.004 (0.004)
0.004 (0.002)
0.001 (0.000)

0.95
0.94
0.99

0.31 (0.06)
0.54 (0.07)
0.82 (0.07)

0.62 (0.02)
0.59 (0.03)
0.82 (0.07)

0.046 (0.048)
0.037 (0.002)
0.026 (0.002)

1.18 (0.04)
0.85 (0.02)
0.78 (0.02)

0.002 (0.001)
0.002 (0.001)
0.001 (0.000)

0.97
0.96
1

Nonequilibrium transport model
Iron column
FastIntermediate
Slow
Copper-coated ironcolumnFastIntermediateSlow

0.02 (0.01)
0.04 (0.01)
0.18 (0.18)

0.55 (0.02)
0.64 (0.05)
0.21 (0.04)

0.80 (0.03)
0.52 (0.07)
2.86 (0.39)

0.042 (0.002)
0.048 (0.007)
0.019 (0.001)

0.145 (0.029)
0.118 (0.109)
0.021 (0.004)

1.05 (0.04)
0.90 (0.07)
1.23 (0.05)

0.003 (0.003)
0.002 (0.005)
0.001 (0.001)

0.272 (0.079)
0.090 (0.046)
0.080 (0.019)

0.96
0.98
0.98

0.03 (0.00)
0.02 (0.02)
0.05 (0.07)

0.58 (0.02)
0.51 (0.03)
0.18 (0.15)

0.83 (0.03)
0.65 (0.04)
1.17 (0.67)

0.037 (0.001)
0.037 (0.001)
0.022 (0.007)

0.071 (0.008)
0.066 (0.015)
0.028 (0.026)

1.16 (0.02)
0.89 (0.02)
0.70 (0.08)

0.001 (0.003)
0.001 (0.001)
0.001 (0.011)

0.139 (0.058)
0.070 (0.006)
0.065 (0.019)

0.98
1
0.99

† ␭, dispersivity (⫽hydrodynamic dispersion/velocity); Kd, distribution coefficient; f, fraction of Type-1 sorption sites; ␣, first-order mass transfer constant;␥, reaction rate constant; r 2, coefficient of determination.
‡ Subscripts “TCE” and “ethylene” signify parameters for the respective breakthrough curve.

f. Fitted TCE breakthrough curves obviously did notcontain enough information to allow simultaneous fitting of five parameters of the nonequilibrium transportmodel. This was the case especially for the slow flow rate
experiments, when most TCE was already transformed
before reaching the end of the soil column and fitting
was applied to the breakthrough curves with relatively
small concentrations (less than one hundredth of theinitially applied concentration). As a result, optimized
parameters were hardly identifiable, confidence in them
was relatively low, and also the predictions of the ethylene breakthrough curves were not very good. This problem was overcome when both TCE and ethylene breakthrough curves were fitted simultaneously. Confidence
intervals of all optimized parameters, as well as theircross-correlations, were reduced dramatically for both
equilibrium and nonequilibrium models.
The nonequilibrium model described the TCE andethylene breakthrough curves significantly better for
the fast flow rates for both Fe and Cu–Fe columns thanthe equilibrium model. However, as the flow rate decreased, differences between the equilibrium and nonequlibrium model fits decreased until they were nearly
identical for the slow flow rate. This trend was moreprevalent when the inverse model solution was applied
to both TCE and ethylene, and not just to TCE, as wasdone by Casey et al. (2000b). This trend also suggested
that some type of mass transfer limitation existed at thefaster flow rates, such as diffusion to the iron surface(Burt, 1999), a process that exhibits itself as a kineticallycontrolled sorption. Burris et al. (1998) suggested thata rate-limiting step may be present in the transformationof TCE as it desorbs from reactive sites on zero-valent
metal. Although the simultaneous inverse fit to the TCE
and ethylene breakthrough curves can provide more in-sight into which models best describe the data, more experiments need to be performed to verify this assertion.
The more complex nonequilibrium transport model
has more parameters, which should improve the fit of
the model to the data. However, good model fits do notnecessarily mean more accurate identification of theunderlying transport processes because the model solutions may not be unique, resulting in unrealistic parameter estimates or large confidence intervals. Therefore,
complex transport models need to be used with discretion, by using as many as possible independent estimatesof unknown transport parameters.
To verify the results found from this study, some of themodel parameters were compared with independently
estimated values from previous batch and degradation experiments. Numerous zero-valent metal degradation
experiment studies exist where first-order degradation
rates for TCE have been reported. For example, Tratnyek et al. (1997) summarized a collection of degradation rates (Fig. 3) that were normalized according tosurface area (Johnson et al., 1996). The normalized TCE
degradation rates from this study fell within the rangeof previously reported values (Fig. 3), but they were at
the low end of the range. Burt (1999) used batch andcolumn experiments to study the degradation of anotherchlorinated aliphatic hydrocarbon, perchloroethylene,in the presence of zeolites impregnated with zero-valent
metals. He found that the degradation rate values estimated from the column experiments were lower thanvalues estimated from batch experiments and suggested
that the difference was caused by physical mass transfer
limitations. This may suggest why the degradation rate
values from this study fell at the lower end of the range
reported by previous researchers. Furthermore, a linearized Kd value (1.47 L kg⫺1 ) from Burris et al. (1995)

CASEY & ŠIMŮNEK: ANALYSES OF TRANSPORT OF CHLORINATED HYDROCARBONS

Fig. 3. A comparison of normalized degradation rates from this study
to previous studies. The normalized degradation rates were obtained from curve fits using the (a ) equilibrium and (b ) nonequilibrium sorption models. Figure adapted from Tratnyek et al. (1997)
and is reprinted by permission of Ground Water Monitoring &Remediation (Copyright 1997).

was calculated and found to be within the range of Kd
values obtained in this study (Table 2).

CONCLUSION
The HYDRUS-1D model was successfully modified
to include inverse solutions for solutes undergoing transport and transformation. The inverse technique was applied to sample TCE and ethylene breakthrough curves
and provided more stabile and accurate estimates of thetransport parameters. The improvement lead to morereliable identification of underlying transport processes,
which was indicated by excellent correlation between
the model predictions and measured data, notwithstanding added constraints to the inverse solution. Confidence intervals of optimized parameters, obtained byanalyzing TCE and ethylene breakthrough curves simultaneously, were significantly reduced compared withthose obtained using only the TCE breakthrough curve.
The parameters that were estimated using the modified
HYDRUS-1D model were consistent with independently obtained parameters from previous studies. The
inverse application presented in this study should lendbetter understanding of subsurface transport processes
involving solutes that undergo transformation reactions.
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Seasonal Leaching and Biodegradation of Dicamba in Turfgrass
J. W. Roy, J. C. Hall, G. W. Parkin,* C. Wagner-Riddle, and B. S. Clegg
ABSTRACTThe leaching of surface-applied herbicides, such as dicamba (2methoxy-3,6-dichlorobenzoic acid), to ground water is an environmental concern. Seasonal changes in soil temperature and water content,
affecting infiltration and biodegradation, may control leaching. The
objectives of this study were to (i) investigate the leaching of dicamba
applied to turfgrass, (ii) measure the degradation rate of dicamba insoil and thatch in the laboratory under simulated field conditions,and (iii) test the ability of the model EXPRES (containing LEACHM)
to simulate the field transport and degradation processes. Four field
lysimeters, packed with sandy loam soil and topped with Kentucky
bluegrass (Poa pratensis L.) sod, were monitored after receiving three
applications (May, September, November) of dicamba. Concentrations of dicamba greater than 1 mg L⫺1 were detected in soil water.
Although drying of the soil during the summer prevented deep transport, greater leaching occurred in late autumn due to increased infiltration. From the batch experiment, the degradation rate for dicamba
in thatch was 5.9 to 8.4 times greater than for soil, with a calculated
half-life as low as 5.5 d. Computer modeling indicated that the soil
and climatic conditions would influence the effectiveness of greater
degradation in thatch for reducing dicamba leaching. In general,
EXPRES predictions were similar to observed concentration profiles,
though peak dicamba concentrations at the 10-cm depth tended tobe higher than predicted in May and November. Differences between
predictions and observations are probably a result of minor inaccuracies in the water-flow simulation and the model’s inability to modify
degradation rates with changing climatic conditions.

Leaching of pesticides through the soil to the groundwater is a concern since these chemicals may affect
the quality of drinking water supplies and surface water
ecosystems. Dicamba, a postemergent herbicide commonly used to control broadleaf weeds in turfgrass, hasbeen detected in ground water (Koterba et al., 1993;
Cox, 1994). The acceptable limit for dicamba in drinking
water is 200 ␮g L⫺1 in the United States and 120 ␮g
L⫺1 in Canada (Caux et al., 1993). Based on numerous
J.W. Roy, G.W. Parkin, and C. Wagner-Riddle, Dep. of Land Resource Science, and J.C. Hall and B.S. Clegg, Dep. of Environmental
Biology, Univ. of Guelph, Guelph, ON, Canada N1G 2W1. J.W. Roy,current address: Dep. of Earth Sciences, Univ. of Waterloo, Waterloo,
ON, Canada N2L 3G1. Received 26 May 2000. *Corresponding author(gparkin@lrs.uoguelph.ca).
Published in J. Environ. Qual. 30:1360–1370 (2001).

studies in Canada, Caux et al. (1993) calculated that 8%of the surface water and 2% of the ground water samples
contained detectable amounts of dicamba. Cohen et al.
(1990) tested the ground water under various golfcourses on Cape Cod, MA, and detected dicamba in 1of the 16 monitoring wells.
Most researchers have found only very low levels of
dicamba in infiltrating water and low total mass ofleached dicamba when applied to turf. For lawn or golf
green conditions, few of the percolate samples collected
between 0.10 to 0.20 m below surface had concentrations
exceeding 10 ␮g L⫺1 (Gold et al., 1988; Smith and Bridges, 1996; Snyder and Cisar, 1997). In these previous
studies applications took place from spring to late fall,with rates ranging from 0.11 to 0.28 kg ha⫺1. Althoughsoil cores taken by Snyder and Cisar showed noticeable
peaks of dicamba concentration in soil and thatch
shortly after application, these rapidly declined over thefollowing 2 wk.
In a field study by Harrison et al. (1993), relatively
high concentrations of dicamba were measured in runoff and/or percolate on sloped turf grown on clay topsoil. They applied dicamba at 0.28 kg ha⫺1 in July, August, September, October, and November over 2 yr. The
peaks in concentration for leachate samples collected
at the 0.15-m depth coincided with the first major irrigation or rainfall within a week after application, although
Harrison et al. (1993) considered the irrigation events
extreme. The mean concentrations (three replicate samples) of dicamba in leachate following these events were11, 21, 22, 118, and 57 ␮g L⫺1.
Only recently have researchers modeled the transportof solutes applied to turfgrass. The GLEAMS model
greatly overpredicted pesticide leaching below turf
(Smith et al., 1993). A number of researchers (Pennell
et al., 1990; Costa et al., 1994; Brown et al., 1996) indicated that LEACHM (Wagenet and Hutson, 1987) simulates solute transport in unsaturated soil as well or
better than other models. However, LEACHM predicted significantly higher dicamba concentrations inleachate and longer travel times for dicamba transport
Abbreviations: GC–MS, gas chromatography–mass spectrometry;
HPLC, high pressure liquid chromatography.