Journal of Contaminant Hydrology 89 (2007) 107 – 135
www.elsevier.com/locate/jconhyd

Transport of sulfadiazine in soil columns —Experiments and modelling approaches
Anne Wehrhan a,⁎, Roy Kasteel a , Jirka Simunek b , Joost Groeneweg a ,Harry Vereecken aaAgrosphere, ICG IV, Forschungszentrum Jülich GmbH, Leo-Brandt Str., 52425 Jülich, Germany
Department of Environmental Sciences, University of California, Riverside, CA, 92521, USAb

Received 2 November 2005; received in revised form 14 July 2006; accepted 13 August 2006
Available online 6 October 2006

Abstract
Antibiotics, such as sulfadiazine, reach agricultural soils directly through manure of grazing livestock or
indirectly through the spreading of manure or sewage sludge on the field. Knowledge about the fate ofantibiotics in soils is crucial for assessing the environmental risk of these compounds, including possible
transport to the groundwater. Transport of 14C-labelled sulfadiazine was investigated in disturbed soilcolumns at a constant flow rate of 0.26 cm h− 1 near saturation. Sulfadiazine was applied in different
concentrations for either a short or a long pulse duration. Breakthrough curves of sulfadiazine and the nonreactive tracer chloride were measured. At the end of the leaching period the soil concentration profiles were
determined. The peak maxima of the breakthrough curves were delayed by a factor of 2 to 5 compared tochloride and the decreasing limbs are characterized by an extended tailing. However, the maximum relative
concentrations differed as well as the eluted mass fractions, ranging from 18 to 83% after 500 h of leaching. To
identify relevant sorption processes, breakthrough curves of sulfadiazine were fitted with a convective–
dispersive transport model, considering different sorption concepts with one, two and three sorption sites.
Breakthrough curves can be fitted best with a three-site sorption model, which includes two reversible kinetic
and one irreversible sorption site. However, the simulated soil concentration profiles did not match theobservations for all of the used models. Despite this incomplete process description, the obtained results have
implications for the transport behavior of sulfadiazine in the field. Its leaching may be enhanced if it isfrequently applied at higher concentrations.
© 2006 Elsevier B.V. All rights reserved.
Keywords: Sulfadiazine transport; Antibiotics; Soil column; Breakthrough curve; Transport models; Sorption models⁎ Corresponding author. Now working at: Federal Environment Agency, postbox 1406, 8 06813 Dessau, Germany.
Tel.: +49 340 2103 3151; fax: +49 340 2104 3151.
E-mail address: anne.wehrhan@uba.de (A. Wehrhan).
0169-7722/$ - see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.jconhyd.2006.08.002

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1. Introduction
Among other veterinary pharmaceuticals sulfadiazine (SDZ), which belongs to the groupof sulfonamides, is a widely used antimicrobial substance in intensive livestock production totreat and prevent diseases (Thiele-Bruhn, 2003; Boxall et al., 2004). Up to 40% of theadministered sulfonamides are eliminated as microbial active parent substances with theanimal excretions (Kroker, 1983). Manure is dropped directly onto the pastures by grazing
livestock or spread onto agricultural soils after storage as fertilizer (Jørgensen and HallingSørensen, 2000). Concentrations of SDZ measured in pig manure range between 0.3 and198 mg of SDZ per kg depending on medication, dilution and age of the manure (Höper etal., 2002; Grote et al., 2004; Hamscher et al., 2005). As a result of the wide distribution ofmanure in the environment, sulfonamides are frequently found at concentration levels between
a few and 100 ng L− 1 in surface waters of Northwestern Germany (Christian et al., 2003).
Due to low extraction efficiencies (Kreuzig et al., 2003; Hamscher et al., 2005), there are no
reliable data for typical SDZ concentrations in soils. The risk of surface water contaminationis enhanced by surface runoff from manured fields (Burkhardt et al., 2005; Kay et al., 2005a)
or in drained arable lands. Peak concentrations of about 0.6 mg L− 1 of sulfachloropyridazine
and 0.03 mg L− 1 of oxytetracycline, two other antibiotic substances used in pig breeding,were found in drainage water after the application of contaminated pig manure (Kay et al.,2004).
During monitoring of pharmaceuticals in groundwater in southwest Germany, SDZ wasfound in one out of 105 samples (Sacher et al., 2001). In contrast to another sulfonamide(sulfamethazine) or tetracyclines, SDZ was not detected in the soil or groundwater after theapplication of contaminated pig manure to a field site (Hamscher et al., 2005). Possible
reasons for the fast dissipation of SDZ compared to the other substances are either a faster
degradation or transformation, strong sorption in non-extractable fractions or low extraction
efficiencies of soil analysis (Hamscher et al., 2005). It is known that the recovery of SDZ fromspiked soil samples decreases with time from 74% to 18% for samples extracted 5 min or
7 days after spiking (Hamscher et al., 2005). The contact times of the antibiotics and the soil
matrix are typically far longer in the field, provided that very fast degradation can be
excluded.
Mineralization of 14C-labelled SDZ to 14CO2 in bovine manure, soil or soil manure slurries isless than 2% after 102 days (Kreuzig and Höltge, 2005), which we also found in separate
investigations with the same soil without manure (data not shown). However, Kreuzig and Höltge
(2005) found that the dissipation of SDZ in the extracts was much faster (after one week only 40,
20 or 5% of the initially applied 14C was detectable in manure, soil or soil manure slurries,
respectively). They attributed this to the fixation of SDZ or its transformation products as nonextractable residues. They also detected up to four unidentified transformation products by radio
thin layer chromatography in the remaining extractable fraction. This study was in contrast toanother investigation, where no substances other than SDZ were found in comparable extracts(Kreuzig et al., 2003).
Looking into the pharmacokinetics, one of these metabolites might be acetyl-SDZ. Withintreated pigs, SDZ is metabolized to the N4-acetyl-sulfadiazine and both substances are mainly
eliminated by renal excretion (Kroker, 1983; Grote et al., 2004) and thus found in manure.
However, de-alcylation leads to an increasing concentration of SDZ in stored manure (Berger
et al., 1986; Grote et al., 2004). Although those studies focused on the metabolism in manure, theresults of Kreuzig and Höltge (2005) and our separate experiments (unpublished data) indicate

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

109

that transformation reactions might also occur in soils. Additional to acetyl-SDZ, Pfeifer et al.
(2005) detected hydroxy-SDZ in pig manure. In contrast to acetyl-SDZ, hydroxy-SDZ can still be
active against different bacteria strains. It is therefore essential to investigate the fate of both, theparent and possible transformation products.
To prevent further environmental contamination and possible adverse effects of the antimicrobial substances on soil microbial populations, an understanding of the environmental fateof these compounds is necessary (Jørgensen and Halling-Sørensen, 2000). Apart from the routeof entry, the fate of pharmaceuticals in the environment is comparable to other organic
chemicals, such as pesticides. The literature on sorption and transport of organic chemicals insoils is for instance compiled in the review articles by Pignatello and Xing (1996) and Flury(1996). To assess the mobility of pollutants in the environment, knowledge about their
persistence and sorption behavior is crucial. Until now the sorption/desorption processes of SDZ
in soils are not thoroughly investigated. Sorption studies with sulfadiazine and othersulfonamides and different soils showed a Freundlich-type behavior with typical equilibriumtimes of 16 h (Thiele-Bruhn and Aust, 2003). Formation of non-extractable residues of 14Clabelled SDZ was observed in a clayey silt (Kreuzig et al., 2003). Whereas about 50% of SDZ
was not extractable after three days of incubation in this study, this fraction increased to about
90% after 28 days. Therefore, concentration- and time-dependent and possibly also irreversible
sorption can be expected in soils.
Process-oriented studies are scarce in literature concerning the transport of SDZ in soils.
The mobility of sulfonamides in soils is assumed to be high, based on their physicochemical
properties (Tolls, 2001). However, incomplete breakthrough of SDZ was observed in severaltransport studies. SDZ was rarely found in the leachate of column and plot studies, and mostof the applied SDZ was retained in the upper part of the soil (Kreuzig and Höltge, 2005). Fast
sorption of SDZ into non-extractable pools was reported in leaching experiments with
undisturbed soil columns, after application of contaminated manure (Kreuzig and Höltge,2005). Sulfachloropyridazine, which is a sulfonamide similar to SDZ, was found to be quite
mobile, but also readily degradable (Boxall et al., 2002; Kay et al., 2004, 2005a,b). The
component was classified as being mobile in different soils from two-days batch sorption
experiments, which was additionally verified in column studies (Boxall et al., 2002).
However, the leached mass fraction was lower than expected, and the non-recovered mass inthe experiments was attributed to degradation (Boxall et al., 2002; Kay et al., 2005b). Similar
observations were also reported for sulfamethoxazole: leaching was shown to depend on (i)the applied mass, (ii) irrigation intensity and (iii) soil type (Drillia et al., 2005), which hints
towards a soil dependent, non-linear and time-dependent sorption of the investigatedsulfonamide.
To our knowledge transport and sorption mechanisms of sulfadiazine have not yet beensystematically analyzed in column experiments. The objective of this study was to investigate thetransport behavior of sulfadiazine in disturbed soil columns at a constant flow rate near saturation.
We especially focus on the effect of concentration on the fate of SDZ, by changing the input
concentration and/or pulse duration. Although the antibiotics enter the soil environment typicallyas ingredients of manure, the experiments were performed without manure to circumvent any
changes in soil properties (e.g. pH, ionic strength, dissolved and particulate organic matter) andtheir effects on solute transport. 14C-labelled SDZ was used to ensure complete mass balances. To
identify relevant sorption processes, measured breakthrough curves (BTCs) and soil concentration
profiles of SDZ were fitted with a convective–dispersive transport model considering different
sorption concepts.

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2. Theory of solute transport
The transport of non-degradable dissolved substances in homogeneous soils with a constantwater content and steady state flow conditions is typically described by the convection–
dispersion equation (CDE) (e.g. Hillel, 1998):
ACt
A2 C
AC
¼ Dh 2 −jw
Az
Az
At

;

ð1Þ

where t is time [T], z is depth [L], D is the hydrodynamic dispersion coefficient [L2T− 1], θ is thevolumetric water content [L3L− 3], jw is the water flow density [L T− 1], C is the soluteconcentration in the liquid phase [M L− 3] and Ct is the total mass of solute per unit volume of soil
[M L− 3]. For non-volatile compounds Ct is given as the sum of concentrations in the dissolved
and sorbed phase:
Ct ¼ hC þ qS;

ð2Þ

where ρ is the soil bulk density [M L− 3] and S is the sorbed solute concentration [M M− 1].
2.1. Sorption models
Various sorption concepts are available to describe the interaction of dissolved substanceswith the soil material. These sorption concepts differ with respect to the involved sorption
isotherm (linear or non-linear), the assumptions made concerning the time-dependency(instantaneous or rate-limited) and reversibility of the sorption process (reversible orirreversible). Up to three sorption regions were considered in our study. Multiple sorption
regions are considered in sorption models to represent the heterogeneity of the soil material
with respect to its sorption properties as well as differences in the accessability of thepotentially sorptive surfaces. However, these sorption regions are only conceptual and do
not reflect well-defined fractions of the soil material. We compare the isotherm-based
distribution models to the attachment/detachment approach. Whereas the former approachdescribes the equilibrium distribution between phases by an adsorption isotherm, the latter isbased on multiple kinetic processes. It was introduced to describe the transport of small
particles or bacteria through porous media (e.g. Schijven and Hassanizadeh, 2000; Bradford
et al., 2003). The solute–soil–water distribution models considered in this study aresummarized in Fig. 1.
2.2. Isotherm-based models
A comprehensive mathematical derivation of the applied sorption models is given elsewhere indetail (e.g. Streck et al., 1995). Therefore, we give here only their implementation into the solutetransport equation. The combination of Eqs. (1) and (2) results in:
h

AC
AS
A2 C
AC
þq
¼ hD 2 −jw
At
At
Az
Az

:

ð3Þ

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111

Fig. 1. Structures of the applied models. The boxes labelled with C represent the liquid phase with concentration C, theboxes Si, with i = 1,2,3 represent the three sorption sites with the respective concentrations. The arrows indicate thesorption process, where Kd is the distribution coefficient, Kf and m are the Freundlich coefficient and exponent, á2 is thereversible ad- and desorption rate, βi and γi are the one-way attachment and detachment rates, respectively. Simplified
versions of each model were derived by omitting one or two sorption sites: The combinations for reversible and irreversiblemodels are given below the models. The model names are composed of the number of sites, S (1–3), number of rates, R(0–5), sorption concept (lin: linear and Freu: Freundlich sorption isotherms, att: attachment/detachment model) andreversibility of the sorption process (rev: reversible, irrev: irreversible).

2.2.1. One-site equilibrium sorption
For instantaneously and reversibly sorbing substances Eq. (3) can be rewritten as:
RAC
A2 C AC¼ D 2 −v
;
At
Az
Az

ð4Þ

where v = jw / θ is the pore water velocity [L T− 1] and R [−] is the retardation factor:
q AS
;
ð5Þ
h AC
where ∂S / ∂C is the first derivative of a relationship between the concentration in the solid (S) andliquid (C ) phases, expressed by the sorption isotherm. The linear and non-linear (Freundlich)isotherms are given by:
R¼1þ

S ¼ Kd C

;

ð6Þ
3

−1

where Kd is the soil–water distribution coefficient [L M ] and:S ¼ Kf C m;

ð7Þ

1 − m 3m
−1
L Msoil] and m is the dimensionlesswhere Kf is the Freundlich distribution coefficient [Msolute

Freundlich exponent. Note that the linear isotherm is a special case of the Freundlich isotherm for
m = 1. The retardation factor R is given by:q
ð8Þ
R ¼ 1 þ Kf mC m−1 :h
The 1S0R-lin-rev and 1S0R-Freu-rev models (Fig. 1) are given by Eqs. (4) and (8).

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A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

2.2.2. One-site, rate-limited, reversible sorption
If the equilibrium distribution of the solute between solid and liquid phases cannot be
considered instantaneous, a kinetic term may be introduced (Fortin et al., 1997):dS¼ aðKf C m −SÞ
dt

;

ð9Þ

where α is the adsorption/desorption rate coefficient [T− 1]. The combination of Eqs. (3) and (9)(van Genuchten and Wierenga, 1976) yields the 1S1R-lin-rev and 1S1R-Freu-rev models (Fig. 1,
the subscript 2 is dropped in the equation for simplicity in the one-site model).
2.2.3. Two-site, rate-limited, reversible sorption
Two-site sorption to instantaneous (S1) and rate-limited sorption sites (S2) is described by thefollowing set of equations (van Genuchten and Wagenet, 1989; Simunek et al., 1998):
S ¼ S1 þ S2

;

ð10Þ

S1 ¼ f K f C m

;

ð11Þ

dS2
¼ a2 ðð1−f ÞKf C m −S2 Þ ;
dt

ð12Þ

where f is the fraction of equilibrium sites (S1), and α2 is the sorption rate coefficient [T− 1].
Together with Eq. (3) it gives the 2S1R-lin-rev and 2S1R-Freu-rev models (Fig. 1).
2.2.4. Irreversible sorption
Irreversible sorption is represented as a first-order kinetic sink of solute in the water phase.
This process is equivalent to the description of the first-order degradation from the water phase(Prata et al., 2003) and is given by Eq. (13), assuming that sorption sites S3 exhibit irreversible
sorption:
AS3 h¼ b3 C
q
At

;

ð13Þ

where β3 is the irreversible adsorption rate coefficient [T− 1]. In the three-sites two-rates
irreversible sorption models (3S2R-lin-irrev and 3S2R-Freu-irrev) total sorbed concentration S isthen given by:
S ¼ S1 þ S2 þ S 3

;

ð14Þ

where sorption characteristics for S1 and S2 are described by Eqs. (11) and (12), respectively. In
the 2S2R-lin-irrev and 2S2R-Freu-irrev models the instantaneous sorption sites S1 are omitted( f = 0), whereas the rate-limited reversible sorption sites S2 are omitted ( f = 1) in the 2S1R-linirrev and 2S1R-Freu-irrev models.

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

113

2.3. Attachment/detachment models
In the attachment/detachment concept all processes are first-order and rate-limited. Reversible
attachment/detachment processes are given by:ASi h¼ bi C−gi SiqAt; i ¼ 1; 2

;

ð15Þ

where βi are the attachment and γi the detachment rate coefficients [T− 1] for the corresponding
attachment/detachment sites Si. If detachment is omitted, the second term on the right hand side ofEq. (15) goes to zero. Thus, Eq. (15) is equivalent to Eq. (13), i.e. it describes irreversible
sorption. Equally to the isotherm-based models the total sorbed concentration is given by Eq.
(14). The attachment/detachment model with two reversible and one irreversible site (3S5R-attirrev) is given by the combination of Eqs. (3, 13–15) (Schijven and Šimu˙nek, 2002). Simpler
attachment/detachment models with less sites or rates are derived by setting selected rate
parameters to zero: β3 = 0 in the 2S4R-att-rev model, γ2 = β2 = 0 in the 2S3R-att-irrev model andβ3 = γ2 = β2 = 0 in the 1S2R-att-rev model.
2.3.1. Comparison of isotherm-based and attachment/detachment concept
In the attachment/detachment concept the ratio of the first-order attachment and detachment
rate coefficients describes the tendency of the solute to distribute in either the liquid or the solid
phase. This eventually results in linear equilibrium distribution isotherms, such as the isothermbased models with linear sorption. However, the concept of the isotherm-based and the attachment/
detachment model differs in whether the interaction occurs to the bulk soil or to only one fraction( f, (1 − f )) of the bulk soil. Whereas the sorption parameters of the isotherm-based modes are
independent of the experimental conditions, the attachment/detachment model parameters dependon θ and ρ and are therefore not readily comparable between varying soil to solution ratios.
Despite the difference in mathematical formulation, the attachment/detachment model can beparameterized in such a way, that it is equivalent to the linear sorption model with a similar numberof rate-limited sorption sites (e.g. 1S1R-lin-rev equals 1S2R-att-rev, and 2S2R-lin-irrev equals
2S3R-att-irrev). If the attachment and detachment rates in one sorption site are much fastercompared to the other processes, it can be described as instantaneous. In this case the models
2S1R-lin-rev and 2S4R-att-rev as well as 3S2R-lin-irrev and 3S5R-att-irrev are equivalent, too.
However, the 3S5R-att-irrev model is more flexible than the 3S2R-lin-irrev model because it
considers all sorption processes to be rate-limited.
3. Materials and methods
All transport experiments were done with the antimicrobial substance sulfadiazine (IUPACname: 4-amino-N-pyrimidin-2-yl-benzenesulfonamide, Fig. 2). Selected physicochemical
properties are listed in Table 1. The transport studies were conducted in repacked soil columns
near water saturation. Three experiments with different input scenarios (A, B, C) were performed
in order to investigate the effect of concentration and pulse duration on the fate of SDZ (Table 2).
Whereas in experiments A and B solute was applied for a long pulse duration, solute was appliedwith a short pulse in experiment C. High solute concentrations were applied in experiments A and
C. Only about one tenth of that concentration was applied in experiment B. Thus, the total applied
solute masses were approximately equal for experiments B and C.

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A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

Fig. 2. Chemical structure of sulfadiazine (SDZ). The 14C-labelling is in the phenyl-ring with a specific radioactivity of
3.46 MBq mg− 1.

3.1. Soil columns
The soil material was collected from the upper 30 cm of an Eutric Cambisol which was used as
grassland in the past. The soil is classified as a silty loam and characterized as described in Table 3.
Field moist soil was sieved (2 mm) and stored at 4 °C in the dark until usage.
The columns were made of stainless steel (inner diameter and height were 8.5 cm and 10 cm,
respectively). They were mounted on a porous ceramic plate (high flow, air-entry point N 1 bar).
The outflow was connected to a fraction collector. An irrigation device with 12 glass needles wasplaced on top of the column. An HPLC-pump (high performance liquid chromatography) supplieda constant irrigation from a reservoir. No pressure was applied at the bottom of the soil column.
Wet soil (gravimetric water content of 40%) was packed in the columns in small increments,
each compacted with a metal stick, up to a total height of 9 cm. Due to the sticky properties of thefine textured soil, the wet soil could not be compacted to a typical field soil bulk density. A
density of about 1 g cm− 3 (Table 4) assured the maintenance of constant flow rates. A 0.5 cm
thick layer of coarse quartz sand was put on top of the packed soil in order to provide a more
uniform distribution of water and to prevent splashing of the soil material. This sand was burnt inan oven at 450 °C for 24 h to remove any organic contamination. The soil columns were saturated
from the bottom with a 0.01 M CaCl2 solution for three days.
3.2. Transport experiments
The soil columns were irrigated at a constant rate of approximately 0.26 cm h− 1 for four days
to establish steady state flow conditions. The pistons of the pump were flushed with water once a
day to prevent salt precipitation and drying. Although the flow rate was regulated by the HPLCTable 1
Selected physicochemical properties of sulfadiazine
Molecular formulaCAS†
Molecular mass
pKa1 and pK ‡a2
Melting point
Vapor pressure
Henry constant
Solubility in water
Octanol/water distribution coefficientSpecific radioactivity§[g mol−1][°C][Pa][Pa m3 mol− 1][mg L− 1][MBq mg− 1]

C10H10N4O2S
68-35-9250.28
1.57 and 6.50
250
5.745 × 10− 6
1.60 × 10− 5
13 to 77
0.76
3.46

Data were taken from the supplier of the non-labelled SDZ: Sigma Aldrich, Taufkirchen, Germany. †Registration numberof the Chemical Abstract Service; ‡acidity constants; §for the labelled compound supplied by the Institute of Isotopes Co.,
Ltd., Budapest, Hungary.

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

115

Table 2
Experimental conditions of the column experiments
Soil column

C†0(mg L− 1)

‡
Vin
(L)

Δt§in
(h)

m¶in
(mg)

M#app
(g m− 2)j††w
(cm h− 1)

A
B
C

5.70
0.57
5.70

1.047
1.032
0.094

67.8
68.0
7.0

5.97
0.526
0.539

1.052
0.093
0.095

0.266
0.260
0.262

†

SDZ concentration in the application solution, ‡volume of application solution, §pulse duration, ¶applied mass, #appliedmass per soil surface area, ††irrigation rate.

pump, it was additionally controlled by weighing the solution loss from the reservoir per unit time
as well as the leached volume in the single fractions.
A defined volume of the application solution of chloride or SDZ was irrigated on top of thecolumn and subsequently leached with the 0.01 M CaCl2 solution at the same flow rate. The
applied volume was determined by the mass difference in the reservoir.
Measured concentrations in single fractions of the leachate were corrected for evaporation
losses (approximately 4.5 × 10− 6 L h− 1) during the open sample storage in the fraction collector.
For a better comparison between the experiments, concentrations in the outflow were normalized
to their corresponding input concentrations (C0).
3.2.1. Chloride
A breakthrough curve of chloride as a non-reactive tracer was determined for each packed soilcolumn to characterize the flow behavior of water itself. The chloride was applied as a 2-h pulse
Table 3
Some selected physical and chemical properties of the soil material
Parameter
Texture†:Clay (b0.002 mm)
Fine silt (0.002–0.006 mm)
Medium silt (0.006–0.020 mm)
Coarse silt (0.020–0.063 mm)
Fine sand (0.063–0.200 mm)
Medium sand (0.200–0.630 mm)
Coarse sand (0.630–2.000 mm)
Clay minerals§:
Smectite
IlliteChlorite
Specific surface area
Chemical analysis†:
pH
P¶tot
CEC#
C††
org
CaCO‡‡
3

Unit

Value

[% mass]‡[% mass][% mass][% mass][% mass][% mass][% mass]

23
7
14
22
19
11
4

[%]
[%]
[%]
[m2 g−1]

25
25
50
4.96

[mg kg− 1][meq 100 g− 1][% mass][% mass]

6.1
1292
17.4
3.3
b3

Soil was air dried and sieved to 2 mm prior to the analysis. †Analysis were done by standard procedures at the laboratory of
the LUFA (Landwirtschaftliche Untersuchungs-und Forschungsanstalt) in Speyer, Germany. ‡The mass fractions are basedon the total mass of soil. §Clay minerals were analyzed by X-ray diffraction at the Institute of Soil Science and Soil
Ecology at the University of Bonn, Germany. ¶Total content of phosphorous, #cation exchange capacity, ††content oforganic carbon, ‡content of carbonate.

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A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

Table 4
Properties of the soil columns and the experimental conditions
Soil column

jw(cm h− 1)ρ(g cm− 3)v(cm h− 1)θ(cm3cm− 3)

D(cm2 h− 1)

λ
(cm)

EF†

A
B
C

0.266
0.260
0.262

0.89
0.99
0.84

0.437
0.492
0.543

0.609
0.528
0.483

0.580
0.191
0.258

1.329
0.388
0.475

0.990
0.997
0.983

The irrigation rate, jw, and the soil bulk density, ρ, were determined experimentally. The pore water velocity, v, and thedispersion coefficient, D, were fitted to the BTCs of chloride. The volumetric water content, θ, and the dispersivity, λ,were calculated.
†
Modelling efficiency according to Loague and Green (1991): EF = (Σ(Oi − Omean)2 − Σ(Oi − Pi)2) / (Oi − Omean)2, where Oi
and Pi are the observed and predicted values, respectively and Omean is the arithmetic mean of the observed values.

with an input concentration C0(Cl−) of 1.0 g L− 1 as CaCl2. The leachate was collected in hourly
fractions of approximately 15 mL for analysis until a constant background level was reached.
The chloride concentration in the leachate was determined by measuring the electricalconductivity. The electrical conductivity linearly correlates with the concentration of CaCl2
within the concentration range of the samples. Solutions with known concentrations of CaCl2
were used to determine the calibration curve.
3.2.2. Sulfadiazine
The application solution of SDZ was prepared in 0.01 M CaCl2 solution by addition of theappropriate amount of stock solution (500 mg SDZ L− 1 dissolved in acetonitrile). For experiment
A 14C-labelled SDZ and non-labelled SDZ were mixed (1:4, m:m) to reduce the consumption of
the labelled compound. In experiments B and C the 14C-labelled SDZ was not diluted with nonlabelled SDZ to ensure adequate sample concentrations for analysis. The SDZ input solution wasapplied using the same steady irrigation rate as for chloride experiments. After application SDZ
was eluted for 500 h, which corresponds to approximately 20 pore volumes. Detailed information
about the experimental conditions is listed in Table 2.
The concentration of SDZ in the outflow was determined by measuring its 14C-radioactivity.
An aliquot of the sample was mixed with 10 mL of an appropriate scintillation cocktail andmeasured by liquid scintillation counting (LSC). The detection limit of the LSC-method is0.25 Bq per sample. The measuring volume V of the sample was chosen according to its expected
specific radioactivity, varying from 0.1 to 5 mL for high and low specific radioactivities,
respectively. Each sample was measured in triplicate. All measured values were corrected for the
background radiation measured in a blank sample. The corresponding specific radioactivity Aspec[T− 1 L− 3] was calculated from the measured radioactivity A [T− 1].
The equivalent SDZ concentration of the sample was determined after division by the specificradioactivity of the applied SDZ, Aspec (SDZ) [T− 1 M− 1] (0.865 and 3.46 MBq mg− 1 forexperiment A and experiments B and C, respectively), assuming that 14C-radioactivity is linearly
related to SDZ. If any transformation products were present the resulting total SDZ concentrations
are the sum of both, parent and transformation products, given in mass equivalents of SDZ(molecular mass = 250.28 g mol− 1).
At the end of each leaching experiment, the soil was sliced at 0.5 or 1 cm depth intervals todetermine the concentration distribution of SDZ in the column. For all samples the water content
was determined gravimetrically. Prior to analysis the dry soil samples were ground andhomogeneously mixed. The SDZ concentration in soil was determined by measuring the 14C-

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

117

radioactivity after total combustion of the soil samples with the help of an oxidizer. Threereplicates of 0.500 g of each soil sample were combusted at 900 °C. The evolving gas was washedinto a scintillation cocktail. Here, 14CO2 was trapped and subsequently measured by LSC. The
14
C-analysis in both solid and liquid phases was insensitive to matrix effects and did not require
any extraction steps.
The performance of the method was checked in each measuring series. Blanks were run before
and after the samples to check for background contamination and cross contamination during themeasurement. The recovery of the method is defined as the ratio of measured radioactivities in ablank sample spiked with a known amount of 14C prior to combustion to the radioactivity in ablank sample where 14C was spiked to the scintillation cocktail after combustion. Measurement
series with a recovery b 92% were repeated.
The total concentration of SDZ in the soil [M(SDZ) M− 1(soil)] is calculated from the mass ofthe soil, the specific radioactivity of the applied SDZ Aspec (SDZ), and the measured radioactivity
corrected for the corresponding recovery. As discussed for the liquid phase concentrations above,
SDZ concentrations in the solid phase refer to the sum of both, the parent compound and its
transformation products, given in mass equivalents of SDZ. Note that the soil concentration is thesum of the sorbed and dissolved solute per unit mass of soil.
3.3. Parameter estimation
Water flow and solute transport in the soil columns were treated as one-dimensional problems
in mathematical simulations. The water content was assumed to be constant in space and timethroughout the experiment. Any variations in water content were assumed to be negligible,
because the columns were homogeneously packed, water-saturated at the bottom and irrigatedwith a constant rate at the top. The columns were assumed to be initially solute free (Cl− or SDZ).
A flux concentration boundary was assumed at the top and a zero concentration gradient at thebottom of the column.
3.3.1. Conservative tracer chloride
The transport parameters v and D were determined by fitting the analytical solution of the
CDE (Eq. (4) with R = 1) with appropriate initial and boundary conditions to the observed BTC
using the CXTFIT code (Toride et al., 1999). To account for variations in mass balance, the input
concentration was also fitted. From D, v and jw the volumetric water content θ = jw / v and thedispersivity λ = D / v were calculated and used to fix the water flow for the transport simulations
with the reactive tracer SDZ.
3.3.2. Reactive tracer SDZ
Since SDZ exhibits non-linear sorption and no analytical solution exists for such transport
behavior, we used the numerical code HYDRUS-1D (Simunek et al., 1998) to describe thetransport experiments. HYDRUS-1D is a finite element code that provides numerical solutions forvarious transport models described above. The Galerkin finite element method with a Crank–
Nicholson time weighting scheme was used to solve the governing solute transport equations.
HYDRUS-1D includes an inverse parameter optimization method based on the Levenberg–
Marquardt algorithm. For the numerical calculations the soil profile was discretized into 101
evenly distributed nodes. The maximum time step was chosen small enough to assure a massbalance error smaller than 1%. The model was run with gravity driven flow, where the hydraulicconductivity at the prevailing water content was set equal to the irrigation rate jw.

118

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

Fig. 3. Breakthrough curves of SDZ in the three columns plotted on a linear (a) and a logarithmic (b) scale.

HYDRUS-1D was used either in a predictive manner with fixed transport parameters or in an
inverse mode to fit one or more parameters of a sorption model to the experimental data. In thelatter case the experimental data of the BTC were in selected cases internally log10-transformed toincrease the weighting on the BTC tailing. The soil concentration profile data were nottransformed. Unit weights were assigned to all residuals. Either BTC, profile or both data sets
were used in the fitting procedure. To evaluate the goodness of fit we calculated the modelling
efficiency for the non-transformed (EF) and log10-transformed BTC data (EFlog) according to
Loague and Green (1991). A modelling efficiency equal to 1 indicates perfect agreement of themodel and the data. If the modelling efficiency is negative, the arithmetic mean of the data is abetter description for the data set than the model. The sum of squares was also calculated for the
non-transformed (SSQ) and log10-transformed data (SSQlog). Due to different orders ofmagnitude of the concentration values in the peak and tailing of the BTC, a mismatch in the peakconcentrations affects EF or SSQ more than deviations in the tailing. Deviations in the low
concentration range (at the beginning and the end of the BTC) result in a larger SSQlog and asmaller EFlog. Because transformation reactions can not be ruled out during our experiments, we
focused on an effective transport description for the sum of SDZ and possible transformation

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

119

Table 5Mass recovery of 14C-radioactivity after the column experiments
Soil column

In leachate(%†)

In soil column(%)

Total recovery
(%)

A
B
C

82.7
60.7
17.8

14.5
38.3
81.8

97.2
99.0
99.6

†

Mass fractions are given in percent of the applied mass, min (Table 2).

products. However, as the identity and fate of the possible transformation products are still
unknown, the sum of SDZ and potentially active or re-transferable transformation products is ofenvironmental concern. This lumped characterization can be used for a first risk assessment. Thiswas previously done by Prata et al. (2003) and Casey et al. (2004), who also used 14C-labelled
compounds for their experiments. Despite the determination of transformation products in theleachate, they applied their models to the measured 14C-data and the modelling resulted in an
effective description of the transport behavior of the parent substance and its transformation
products.
4. Results
4.1. Transport and breakthrough curves of chloride
The transport parameters D and v that were fitted to the chloride BTCs are listed in Table 4.
Although the obtained parameters were not identical for all three columns, the physicalequilibrium CDE was able to describe all BTCs. It was, thus, concluded that no non-equilibrium
processes affected the chloride transport and that there was no stagnant water. Relatively large
differences in water contents between the three columns were likely due to the packing procedurethat was difficult to standardize. To account for these variations in the flow field between
columns, the transport parameters were individually determined for each column.

Fig. 4. Soil concentration profiles of resident 14C concentrations in the three columns.

120

Model

Fit†

linear sorption models
1S0R-lin-rev
Lin
1S1R-lin-rev

Lin

2S1R-lin-rev

Lin

2S1R-lin-rev

Log

2S1R-lin-irrev

Lin

2S2R-lin-irrev

Lin

3S2R-lin-irrev

Log

Freundlich sorption models
1S0R-Freu-rev
Log
1S1R-Freu-rev

Log

2S1R-Freu-rev

LinKf(kg − 1L3mmg1−m)m

α2(h− 1)

fβ3(h− 1)

EF‡EF§log

SSQ¶

SSQ††
log

EM‡‡
(%)

1.13 × 10+ 0(8.77 × 10+ 0)
1.25 × 10+ 0(2.72 × 10− 2)
4.39 × 10+ 0(2.67 × 10− 1)
1.54 × 10+ 0(2.20 × 10− 2)
9.10 × 10− 1(1.02 × 10− 2)
9.46 × 10− 1(9.85 × 10− 3)
1.61 × 10+ 0(4.65 × 10− 2)

1#

0#

1#

0#

0.864

− 1.675

42.1

731

99

1#

8.67 × 10− 2(6.23 × 10− 3)
3.19 × 10− 3(2.72 × 10− 4)
6.55 × 10− 3(2.80 × 10− 4)
0#

0#

0#

0.956

0.407

13.7

162

99

1.97 × 10− 1(1.16 × 10− 2)
5.83 × 10− 1(8.13 × 10− 3)
1#

0#

0.996

0.216

1.30

214

89

0#

0.931

0.997

21.2

0.88

98

0.991

− 3.576

2.80

1251

73

3.76 × 10− 1(4.20 × 10− 2)
7.08 × 10− 3(1.44 × 10− 3)

0#

0.994

− 1.715

1.89

742

77

5.95 × 10− 1(1.84 × 10− 2)

1.40 × 10− 2(3.33 × 10− 4)
1.17 × 10− 2(3.56 × 10− 4)
4.67 × 10− 3(3.56 × 10− 4)

0.987

0.997

4.12

0.71

88

0#

1#

0#

0.263

− 0.547

228

423

99

8.12 × 10− 2(1.81 × 10− 3)
3.32 × 10− 3(2.78 × 10− 4)

0#

0#

0.980

0.987

6.22

3.50

97

2.03 × 10− 1(1.16 × 10− 2)

0#

0.996

0.617

1.22

105

88

7.61 × 10− 1(1.65 × 10− 1)
2.48 × 10+ 0(4.86 × 10− 2)
4.55 × 10+ 0(2.68 × 10− 1)

1#
1#
1#
1#
1#
5.04 × 10− 1(1.65 × 10− 1)
5.27 × 10− 1(4.96 × 10− 3)
9.51 × 10− 1(1.55 × 10− 2)

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

Table 6
Fitting parameters of the different isotherm-based (upper part) and attachment/detachment (lower part) models for column ALog

2S1R-Freu-irrev

Lin

2S2R-Freu-irrev

Log

3S2R-Freu-irrev

Log

Model

Fit†

2.40 × 10+ 0(5.21 × 10− 3)
1.05 × 10+ 0(3.55 × 10− 2)2.31 × 10+ 0(3.61 × 10− 2)2.33 × 10+ 0(3.21 × 10− 2)

3.34 × 10− 1(9.94 × 10− 4)
9.03 × 10− 1(2.10 × 10− 2)
4.89 × 10− 1(1.14 × 10− 2)
4.88 × 10− 1(1.63 × 10− 2)

1.09 × 10− 1(1.47 × 10− 4)
0#1.72 × 10− 3(5.71 × 10− 6)
1#

7.78 × 10− 2(2.55 × 10− 3)
7.35 × 10− 2(4.61 × 10− 5)0#β1(h− 1)

γ1(h− 1)
8.74 × 10− 2(6.47 × 10− 3)
3.94 × 10− 1(4.98 × 10− 2)
6.76 × 10− 1(1.15 × 10− 1)
3.94 × 10+ 2(2.02 × 10+ 2)
2.53 × 10+ 0(1.80 × 10+ 0)

Attachment/detachment models
1S2R-att-rev
Lin1.59 × 10− 1(1.10 × 10− 2)
2S3R-att-irrev
Lin
5.44 × 10− 1(6.65 × 10− 2)
2S4R-att-rev
Lin8.82 × 10− 1(1.45 × 10− 1)
2S4R-att-rev
Log 5.13 × 10+ 2(5.29 × 10+ 2)
3S5R-att-irrev
Lin
3.05 × 10+ 0(2.14 × 10+ 0)

0#

0.837

0.554

50.6

122

95

0.992

− 0.232

2.55

337

73

0.975

0.995

7.43

1.28

80

3.63 × 10− 3(1.17 × 10− 2)

1.41 × 10− 2(3.13 × 10− 4)
8.96 × 10− 3(9.87 × 10− 4)
1.02 × 10− 2(8.60 × 10− 4)

0.966

0.995

10.64

1.35

78

β2
(h− 1)

γ2(h− 1)

β3(h− 1)

EF‡EF§log

SSQ¶

SSQ††
log

EM‡‡
(%)

0#

0#

0#

0.956

0.403

13.7

163

99

0#

0#

0.994

− 1.760

1.90

755

77

1.44 × 10− 2(3.47 × 10− 4)
6.22 × 10− 3(2.80 × 10− 4)
1.17 × 10− 2(6.18 × 10− 4)

2.44 × 10− 3 (2.34 × 10− 4)

1.18 × 10− 2(3.51 × 10− 4)
0#

0.997

0.842

1.00

43.2

88

6.95 × 10− 3 (2.86 × 10− 4)

0#

0.930

0.997

21.6

0.84

98

1.41 × 10− 2 (1.46 × 10− 3)

7.68 × 10− 3(3.82 × 10− 4)

0.998

0.867

0.61

36.4

83

The eluted mass fraction in the experiment was 82.7%.
Standard errors are given in parenthesis. †Denotes whether the models was fitted to the non-transformed (lin) or log10-transformed concentration data (log); ‡modelling efficiency
according to Loague and Green (1991) calculated for non-transformed data: EF = (∑ (Oi − Omean)2 − ∑(OI − Pi)2) / ∑(Oi − Omean)2, where Oi and Pi are the observed and predictedvalues, respectively and Omean is the arithmetic mean of the observed values; §modelling efficiency calculated on the basis of the log10-transformed data; ¶sum of squares calculatedon the basis of the non-transformed data; ††sum of squares calculated on the basis of the log10-transformed data; ‡‡eluted mass fraction; #fixed parameters.

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

2S1R-Freu-rev

121

122

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

Fig. 5. Normal (a) and semi-log (b) plots of the BTC for column A and different fits of the one-site models. The models
with Freundlich sorption were fitted to the log10-transformed data.

4.2. Transport of SDZ — experimental results
The peak maxima of different treatments were delayed relative to chloride by a factor of 2 to 5
(Fig. 3), which is an arbitrary measure for residence time. The decreasing limb of each BTC is
characterized by an extended tailing that exhibits a rather constant slope after about 60 cm of
cumulative outflow in the semi-log plot (Fig. 3b). Within the experimental duration of
approximately three weeks, a complete breakthrough of SDZ was not achieved due to the
pronounced tailing. The BTCs differed in the maximum concentrations as well as the eluted massfractions. Despite the comparable amount of cumulative irrigation in all experiments, the eluted
mass fraction was considerably higher for the experiments with the long pulse application A andB (83 and 61%, respectively) as compared with the short pulse application (experiment C), where
only 18% was leached (Table 5).
Concentration profiles of SDZ for the columns with the long pulse application (A, B) showed
the highest concentrations at the top of the column, with concentrations steadily decreasing
towards the bottom (Fig. 4). In the column with the short pulse application (C) soluteconcentrations were relatively uniformly distributed. Concentrations were slightly higher

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

123

Fig. 6. Semi-log plot of the BTC of column A and different model fits with a) two-site reversible and b) two- or three-site
irreversible sorption models. For each model in Fig. 6a both fits to the non-transformed (solid lines) and to the log10transformed (dashed or dotted lines) are given. In Fig. 6b the 2S1R-lin-irrev, 2S2R-lin-irrev, 2S1R-Freu-irrev, 2S3R-attirrev models were fitted to the non-transformed data, the other four models to the log10-transformed data.

between 2 and 6 cm depth of the column. The difference between the applied and the recovered
mass was less than 3% of the applied mass for all experiments (Table 5).
4.3. Transport of SDZ — modelling results
The breakthrough curves of SDZ were fitted using HYDRUS-1D assuming different solute–soil–water interaction concepts. The various transport models and their corresponding fits are
discussed below in detail for column A. The model complexity was increased from one-siteequilibrium models to more complex multiple-site models with reversible or irreversible sorption.
The fitted parameters and further details are given in Table 6.
4.3.1. One-site sorption models
Fig. 5 shows the fit of the various one-site models in normal and semi-log representation. In
general all one-site sorption models overestimated the leaching of SDZ. They could not

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A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

Fig. 7. Semi-log plot of the BTC of column B (a) and C (b) and different fits of two- or three-site irreversible models. For
column B (a) the 3S2R-Freu-irrev and the 3S5R-att-irrev models were fitted to the log10-transformed data, while the othertwo models to the non-transformed data. For column C (b) all models were fitted to the log10-transformed data.

account for the mass remaining in the soil column at the end of the experiment (Table 6).
Notice that if sorption was assumed to be rate-limited and reversible, the predicted curves withthe linear sorption (1S1R-lin-rev) and the kinetic attachment/detachment model (1S2R-att-rev)
are almost identical since the models are mathematically equivalent. Only the curve fitted with
the Freundlich rate-limited reversible sorption (1S1R-Freu-rev) described approximately themain features of the observed BTC. Although the maximum peak concentration and thedecreasing limp were only slightly overestimated the difference in the mass balance was still
relatively large (14%, Table 6). Both models involving Freundlich sorption isotherms werefitted to the log10-transformed data, which gives more weight to the lower concentrations in thetailing. More weight is placed on the peak concentrations in the non-transformed data. Eachmodel was fitted to the non-transformed and the log10-transformed concentration data. To
select one fit for presentation, we focused on the ability of the model to match the tailing. Thisrather subjective choice is not always supported by the modelling efficiency or the sum ofsquares. Because the models involving kinetic sorption matched the observations better, butModelFit†

Kf(kg− 1L3m mg1−m)m

α2(h− 1)

fβ3(h− 1)

EF‡EF§log

SSQ¶

SSQ††
log

EM‡‡
(%)

Linear sorption model
3S2R-lin-irrev

Lin

6.49 × 10− 1(2.72 × 10− 2)

1#

7.53 × 10− 2(1.13 × 10− 2)2.46 × 10− 1(5.18 × 10− 2)

3.29 × 10− 2(8.52 × 10− 4)

0.988− 9.89

0.016

828

59

4.61 × 10− 1(1.02 × 10− 2)
6.08 × 10− 1(2.14 × 10− 1)

4.98 × 10− 1(5.47 × 10− 2)
4.54 × 10− 1(1.40 × 10− 1)

7.80 × 10− 2(2.42 × 10− 3)
2.76 × 10− 2(7.92 × 10− 3)

0#

0.993

− 0.687

0.009

128

56

2.10 × 10− 3(1.62 × 10− 2)2.80 × 10− 2(4.19 × 10− 4)
2.53 × 10− 2(1.18 × 10− 4)

0.931

0.264

0.096

55.9

59

β1
(h− 1)

γ1(h− 1)

β2(h− 1)

γ2(h− 1)

β3(h− 1)

EF‡EF§log

SSQ¶

SSQ††
log

EM‡‡
(%)

1.37 × 10− 1(5.75 × 10− 2)

1.10 × 10− 1(5.16 × 10− 2)

1.29 × 10− 2(3.16 × 10− 3)

4.66 × 10− 3(2.27 × 10− 3)

2.49 × 10− 2(6.97 × 10− 3)

0.981

0.686

0.026

23.8

59

Freundlich sorption models
2S2R-Freu-irrev
Lin
3S2R-Freu-irrev

Model

Log
Fit†

Attachment/detachment model
3S5R-att-irrev
Log

The eluted mass fraction in the experiment was 60.7%.
Standard errors are given in parenthesis. †Denotes whether the model was fitted to the non-transformed (lin) or log10-transformed concentration data (log); ‡modelling efficiency
according to Loague and Green (1991) calculated for non-transformed data: EF = (Σ(Oi − Omean)2 − Σ(Oi − Pi)2) / Σ(Oi − Omean)2, where Oi and Pi are observed and predicted values,
respectively and Omean is the arithmetic mean of the observed values; §modelling efficiency calculated on the basis of the log10-transformed data; ¶sum of squares calculated on thebasis of the non-transformed data; ††Sum of squares calculated on the basis of the log10-transformed data; ‡‡eluted mass fraction; #fixed parameters.

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

Table 7
Fitting parameters of the different isotherm-based (upper part) and attachment/detachment (lower part) models for column B

125

126

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

Fig. 8. Measured and modelled soil profiles of resident 14C concentrations in column A. The reversible models are given in
Fig. 8a, the irreversible models in Fig. 8b.

still not sufficiently, model complexity should be enhanced to reflect all observed features of
the BTC. Therefore, an additional site with kinetic reversible sorption was included in thefollowing models.
4.3.2. Two-site reversible sorption models
The curves fitted to both, the log10- and non-transformed data using the two-site reversible
sorption models are plotted in Fig. 6a. Only the semi-log plot is given because the description of
the tailing is especially interesting. The performance of all models was rather similar. The models
fitted to the non-transformed data matched well the peak, but overestimated the tailing, whereas
the models fitted to the log10-transformed data overestimated the peak concentrations, but
described the tailing well. Despite the mismatch in the tailing of the models fitted to the nontransformed data, EF is larger than for the models fitted to the log10-transformed data. Whereas
EFlog is always smaller than EF for the models fitted to the non-transformed data, EFlog is larger oronly slightly smaller than EF for the models fitted to the log10-transformed data (Table 6). Since
the loss in modelling efficiency (EF − EFlog) is smaller for the models fitted to the log10transformed data, these fits were preferred. Similarly as for the one-site models, the linear sorption

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

127

Fig. 9. Measured and modelled soil profiles of resident 14C concentrations in column B (a) and C (b).

model 2S1R-lin-rev and the attachment/detachment model 2S4R-att-rev provided almost
identical fits. This indicates that the attachment/detachment rates on one fraction of sorption
sites are fast compared to the transport velocity and can thus be approximated by instantaneous
sorption. However, the leached mass fraction was still overestimated in all two-site rate-limited
reversible sorption models. At least one process is, thus missing that can account for the solute
mass remaining in the soil column. While sorption is often assumed to be a reversible process,desorption kinetics may be very slow compared to the duration of the experiment and sorption
may then appear to be irreversible. Whether irreversible sorption processes can account for themass remaining in the soil column and describe the observed BTC was tested with the following
models that consider irreversible sorption.
4.3.3. Two- or three-site irreversible sorption models
The curves fitted with models considering two or three sorption sites with one site being
irreversible are presented in Fig. 6b. The optimized parameters are given in Table 6. The peakconcentrations were well described by all irreversible models. However, all two-site models
except the 2S2R-Freu-irrev model failed to predict the extended tailing (Fig. 6b) andunderestimated the leached mass fraction (Table 6). The simulated curves of the 2S2R-lin-irrev

128

Model

Fit†

Kf
(kg− 1 L3m mg1−m)m

α2(h− 1)

fβ3(h− 1)

EF‡EF§log

SSQ¶

SSQ††
log

EM‡‡
(%)

Linear sorption model
3S2R-lin-irrev

Lin

6.15 × 10+ 0(8.16 × 10− 1)

1#9.41 × 10− 3(2.05 × 10− 3)

1.65 × 10− 1(2.32 × 10− 2)

1.06 × 10− 1(7.23 × 10− 3)

0.968

0.526

0.003

24.3

17

8.59 × 10− 1(4.55 × 10− 4)
7.07 × 10+ 0(1.20 × 10+ 0)

2.03 × 10− 1(1.58 × 10− 4)
1.06 × 10+ 0(4.00 × 10− 2)

1.99 × 10− 1(1.19 × 10− 4)
8.22 × 10− 3(1.90 × 10− 3)

0#

0.753

0.760

0.023

12.3

19

1.74 × 10− 1(2.72 × 10− 2)

8.63 × 10− 2(1.54 × 10− 4)
1.06 × 10− 1(7.39 × 10− 3)

0.927

0.544

0.007

23.3

17

β1
(h− 1)

γ1(h− 1)

β2(h− 1)

γ2(h− 1)

β3(h− 1)

EF‡EF§logSSQ¶

SSQ ††
log

EM ‡‡
(%)

5.91 × 10+ 0(3.54 × 10+ 0)

2.81 × 10+ 0(1.95 × 10+ 0)

7.45 × 10− 2(1.55 × 10− 2)

8.51 × 10− 3(1.99 × 10− 3)

1.05 × 10− 1(7.46 × 10− 3)

0.918

0.544

0.007

23.3

18

Freundlich sorption models
2S2R-Freu-irrev
Log
3S2R-Freu-irrev

Model

Log
Fit†

Attachment/detachment model
3S5R-att-irrev
Log

The eluted mass fraction in the experiment was 17.8%.
Standard errors are given in parenthesis. †Denotes whether the model was fitted to the non-transformed (lin) or log10-transformed concentration data (log); ‡modelling efficiency
according to Loague and Green (1991) calculated for non-transformed data: EF = (Σ(Oi − Omean)2 − Σ (Oi − Pi)2) / Σ(Oi − Omean)2, where Oi and Pi are the observed and predictedvalues, respectively and Omean is the arithmetic mean of the observed values; §modelling efficiency calculated on the basis of the log10-transformed data; ¶sum of squares calculatedon the basis of the non-transformed data; ††sum of squares calculated on the basis of the log10-transformed data; ‡‡eluted mass fraction; #fixed parameters.

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

Table 8Fitting parameters of the different isotherm-based (upper part) and attachment/detachment (lower part) models for column C

A. Wehrhan et al. / Journal of Contaminant Hydrology 89 (2007) 107–135

129

and the 2S3R-att-irrev model were identical, as expected. In case of the Freundlich sorption(2S2R-Freu-irrev), the observed and predicted BTCs were in close agreement, apart from a slightunderestimation of concentrations in the beginning of the decreasing limb. The calculated eluted
mass fraction (80%) was close to the observed fraction, too. An additional instantaneous sorption
site (3S2R-Freu-irrev) did not further improve the model performance.
The additional sorption site in the three-site model with linear sorption (3S2R-lin-irrev) and theattachment/detachment model (3S5R-att-irrev) resulted in a very good fit of the tailing and only aslight overestimation of the peak concentrations. Both predicted curves were nearly identical witha leached mass fraction of about 88%. In general, the long tailing characterized by two distinct
slopes of the measured BTC required a model that either considered two sorption sites withkinetic desorption, such as 3S2R-lin-irrev or 3S5R-att-irrev, or one kinetic desorption site
combined with non-linear sorption/desorption, such as 2S2R-Freu-irrev or 3S2R-Freu-irrev. The
large standard errors of the estimated parameters (Table 6) should, however, be recognized as ahint for overparameterization of the used models.
In terms of EF and SSQ, the 3S5R-att-irrev model performed slightly better than models withthree-site isotherm-based irreversible sorption and the 2S2R-Freu-irrev model. Note that incontrast to the other two models, the 3S5R-att-irrev model was fitted to the non-transformed data.
The comparability of EF and SSQ (EFlog and SSQlog) is therefore limited. But from only one
measured BTC it cannot be decided whether (i) sorption is linear or non-linear, nor (ii) if two or
three kinetic sorption sites are required, nor (iii) whether the fast sorption process can beapproximated by instantaneous sorption. Therefore, the ability of the four models, which
performed best for experiment A, was tested to describe the two BTCs measured under different
application protocols.
4.3.4. Model description for different application protocols
Model fits and their parameters for experiment B are given in Fig. 7a and Table 7, respectively.
The 2S2R-Freu-irrev model described the peak of the BTC well, but underestimated the tailingand, thus, the eluted mass fraction. Out of the three-site models only the 3S5R-att-irrev model
matched the observed BTC as well as the eluted mass fraction (52%). The other three-site models
either failed to describe the shape of the peak (3S2R-Freu-irrev) or the tailing (3S2R-lin-irrev).
Since the 3S5R-att-irrev differs from the 3S2R-lin-irrev model, attachment/detachment rates on
the fast kinetic sites was too slow to be approximated by instantaneous sorption.
The simulated BTCs for experiment C with the short application pulse are plotted in Fig. 7b.
The three-site models are nearly identical, and all curves roughly described the observed BTC.
The highest peak concentration and concentrations in the beginning of the tailing (between 20 and
40 cm of cumulative outflow) were underestimated. The 2S2R-Freu-irrev model predicted thelatter part better, but underestimated the concentrations in the tailing. As was observed forexperiment A with the same input concentration, the fast attachment/detachment process in the
3S5R-att-irrev model could be approximated by instantaneous sorption (3S2R-lin-irrev). Because
the fitted Freundlich exponent was close to 1, the simulated curve with the 3S2R-Freu-irrev
model was almost identical to the latter two models.
Thus, only the 3S5R-att-irrev model was flexible enough to predict the observed BTCs of all
three experiments. Note that the standard errors of the five estimated rate parameters are relatively
large. Hence, the accuracy of the estimates is reduced, which might be a result of the highflexibility of the model. As already known in soil physics the results demonstrate that experimentswith different boundary conditions are necessary to identify the relevant sorption processes.
Although it is highly unlikely that, because of the complexity of the sorption processes, the130

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Fig. 10. Measured, fitted and predicted BTCs with the 3S5R-att-irrev model for experimental conditions A (a), B (b) and C(c).

calibrated parameters represent unique solutions of the inverse problem, they did provide a very
good description of the measured BTCs. However, the optimal parameter sets differed widely
between the three experiments. Variation of other boundary conditions, such as irrigation rate,
might help to further elucidate possible sorption processes.
4.3.5. Concentration profiles
Simulated concentration profiles for the different sorption models are given in Figs. 8 and 9.
None of the simulated profiles matched the measurements, despite good fits for the BTCs.

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131

Including observed concentration profile data in the numerical inversion of models withirreversible sorption did not result in a parameter set that could considerably better simulate themeasured soil concentration profiles (data not shown).
A first-order irreversible sorption process results in an exponential decrease in the soil
resident concentration profile. However, no parameter combination was found for experiments
A and B to match all features of the profile concentrations under the prevailing boundary
conditions, i.e. the high concentrations in the upper part followed by the steep concentration
gradient and the constant concentration level in the lower part of the column. Still, only
models involving irreversible sorption processes were able to predict higher resident concentrations at the top than at the bottom of the column (Fig. 8a and b) after long leaching
periods.
In experiment C a more uniform soil concentration distribution was observed (Fig. 9b). To
account for the large mass fraction remaining in the column, the fitted irreversible sorption
rate was larger in all models than for experiments A or B. However, the modelled soil
concentration gradient was steepest for this set of parameters, and did not match the observed
shape.
4.3.6. Parameter comparison and predictability
Although the 3S5R-att-irrev model might not be the adequate process description, theoptimized parameter values for the different experiments (Tables 6, 7 and 8) showed some trends.
The comparability of the parameter sets is justified by the fact that soil to solution ratios are
similar in all columns. Since most mass was retained in the soil in experiment C parameter β3 andsorption affinity were both the highest for this experiment. The attachment rate coefficient
towards the irreversible sorption site β3 irreversibly removes solute mass from the transportdomain. Sorption affinity reduces the solute transport velocity compared to the water flow and canbe estimated from the ratio between the attachment and the detachment rate coefficients (βi / γi).
The slow reversible attachment/detachment rate coefficients were within the same range, whereas
the rate coefficients for the fast sorption site differed by three orders of magnitude, with the largest
values for experiment A and smallest for experiment B.
However, if the 3S5R-att-irrev model included all relevant processes occurring during theexperiments and if its parameters were constant (i.e. concentration independent), the optimal
parameters for all experimental conditions should be identical. The predictive power of the 3S5Ratt-rev model was tested to describe the BTCs. The optimal parameter set for one experiment wasused to predict the BTC for the other two application scenarios (Fig. 10). The earliest
breakthrough was always predicted using the parameters of experiment B, the latest using theparameters of experiment C. The observed peak concentrations and the eluted mass fractions were
never met by the forward calculations, because the values of β3 were too different. However, thetailing is described well by all parameter combinations (Fig. 10). The tailing of the BTC cannot
proceed faster than exp(−αslowt), suggesting that it drops with exp(−βt), where β = αslow − δ with
δ N 0 (Vereecken et al., 1999). Here β is the slope of the tailing in the semi-log plot for two-sitekinetic sorption models (equivalent to the 2S2R-lin-rev or 2S4R-att-rev models) and αslow is thesmallest sorption rate coefficient. For the 3S5R-att-irrev model the determining rate coefficientfor the tailing is the smallest desorption rate γ2, because the irreversible sorption process does not
influence the slope of the tailing. For all sets of parameters, the values of γ2 are in the same orderand thus the slopes of the tailing are expected to be similar, too. Due to the differences in the fitted
3S5R-att-irrev model parameters for the three experiments, we did not expect to find a set ofparameters that fits all experiments equally well by simultaneous fitting. We thus, did not add an

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option for simultaneous fitting of multiple experiments to the applied version of the HYDRUS-1Dmodel.
5. Discussion
Incomplete breakthrough of sulfonamides has previously been reported during transport ofSDZ (Kreuzig and Höltge, 2005), sulfachloropyridazine (Boxall et al., 2002; Kay et al., 2005b)
and sulfamethoxazole (Drillia et al., 2005). However, the effect of different boundary conditions
regarding the solute application on the transport was not yet investigated. Kreuzig and Höltge
(2005) found only 4% of the applied SDZ in the leachate compared to 43% of a simultaneously
applied conservative tracer. They also found more than 60% of the applied 14C-labelled SDZ as
non-extractable residues in the upper 5 cm of the column after 6 days of irrigation. The resulting
concentration profile is in accordance with our studies, although detailed information about the
BTCs was lacking. Low recoveries were shown for SDZ by Kreuzig et al. (2003) or Hamscher
et al. (2005), especially for aged soil residues. Because of the lack of proved degradation products,
the missing mass may as well be non-extractable, apparently irreversibly sorbed parent substance.
The model concept proposed to describe the transport of sulfamethoxazole included non-linear
Freundlich sorption as well as a rate-limited mass transfer between the flowing bulk liquid phaseand a stagnant water film attached to the soil particles (Drillia et al., 2005). However, for soils withlittle organic material, a strong sorption hysteresis was also observed, which might be described bya second, slower reversible or even an irreversible sorption process (Drillia et al., 2005). Due to its
two ionizable functional groups, the charge of SDZ depends on the prevailing pH-value. Although
the pH-dependent species of SDZ exhibit different sorption properties (e.g. Gao and Pedersen,
2005), the proposed model concepts did not account for pH-speciation. This is justified because pH
did not change during the experiments. Thus, the ratio of the dominant species was assumed to beconstant. Because the neutral and the anionic species were dominant in the column experiments,
cation exchange as one of the sorption processes may be negligible. Anion sorption of SDZ on
positively charged iron oxides might be anticipated. In independent batch sorption experiments
sorption of 14C-sulfadiazine was determined to be non-linear and rate-limited, whereas desorption
is very slow or even irreversible (data not shown). As already reported by Tolls (2001) for various
pharmaceuticals, common sorption concepts (KOC, linear equilibrium isotherms) are inappropriate
for the description of these experiments. This rather complex sorption behavior will be addressedin a forthcoming article.
Although process-oriented transport studies for veterinary pharmaceuticals are still rare,comparable experimental protocols are commonly used for the estimation of the transportparameters for other environmental pollutants, such as pesticides or bacteria. Prata et al. (2003)
described the BTC of the herbicide atrazine in repacked soil columns well with the 3S2R-lin-irrev
model. The irreversible sorption process accounted for 40 to 50% of the applied mass remaining
in the soil column after the leaching period, while even the concentration profile was relatively
well reproduced. A similar long tailing due to chemical non-equilibrium sorption was observed
for the hormone testosterone in repacked soil columns (Casey et al., 2004). They successfully
described the observed BTCs with a one-site kinetic Freundlich sorption model, having a firstorder degradation in the solid phase. The attachment/detachment concept gave the best
predictions for all experiments. This approach is commonly used to describe the transport of small
particles such as bacteria or viruses in soils or aquifers (Schijven and Hassanizadeh, 2000). In
these studies the characteristic soil concentration profiles and the extended tailing are often
observed (Schijven et al., 2002; Bradford et al., 2002, 2003). However, in particle transport

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133

studies additional processes, such as blocking, filtration or straining are included to describe how
the size of the particles and their surface properties affect the transport behavior. The required
parameters can even be determined independently (Bradford et al., 2002, 2003). These authors
considered, for example, blocking as depth-dependent. This concept results in high resident
concentrations near the source of the particle release, i.e. the top of the column with very steep
concentration gradients.
However, a depth-dependent process, which might better describe the observed soil concentration
profiles in this study, cannot be justified for a solute such as SDZ. Nevertheless, the poor model
performance for the concentration profiles is a hint that at least one process is lacking in the model.
Since our chemical analysis of SDZ was restricted to 14C only, we have no information available on
possible transformation reactions of the 14C-labelled parent compound and its daughter products inthe leachate or the soil. Transformation might affect the overall transport in the following manner: It
is anticipated that transformation products exhibit different sorption properties (isotherm, kinetics,
reversibility) as compared to the parent compound. In contrast to the parent compound which isapplied on top of the soil column, the transformation products are formed during the course of theexperiment within the soil column. The concentration of the parent compound consequently
decreases. The concentrations of the transformation products may increase or decrease according totheir sorption properties and their successive transformation. The simultaneously occurring sorption
and transformation processes that may depend on time and concentration, result in different BTCs
and soil concentration profiles than predicted with the presented effective models for 14C-SDZ. An
estimation of the effect of the occurrence of transformation products during the experiments would
be highly speculative, since only the superimposed BTCs and soil concentration profiles of theparent and possible transformation products were determined by 14C-analysis. Additionally there is
too little information in the literature on the identity, concentration, transformation pathways,
transformation kinetics and sorption properties of the transformation products. To our knowledge no
information exists on the fate of acetyl-SDZ and hydroxy-SDZ, two of the known transformation
products of SDZ, in soils.
6. Conclusions
The transport of SDZ depends on the application protocol of the solute, i.e. the input
concentration and the pulse duration. The observation of low concentrations in the tailing andthe determination of soil resident concentrations was only possible due to the 14C-analysis.
The observed differences in peak concentrations and eluted mass fraction are caused by timeand concentration-dependent sorption processes. Only the complex three-site kinetic sorption
model with two reversible and one irreversible sorption site was flexible enough to describe
the complete observed BTCs for the various application scenarios. Despite the good agreement
for the BTCs, the observed and modelled concentration profiles in the soil differed substantially. Therefore, common approaches for process identification on the basis of the main
peak breakthrough without the observation of the tailing and the concentration profile areprecarious. Reasons for the discrepancy between observations and model predictions might be:(i) possible transformation reactions, which were out of the scope of the experimental andmodel investigations, (ii) inappropriate mathematical concepts for the sorption processes, i.e.
isotherms and rate-laws and (iii) the assumption of sorption irreversibility. Although SDZ
reaches the soil environment typically as ingredient of manure, the results imply that leachingof SDZ might be enhanced if applied in higher concentrations on soils near water saturation
shortly before the next rain event.

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