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1673
Environmental Toxicology and Chemistry, Vol. 18, No. 8, pp. 1673–1678, 1999
q
1999 SETAC
Printed in the USA
0730-7268/99 $9.00
1
.00
IMPACT OF GRAIN SCALE HETEROGENEITY ON SLOW SORPTION KINETICS
S
YBILLE
K
LEINEIDAM
,H
ERMANN
R
U
¨GNER
, and P
ETER
G
RATHWOHL
*
Geological Institute, University of Tu¨bingen, Sigwartstraße 10, 72076 Tu¨bingen, Germany
(
Received
14
April
1998;
Accepted
22
January
1999)
Abstract—Groundwater contamination by dissolved organic compounds frequently occurs in valley aquifers that consist of highly
heterogeneous sand and gravel sediments. Remediation and risk assessment (e.g. reactive transport modeling) requires detailed
information on the sorption/desorption kinetics in such aquifer materials. In this paper we present data on slow sorption kinetics
of phenanthrene and the composition of several aquifer materials that are typical for southern Germany and Switzerland. The
heterogeneity of the aquifer material is described in terms of the physical and chemical properties (e.g., grain size, organic carbon
content, intraparticle porosity, sorption parameters, and rate constants for intraparticle diffusion) of the sediment constituents
(lithocomponents). Phenanthrene sorptive uptake in a heterogeneous bulk sample can be predicted using a numerical model only
if the composition and geochemical heterogeneity (different sorptivities and porosities of the lithocomponents) are considered. It
could be shown that even within a narrow grain size fraction, the geochemical heterogeneity has tobe incorporatedfortheprediction
of long-term sorptive uptake or release of organic contaminants.
Keywords—Heterogeneity Sorption kinetic Numerical modeling Aquifer material
INTRODUCTION
Groundwater contaminations are frequently found in shal-
low aquifers that comprise heterogeneous unconsolidated sand
and gravel sediments. Remediation efforts over the last several
decades have revealed that the time scale for complete cleanup
of such aquifers can be extremely long because of diffusion-
limited sorption and desorption processes [1–3]. Pignatello and
Xing [4] provide a summary of slow sorption mechanisms for
natural particles. Contaminant transport experiments at the lab-
oratory and field scale have demonstrated that nonequilibrium
conditions frequently occur in aquifers (e.g., retardation factors
increased with time and transport distance or column length,
respectively [5–8]). Diffusion models have been used to de-
scribe long-term sorption and desorption kinetics, but in most
cases the aquifer samples were treated and characterized as a
bulk material (homogeneous sample). The application of a
single component diffusion model that is based on the average
properties of a heterogeneous sample has resulted in unreal-
istically high tortuosity factors for pore diffusion [3,9,10]. Ball
[9] first discussed this issue for sorptive uptake of chlorinated
compounds in Borden sand. Pedit and Miller [11] showed that
the incorporation of different particle size classes into the sorp-
tive uptake model resulted in a better fit of measured sorption
data. They also pointed out that the different equilibrium sorp-
tion capacities of the grain size fractions can be more important
than particle size differences. Barber et al. [12,13] found that
even within a single grain size fraction, equilibrium sorption
capacities can vary by a factor of four to seven for the magnetic
fraction (reactive fraction) as compared to the bulk sample.
The shale-like (reactive) fraction dominated the bulk sorption
behavior in soil samples [14]. In response to these findings,
the sorption and desorption behavior of pollutants in hetero-
* To whom correspondence may be addressed
(peter.grathwohl@uni-tuebingen.de).
Presented at the 218th Meeting of the American ChemicalSociety,
Las Vegas, NV, USA, September 7–11, 1997.
geneous samples were successfully modeled using a range of
kinetic parameters (e.g., a gamma distribution of first-order
rate constants [15–17]).
Most aquifer materials consist of a mixture of grains of dif-
ferent sizes and properties (e.g., density, intraparticle porosityand
organic carbon content). The bulk properties depend mainly on
the petrography of the source rocks (source of the lithocompo-
nents) and the sediment transport distance (separation and ac-
cumulation due to weathering and transport processes affect the
petrographic composition and the grain size distribution of the
aquifer sediments). The lithocomponents are fragments of lime-
stones, sandstones, mudstones, shales, igneous rocks, and so on
and minerals (e.g. quartz, feldspar, and calcite).
The objectives of this paper are (1) to provide a compre-
hensive data set on physical and chemical properties of typical
heterogeneous aquifer materials (sand and gravel) and (2) to
show that long-term sorptive uptake of organic contaminants
can be predicted adequately if the natural sample heterogeneity
is considered. The impact of sample heterogeneities on sorp-
tive uptake as well as modeling artifacts (e.g., prediction of
equilibration time and derivation of tortuosity factors) using
single-component models are illustrated.
Diffusion-limited sorptive uptake in heterogeneous samples
It is widely accepted that slow sorption and desorption
processes are due to diffusion-limited transport of solutes to
sorption sites inside of particles or soil aggregates [1,2,18,19].
Consequently, the diffusion equation (Fick’s 2
nd
Law) in spher-
ical coordinates is commonly used to describe the sorption/
desorption kinetics [20]:
2
]
C
]
C
2
]
C
5
D
1
(1)
a2
[]
]
t
]
rr
]
r
where
C, t,
and
r
denote concentration (
m
g/L), time (s), and
the radial distance (cm) from the center of a spherical grain,
respectively. The term
D
a
(cm
2
/s) is the apparent diffusion
1674
Environ. Toxicol. Chem.
18, 1999 S. Kleineidam et al.
Table 1. Properties of the lithocomponents (grain size fractions) investigated
Origin/lithocomponents Solid density
(g/cm
3
)
e
(
2
)
f
oc
(mg/g) CaCO
3
(
2
)
K
Fr
/
l
/
n
(L kg
2
1
)/(
2
)
Hu¨ntwangen
Dark-colored limestone (DL)
Dark-colored sandstone (DS)
Light-colored limestone (LL)
Light-colored sandstone (LS)
Quartz and feldspar minerals (Qz)
Igneous and metamorphic rocks (Met)
2.74
2.67
2.73
2.67
2.64
2.71
0.0035
0.015
0.011
0.046
0.0014
0.0047
0.41
6
0.02
0.62
6
0.06
0.23
6
0.02
0.32
6
0.03
0.04
6
0.01
a
0.16
6
0.01
0.86
0.37
0.81
0.33
0.025
,
0.005
355/0.58
977/0.50
47.9/0.65
85.1/0.64
1.4/0.92
0.38/1.15
Singen
Dark-colored limestone (DL)
Dark-colored sandstone (DS)
Light-colored limestone (LL)
Light-colored sandstone (LS)
Quartz and feldspar minerals (Qz)
Igneous and metamorphic rocks (Met)
Coal particles
2.70
2.69
2.72
2.70
2.64
2.70–2.84
0.79
0.0034
0.016
0.0089
0.046
0.0014
0.0048
0.006
0.85
6
0.06
0.90
6
0.14
0.24
6
0.04
0.29
6
0.08
0.04
6
0.003
0.07
6
0.01
400
6
0.20
0.67
0.37
0.72
0.39
0.014
,
0.005
,
0.005
Neckar River, Horkheim
Triassic dark limestone (MsK)
Jurassic light limestone (JK)
Triassic light sandstone (SS)
Bunter sandstone (BS)
2.73
2.73
2.65
2.64
0.0070
0.012
0.080
0.10
0.34
6
0.03
0.22
6
0.03
0.25
6
0.02
0.04
6
0.01
0.95
0.94
0.34
,
0.005
182/0.67
20.2/0.75
30.4/0.66
3.2/0.67
Quartz (Qz) 2.64 0.0014 0.04
6
0.01
,
0.005 1.4/0.92
Neckar River, Hirschau
Triassic dark limestone (MsK)
Jurassic light limestone (JK)
Triassic light sandstone (SS)
2.72
2.72
2.67
0.0057
0.016
0.080
0.80
6
0.03
0.73
6
0.03
0.59
6
0.01
0.95
0.94
0.29
156/0.72
58.0/0.83
78.9/0.76
Neckar River, Hirschau (grain size fractions
,
1.0 mm)
0.063–0.125 mm
0.125–0.25 mm
0.25–0.5 mm
0.5–1.0 mm
2.71
2.70
2.66
2.67
0.020
0.019
0.016
0.0093
1.3
6
0.13
1.3
6
0.13
0.63
6
0.01
0.33
6
0.02
0.5
0.52
0.40
0.33
282/0.69
137/0.69
57.3/0.64
35.2/0.73
a
Detection limit of the organic carbon measurements. For the distribution of the lithocomponents in the grain size fractions, see Figure 1.
coefficient that, in a water-saturated porous particle (pore dif-
fusion), can be defined as
D
e
aq
D
5
(2)
a
(
e1
K
r
)
t
df
where
D
aq
(cm
2
/s),
e
(
2
),
r
(g/cm
3
), and
K
d
(L/kg) denote the
aqueous diffusion coefficient, the intraparticle porosity, the
bulk density of the particle, and the distribution coefficient
(ratio of sorbed to dissolved concentrations), respectively;
t
f
(
2
) is the tortuosity factor that cannot be measured indepen-
dently and therefore is often used as fitting parameter; and
t
f
can be estimated on the basis of the intraparticle porosity,
analogous to the electrical conductivity in porous media [21]
(e.g.,
t
f
5e
1
2
m
, where
m
is an empirical exponent that in
sedimentary rocks is usually close to 2 [22,23]). It should be
noted that for nonlinear sorption isotherms,
K
d
, and thus
D
a
,
becomes a function of the concentration, and numerical so-
lutions are required to solve Equation 1. As pointed out by
several authors [24,25], Equation 1 is valid for a mixture of
particles of only a limited size distribution, that is, within one
order of magnitude. A fraction of instantaneous sorption (
x
i
)
was introduced into the analytical solutions of Equation 1 [1]
to account for a fast sorption rate. Because in the heteroge-
neous aquifer sediments
D
a
can vary significantly even within
a single grain size fraction (arising from different
e
and
K
d
of
the lithocomponents), numerical models have to be used to
solve Equation 1. Modeling in this paper is based on the finite
difference method and the Crank-Nicholson approach [26].
Input data are parameters describing the physical heterogeneity
of the sample (grain size distribution and petrographic com-
position) and the physicochemical properties of the lithocom-
ponents (
e
and
t
f
as well as the Freundlich sorption isotherm,
K
Fr
,1/
n
). The sorption data for the lithocomponents as well
as for the grain size fractions
,
2 mm were measured in equi-
librium- and long-term batch experiments [27,28].
MATERIALS AND METHODS
Samples were collected from three gravel pits (outcrops of
fluviatile sediments) and one borehole in southwestern Ger-
many and Switzerland. The sand and gravel samples consist
of typical lithocomponents that are erosional products (frag-
ments of mainly sedimentary rocks) of either German Triassic
and Jurassic rocks (Hirschau and Horkheim) or of alpine origin
(Hu¨ntwangen and Singen). They were split into eight grain-
size fractions by dry sieving. Petrographically uniform grains
were separated from the gravel and coarse sand fractions to
obtain homogeneous samples consisting of one specific class
of lithocomponents (Table 1). Because the separation of the
lithocomponents was based only on the petrography of the
constituents (by visual appearance of the wet gravels), a class
of lithocomponents consists of grains of similar depositional
environments (e.g., dark colored marine limestones) but might
be derived from different geological rock formations (e.g.,
Triassic, Jurassic, and Cretaceous for the samples of alpine
origin). The petrographic composition of one sand fraction
(Singen) was determined in a thin section using a point counter.
In general, for grain size fractions smaller than 1 mm, only
Slow sorption kinetics in heterogeneous aquifer materials
Environ. Toxicol. Chem.
18, 1999 1675
Fig. 1. Typical petrographic composition of the gravel and coarse sand fractions of the sampled sites/sediments. Data are based on average
values of two to six samples derived from different lithofacies (differences among samples of one site are mainly in grain size distribution and
not in petrographic composition). The Hu¨ntwangen and Singen samples represent glaciofluviatile alpine-derived sediments from the last ice age.
Horkheim and Hirschau samples are Quaternary sediments from the Neckar River valley. The petrographic composition of grain size fractions
used in the sorption kinetic studies are marked by dashed lines. Met
5
metamorphic rock, Qz
5
quartz, SS
5
sandstone, LS
5
light sandstone,
DS
5
dark sandstone, DL
5
dark-colored limestone, BS
5
Bunter limestone, JK
5
Jurassic limestone, MsK
5
Triassic limestone.
bulk parameters were measured. The petrographic composi-
tions of the grain size fractions are given in Figure 1.
Physical and chemical properties were measured for all
lithocomponents (Table 1) and the sand fractions less than 2
mm (a selection is given in Table 1). Details on the methods
are described elsewhere [27,28]. In brief, the carbonate content
(CaCO
3
) of a sample was measured by dissolution in hydro-
chloric acid and back-titration of the residual HCl with NaOH;
phenolphthalein was used as an indicator. The organic carbon
content (
f
oc
) was measured using dry combustion under pure
oxygen at temperatures of 750
8
C (Model 183 Boat Sampling
Module, Rosemount Inc., Santa Clara, CA, USA) and infrared
detection of the evolved CO
2
(Horiba PIR-2000, Horiba LTD,
Tokyo, Japan). The intraparticle porosity (
e
) was determined
by mercury intrusion and nitrogen adsorption (Autopore 9220
and ASAP 2010, Micromeritics Norcross, GA, USA). The sol-
id density was measured with a He-pycnometer (Accupyc
1330, Micromeritics).
The sorption equilibrium and the sorption kinetics of the
heterogeneous samples were studied using phenanthrene as a
chemical probe (octanol:water coefficient log
K
ow
5
4.63; wa-
ter solubility
5
1.29 mg/L). Phenanthrene was analyzed by
HPLC using fluorescence detection. The experiments werecar-
ried out using a batch technique described in detail in Schu¨th
[29] and Ru¨gner et al. [28]. All batch tests were conducted in
triplicates in crimp-top reaction vials sealed with Teflon
t
-lined
butyl rubber septa. Blank samples were monitored over the
same experimental time period. Sorption to the aquifer solids
was determined on the basis of mass balance considerations.
Mass balances were evaluated at the end of the experiments
by extracting the solids using hot methanol. In general, re-
covery rates were close to 100% (for more detailed infor-
mation, see [28]). Comprehensive data on sorption isotherms
and sorptive uptake of phenanthrene by the specific lithocom-
ponents are given elsewhere [27,28].
RESULTS AND DISCUSSION
Characterization of the lithocomponents
Organic carbon content and intraparticle porosity are dis-
tinctly different in the various lithocomponents investigated.
In general, the dark-colored lithocomponents (Triassic lime-
stone [MsK], dark-colored limestone [DL], and dark sandstone
[DS]) contain higher fractions of organic carbon than the light-
colored components (Jurassic limestone [JK], light-colored
limestone [LL], and light-colored sandstone [LS]). Organic
carbon contents of the igneous and metamorphic rock frag-
ments (Met) are very low and close to the detection limit for
the quartz and feldspar monominerals (Qz/Fds). Coal frag-
ments were identified in the coarse sand fraction of the Singen
sample. Intraparticle porosities for the lithocomponents are
given in Table 1. In general, lower values were measured in
the limestone fragments than in the sandstone fragments.
Composition of the gravel and sand fractions
The source rock area of the Neckar River sediments is
dominated by limestones. The fraction of micritic dark-colored
MsK was slightly higher than the fraction of light-colored JK.
Sandstones (SS) occur in minor quantities. Although the two
alpine-derived sediments (Singen and Hu¨ntwangen) were de-
1676
Environ. Toxicol. Chem.
18, 1999 S. Kleineidam et al.
Fig. 2. Simulation of diffusion limited sorptive uptake in a batch
experiment of a heterogeneous sample. The sample consists of five
components accounting for 20% of the equilibrium sorption capacity
each. The curves 1 to 5 are numerical solutions of Equation 1 for
each component. Rate constants 1–5: 8.6
3
10
2
9
s
2
1
(Qz); 2.1
3
10
2
9
s
2
1
(BS); 4.1
3
10
2
10
s
2
1
(SS); 1.9
3
10
2
11
s
2
1
(JK); 3.9
3
10
2
11
s
2
1
(MsK).
Fig. 3. Phenanthrene sorptive uptake data and modeling for a bulk
sample (Neckar River, Hirschau) consisting of different grain size
fractions (0.063–8 mm) and different lithocomponents. Solid line:
Prediction of the sorptive uptake in the heterogeneous sample (pure
forward modeling) based on seven grain size fractions and petro-
graphic composition of the grain size fractions
$
1 mm (making up
70% of the bulk). Physical and chemical parameters as well as the
weight fractions are given in Tables 1 and 2. Dotted line: Best fit to
measured data using a single-component model; the tortuosity factor
(
t
f
) is the fitting parameter in the numerical model and
t
eq
is the time
to reach 99% of the sorption equilibrium. Dashed line: Best fit as
above but including a fraction of instantaneous uptake (
x
i
).
posited at the same time period, the lithocomponents show a
different distribution pattern because of different Rhine glacier
lobes that were connected to two different source rock areas.
Whereas the gravels in the Singen Basin are dominated by
igneous and Met rocks and Qz/Fds, the sediments in Hu¨nt-
wangen contain higher fractions of the sedimentary rocks. DL
and fine-grained turbiditic DS occur in similar fractions in both
outcrops. Light-colored limestone and LS are more frequently
found in the Hu¨ntwangen gravel fractions. The petrographic
composition of all samples is illustrated in Figure 1. At all
sites, the petrographic composition of the sand fraction (start-
ing at
,
2 mm) is significantly different from the gravel fraction
because of higher quartz and feldspar levels in the sand fraction
(Fig. 1). The highest quartz levels coincide with a minimum
of carbonate and organic carbon content within the medium
sand fraction. This is especially true for the medium sand
fraction (0.25–0.5 mm) of the Singen sample, which was com-
posed of 50% quartz. The quartz mineral size is in the range
of 0.25 to 0.5 mm. The amount of quartz minerals also in-
creases with transport distance, as seen in the Horkheim sed-
iments, which were deposited 150 km downstream of the Hir-
schau material and already contain 51% of quartz in the 1- to
2-mm grain size fraction compared to 25% in Hirschau. The
origins of the quartz minerals are weathered igneous and meta-
morphic rocks (granites and gneiss) and sandstones. Coal frag-
ments in the sand fractions of the Singen sample make up a
maximum of 1% and are therefore not incorporated in Figure
1. Measured
f
oc
in the bulk sample and calculated
f
oc
based on
the composition of the 1- to 2-mm grain size fractions are
within a 15% error level.
Influence of the sample heterogeneity on sorption kinetics
The rates of sorptive uptake depend on the properties of
the lithocomponents and the grain size. According to the dif-
ferences in
f
oc
and
e
, both equilibrium sorption capacity and
the sorption kinetics of phenanthrene are significantly different
for the lithocomponents, as described elsewhere [27,28]. In
brief, dark-colored components containing high organic carbon
content showed generally high sorption capacities and, because
of low intraparticle porosities, very slow sorption kinetics. For
most grain sizes of 2 to 4 mm after 500 d, less than 10% of
the equilibrium was reached. Although the light-colored lime-
stones showed smaller sorption capacities and faster sorption
kinetics, several months to years were still necessary to reach
equilibrium. Sorption equilibrium within 100 d was reached
only for the SS. Equilibrium within days was reached for the
monominerals (Qz) and igneous and Met rock fragments.
Figure 2 shows a calculated example of sorptive uptake in
a batch experiment for a sample made up of five lithocom-
ponents (Qz, BS, SS, JK, and MsK). The bulk sorptive uptake
results from the superposition of the sorptive uptake of the
different lithocomponents. Components with fast sorption ki-
netics (BS and Qz) can reach equilibrium within days. The
following constant increase in sorptive uptake due to slower
sorbing components (MsK and JK) results in a desorption of
the early-equilibrated (fast-sorbing) particles. The bulk sorp-
tive uptake will be dominated by the fast-sorbing components
at short time periods and by the slow-sorbing components in
later time periods. From Figure 2, it is obvious that a single
component model cannot adequately describe the sorptive up-
take in heterogeneous materials.
Figure 3 shows sorption kinetics, which were measured in
a heterogeneous bulk sample from the Neckar River (Hir-
schau). The sorptive uptake was predicted using a numerical
solution of Equation 1 [26] based solely on the bulk sample
composition (seven grain size fractions), the petrographic com-
position (grain size
.
1 mm making up 70% of the bulk; Fig.
1), and the properties of the lithocomponents (see Table 1)
comprising each grain size fraction (Table 2). Good agreement
was achieved between the model prediction and the data (mean
weighted squared error
5
0.031). If the heterogeneity of the
sample is ignored and the numerical modeling is based on the
bulk sorption isotherm data and the average porosity (single-
component model), a reasonable fit can be obtained only for
a certain time period (10–100 d, error
5
0.32). This fit can
be improved if the model accounts for a fraction of instan-
taneous sorption (
x
i
). For time periods up to 500 d (experi-
Slow sorption kinetics in heterogeneous aquifer materials
Environ. Toxicol. Chem.
18, 1999 1677
Table 2. Components and weight fractions used for the numerical
modeling (multicomponent models)
a
Components No.
S
weight
fraction
(%)
Weight fraction of lithocompo-
nents
in grain size fractions (%)
Grain size fraction 0.063–8 mm of the Neckar River Valley (Hirschau)
sample (Fig. 3)
MsK
(%) JK
(%) SS
(%) Qz
(%)
0.063–0.125 mm
0.125–0.25 mm
0.25–0.5 mm
0.5–1.0 mm
1
2
3
4
2.8
4.12
13.16
12.51
grain size
fractions nos.
1–4 were not
separated into
lithocomponents
1.0–2.0 mm
2.0–4.0 mm
4.0–8.0 mm
5–8
9–12
13–16
9.31
18.27
39.83
37.6
47.6
52.4
32.1
40.2
41.5
5.7
5.0
4.8
24.7
7.1
1.3
Grain size fraction 2.0–4.0 mm of the Neckar River valley (Horkheim)
sample (Fig. 4)
MsK
(%) JK
(%) SS
(%) QZ
(%) BS
(%)
2–4 mm 1–5 100.0 25.5 49.0 5.8 12.6 7.1
Grain size fraction 2.0–4.0 mm of the Hu¨ntwangen sample (Fig. 4)
DL
(%) DS
(%) LL
(%) LS
(%) Met
(%)
2–4 mm 1–5 100.0 26.5 18.3 24.6 11.1 19.5
a
For
K
Fr
,
l
/
n
,
e
, and solid density, see Table 1.
Fig. 4. Sorptive uptake of phenanthrene for the fine gravel fraction
(2–4 mm) in the Neckar River, Horkheim and Hu¨ntwangen sample.
Solid lines: Calculated sorptive uptake based on the petrographic com-
position of the grain size fractions (multicomponent model).Physical
and chemical parameters as well as the weight fractions are given in
Tables 1 and 2. Dotted lines: Single-component model fitted to 1 to
10 d of the calculated sorptive uptake data. Dashed lines: Single
component model fitted to 50 to 500 d of the calculated data using
x
i
.
mental data),
x
i
leads to a lower error (0.022), but in both cases
the single-component model cannot account for the long-term
sorption behavior (larger grain sizes and slow sorbing litho-
components) and will underestimate the time needed for equil-
ibration. It has to be pointed out that the single-component
models are just fits to experimental data, whereas the multi-
component model approach is a true prediction of the sorptive
uptake.
Figure 4 shows some further artifacts that occur if asingle-
component model is used for the interpretation of sorptive
uptake data even in a narrow grain size fraction of a hetero-
geneous sample (the 2- to 4-mm grain size fractions of the
Horkheim and Hu¨ntwangen samples). The two samples consist
of different lithocomponents (Fig. 1) and also have different
average properties (
f
oc
and
e
, Table 1), which result in different
equilibrium
K
d
values and equilibration times. Independently
measured sorption properties and diffusion rate constants of
the lithocomponents are illustrated elsewhere [28]. The single-
component model (based on the equilibrium sorption isotherms
and the average porosities of the grain size fractions) was fitted
to the calculated sorptive uptake data for the heterogeneous
grain fractions within two different time periods (1–10 d and
50–500 d). For the longer time period, a fraction of instan-
taneous sorption (
x
i
) was incorporated in the single-component
model, resulting in a better fit of the early sorptive uptake due
to fast-sorbing lithocomponents. The long-term sorption ki-
netics are governed by the slowest-sorbing lithocomponents.
Therefore, attempting to fit data from a heterogeneous sample
with a single-component model will lead to an underestimation
of the time for equilibrium (
t
eq
5
the time to reach 99% of
equilibrium sorption). This phenomena is due to the fact that
in calculating the time required for equilibrium experimentally,
the impact of the slowest-sorbing lithocomponent is under-
estimated. This is clearly shown by comparing the sorption
rates derived using a single-component model (Horkheim 10
d, 500 d,
t
eq
5
2,090 d, 4,300 d; Hu¨ntwangen 10 d, 500 d,
t
eq
5
7370 d, 11,200 d) with those calculated for a heterogeneous
model (Horkheim
t
eq
5
16,900 d, Hu¨ntwangen
t
eq
5
84,700
d). It should be noted that these relatively long equilibration
times depend on the grain size squared (are 100 times shorter
for a medium sand of 0.2- to 0.4-mm grain size). Also, cal-
culated tortuosity factors (Eqn. 2) are higher than expected
from the average porosity of the grain size fraction (the bulk
porosity is dominated by relatively porous lithocomponents),
and they increase with time (Horkheim 10 d, 500 d,
t
f
5
156,
350). The influence of slow-sorbing lithocomponents increases
with time, until finally only the slowest-sorbing lithocompo-
nent will govern the bulk sorptive uptake. For remediation
efforts, this long-term sorption behavior is of special interest.
SUMMARY AND CONCLUSIONS
All the samples investigated were highly heterogeneous
because of different source areas of the sediments and show
different petrographic compositions (different lithocompo-
nents). Depending on the source rock properties, the litho-
components have different
e
,
f
oc
, and CaCO
3
contents. There-
fore, the bulk parameters of the grain size fractions depend on
the lithocomponents and their distribution, which is influenced
by separation processes during transport and sedimentation.
The heterogeneity of the sample has to be incorporated in
the modeling of sorption/desorption kinetic data to achieve a
long-term prediction. As demonstrated in Figures 3 and 4,
artifacts must result from applying a single-component model
to heterogeneous samples. Both
t
eq
and
t
f
depend on the avail-
able data base (e.g., time scale of data collection in a batch
experiment) if the single-component model is fitted to sorptive
uptake in a heterogeneous sample. Long-term sorptive uptake
and desorption cannot be predicted from short-term data in a
heterogeneous sample. If initially fast sorption is modeled by
introducing a fraction of instantaneous sorptive uptake, an ac-
curate prediction of the time needed for equilibration is still
not possible. In all cases, equilibration times and consequently
the tailing in desorption will be underestimated. Tortuosity
1678
Environ. Toxicol. Chem.
18, 1999 S. Kleineidam et al.
factors can be far to high compared to the
t
f
expected from
the average intraparticle porosity of the bulk sample (e.g.,
t
f
ø
1/
e
). This holds even for a narrow grain size fraction and
depends on the variability of the lithocomponents involved.
Acknowledgement
—Funding for this work was provided by the Ger-
man Research Foundation through Grant Gr-971/5-1/2 to H. Ru¨gner
and the SFB 275, C3 Quaternary gravel bars: Sedimentology, Hy-
drogeology and Climate History Grant to S. Kleineidam. The man-
uscript benefited from reviewers’ comments.
REFERENCES
1. Ball WP, Roberts PV. 1991. Long-term sorption of halogenated
organic chemicals by aquifer material. 2. Intraparticle diffusion.
Environ Sci Technol
25:1237–1249.
2. Grathwohl P, Reinhard M. 1993. Desorption of trichloroethylene
in aquifer material: Rate limitation at the grain scale.
Environ Sci
Technol
27:2360–2366.
3. Farrell J, Reinhard M. 1994. Desorption of halogenated organics
from model solids, sediments and soil under unsaturated condi-
tions. 2. Kinetics.
Environ Sci Technol
28:63–72.
4. Pignatello JJ, Xing B. 1996. Mechanisms of slow sorption of
organic chemicals to natural particles.
Environ Sci Technol
30:
1–11.
5. Roberts PV, Goltz MN, Mackay DM. 1986. A natural gradient
experiment on solute transport in a sand aquifer. 3. Retardation
estimates and mass balances for organic solutes.
Water Resour
Res
22:2047–2058.
6. Ptacek CJ, Gillham RW. 1992. Laboratory and field measurements
of non-equilibrium transport in the Borden aquifer, Ontario,Can-
ada.
J Contam Hydrol
10:119–158
7. Brusseau ML, Jessup RE, Rao RSC. 1991. Nonequilibrium sorp-
tion of organic chemicals: Elucidation of rate limiting processes.
Environ Sci Technol
25:134–142.
8. Schu¨th C, Grathwohl P. 1994. Nonequilibrium transport of PAHs:
A comparison of column and batch experiments.
Proceedings,
International Association for Hydraulic Research Symposium,
Zu¨rich, Switzerland, April 11–15, pp 143–148.
9. Ball WP. 1989. Equilibrium sorption and diffusion rate studies
with halogenated organic chemicals and sandy aquifer material.
PhD thesis. Stanford University, Palo Alto, CA, USA.
10. Harmon TC, Roberts PV. 1994. Comparison of intraparticle sorp-
tion and desorption rates for a halogenated alkene in a sandy
aquifer material.
Environ Sci Technol
28:1650–1660.
11. Pedit JA, Miller CT. 1994. Heterogeneous sorption processes in
subsurface systems. 1. Model formulations and applications.
En-
viron Sci Technol
28:2094–2104.
12. Barber LB, Thurman ME, Runnells DD. 1992. Geochemical het-
erogeneity in sand and gravel aquifer: Effect of sediment min-
eralogy and particle size on the sorption of chlorobenzenes.
J
Contam Hydrol
9:35–54.
13. Barber LB. 1994. Sorption of chlorobenzenes to Cape Cod aquifer
sediments.
Environ Sci Technol
28:890–897.
14. Weber WJ, McGinley PM, KatzLE. 1992. A distributed reactivity
model for sorption by soils and sediments. 1. Conceptual basis
and equilibrium assessments.
Environ Sci Technol
26:1955–1962.
15. Chen W, Wagenet RJ. 1995. Solute transport in porous media
with sorption-site heterogeneity.
Environ Sci Technol
29:2725–
2734.
16. Haggerty R, Gorelick SM. 1995. Multiple-rate mass transfer for
modeling diffusion and surface reactions in media withpore-scale
heterogeneity.
Water Resour Res
31:2383–2400.
17. Werth CJ, Cunningham JA, Roberts PV, Reinhard M. 1997. Ef-
fects of grain-scale mass transfer on the transport of volatile or-
ganics through sediments 2. Column results.
Water Resour Res
33:2727–2740.
18. Crittenden JC, Hutzler LM, Geyer DG, Oravitz JL, Friedman G.
1986. Transport of organic compounds with saturated ground-
water flow: Model development and parameter sensitivity.
Water
Resour Res
22:271–284.
19. Steinberg SM, Pigantello JJ, Sawhney BL. 1987. Persistence of
1,2-Dibromethane in soils: Entrapment in intraparticle micro-
pores.
Environ Sci Technol
21:1201–1208.
20. Crank J. 1975.
The Mathematics of Diffusion,
2nd ed. Cambridge
University Press, Oxford, UK.
21. Archie GE. 1942. The electrical resistivity log as an aid in de-
termining some reservoir characteristics. Transactions of the So-
ciety of Mining Engineers of American Institute of Mining, Met-
allurgical and Petroleum Engineers 146:54–61.
22. Engelhardt von W. 1960.
Der Porenraum der Sedimente,
2. Band.
Springer-Verlag, Berlin, Germany.
23. Grathwohl P. 1998.
Diffusion in Natural Porous Media: Con-
taminant Transport, Sorption/Desorption and Dissolution Ki-
netics.
Kluwer, Boston, MA, USA.
24. Wu S, Gschwend PM. 1986. Sorption kinetics of hydrophobic
organic compounds to natural sediments and soils.
Environ Sci
Technol
20:717–725.
25. Mathews AP, Zayas IJ. 1989. Particle size and shape effects on
adsorption rate parameters.
J Environ Eng.
115:41–55.
26. Ja¨ger R, Liedl R. 1999. Prognose der Sorptionskinetik organischer
Schadstoffe in heterogenem Aquifermaterial.
Grundwasser
(in
press).
27. Kleineidam S, Ru¨gner H, Grathwohl P. 1999. Organic matter
facies and equilibrium sorption of phenanthrene.
Environ Sci
Technol
(in press).
28. Ru¨gner H, Kleineidam S, Grathwohl P. 1999. Longterm sorption
kinetics of phenanthrene in aquifer materials.
EnvironSci Technol
(in press).
29. Schu¨th C. 1994. Sorptionskinetik und Transportverhalten von po-
lyzyklischen aromatischen Kohlenwasserstoffen (PAK) im
Grundwasser—Laborversuche. PhD thesis. University of Tu¨-
bingen, Germany.
