HydrologicalSciences-Journal-des
Sciences
Hydrologiques,
42(2)
April
1997
245
Nonequilibrium
transport and sorption of organic
chemicals
during aquifer remediation
CORS
VAN DEN BRINK
IWACO,
Consultants
for
Water
&
Environment,
PO Box
8064,
9702
KB
Groningen,
The Netherlands
WILLEM
J. ZAADNOORDIJK
[WACO,
Consultants
for
Water

pendant la restauration d'un aquifère
Résumé Les opérations de restauration d'aquifères interviennent souvent tardivement.
En général, la concentration élevée en éléments chimiques indésirables décroît
rapidement dès le début de l'opération, puis intervient une période pendant laquelle la
diminution de concentration est à peine observable. Parfois même, la concentration
augmente à nouveau après l'arrêt du traitement des eaux souterraines. Ce phénomène
est causé par un transport et une désorption retardés (tailing). Ce retard est lié au fait
que l'arrêt de l'opération ne signifie pas que l'équilibre est atteint pour le transport et la
désorption des éléments. Afin de prédire les effets de ce retard, IWACO a développé
le programme informatique de modélisation, SORWACO, qui décrit le comportement
des substances en solution le long d'un filet d'écoulement. Aussi bien les processus
pour lesquels l'équilibre est atteint rapidement que ceux pour lesquels il est atteint
lentement ont été pris en compte. Le programme a été vérifié par rapport aux courbes
de dégradation observées sur colonnes expérimentales et décrites dans la littérature.
Les paramètres du programme ont été calés en utilisant les données de plusieurs
expérimentations. Les valeurs des paramètres obtenues décrivent précisément le
transport pour différentes vitesses d'écoulement. Le fait que de bons résultats puissent
être obtenus sur un site spécifique même en l'absence d'un grand nombre de données
le concernant, fait que le programme est un outil fiable pour la conception des
opérations de restauration. Le programme est en particulier utile lorsque des modèles
tridimensionnels ou stochastiques détaillés ne peuvent être utilisés par manque de
données de base en quantité suffisante. Dans cet article, l'utilisation du programme est
Open for
discussion
until I
October 1997
246
Cors
van den Brink
& Willem

(e.g. bulk density, porosity, and organic carbon content of the soil).
The equilibrium of the pollutant between the groundwater and the solid phase of
the soil is described by a Freundlich isotherm. This nonlinear sorption isotherm does
not vary in time.
Sorption takes place at the so-called "sorption sites" of the soil. Two classes of
sorption sites are distinguished (Boesten, 1986; Brasseau, 1992b). The sorption sites
of class 1 are continuously in equilibrium. The class 2 sorption sites are not
continuously in equilibrium with the soil solution. The rate of (de)sorption at class 2
sites is driven by the shortage (or excess) of the sorbed amount relative to the
concentration in the soil liquid phase, which in turn depends on the properties of the
solute/soil combination and the velocity of the groundwater. When such a sorption
shortage or excess exists one talks about "sorption related nonequilibrium".
The soil liquid phase is divided into a fast and a slow moving portion to account
for the variations in velocity that occur in a porous medium. The exchange of
pollutant between these portions is driven by the concentration difference and is
Nonequilibrium transport
and
sorption
of
organic chemicals
during aquifer remediation 247
further determined by the extent of the slow and fast moving portions of the liquid
phase, the respective velocities, and the diffusivity. A "transport related
nonequilibrium" exists if the concentrations are not equal and there is exchange
between the portions of the liquid phase.
The program SORWACO takes both the transport and sorption related
nonequilibrium into account. It calculates the concentration of the pollutant in each
cell at every time step. The concentration in the water flowing out of the last cell is
the concentration of the water that enters the purification or discharge system.
It is possible to calculate the impact of intermittent groundwater recovery on both

(2)
248
Cors
van den Brink
& Willem
J.
Zaadnoordijk
J = QVC<D
%
} (3)
R,=
k,c (4)
in which c denotes the concentration in the soil liquid phase, 9 the volumetric
soilwater content [L
3
L"
3
], p the bulk density of the soil [M L/
3
], S the adsorbed
concentration [M M"
1
], v the average pore water velocity [L t"
1
], D the dispersion
coefficient and k, the decay rate.
Equations (1) to (4) do not suffice for the description of contaminant transport
which includes tailing. Two phenomena will be added to arrive at a set of equations
that is capable of simulating properly transport with tailing: transport related non-
equilibrium and sorption related nonequilibrium.

(5b)
where the subscripts / and s refer to fast moving and slow moving liquid regions
respectively, and J
Hs
is the exchange between the fast moving and slow moving
liquid phase:
Nonequilibrium transport and sorption of
organic chemicals
during aquifer
remediation
249
Jf^„=k
s
j(c
f
-C
s
) (6)
The mass transfer coefficient, k
sf
, in equation (6) determines the rate of exchange
between the two liquid regions. This rate is proportional to the difference in
concentration between the fast and slow moving portions of the soil liquid phase.
In the derivation of equations (5) and (6) no restrictions have been made on the
adsorption in both regions. Thus, the adsorption around the larger pores (fast moving
portion) can be different from that of the micropores (slow moving region) in
SORWACO, as is the case in reality.
Sorption related nonequilibrium
The equations presented so far do not describe the relationship between the adsorbed
concentration S and the solute concentration c. In the literature both equilibrium

and F
2
refer to the ratio between the class 1 and class 2 sorption sites. For
field application there is usually no information on the values of F, and F
2
. A value
of 0.7 is then used for F,. This value is based on measurements on adsorption
kinetics carried out by Boesten (1986). The parameter K
F
denotes the Freundlich
sorption coefficient [L
3/n
M"
1/n
] and n the Freundlich exponent. It is assumed that K
F
is the same for both the class 1 and class 2 sites because sufficient information on the
sorption is not available for field sites (Brusseau, 1992b). It may be concluded from
the experimental work of Boesten (1986) that the total amount of sorption sites
250
Cors
van den Brink
& Willem
J.
Zaadnoordijk
exceeds the amount measured in short term sorption experiments. The practical
consequence of these results is that the sum of the parameters F
x
and F
2

v
"
the equilibrium amount sorbed
at the class 2 sites corresponding to the current soil liquid concentration c
(equation (8)).
This approach, in which the sorption and transport related nonequilibrium are
described explicitly, is using almost the same theoretical framework as the two-
domain approach of Brusseau (1992b). A difference is the capability of SORWACO
to describe the sorption by a nonlinear sorption isotherm. In addition, the soil liquid
is divided into two regions with different flow velocities, instead of a mobile and an
immobile region. However, the main difference consists of concepts which facilitate
practical use:
- SORWACO describes the transport along a pathline in three-dimensional
groundwater flow (and not uniform flow);
- SORWACO uses the concentrations in the soil liquid phase as input, and
calculates the total mass which is usually not measured; and
- parameter values from the literature work well with SORWACO (except for
organic carbon content for which some measurements are usually available).
In practical cases, the first goal of a field investigation is to determine the extent
of the contamination. In an early stage of the investigation, not much effort is given
to the collection of data that are needed to predict the duration of the aquifer
remediation. In a later stage, when it has been decided to carry out a remediation,
additional data can be collected to establish better input data for SORWACO.
Moreover, as results of the remediation become available, they can be used to further
improve the SORWACO model.
IMPLEMENTATION IN THE PROGRAM SORWACO
Equations have been given in the previous sections for the fast and slow moving
region and the class 1 and class 2 sites separately. The way they are implemented in
the program SORWACO is illustrated in Fig. 1. The two soil liquid regions are
indicated by boxes as well as the solid phase. The sorptions by the class 1 and class 2

x
+ C
f
(12)
The amount in the slow moving soil liquid phase is equal to (equations (2) and (7)):
C, =
e,c.,
+
p(l-/)(S
u
+5
2
,,) (13)
where S
s
is the adsorbed concentration related to the slow moving region of the soil
(expressed per unit mass of soil assigned to this region) and / is the mass fraction of
the solid phase assigned to the fast moving region.
Since only class 1 sites are associated with the fast moving soil liquid phase, the
total amount in this phase is given by:
C,=Q
f
c
f
+
fpS
if
(14)
where S
f

water leaves the model with the concentration calculated for the final cell.
The equations are converted into an iterative finite difference algorithm. The
iterations are necessary since the amount sorbed by the class 1 sites depends
nonlinearly on the soil liquid concentration (equation (8)). Therefore this amount is
calculated by applying equations (8) and either (13) or (14) alternatively at the
beginning of each time step. At the end of each time step the values of the total
amounts, C
s
and C
f
, are calculated by means of equations (5a) and (5b).
COMPARISON WITH COLUMN EXPERIMENTS
Use of the program SORWACO was evaluated by comparing the laboratory results
of column experiments from the literature with the breakthrough curves calculated by
means of SORWACO. The impact of variations in pore water velocity on the
nonequilibrium sorption and transport of organic chemicals was investigated by
Brasseau et al . (1991) and Brusseau (1992a). In those studies, miscible displacement
experiments were carried out with different organic chemicals and aquifer media
having low organic carbon contents (0.02-0.39%). Four column experiments were
evaluated. The experiments analysed, with respect to the type of sorbent, chemical,
and (nonequilibrium) parameters, are listed in Table 1. The values of the parameters
F
l
and F
2
have been taken from Brusseau (1992a) initially and verified during the
calibration. The dispersion coefficient D has been assumed to be equal to zero.
The parameters for the Lula medium were calibrated using the breakthrough
curve for the low pore water velocity (5 cm h
1

0.27
0.27
0.21
0.21
(h
1
)
0.003
0.003
0.01
0.01
(h
1
)
0.70
0.70
0.07
0.07
/
0.5
0.5
0.7
0.7
*",
0.5
0.5
0.7
0.7
F
2

J*5
È
m
-4
f
J
i _
r
iH|Ljl
•t^fB==l
^=
=*F «" a»
4 5 f
Flux
Factor
10
Brusseau
[1992]
+ v=5
cm/hr
•
v=45
SORWACO
— v=5
cm/hr
v=45
Fig. 2 Measured (Brasseau, 1992) and calculated (SORWACO) breakthrough curves
for Lula medium.
0.6
o

v=86
Fig. 3 Measured (Brusseau, 1992) and calculated (SORWACO) breakthrough curves
for Eustis medium.
velocity breakthrough curve. The RMS of the residuals for the predicted values of the
high velocity experiment was 0.043.
For the Eustis medium, the parameters could not all be calibrated using only the
low velocity experiment. However, the combined calibration of both the low and the
high velocity experiment showed that they could be described with one single set of
SORWACO parameters. The RMS of the residuals was 0.039 for the low and 0.016
for the high velocity experiment respectively. The breakthrough curves are given in
Fig. 3.
254
Cors
van den Brink
& Willem
J.
Zaadnoordijk
The calibration resulted in higher values for k
dl
than for k
st
This implies that the
asymmetry of the breakthrough curves is mostly due to transport related non-
equilibrium at low pore water velocities and to sorption related nonequilibrium at
high velocities.
The leftward shift with higher velocity also indicates nonequilibrium (Brusseau,
1992a). As could be expected from the differences in flow velocity, the leftward shift
is greater for the Eustis medium than for Lula medium since the ratios of the high
and low velocities in both experiments are equal to 215 and 9 respectively. The
analysis of the column experiments shows that the operation of SORWACO is

fine sand
silty sand
and clay
-30 m
fine and
coarse sand
Fig. 5 Overview of the subsoil
The extent and degree of soil and groundwater contamination have been
investigated in several phases of drilling, sampling and analysing. From 1985 to
1990 a total of 100 boreholes were made with a hand auger ranging in depth from 2
to 5 m. In addition 10 soil borings were made with the cable tool percussion method,
ranging in depth from 12 to 50 m. A total of 117 soil samples and 360 groundwater
samples obtained from these borings were analysed. The concentration of benzene
was much higher than the concentration of the other contaminants that were not
removed together with the upper layer of the subsoil (mainly BTEX). Benzene has a
relatively high mobility and a low allowed concentration 0.2 u.g l"
1
(recently
increased to 1 ug l"
1
) in groundwater. Benzene is the only contaminant that has
migrated away from the area of the gas production site. Thus it remains the most
critical contaminant during the remediation and was selected as the contaminant to be
modelled.
-^7 surface level
" ~~ Tj groundwater table
at -1.8m
-14 m
-150 m below surface
256

with approximately 400 kg of volatile organic hydrocarbons and 4000 kg of mineral
oil.
Approximately 1000 kg of volatile aromatic hydrocarbons have leached into the
groundwater, resulting in contamination of 400 000 m
3
of groundwater. The plume
of contaminated groundwater reaches a depth of at least 50 m and is 250 m in length.
Application
The design of the remediation consists of 10 recovery wells (Fig. 7). The
groundwater flow pattern during the remediation was calculated with the program
AQ-AS (RIVM, 1991). Based on the groundwater flow pattern and the spreading of
benzene, the contaminant to be modelled, a representative pathline to the recovery
wells was selected, which is indicated in Fig. 7.
Nonequilibrium transport and sorption of organic chemicals during aquifer remediation 257
A/
C ho r
ocler ist ic paihline
Fig. 7 Location of the recovery wells used for the remediation.
Both the travel time of the groundwater and the concentration of benzene along
the pathline was used as input for SORWACO. The distance travelled and the travel
time determined the average velocity of the groundwater flow. The flow was divided
into a slow (40%) and a fast moving portion (60%), with velocities of 0.022 and 1.7
times the average velocity respectively. The mass transfer coefficient between the
slow moving and the fast moving liquid phases is mainly influenced by the diffusion
rate and distance. This is strongly dependent on the geological formation. From
Goltz & Roberts (1988) it could be derived that an estimate for this first-order mass
transfer coefficient, could be written as:
where D
0
is the liquid diffusion coefficient, X the tortuosity, b the characteristic length

) and the partitioning coefficient K
oc
. The organic
carbon content of the aquifer was analysed during the field and laboratory research.
The average mass fraction
(M
oc
)
was 0.07%. The most crucial parameter determining
the behaviour of the solute is the partition coefficient K
oc
(m
3
kg
4
). This coefficient
describes the affinity of solutes to organic carbon. The value of K
oc
was 87.1
1
kg
4
(
10
logK
oc
= 1.94, Montgomery & Welkom, 1990). This resulted in K
F
= 61 x 10"
6

da
I
„ 0.01 '
3
0 0.001
S
"c
S 0.0001
c
o
o
1
1E-05
C
0)
n
1
E-06| K+—
1E-07^
- 1 1 , ,
0 200 400 600 800 1000 1200
time (days)
| Measured in wells
| • well
1
-+- well 2
Fig. 8 Concentration development of the measured and predicted concentrations.
SORWACO
-**— calibrated —t— equilibrium
Nonequilibrhim

nonequilibrium
(k
d2
).
Based on the concentration development during the remediation and a
quantitative insight into the effects of nonequilibrium, a well motivated decision can
be made with respect to after-care and the remaining risks at the end of the aquifer
remediation operation. This can be seen from Fig. 9 which shows the current
recovery scheme continued for five years resulting in a benzene concentration of ca.
3.5 u.g l"
1
in the extracted groundwater. After this first period there are three
scenarios:
- continuation of current recovery;
10 month periods of recovery are alternated with a two month period without
recovery; and
- two month periods of recovery are alternated with a 10 month period without
recovery.
0.00013
S
1
E-05E
o 1E-06=
ç 1E-07
1E-08
6 7
time (years)
continuous
recovery
-« 10month recov. i 2month recov.

Is
U
a
oui
o
is
T)
c
cd
>,
w
<D
>
O
rec
ush
»H
o
a
ctor
<2
•a
<IJ
>
OUI
PH
nn
g
«3
c

O ON
^|- 00
ON ON
ON
OOC^t-^ONONONONON
(nr^^ooNONONONONONON
^-OOONONONONONONONON
ONONONONONONONONONON
^f m ~H o O O O
o-*—<
<N c-) m CN ci m m
—<(Nifi->j-in>dr-ododo6
r-
NO
t- » r~
O
ON
Tf 00
ON
ON ON
00(Nt^ONONONONON
mï^NOONONONONONONON
^TOOONONONONONONONON
ONONONONONONONONONON
•sf c<~>
T* o O O O
*-<cNmTi-iONCt ooON^
Ê-
•B
"S

Flush 3.1 2.6 0.5
factor
An evaluation of the removed fraction of the total benzene during the
remediation operation and per unit volume is shown in Fig. 10. The concentration
decrease during the remediation operation was maximal in the case of a continuous
recovery. However, the removed total fraction of benzene per unit volume
(expressed as flush-factor) shows a significant increase. This phenomenon has been
illustrated in more detail by the evaluation of Harvey et al . (1994). The changes of
the concentration after the remediation has ended differ for the three scenarios
(compare Table 2). This is illustrated by Table 4.
Table 4 Concentration increase during the first two years after the remediation for the three scenarios.
Concentration increase
Absolute
im r
1
)
Relative
Continuous
0.30
158%
recovery Alternating 10 months
recovery and 2 months
rest
0.32
145%
Alternating 2 months
recovery and 10 months
rest
0.69
25%

Ad
//' »'•'•
* 1
,1:7::,^
/
,.]
1400 1800 2200 2600
Time (days since start of operation)
3000
continuous
recovery
10month recov.
2month none
2month recov.
10month none
Fig. 10 Removed fraction of benzene for alternative recovery scenarios: (a) as function of flush
factor; and (b) as function of remediation time.
velocity of the soil liquid phase as this occurs towards the recovery wells during a
remediation. Both sorption and transport related nonequilibrium processes are imple-
mented.
Evaluation of column experiments has shown that the program is able to predict
the breakthrough curve well, after the nonequilibrium parameters have been fitted
using the results of a situation with quite different flow velocities. It was concluded
that the implementation of the nonequilibrium processes in the program is very useful
for the planning and evaluation of an aquifer remediation operation.
In the case study described, the prediction of the course of the remediation
operation (in 1991) has been sufficiently accurate for the planning of the duration of
the operation as well as for the scale of the purification plant. It has been indicated
Nonequilibrium transport and sorption of organic chemicals during aquifer remediation 263
that after the rather sharp concentration decrease over the first 400 days, the

Physico-Chemical
Models,
Elsevier, Amsterdam, The Netherlands.
Brusseau, M. L. (1992a) Nonequilibrium transport of organic chemicals: The impact of pore-water velocity. /. Contain.
Hydrol. 9, 353-368.
Brusseau, M. L. (1992b) Transport of rate-limited sorbing solutes in heterogeneous porous media: application of a one-
dimensional multifactor nonideality model to field data.
Wat.
Resour.
Res. 9, 2485-2497.
Brusseau, M. L., Jessup, R. E. & Rao, P. S. C. (1991) Nonequilibrium sorption of organic chemicals: Elucidation of
rate-limiting processes.
Environ.
Sci.
Technol.
25, 134-142.
Coats,
K. H. & Smith, B. D. (1964) Dead-end pore volume and dispersion in porous media. J. Soc. Petrol. Engng 4,
73-81.
Goltz, M. N. & Roberts, P. V. (1988) Simulations of physical solute transport models: Application to a large-scale field
experiment. J.
Contam.
Hydrol.
3(1),
37-63.
IWACO (1991) Initial estimates of concentrations at Sappemeer site. Draft report for NAM. IWÀCO, Groningen, The
Netherlands.
Koorevaar, P., Menelik, G. & Dirksen, C. (1983)
Elements
of

10, 159-177.
Ptacek, C. J. & Gilham, R. W. (1992) Laboratory and field measurements of nonequilibrium transport in the Borden
aquifer, Ontario, Canada. /.
Contam.
Hydrol. 10(2), 119-158.
Stagnitti, F., Parlange, J. Y., Steenhuis, T. S., Nijssen, B. & Lockington, D. (1993) Modelling the migration of water
soluble contaminants through preferred flow paths in the soil. In: Proc.
Groundwater Quality Management
Conf.
(Tallinn Estonia, September 1993), ed. by K. Kovar & J. Soveri. IAHS Publ. no. 220.
RIVM (1991) AQ-AS
Computer Program Package
for
Groundwater Pathlines
and
Isochrones,
Analytical Solutions.
AQUIfer SOFTware
Systems.
National Institute of Public Health and Environmental Protection (RIVM), Bilthoven,
The Netherlands.
van den Brink, C. (1987) Simulation of the leaching of atrazin to groundwater (in Dutch). MSc Thesis, Agricultural
264 Cors van den Brink & Willem J. Zaadnoordijk
University Wageningen, The Netherlands.
van Genuchten, M. Th. (1981) Nonequilibrium transport parameters from miscible displacement experiments. Report
no.
116,
US Dept
of
Agriculture,