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Journal of Contaminant Hydrology 78 (2005) 87–103
www.elsevier.com/locate/jconhyd
Numerical simulations of radon as an in situ
partitioning tracer for quantifying NAPL
contamination using push–pull tests
B.M. Davisa,*, J.D. Istokb,1, L. Semprinib,1
aChevronTexaco Energy Technology Co., PO Box 1627, 100 Chevron Way, Richmond, CA 94802, USAbDepartment of Civil, Construction and Environmental Engineering, Oregon State University,
Corvallis, OR 97331, USA
Received 6 October 2003; received in revised form 24 March 2005; accepted 31 March 2005
Abstract
Presented here is a reanalysis of results previously presented by Davis et al. (2002) [Davis, B.M.,
Istok, J.D., Semprini, L., 2002. Push–pull partitioning tracer tests using radon-222 to quantify non-
aqueous phase liquid contamination. J. Contam. Hydrol. 58, 129–146] of push–pull tests using radon
as a naturally occurring partitioning tracer for evaluating NAPL contamination. In a push–pull test
where radon-free water and bromide are injected, the presence of NAPL is manifested in greater
dispersion of the radon breakthrough curve (BTC) relative to the bromide BTC during the extraction
phase as a result of radon partitioning into the NAPL. Laboratory push–pull tests in a dense or
DNAPL-contaminated physical aquifer model (PAM) indicated that the previously used modeling
approach resulted in an overestimation of the DNAPL (trichloroethene) saturation (Sn). The
numerical simulations presented here investigated the influence of (1) initial radon concentrations,
which vary as a function of Sn, and (2) heterogeneity in Sn distribution within the radius of influence
of the push–pull test. The simulations showed that these factors influence radon BTCs and resulting
estimates of Sn. A revised method of interpreting radon BTCs is presented here, which takes into
account initial radon concentrations and uses non-normalized radon BTCs. This revised method
produces greater radon BTC sensitivity at small values of Sn and was used to re-analyze the results
from the PAM push–pull tests reported by Davis et al. The re-analysis resulted in a more accurate
0169-7722/$ -
doi:10.1016/j.
* Correspon
E-mail add
lewis.semprini1 Fax: +1 54
see front matter D 2005 Elsevier B.V. All rights reserved.
jconhyd.2005.03.003
ding author. Fax: +1 510 242 1380.
resses: bmda@chevrontexaco.com (B.M. Davis), jack.istok@orst.edu (J.D. Istok),
@orst.edu (L. Semprini).
1 737 3099.
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–10388
estimate of Sn (1.8%) compared with the previously estimated value (7.4%). The revised method was
then applied to results from a push–pull test conducted in a light or LNAPL-contaminated aquifer at
a field site, resulting in a more accurate estimate of Sn (4.1%) compared with a previously estimated
value (13.6%). The revised method improves upon the efficacy of the radon push–pull test to
estimate NAPL saturations. A limitation of the revised method is that dbackgroundT radon
concentrations from a non-contaminated well in the NAPL-contaminated aquifer are needed to
accurately estimate NAPL saturation. The method has potential as a means of monitoring the
progress of NAPL remediation.
D 2005 Elsevier B.V. All rights reserved.
Keywords: NAPL; Tracers; Partitioning; Single-well tests; Radon
1. Introduction
Partitioning interwell tracer tests have been used to quantify nonaqueous phase liquid
(NAPL) saturations in laboratory and field settings of saturated groundwater flow (Jin et
al., 1995; Nelson and Brusseau, 1996; Annable et al., 1998; Nelson et al., 1999; Young et
al., 1999). Recently, single-well dpush–pullT partitioning tracer tests have been used to
quantify NAPL saturations (Davis et al., 2002, 2003; Istok et al., 2002). In a push–pull
test, an injection solution containing partitioning and conservative tracers is injected
(dpushedT) into an aquifer through a well. The solution/groundwater mixture is then
extracted (dpulledT) from the same well. These tests have involved the use of both dex situT(i.e., injected) and din situT (i.e., naturally occurring radon) partitioning tracers. For the ex
situ tracer method, partitioning and conservative (e.g., bromide) tracers are injected into
the aquifer, while for the in situ tracer method, a radon-free injection solution (containing a
conservative bromide tracer) is injected into the aquifer. In both cases, the presence of
NAPL is indicated by a greater dispersion of the extraction phase breakthrough curve
(BTC) for the partitioning tracer relative to a conservative tracer (Schroth et al., 2000).
In situ radon that is generated by aquifer solids (t1/2=3.83 days) has been used as a
partitioning tracer for locating and quantifying dense or DNAPL saturation (Semprini et
al., 1993, 1998, 2000; Davis et al., 2002, 2003) and light or LNAPL saturation (Hunkeler
et al., 1997; Davis et al., 2002). The steady-state or dbackgroundT radon concentration in
groundwater (Cw,bkg) is a function of the radium content (CRa, mass/mass) and radon
emanation power (Ep, unitless) of the aquifer solids and the bulk density (qb) and porosity
(n) of the aquifer as described by (Semprini et al., 2000):
Cw;bkg ¼CRaEpqb
nð1Þ
Model equations for the equilibrium partitioning of radon and the secular equilibrium that
is achieved between radon emanation and decay are provided by Semprini et al. (2000)
and Davis et al. (2002). The models are based on linear partitioning, with the partition
coefficient (K) for radon defined as:
K ¼ Cn
Cw;nð2Þ
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–103 89
where Cn is the concentration of radon in the NAPL, and Cw,n is the concentration of
radon in the aqueous phase in the presence of NAPL. Partition coefficients may be
determined using the methodology of Cantaloub (2001) and range from 37 (o-xylene) to
50 (trichloroethene, or TCE) to 61 (cyclohexane). As groundwater flows through a NAPL-
contaminated zone of an aquifer, radon in NAPL will obtain a concentration in equilibrium
with radon in groundwater. Because radon is continually being generated by aquifer solids
and is continually decaying, and because groundwater flow is typically slow, a closed-
system equilibrium equation (Eq. (3)) describes radon concentrations in water and NAPL.
Model simulations by Semprini et al. (2000) show that if transport through the NAPL-
contaminated zone is long enough for equilibrium to be achieved, radon concentrations
can be described by Eq. (3):
CnSn þ Cw;nSw ¼ Cw;bkg ð3Þ
Based on linear radon partitioning between NAPL and water (Eq. (2)), radon concentration
in the water phase is given by a rearranged Eq. (3):
Cw;n ¼Cw;bkg
1þ Sn K � 1ð Þ ð4Þ
where Cw,n is a non-linear function of Sn and K. This non-linear relationship is shown in
Fig. 1, using a K =50. Eq. (4) can be further rearranged to solve for the NAPL saturation in
an aquifer as a function of Cw,bkg, Cw,n, and K:
Sn ¼Cw;bkg
Cw;n� 1
�1
K � 1ð Þ
���ð5Þ
Note that Eq. (5) does not require estimation of radon retardation (R) via a push–pull test
in order to calculate Sn. However, radon retardation during transport can be used to
Sn (%)
0 5 10 15 20
Cw
,n (
pC
i/L)
0
50
100
150
200
Fig. 1. Aqueous phase radon concentrations (Cw,n) as a function of NAPL saturation, plotted using Eq. (3) with a
background radon concentration (Cw,bkg)=200 pCi/l and K =50.
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–10390
determine NAPL saturation. The retardation factor for a partitioning tracer is given by
(Dwarakanath et al., 1999):
R ¼ 1þ KSn
Swð6Þ
If K is known and R is estimated using a push–pull test, Sn can be determined using:
Sn ¼R� 1
Rþ K � 1ð7Þ
Push–pull tests using radon as a partitioning tracer were performed in laboratory
physical aquifer models (PAMs) containing TCE (Davis et al., 2002). Experimental
conservative (bromide) tracer and radon extraction phase BTCs were fitted to an
approximate analytical solution to estimate R, which was then used to calculate Sn.
This approach resulted in an overestimation of Sn compared to the NAPL saturation
emplaced in the PAM. Furthermore, the numerical modeling in Davis et al. (2002)
assumed that radon behaved similarly to an injected tracer. Although these
simulations accounted for radon partitioning between the NAPL and aqueous phases
during the push–pull test, they did not account for steady-state radon partitioning
into NAPL prior to the test. The pre-test radon concentrations are in fact reduced in
the presence of NAPL, with the steady-state radon concentration being a non-linear
function of Sn (Eq. (4)). Also, the model construct did not agree with the actual
conditions in the PAM. For example, the model assumed that NAPL was distributed
throughout the PAM sediment, while in the laboratory push–pull tests, the NAPL-
contaminated zone existed in only part of the PAM’s sediment. The heterogeneous NAPL
distribution will affect initial radon concentrations and partitioning behavior during the
push–pull test. As will be shown, this heterogeneous distribution can affect estimations of
R and Sn.
The goal of this study was to examine two factors that can influence the interpretation
of push–pull tests for estimating Sn: (1) the influence of NAPL on initial (i.e., pre-
injection) phase radon concentrations, and (2) heterogeneous NAPL saturation distribu-
tions. A revised method of interpreting radon BTCs is presented, which results in more
accurate estimates of Sn and in an increase in sensitivity of the estimation method at small
values of Sn. This method was then used to re-estimate values of Sn in previously
conducted laboratory and field push–pull tests.
2. Methods
Simulations were performed with the STOMP code (White and Oostrom, 2000), a fully
implicit volume-integrated finite difference simulator for modeling one-, two-, and three-
dimensional groundwater flow and transport. The simulator models the advective/
dispersive equation, with linear equilibrium partitioning. STOMP has been extensively
tested and validated against analytical solutions and other numerical codes (Nichols et al.,
1997). Simulations were based on a hypothetical push–pull test conducted in a 5 cm
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–103 91
diameter well over a 91.4 cm long screened interval of an aquifer. The model aquifer is
based on an aquifer composed of sediment from the Hanford Formation, an alluvial
deposit of sands and gravels of mixed basaltic and granitic origin (Lindsey and Jaeger,
1993) previously used in laboratory push–pull tests. Solid density (qs)=2.9 g/cm3,
porosity (n)=0.35, calculated bulk density (qb)=1.89 g/cm3, and longitudinal dispersivity
(aL)=4.0 cm were used in all the simulations. Simulations incorporated an injection
volume of 250 l and an extraction volume ranging from 500 to 2000 l. Injection and
extraction pumping rates were constant at 1 l/min with no rest period between the injection
and extraction phases. The computational domain consisted of a line of 500 nodes with a
uniform radial node spacing of Dr =1.0 cm. The model geometry and injection volumes
resulted in the injection solution traveling 48 cm from the well, as measured by the travel
distance to half the solution injection concentration of the conservative tracer (C/C0=0.5).
Simulations were performed using time-varying third-type flux boundary conditions to
represent pumping at the well, with a constant hydraulic head. Constant head and
zero solute flux boundary conditions were used to represent aquifer conditions at
r =500 cm.
Specified NAPL saturations were modeled using TCE with a value of K =50 for radon
(Davis et al., 2003). To simplify the modeling procedure, NAPL saturations (Sn) were
incorporated into the model using solid:aqueous phase partition coefficients, which
enabled the model to mimic radon partitioning into NAPL as radon partitioning into
aquifer solids. These two partitioning processes are similar for radon. First, Eq. (6) was
used to determine a retardation factor (R) for a given ratio of Sn to water saturation (Sw).
Second, this calculated R value, the sediment porosity, and the bulk density were used to
determine a solid:aqueous phase partition coefficient (Kd):
Kd ¼ R� 1ð Þ n
qb
��ð8Þ
Simulations were performed with specified Sn values from 0% to 15.25%, which
corresponds to retardation factors (R) ranging from 1 to 10, respectively. The effects of
initial radon concentrations and Sn heterogeneity on simulation results were investigated
with three sets of simulations, with NAPL extending homogeneously from (1) r =500
cm, (2) r =48 cm (corresponding to the maximum travel radius of a conservatively
transported tracer, as defined by C/C0=0.5), and (3) r =24 cm (corresponding to half the
maximum travel radius of a conservatively transported tracer), where r is the radial
distance from the injection/extraction well. An initial radon concentration of 200 pCi/
l (corresponding to Sn=0%) was emplaced at r N48 cm for the second set of simulations
and at r N24 cm for the third set of simulations. Each simulation utilized (1) an injection
radon concentration of 0 pCi/l, which corresponds to the true radon injection
concentration in laboratory and field push–pull tests, and (2) an initial radon
concentration in the model that varied in space as a function of Sn. The simulations
involving the PAM and field tests are described below. All simulations and PAM and
field push–pull tests were performed over time periods such that the effects of radon
emanation and decay on radon concentrations could be neglected (i.e., Ve/Vi =2 was
obtained in V12.5 h, where Vi is the volume of solution injected and Ve is the volume of
solution extracted at a given time).
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–10392
3. Results and discussion
3.1. Injection phase results
Fig. 2 shows radon concentration spatial profiles at the end of the injection phase of a
simulated push–pull test (corresponding to Ve /Vi =0) for Sn values of 0–4% and for
different distributions of NAPL. When Sn=0%, the radon-free injection solution is
transported to r =48 cm, as measured by half the initial radon concentration (C/C0=0.5) at
the injection well (i.e., one manner in which to measure transport distance). In contrast,
when Snp 0% over a specified portion of the model domain, radon is retarded. When
Sn=4% for rV500 cm (i.e., a homogeneous NAPL distribution) and the initial radon
concentration in the model is 68 pCi/l (Eq. (4)), the radon-free injection solution is
transported only to r =26 cm, as measured by half the initial radon concentration at the
injection well, due to retardation resulting from radon partitioning into the NAPL during
transport. When Sn=4% for rV48 cm and Sn=0% for r N48 cm (i.e., a heterogeneous
NAPL distribution), the injection solution is again transported only to r =26 cm. A two-
step radon concentration profile results from this heterogeneous NAPL distribution. When
Sn=4% for rV24 cm and Sn=0% for r N24 cm, the radon-free injection solution is
retarded as indicated by the profile, but the concentration increases rapidly as the radial
distance increases. Thus, when the portion of the model domain containing NAPL
decreases, the profiles tend towards the zero saturation case. Radon concentration profiles
are influenced by both radon partitioning between the aqueous phase and NAPL prior to
the push–pull test, and radon partitioning between the injection solution and NAPL during
the test. Heterogeneity in NAPL distribution affects radon concentration profiles due to the
partitioning processes and mixing of water with different initial radon concentrations
during the test.
0 20 40 60 80 1000
50
100
150
200Sn=4% to 500cm
Sn=4% to 48cm
Sn=4% to 24cm
Sn=0% to 500cm
radial distance (cm)
Cw
,n (
pC
i/L)
Fig. 2. Simulated radon concentration profiles (Cw,n) at the end of the injection phase of push–pull tests with no
NAPL (Sn=0% to 500 cm); heterogeneous NAPL saturation (Sn=4% to 48 cm) and (Sn=4% to 24 cm); and
homogeneous NAPL saturation (Sn=4% to 500 cm).
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–103 93
3.2. Extraction results—concentration profiles
3.2.1. Radon concentration profiles for different degrees of fluid extraction
Simulated radon concentration profiles as a function of the volume of groundwater
extracted are presented in Fig. 3. Note that the volume of injection solution/groundwater
extracted (Ve) is divided by the total volume of injection solution injected (at the end of the
injection phase, Vi) to calculate dimensionless time (Ve/Vi) during the extraction phase. For
the case of Sn=4% for rV500 cm (i.e., a homogeneous NAPL distribution), radon
concentrations increase with time as the injection solution/groundwater mixture is
extracted from the well (Fig. 3a). The initial radon equilibrium concentration was 68
pCi/l for rV500 cm (Eq. (4)). The radon concentration at the well (r =0 cm) is 63% of the
initial radon concentration at Ve/Vi =1, 89% at Ve/Vi =2, and 96% at Ve/Vi =3. Thus, as
extraction proceeds, radon concentrations approach but do not exceed the initial radon
concentration.
Profiles for a heterogeneous NAPL distribution when Sn=4% for rV48 cm and Sn =
0% for r N48 cm are shown in Fig. 3b. The initial equilibrium radon concentration was 68
pCi/l for rV48 cm and 200 pCi/l for r N48 cm (shown with a step-function concentration
change for simplicity). The radon concentration measured at the well (r =0 cm) is 63% of
the initial radon concentration at Ve /Vi =1, 103% at 2, and 153% at 3, and increases to
291% at 8. As the extraction proceeds, radon concentrations at the well exceed the initial
radon concentration due to the influx of water with a radon concentration of 200 pCi/l.
Such a response in push–pull tests might be utilized in identifying heterogeneous NAPL
distributions.
Fig. 3c shows the profiles that result from the heterogeneous distribution when Sn=4%
for rV24 cm and Sn=0% for r N24 cm. Radon concentrations increase more quickly
with time as the injection solution/groundwater mixture is extracted from the well
compared to the previous simulation. Radon concentrations at the well exceed the
initial radon concentration at the well after just Ve/Vi =1 due to the influx of water
with a radon concentration of 200 pCi/l. Thus, as NAPL is concentrated closer to
the well, radon concentrations more rapidly exceed initial values at the well as the
extraction phase proceeds. Conversely, if NAPL saturations are distributed farther
from the well, radon concentrations would possibly not approach initial values at the
well.
3.3. Extraction phase results—breakthrough curves
Usually the only radon concentration data available at field sites are obtained from the
well in which the push–pull test is conducted. To investigate radon BTC behavior, a set of
six simulations was performed for each of the homogeneous and heterogeneous NAPL
distributions. Simulations performed for the homogeneous NAPL distribution are
presented in Fig. 4a, while those for the heterogeneous NAPL distributions are presented
in Fig. 4b and c. Each simulation represented a different value of Sn. For homogeneous
NAPL distributions (Fig. 4a), as the extraction phase approaches Ve /Vi =2, radon
concentrations approach but do not exceed their initial value at the well. Radon
concentrations approach initial values at the well more slowly as Sn increases due to the
initial conditionsVe/Vi = 0
Ve/Vi = 1
Ve/Vi = 2
Ve/Vi = 4
0 20 40 60 80 100
0 20 40 60 80 100
0 20 40 60 80 100
initialVe/Vi = 0
Ve/Vi = 1
Ve/Vi = 2
Ve/Vi = 4
Ve/Vi = 6
Ve/Vi = 8
initialVe/Vi = 0
Ve/Vi = 1
Ve/Vi = 2
Ve/Vi = 4
Ve/Vi = 6
Ve/Vi = 8
0
50
100
150
200
0
50
100
150
200
0
50
100
150
200
Cw
,n (
pC
i/L)
Cw
,n (
pC
i/L)
(b)
(a)
(c)
radial distance (cm)
radial distance (cm)
radial distance (cm)
Cw
,n (
pC
i/L)
Fig. 3. Simulated radon concentration profiles (Cw,n) during the extraction phase of a push–pull test. (a) Sn=4%
for r V500 cm; (b) Sn=4% for rV48 cm; Sn=0% for r N48 cm; (c) Sn=4% for r V24 cm; Sn=0% for r N24 cm.
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–10394
0.0 0.5 1.0 1.5 2.0
0.0 0.5 1.0 1.5 2.0
Cw
,n (
pC
i/L)
Cw
,n (
pC
i/L)
(a)
(b)
(c)
0
50
100
150
200
0
50
100
150
200
0
50
100
150
200
0.0 0.5 1.0 1.5 2.0
Sn=0%,R=1
Sn=1.96%,R=2
Sn=5.66%,R=4
Sn=9.09%,R=6
Sn=12.28%,R=8
Sn=15.25%,R=10
Sn=0%,R=1
Sn=1.96%,R=2
Sn=5.66%,R=4
Sn=9.09%,R=6
Sn=12.28%,R=8
Sn=15.25%,R=10
Sn=0%,R=1
Sn=1.96%,R=2
Sn=5.66%,R=4
Sn=9.09%,R=6
Sn=12.28%,R=8
Sn=15.25%,R=10
Ve/Vi
Ve/Vi
Ve/Vi
Cw
,n (
pC
i/L)
Fig. 4. Simulated radon breakthrough curves during the extraction phases of six push–pull tests. (a) Sn=0–
15.25% for r V500 cm; (b) Sn=0–15.25% for rV48 cm; Sn=0% for r N48 cm; (c) Sn=0–15.25% for r V24 cm;
Sn=0% for r N24 cm.
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–103 95
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–10396
increase in dispersion of the radon BTC (Schroth et al., 2000). Radon BTCs show the
greatest sensitivity at small values of Sn, which is due to the non-linear relationship
between Sn and the initial radon concentration.
The simulations performed for a heterogeneous NAPL distribution (Sn for rV48 cm
and Sn=0% for r N48 cm) are presented in Fig. 4b. As the extraction phase approaches Ve /
Vi =2, radon concentrations approach their initial value at the well. Radon concentrations
would increase beyond the initial radon concentration for SnN0% if Ve /Vi progressed
beyond 2. However, the shapes of the radon BTCs are similar at early times for the two
sets of simulations (Fig. 4a and b), since conditions close to the well dominate the
response.
The third set of six simulations performed with the heterogeneous NAPL distribution
(Sn for rV24 cm and Sn =0% for r N24 cm) are presented in Fig. 4c. As the extraction
phase reaches Ve /Vi =2, radon concentrations approach and exceed their initial value at
the well to a greater degree than when NAPL extended to 48 cm. These percentages vary
as a function of Sn, reaching 165% of the initial value at the well for Sn=1.96%, 239% for
Sn=5.66%, and 189% for Sn=15.25%. The presence of Sn=0% for r N24 cm produces
greater radon concentrations for each simulation as compared to the prior simulations.
Radon concentrations would continue to increase beyond the initial radon concentration
for SnN0% if Ve/Vi progressed beyond 2. The Sn=0% at r N24 cm results in greater slopes
for radon BTCs compared to the previous simulations (Fig. 4a and b). The shape of the
radon BTCs, especially at late time, can be potentially used to investigate heterogeneity in
NAPL distribution.
3.4. Extraction phase results—normalized breakthrough curves
Fig. 5 presents the extraction phase normalized BTCs for the results presented in Fig. 4.
Radon concentrations are normalized to the initial concentrations at the well prior to the
injection phase. For the homogenous NAPL distribution, the normalized concentration
does not exceed 1 at Ve/Vi =2 (Fig. 5a). The effect of increasing dispersion as Sn increases
is apparent (Schroth et al., 2000). A drawback to normalizing to the initial radon
concentration is the decrease in sensitivity of the radon BTCs to small values of Sncompared to the non-normalized method (Fig. 4a). This drawback is a concern when
fitting experimental radon BTCs to simulated BTCs in order to determine a best-fit value
of R in order to estimate Sn.
The normalized BTC for the heterogeneous NAPL distribution where Sn=0% for r N48
cm deviates from the homogenous cases as the extraction volume increases (Fig. 5b). The
deviation becomes even more pronounced when normalized radon BTCs deviate from
those for the heterogeneous NAPL distribution Sn=0% for rN24 cm (Fig. 5c). Thus, the
interpretation of normalized radon BTCs becomes more difficult as heterogeneity in Snincreases.
Fig. 5. Simulated radon breakthrough curves during the extraction phases of six push–pull tests. Radon
concentrations are normalized to the initial radon concentrations at the well for each value of Sn. (a) Sn=0–15.25%
for r V500 cm; (b) Sn=0–15.25% for rV48 cm; Sn=0% for r N48 cm); (c) Sn=0 –15.25% for rV24 cm; Sn=0%
for r N24 cm.
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.0 1.5 2.0
0.0 0.5 1.0 1.5 2.0
0.0 0.5 1.0 1.5 2.0
0.0
0.2
0.4
0.6
0.8
1.0
Sn=0%,R=1
Sn=1.96%,R=2
Sn=5.66%,R=4
Sn=9.09%,R=6
Sn=12.28%,R=8
Sn=15.25%,R=10
Sn=0%,R=1
Sn=1.96%,R=2
Sn=5.66%,R=4
Sn=9.09%,R=6
Sn=12.28%,R=8
Sn=15.25%,R=10
Sn=0%,R=1
Sn=1.96%,R=2
Sn=5.66%,R=4
Sn=9.09%,R=6
Sn=12.28%,R=8
Sn=15.25%,R=10
Ve/Vi
Ve/Vi
Ve/Vi
(c)
(b)
(a)
No
rmal
ized
Cw
,nN
orm
aliz
ed C
w,n
No
rmal
ized
Cw
,n
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–103 97
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–10398
3.5. Revised method for radon BTC interpretation
The use of non-normalized radon BTCs to estimate Sn provides two advantages over
normalized radon BTCs in that (1) the sensitivity of non-normalized radon BTCs to small
values of Sn can be utilized, and (2) the effect of heterogeneity in Sn on the shape of radon
BTCs can be lessened. The revised method for estimating Sn utilizing non-normalized
radon BTCs requires obtaining a dbackgroundT radon concentration (Cw,bkg) from a non-
contaminated portion of the contaminated aquifer. Using this sample as a dbackgroundTconcentration assumes homogeneity in porosity and radon emanation between the non-
contaminated location chosen for the dbackgroundT radon sample and the location with
suspected NAPL contamination where the push–pull test is conducted. To use this revised
method extraction phase, radon and bromide results are plotted in concentration units (pCi/
l for Rn and mg/l for Br�) as a function of Ve /Vi. The y-axis of the plot shows radon
concentrations ranging from 0 at the origin to a maximum value equal to the dbackgroundTconcentration. Bromide concentrations are plotted on a secondary y-axis with concentra-
tions ranging from the injection solution concentration to 0 mg/l, the injection solution
concentration at the origin, and 0 mg/l at the maximum or dbackgroundT radon
concentration. This inverts the bromide concentrations and causes the radon and bromide
BTCs to overlap. Numerical simulations are then performed to best-fit (using a least
squares procedure) the experimental bromide BTC to a non-retarded simulated BTC (i.e.,
with R =1) by varying the sediment dispersivity (aL). The best-fit aL value is then used in
subsequent simulations to best-fit (using a least squares procedure) the experimental radon
BTC to a simulated BTC corresponding to a particular value of R. For each simulated
BTC, Eq. (4) is used to input the initial radon concentration in the model as a function of
Sn and K. The initial radon concentration can be inputted into the model as a homogeneous
or heterogeneous distribution. Eq. (7) is then used to calculate the value of Sn that
corresponds to the best-fit R value.
3.6. PAM push–pull tests re-analysis
The revised method was applied to existing radon and bromide extraction phase data
from push–pull tests performed in wedge-shaped physical aquifer models (PAMs) by
Davis et al. (2002). These push–pull tests were performed in clean sediment (Test 1) and
TCE-contaminated sediment (Test 2), with the contaminated zone (Sn~2%) of Test 2
extending 74 cm from the narrow end of the PAM, beyond which Sn=0%. The tests were
originally modeled by Davis et al. (2002) using normalized BTCs without the
incorporation of initial radon concentrations in the model domain and the lack of NAPL
saturation after 74 cm. This resulted in overestimates of R and the likely Sn in the PAM
(Table 1).
Test 1 was modeled using the revised method, with an average initial radon
concentration of 198 pCi/l (measured in four sampling ports in this PAM before the
test). The bromide data are well fitted by a simulated R =1 BTC, with a best-fit aL=1.9cm, and the radon data were fitted by a simulated R =1.3 BTC (Fig. 6). Both the bromide
and the radon simulations underestimate results during the early stages of extraction. This
likely results from mixing processes not accounted for in the model. The radon retardation
Table 1
Radon retardation factors (R), adjusted retardation factors for the effect of trapped gas (in italics), best-fit
dispersivities (aL), and calculated TCE saturations (Sn) from push–pull tests
From Davis et al. (2002)
(aL best-fit using approximate solution)
Using revised method
(aL best-fit using STOMP)
R aL (cm) Sn (%) R aL (cm) Sn (%)
Test 1, no TCE 1.1 3.2 – 1.3 1.9 –
Test 2, with TCE 5.1/5.0 4.0 7.4 2.2/1.9 3.7 1.8
Results from Davis et al. (2002) are shown on the left, while results using the revised method are shown on the
right. A value of K =50 was used to calculate Sn in the presence of TCE.
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–103 99
in Test 1 is attributed to partitioning of radon between the trapped gas and aqueous phases,
in analogy to what has been described for O2 by Fry et al. (1995):
R ¼ 1þ HccSg
Swð9Þ
where Hcc is radon’s dimensionless Henry’s coefficient and Sg is the trapped gas
saturation. Radon would show a BTC with R =1, if (H cc(Sg/Sw))=0. Using Eq. (9),
Hcc=3.9 (Clever, 1979), and R =1.3, the estimated Sg =7.1%. These values are similar to
those from Davis et al. (2002) (Table 1), who reported a best-fit aL =3.2 cm, R =1.1, and
estimated Sg ranging up to 9.3%. The best-fit R =1.3 also compares favorably to the
retardation factors measured in sampling ports 1 and 2 (located 15 and 30 cm from the
narrow end of the PAM) during the injection phase of Test 1, which ranged from 1.0 to 1.4
(Davis et al., 2002). Similar values of trapped gas saturation were reported by Fry et al.
(1995) for the same sediment material.
Test 2 was also modeled using the revised method, with an average initial radon
concentration of 262 pCi/l (measured in four sampling ports in this PAM prior to TCE
contamination). A simulation was performed in which TCE contamination extended to 74
cm, with uncontaminated sediment at N74 cm. TCE was emplaced in the PAM (as
0.0 0.5 1.0 1.5 2.0
0
20
40
60
80
100
Br- (
mg
/L)
Rn
(p
Ci/L
)
Ve/Vi
Br-
R=1RnR=1.3
0
50
100
150
200
Fig. 6. Radon (pCi/l) and bromide (mg/l) experimental and simulated (R =1 and R =1.3) breakthrough curves
during the extraction phase of a push–pull test performed in a non-contaminated physical aquifer model (Test 1).
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–103100
described in Davis et al., 2002); then, Test 2 was performed after a 3-week static period
allowed radon concentrations to reach N95% of their secular equilibrium value as a result
of concurrent radon emanation from sediment and decay. The bromide data are well fitted
by a simulated R =1 BTC and aL=3.7 cm, and the radon data are fitted by a simulated
R =2.2 BTC (Fig. 7). The radon retardation in Test 2 is attributed to partitioning of radon
between (1) the trapped gas and aqueous phases, and (2) the NAPL and aqueous phases.
The portion of radon retardation due to TCE partitioning was determined by adjusting R to
account for trapped gas partitioning using (Davis et al., 2002):
Radj ¼ RTest 2 � RTest 1 � 1:0ð Þ ð10Þ
where Radj is the adjusted retardation factor, RTest 2 is the retardation factor from Test 2,
and RTest 1 is the retardation factor from Test 1. Using Eq. (10), an adjusted R value of 1.9
is calculated, which results in an estimated Sn=1.8% (Table 1). The fitted aL =3.7 cm
compares favorably with the value of aL=4.0 cm from Davis et al. (2002). Moreover, the
estimated Sn=1.8% compares more favorably with the actual TCE saturation emplaced in
the sediment pack (~2%) than the estimated Sn=7.4% from Davis et al. (2002) (using
K =50). The adjusted R =1.9 compares favorably with the adjusted retardation factors
measured in sampling ports 1 and 2 during the injection phase of Test 2, which ranged
from 1.1 to 1.5 (Davis et al., 2002). Thus, the revised method results in better agreement of
extraction and injection phase estimated R values and subsequent estimations of Sn. The
new estimate of Sn=1.8% is also in agreement with Sn values ranging from 0.7% to 1.6%
from partitioning alcohol push–pull tests performed in this PAM (Istok et al., 2002).
3.7. Field push–pull test application
The revised method was also applied to radon and bromide BTCs from a field test
performed at a former petroleum refinery in the Ohio River valley. As described in Davis
0.0 0.5 1.0 1.5 2.00
Br-
R=1RnR=2.2
0
20
40
60
80
10050
100
150
200
Br- (
mg
/L)
Rn
(p
Ci/L
)
Ve/Vi
Fig. 7. Radon (pCi/l) and bromide (mg/l) experimental and simulated (R =1 and R =2.2) breakthrough curves
during the extraction phase of a push–pull test performed in a TCE-contaminated physical aquifer model (Test 2).
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–103 101
et al. (2002) and Istok et al. (2002), the site consists of glacial outwash deposits that are
contaminated with a mixture of petroleum light or LNAPLs including gasoline, heating
oil, and jet and aviation fuel. Radon samples from a non-contaminated well showed a
maximum concentration of 790 pCi/l. This value was used as the dbackgroundTconcentration for radon. A push–pull test was performed in a contaminated well in which
LNAPL has been detected. Radon concentrations increased and bromide concentrations
decreased smoothly as the test solution/groundwater mixture was extracted from the
aquifer, with the radon BTC being retarded relative to the bromide BTC (Fig. 8).
Numerical simulations were performed for this test, with LNAPL assuming to extend far
beyond the radius of influence of the test. The simulation results fit the bromide BTC to a
simulated R =1 BTC using a best-fit aL=11 cm. This value is less than the value of
aL=20.3 cm from the approximate analytical solution used to fit the normalized bromide
BTC by Davis et al. (2002), where the BTC was adjusted to intersect a normalized
concentration of 0.5 at Ve /Vi =1. Using the revised method and aL=11 cm, the radon BTC
was fit using a simulated R =2.7 BTC. Using the R =2.7, a value of Sn=4.1% was
calculated using Eq. (7) and a value of K =40 for radon in the presence of diesel fuel, as
reported by Hunkeler et al. (1997). Davis et al. (2002) determined an R =7.3 using the
approximate analytical solution to the normalized radon BTC. That R value results in
Sn=13.6%, which is likely an overestimation of LNAPL saturation. Istok et al. (2002)
reported Sn values of V4.0% in this aquifer using partitioning alcohol tracers. The
relatively poor fits of the simulated BTCs to the experimental BTCs likely are a result of
heterogeneities in hydraulic conductivity and porosity in the aquifer and potential impacts
of groundwater flow. In addition, the use of a K value for radon in the presence of diesel
fuel adds uncertainty to the value of Sn=4.1%, since the actual LNAPL composition at the
site is a mixture of LNAPLs. However, the method does provide a more accurate method
to estimate the LNAPL saturation in the vicinity of the well compared to the results of
Davis et al. (2002). Furthermore, a series of similar push–pull tests could be conducted in
this well over time to track the efficacy of remediation and source zone removal.
0.0 0.5 1.0 1.5 2.0
Br-
R=1RnR=2.7
0
20
40
60
80
100 0
200
400
600
800
Ve/Vi
Rn
(p
Ci/L
)
Br- (
mg
/L)
Fig. 8. Radon (pCi/l) and bromide (mg/l) experimental and simulated (R =1 and R =2.7) breakthrough curves
during the extraction phase of a push–pull test performed in a LNAPL-contaminated aquifer.
B.M. Davis et al. / Journal of Contaminant Hydrology 78 (2005) 87–103102
4. Conclusions
The revised method enhances the ability of the radon push–pull test to provide
estimates for Sn at NAPL-contaminated sites. The effect of heterogeneity in Sn on radon
BTCs is lessened, and a greater sensitivity to smaller values of Sn is realized. Also, the
revised method more accurately represents the true condition of in situ radon partitioning
both prior to and during the push–pull test. The method shows promise in providing
estimates for Sn and showing changes in Sn over time as, for example, source zone
remediation is effected. However, the revised method is potentially constrained by the
need to obtain a dbackgroundT radon sample from a non-contaminated well in the
contaminated aquifer. Geologic properties with respect to radon emanation and porosity
must be similar between the contaminated and non-contaminated wells. This may or may
not be the case at a field site. The collection of radon samples from additional non-
contaminated wells emplaced in the NAPL-contaminated aquifer could provide a range of
dbackgroundT values, which could be used in conjunction with the revised method to
provide a range of estimated values of Sn. The simulations presented represent conditions
where radon emanation and decay are not important. Future modeling efforts should
consider including these terms for conditions where they may be important. Also, it should
be noted that estimated values of Sn represent a volume-averaged value, and may or may
not be representative of the true value of Sn at a given location within the radius of
influence of the push–pull test. These uncertainties highlight our view that push–pull test
results provide an estimate of NAPL saturation in the immediate vicinity of the well in
which the test was conducted.
Acknowledgements
This work was funded by the U.S. Department of Defense Environmental Security
Technology Certification Program (project no. 199916) and the U.S. Department of
Energy Environmental Management Science Program (project no. 60158). We also thank
Jennifer Field, Ralph Reed, Jason Lee, Mike Cantaloub, and Melora Park for help with
laboratory methods and activities; Mark Lyverse and Jesse Jones for help with field
activities; Martin Schroth and Mark White for help with STOMP; and Dr. Eduard Hoehn,
Dr. E.O. Frind, and an anonymous reviewer for their helpful comments and suggestions.
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Recommended