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Push-pull tests for estimating effective porosity: expanded analytical solution and in situ application

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The analytical solution to describe the one-dimensional displacement of the center of mass of a tracer during an injection, drift, and extraction test (push-pull test) was expanded to account for displacement during the injection phase to improve the in situ estimation of effective porosity. The truncated equation, which assumes displacement during the injection phase is negligible, may theoretically lead to an underestimation of the true value of effective porosity. In order to experimentally compare the expanded and truncated equations, single-well push-pull tests were conducted among six test wells within a shallow and unconfined aquifer comprised of unconsolidated and heterogeneous silty and clayey fill materials. The push-pull tests were conducted by injecting bromide tracer, followed by a non-pumping period, and subsequent extraction of groundwater. The values of effective porosity from the expanded equation (0.6% to 5.0%) were substantially greater than those from the truncated equation (0.1% to 1.3%). The expanded and truncated equations were compared to data from previous push-pull studies in the literature and demonstrated that displacement during the injection phase may or may not be negligible, depending on the aquifer properties and the push-pull test parameters. The results of the tests presented here also demonstrated that: (1) the spatial variability of effective porosity, within a relatively small study site, can be substantial and (2) the error-propagated uncertainty of effective porosity can be mitigated to a reasonable level (< ± 0.5%). In conclusion, the expanded analytical solution improved the theoretical description of the displacement of a tracer during a push-pull test and the in situ application demonstrated an improvement for the estimation of effective porosity.
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PAPER
Push-pull tests for estimating effective porosity: expanded analytical
solution and in situ application
Charles J. Paradis
1
&Larry D. McKay
1
&Edmund Perfect
1
&Jonathan D. Istok
2
&
Terry C. Hazen
1,3,4,5,6,7
Received: 17 March 2017 /Accepted: 12 September 2017
#The Author(s) 2017. This article is an open access publication
Abstract The analytical solution describing the one-
dimensional displacement of the center of mass of a tracer
during an injection, drift, and extraction test (push-pull test)
was expanded to account for displacement during the injection
phase. The solution was expanded to improve the in situ esti-
mation of effective porosity. The truncated equation assumed
displacement during the injection phase was negligible, which
may theoretically lead to an underestimation of the true value
of effective porosity. To experimentally compare the expand-
ed and truncated equations, single-well push-pull tests were
conducted across six test wells located in a shallow, uncon-
fined aquifer comprised of unconsolidated and heterogeneous
silty and clayey fill materials. The push-pull tests were con-
ducted by injection of bromide tracer, followed by a non-
pumping period, and subsequent extraction of groundwater.
The values of effective porosity from the expanded equation
(0.65.0%) were substantially greater than from the truncated
equation (0.11.3%). The expanded and truncated equations
were compared to data from previous push-pull studies in the
literature and demonstrated that displacement during the in-
jection phase may or may not be negligible, depending on the
aquifer properties and the push-pull test parameters. The re-
sults presented here alsodemonstratedthe spatial variability of
effective porosity within a relatively small study site can be
substantial, and the error-propagated uncertainty of effective
porosity can be mitigated to a reasonable level (< ± 0.5%).
The tests presented here are also the first that the authors are
aware of that estimate, in situ, the effective porosity of fine-
grained fill material.
Keywords Groundwater flow .Heterogeneity .Hydraulic
properties .Hydraulic testing .Tracer tests
Introduction
The effective porosity of saturated porous media is a funda-
mental hydrogeological parameter for modeling the fate and
transport of dissolved-phase contaminants in the subsurface.
Reliable modeling is highly dependent on accurate character-
ization of effective porosity. Field-scale tracer-based methods
are particularly attractive to estimate effective porosity be-
cause they are based on direct measurements of the in situ
transport of a dissolved-phase constituent. The single-well
push-pull test method has been developed to estimate effective
porosity and has been successfully applied in situ (Istok
2013). However, the current analytical model (Hall et al.
1991) assumes the transport of the tracer during the push
phase is negligible, which may or may not be an appropriate
Electronic supplementary material The online version of this article
(https://doi.org/10.1007/s10040-017-1672-3) contains supplementary
material, which is available to authorized users.
*Ter ry C . Ha ze n
tchazen@utk.edu
1
Department of Earth and Planetary Sciences, University of
Tennessee, Knoxville, TN 37996, USA
2
School of Civil and Construction Engineering, Oregon State
University, Corvallis, OR 97331, USA
3
Biosciences Division, Oak Ridge National Laboratory, Oak
Ridge, TN 37830, USA
4
Department of Microbiology, University of Tennessee,
Knoxville, TN 37996, USA
5
Department of Civil and Environmental Sciences, University of
Tennessee, Knoxville, TN 37996, USA
6
Center for Environmental Biotechnology, University of Tennessee,
Knoxville, TN 37996, USA
7
Institute for a Secure and Sustainable Environment, University of
Tennessee, Knoxville, TN 37996, USA
Hydrogeol J
DOI 10.1007/s10040-017-1672-3
assumption in all cases. Theoretically, neglecting to account
for the transport of the tracer during the push phase may lead
to an underestimation of effective porosity. In this study, the
analytical solution to describe the displacement of a tracer
during a push-pull test was expanded to account for the push
phase and then applied in situ toestimate the effective porosity
across six test wells located in a shallow, unconfined aquifer.
Effective porosity can be qualitatively defined as the vol-
ume of the void spaces through which water or other fluids
can travel (by advection) in a rock or sediment divided by the
total volume of the rock or sediment (Fetter 2001). Domenico
and Schwartz (1998) explained that effective porosity implies
some connectivity through the porous medium and is more
closely related to permeability than is total porosity. The def-
inition and conceptualization of effective porosity has led to
the use of more descriptive terms such as mobile porosity,
kinematic porosity, and dynamic porosity. Determining the
appropriate value of effective porosity for groundwater
models can be challenging, due in part, to the spatial hetero-
geneity of porous media. Field-scale tracer-based studies have
shown that effective porosity in granular porous media can
range from 40% (alluvial sediments; fine sands, and glacial
till) to 0.4% (layered medium sand) and in fractured porous
media from 60% (fractured dolomite and limestone) to 0.5%
(fractured chalk) (Gelhar et al. 1992). There is also increasing
evidence that effective porosity is dependent on the scale at
which it is assessed, which suggests that field-scale methods
may be more appropriate to inform groundwater models (Li
1995;Stephensetal.1998).
Methods to estimate effective porosity typically rely on
calculating proxy parameters such as specific yield (Meinzer
1923a) or correlating grain-size distribution and soil-water
characteristic curves to representative values of specific yield
(Meinzer 1923b). Estimation-based methods have the disad-
vantage of being indirect but are relatively simple to conduct.
Methods to calculate effective porosity typically rely on
conducting tracer-based tests and interpretation of subsequent
breakthrough curves (Stephens et al. 1998). Tracer-based
methods have the advantage of being direct but can be rela-
tively difficult to conduct, especially at the field scale.
Moreover, the interpretation of breakthrough curves requires
careful consideration of the properties of the tracer and the
porous mediumfor example, tracer mass transport mecha-
nisms such as: (1) sorption to the porous medium, (2) diffu-
sion from mobile to immobile pore water, (3) volatilization to
the unsaturated zone, and (4) degradation or transformation
are not truly representative of the void spaces through which
water can travel by advection, i.e., effective porosity (Davis
et al. 1980; Turnadge and Smerdon 2014).
Hall et al. (1991) developed a relatively simple tracer-based
method to calculate effective porosity based on conducting
and interpreting the data from a single-well push-pull test. A
single-well push-pull test is conducted by injecting (push
phase) a volume of water containing a tracer into a single well,
followed by a non-pumping period (drift phase), and subse-
quent extracting (pull phase) of groundwater from the same
well in order to generate a breakthrough curve (Istok 2013). A
single-well push-pull test has the threefold advantage of being
direct, simple, and field scale. The Hall et al. (1991)method
was theoretically developed for a confined, homogeneous,
and isotropic aquifer but was experimentally validated at the
field scale in an unconfined, heterogeneous, and sandy
aquifer. Hall et al. (1991) compared the effective porosity
calculated from a single-well push-pull test to a dual-well
natural-gradient test and found that both tests yielded similar
values. However, the Hall et al. (1991) method assumed that:
(1) the transport of the tracer during the push phase was neg-
ligible, and (2) the uncertainty in the calculation of effective
porosity was negligible. Moreover, the Hall et al. (1991)ap-
plication was limited to a single well. Although the
assumptions and spatially limited application by Hall et al.
(1991) may have been valid and appropriate, respectively,
for their case study, they may not be appropriate at other sites
with variable aquifer properties, other push-pull test parame-
ters, and different study objectives.
The purpose of this study was to utilize the single-well
push-pull test method to characterize the magnitude and spa-
tial variability of effective porosity within a shallow, uncon-
fined aquifer. The novelty of this study was threefold: (1) the
expansion of the Hall et al. (1991) analytical solution to in-
clude the transport of the tracer during the push phase, (2) the
performance of an uncertainty analysis for the calculation of
effective porosity, and (3) the assessment of the spatial vari-
ability of effective porosity within the study site.
Materials and methods
Theory
The volume of water injected into, or extracted from, an aqui-
fer at a constant pumping rate, is given by:
V¼Q
jj
tð1Þ
where:
Vvolume of water [L
3
]
Qconstant pumping rate [L
3
/T]
telapsed time during pumping [T]
By convention, the pumping rate (Q) is positive dur-
ing injection and negative during extraction. If the aqui-
fer is confined, homogeneous, and isotropic, and if the
ambient groundwater flow is negligible, the cylindrical
volume of water injected into, or extracted from, a fully
penetrating well, is given by:
Hydrogeol J
V¼πr2bneð2Þ
where:
rradius of water [L]
bsaturated aquifer thickness [L]
n
e
effective porosity [dimensionless]
If the saturated aquifer thickness is constant, equating
Eqs (1)and(2), and rearranging gives:
r¼Q
jj
t
πbne

1=2ð3Þ
Equation (3) describes the leading- or trailing-edge position
of a particle of water within an expanding or contracting cy-
lindrical volume of water as it is injected into, or extracted
from, an aquifer.
Darcys law can be written to include effective porosity as:
v¼
Kdh
dr
ne
ð4Þ
where:
vaverage linear groundwater velocity [L/T]
Khydraulic conductivity [L/T]
dh/drhydraulic gradient [L/L]
Equation (4) describes the average linearvelocityofaparti-
cle of water within an aquifer due to ambient groundwater flow.
Velocity, in general terms, is given by:
v¼Δr
Δtð5Þ
where:
Δrtraveled distance [L]
Δtelapsed time [T]
Equation (5) can be rearranged to give:
Δr¼vΔtð6Þ
Equation (6) describes the average position of a particle of
water within an aquifer due to ambient groundwater flow. The
one-dimensional (1D) displacement of the center of mass of a
tracer, after completion of the injection, drift, and extraction
phases of a push-pull test, is zero (Fig. 1). The displacement of
the center of mass of the tracer is given by:
r1þr2þr3¼0ð7Þ
where:
r
1
displacement during injection [L]
r
2
displacement during drift [L]
r
3
displacement during extraction [L]
The displacement of the tracer during: (1) the injection
phase, is due to injection pumping (r
i
) and ambient ground-
water flow (r
a1
), (2) the drift phase, is due to ambient ground-
water flow (r
a2
), and (3) the extraction phase, is due to extrac-
tion pumping (r
e
) and ambient groundwater flow (r
a3
)
(Fig. 1). The components of the displacement of the center
of mass of the tracer during the push-pull test can be substitut-
ed in Eq. (7)togive:
riþra1
ðÞþra2
ðÞþreþra3
ðÞ¼0ð8Þ
where:
r
i
displacement due to injection pumping [L]
r
a1
displacement due to ambient groundwater flow [L]
r
a2
displacement due to ambient groundwater flow [L]
r
e
displacement due to extraction pumping [L]
r
a3
displacement due to ambient groundwater flow [L]
The components in Eq. (8) can be substituted by their cor-
responding equations given in Eqs. (3)and(6)togive:
Qi
jj
ti
πbne

1=2þvΔta1
"#
þvΔta2
ðÞþQe
jj
te
πbne

1=2þvΔta3
"#
¼0
ð9Þ
The components in Eq. (9), due to injection (first term) and
extraction (fourth term), represent the leading- or trailing-edge
position of the tracer within an expanding or contracting cy-
lindrical volume of water, whereas the components due to
ambient groundwater flow (vΔt
a1
,vΔt
a2
,andvΔt
a3
), repre-
sent the average displacement of the tracer. The average dis-
placement of the tracer, due to injection, occurs when one-half
of the mass of the tracer has been injected and is given by:
Qi
jj
τi¼Qi
jj
ti
2ð10Þ
where:
Q
i
injection rate [L
3
/T]
τ
i
time elapsed from the start of water injection until the
center of mass of the tracer is released [T]
In volumetric terms, Eq. (10) can be rewritten to give:
Vi¼Qi
jj
τið11Þ
where:
Vi= volume of water injected until the center of mass of the
tracer is released [L
3
].
The average displacement of the tracer, due to extraction,
occurs when one-half of the mass of the tracer has been re-
covered and isgiven by integration of the concentration versus
volume data, i.e., the breakthrough curve, as:
Hydrogeol J
Me¼1
2V1
V0CVðÞdV ð12Þ
where:
M
e
one-half of the mass of the recovered tracer [M]
V
0
volume of water recovered at the start of extraction
pumping [L
3
]
V
1
volume of water recovered at the end of extraction
pumping [L
3
]
C(V) concentration of the tracer (C)[M/L
3
] as a function of
the volume (V)[L
3
] of water extracted
The corresponding volume at which one-half of the mass of
the tracer has been recovered is given by evaluating the solu-
tion to Eq. (12)atM
e
by:
Me¼MVe
ðÞ ð13Þ
where:
MVe
ðÞ mass of the tracer (M) [M] as a function of volume
(Ve)[L
3
] at which one-half of the mass of the tracer
has been recovered
It is important to note that the solution to Eq. (12)canbe
estimated numerically, as opposed to solved analytically, and
doing so would allow for estimating Ve. The corresponding
times at which Viand Veoccur are given as:
τi¼Vi
Qi
jj ð14Þ
τe¼Ve
Qe
jj ð15Þ
Substituting Viin Eq. (11), Vein Eq. (13), τ
i
in Eq. (14),
and τ
e
in Eq. (15)forQ
i
τ
i
,Q
e
τ
e
,Δt
a1
,andΔt
a3
in Eq. (9),
respectively, gives:
ViVe
πbne

1=2þvτiþtdþτe
ðÞ¼0ð16Þ
where:
t
d
=Δt
a2
(time elapsed from the end of water injection until
the start of water extraction) [T]
Equation (16) describes the average position of the cen-
ter of mass of the tracer during the injection, drift, and
extraction phases. Rearranging Eq. (16)tosolveforaver-
age linear groundwater velocity gives:
v¼
VeVi
πbne

1=2
τiþtdþτe
ðÞ
ð17Þ
Equating Eqs. (17)and(4), and solving for effective poros-
ity (n
e
)gives:
ne1 ¼πbK2dh
dr

2τiþtdþτe
ðÞ
2
VeVi
ð18Þ
Equation (18) describes effective porosity (n
e1
)asa
function of the aquifer properties, e.g., saturated thickness
(b), hydraulic conductivity (K), and hydraulic gradient (dh/
dr), and the transport of the center of mass of the tracer
during the injection (Vi,τ
i
), drift (t
d
), and extraction (Ve,
τ
e
) phases. Equations (17) and (18) are very similar to the
Leap and Kaplan (1988) and Hall et al. (1991) equations,
respectively.
From Leap and Kaplan (1988):
v¼
Ve
πbne

1=2
tdþτe
ðÞ
ð19Þ
From Hall et al. (1991):
ne2 ¼πbK2dh
dr

2tdþτe
ðÞ
2
Ve
ð20Þ
However, Eqs. (17)and(18) account for the transport of
tracer during the injection phase (Vi,τ
i
), whereas Eqs. (19)
and (20) do not. If the transport of the tracer during the injec-
tion phase is truly negligible, then Viand τ
i
are equal to zero,
and Eqs. (17)and(18) are equivalent to Eqs. (19)and(20),
Fig. 1 Plan-view depiction of the
center of mass of a tracer at the
end of the injection (1), drift (2),
and extraction (3) phases,
r
i
= displacement due to injection,
r
a
= displacement due to ambient
groundwater flow,
r
e
= displacement due to
extraction
Hydrogeol J
respectively. If the transport of the tracer during the injection
phase is not truly negligible, then Viand τ
i
are greater than
zero, and Eq. (17) will yield lower values of average linear
groundwater velocity than Eqs. (19), and (18) will yield higher
values of effective porosity than Eq. (20).
Study site
The study site is in Area 2 of the Oak Ridge Integrated Field
Research Challenge (OR-IFRC) site at the Department of
Energys Oak Ridge Reservation (ORR) in Oak Ridge,
Tennessee, USA (Fig. 2). A typical geologic profile of Area
2 consists of approximately 6 m of unconsolidated and het-
erogeneous materials comprised of silty and clayey fill (most-
ly fine grained soil and clay-rich residuum), related to
historical construction activities, underlain by undisturbed
and clay-rich weathered bedrock (Moon et al. 2006; Watson
et al. 2004; Fig. 3). Slug tests indicated that the hydraulic
conductivity of the fill materials was approximately two or-
ders of magnitude greater than the weathered bedrock, e.g.,
10
6
versus 10
8
m/s, respectively (Fig. 3). The study site
contains 13 monitoring wells (FW218FW230), six of which
were used as test wells (FW220FW225), and one of which
was used as a source well (FW229) for groundwater injectate
for the single-well push-pull tests, as discussed in section
Effective porosity(Fig. 2). The test wells were installed by
direct push coupled with continuous electrical resistivity pro-
filing. The test wells are constructed of 1.9-cm inside diameter
schedule-80 polyvinyl chloride (PVC) pipe and are screened
from 3.7 to 6.1 m below ground surface (mbgs; Fig. 3). The
Fig. 2 Plan-view maps of the study site: acountry map showing study
site location in the southeastern United States, barea map showing study
site location in Area 2 of the OR-IFRC, and cstudy site map showing well
locations, groundwater-level elevations, and groundwater-level elevation
iso-contours (m amsl = meters above mean sea level)
Hydrogeol J
test wells are screened within the fill materials and were ver-
tically terminated at contact with the undisturbed weathered
bedrock; the contact with undisturbed weathered bedrock was
determined by a substantial increase in difficulty of advancing
the direct-push drill string and a concomitant and notable in-
crease in electrical resistivity (Fig. 3). The test wells are fully
screened across the unconfined aquifer (Fig. 3). The source
well is constructed of 5.1-cm inside diameter schedule-40
PVC pipe and is screened from 3 to 7.5 mbgs. The shallow
groundwater aquifer is unconfined and the depth to ground-
water is approximately 3.5 mbgs (Fig. 3). The site-wide aver-
age magnitude and direction of the hydraulic gradient, as de-
termined graphically, is approximately 0.045 m/m and to the
south/southwest, respectively (Fig. 2).
The physical properties of the fill materials, in which the
test wells are screened, are poorly characterized compared to
those at other study sites located within Area 2. This is due, in
part, to environmental safety policies at the site, which is lo-
cated adjacent to highly contaminated areas. As a result of
these policies, it was not feasible to collect core samples for
evaluation of material properties during this study. However,
previous investigations at nearby sites in Area 2 indicate that
fill commonly used in this part of the ORR consisted mainly
of locally obtained silty and clayey material derived from
decomposition of shale and limestone. Fill material at the
study site is expected to be similar in composition. It should
be noted that the chemical and biological properties of the
groundwater system at the study site are better characterized.
A previous study by Paradis et al. (2016)reportedthatdespite
the high level of aquifer heterogeneity within Area 2, the
biogeochemical processes associated with the reduction and
oxidation of uranium within the study site wells (FW218
FW227) were spatially consistent; nevertheless, the spatial
variability of the physical properties of the fill materials,
e.g., effective porosity, were unknown at the time of this study.
Hydraulic gradient
The hydraulic gradient, within the vicinity of each test well,
was estimated using ArcMap (version 10.5) software. The
depth to groundwater, relative to the top of the casing (sur-
veyed to 0.3-cm above mean sea level) of each site well, was
measured using an electronic water level indicator (Solinst)
immediately prior to conducting single-well pumping and
push-pull tests. The depth to groundwater measurements were
converted to meters above mean sea level (m amsl) and
uploaded to ArcMap, along with the coordinates (latitude
and longitude) of each site well, to create a point shape file.
The groundwater elevation data were interpolated, using the
spline tool, to create a digital elevation model (raster file) of
the water table (cell size = 0.15 m, weight = 0, all other pa-
rameters set at default). The slope of the water table was cal-
culated using the slope tool (z-factor = 1.171 × 10
5
,basedon
the latitude of the study site). The average slope, within a 1-m
radius about each test well, was calculated using the zonal
statistics tool. The rationale for a 1-m radius, as representative
of the hydraulic conditions within the vicinity of each test
well, was based on Eq. (3) which describes the leading-edge
position of a particle of water within an expanding cylindrical
volume of water as it is injected into an aquifer, i.e., the max-
imum frontal position of bromide tracer during the injection
phase of a push-pull test. An effective porosity of 5% was
assumed, a priori. For a 20-L injection volume and a saturated
aquifer thickness of 2.5 m, the radius in Eq. (3) would be
approximately 0.25 m. It is important to note that Eq. (3)
ignores heterogeneity and the drift phase of the push-pull tests
which would lead to an underestimation of radius; therefore, a
1-m radius was assumed. The slope at each test well was
converted from degrees to hydraulic gradient values and in-
putted into Eqs. (18)and(20) to estimate effective porosity.
Hydraulic conductivity
The hydraulic conductivity, within the vicinity of each test
well, was estimated by conducting single-well pumping tests.
Single-well pumping tests were conducted according to the
methodology of Robbins et al. (2009) and Aragon-Jose and
Robbins (2011). In brief, groundwater was pumped from each
test well at a constant discharge rate using a peristaltic pump
(Geotech Geopump) and stored in a 208-L plastic drum. The
discharge rate was measured using a graduated cylinder and a
stop watch. The depth to groundwater was measured using an
electronic water level indicator (Solinst). The discharge rate
Fig. 3 Vertical-view conceptual modelof the shallow unconfined aquifer
and construction details of a test well; horizontal exaggeration is 50-fold.
Fill consists of Bsilty and clayey^material
Hydrogeol J
and depth to groundwater were measured sequentially until
steady-state conditions were achieved; steady-state conditions
were defined as a change in drawdown less than 1.2 cm over
the course of 15 min during a constant discharge rate.
Single-well pumping test data were analyzed according to
the general methodology of Robbins et al. (2009) and Aragon-
Jose and Robbins (2011). In brief, the steady-state discharge
and drawdown values, along with the construction details of
the test wells, e.g., saturated screen length and radius of well,
were used to calculate the hydraulic conductivity using the
half-ellipsoid flow equation, described analytically by
Dachler (1936). Graphs showing single-well pumping test da-
ta can be found in the electronic supplementary material
(ESM).
Effective porosity
The effective porosity, within the vicinity of each test well,
was estimated by conducting single-well push-pull tests.
Single-well push-pull tests were conducted according to the
general methodology of Istok (2013). In brief, 23 L of ground-
water (injectate) were collected from the up-gradient well
FW229 (Fig. 2) using a peristaltic pump and stored in a plastic
carboy. Three grams of potassium bromide (KBr; Sigma-
Aldrich) were then added to 20 L of the injectate and mixed
by recirculation using a peristaltic pump for a target concen-
tration of 100 mg/L bromide. During mixing of the injectate,
three samples were collected in 20-ml scintillation vials and
were analyzed for bromide.The concentration of bromide was
determined in the field using a bromide ion selective half-cell
electrode (Thermo Scientific Cat. No. 9435BN) coupled with
a double junction reference electrode (Thermo Scientific Cat.
No. 900200). The minimum detection limit for bromide was
1 mg/L and the reproducibility of bromide measurements was
±2%. Immediately prior to injection, 1 L of groundwater was
purged from the test well (approximately two test well vol-
umes) and three samples were collected and analyzed for the
background concentration of bromide. The push phase of the
test consisted of low-flow (approximately 250400 ml/min)
injection of the 20-L bromide-amended injectate followed im-
mediately by the injection of 3 L of nonamended injectate
(herein referred to as the Bchase^) using a peristaltic pump.
The injection of the chase was conducted to clear the test well
volume (approximately 0.5 L) of the bromide-amended
injectate. The total push time (tracer plus chase) ranged from
approximately 11.5 h. The injectate was then left to drift in
the groundwater system under nonpumping conditions for up
to 2 h. The pull phase of the test consisted of low-flow extrac-
tion (approximately 100 to 300 ml/min) of up to 65 L of
groundwater and sequential collection of 20-ml samples
which were analyzed for bromide.
Single-well push-pull test data were analyzed according to
the general methodology of Istok (2013). In brief, the time (τ
i
)
and volume (Vi) at which the center of mass of bromide was
released were calculated by evaluating Eqs. (10) and (11),
respectively. The concentration of bromide versus the volume
and time elapsed during the pull phase of the tests were gen-
erated to calculate the volume (Ve) and time (τ
e
) at which the
center of mass of bromide was recovered. Veand τ
e
were
calculated by numerical integration of the bromide versus time
data (Thomas et al. 2008). Veand τ
e
were concomitant with
one half of the region between the bromide and volume/time
data. Graphs showing single-well push-pull test data can be
found in the electronic supplementary material (ESM).
Uncertainly analysis
The uncertainty in the measured parameters, e.g., volume
injected/extracted, pumping rate, drawdown, elapsed time,
etc. and the propagated error in the calculated parameters,
e.g., hydraulic gradient, hydraulic conductivity, and effective
porosity, were analyzed according to the BData Analysis
Toolkit # 5: Uncertainty analysis and error propagation^,by
Kirchner (2001). More specifically, the simple rules for sums
and differences, and for products and ratios, were used.
Results
Hydraulic gradient results
The static water table was relatively stable immediately prior
to, and after, conducting the single-well pumping and push-
pull tests (data not shown). The site-wide average magnitude
and direction of the static hydraulic gradient was similar to
pretest conditions, e.g., 0.045 (Fig. 2). The near-well (1-m
radius) hydraulic gradient at each test well, immediately prior
to conducting the push-pull tests, ranged from a low of 0.020
in test well FW224 to a high of 0.085 in test well FW221
(Table 1). The range of hydraulic gradient values were notably
greater than those previously reported at other test sites by
Hall et al. (1991) and Istok (2013).
Hydraulic conductivity results
During the single-well pumping tests, steady-state discharge
and drawdown conditions were achieved within a few minutes
after the tests began and were maintained for approximately
1 h (data not shown). The drawdown was typically less than
10% of the static saturated screen length (data not shown).
Static water levels were stable prior to initiating the pumping
tests and recharge to near-static water levels generally oc-
curred within 0.5 h after pumping stopped (data not shown).
The hydraulic conductivity for each test well was then calcu-
lated by inputting the steady-state discharge and drawdown
values, along with the saturated well screen length and radius,
Hydrogeol J
into the half-ellipsoid flow equation (Dachler 1936). The hy-
draulic conductivity ranged from a low of 2.1 × 10
6
m/s in
test well FW225 to a high of 1.6 × 10
5
m/s in test well
FW224 (Table 1). The range of hydraulic conductivity values
were within those representative of silts and fine sands
(Domenico and Schwartz 1998) and notably less than those
previously reported at other test sites by Hall et al. (1991)and
Istok (2013)(Table1).
Effective porosity results
The breakthrough curves of bromide, during the pull phase of
the tests, showed sharp and short-lived increases followed by
gradual and non-linear decreases (Fig. 4). It is important to
note that the concentrations of bromide in the test wells prior
to injection were below the minimum detection limit (~1 mg/
L) and that the concentration of bromide in the injectate was
near the target concentration (~100 mg/L; data not shown).
The time (τ
e
) from the start of the pull phase until the center
of mass of bromide was recovered ranged from a low of 0.85 h
(3,077 s) in test well FW223 to a high of 1.14 h (4,087 s) in
test well FW222 (Fig. 4; Table 2). The corresponding volume
(Ve)atwhichthecenterofmassofbromidewasrecovered
ranged from a low of 6 L (0.006 m
3
) in test well FW225 to a
high of 15 L (0.015 m
3
) in test well FW221 (Fig. 4; Table 2).
The saturated aquifer thickness (~2.4 m) was similar
among all test wells (Table 2). The drift times (t
d
)weresimilar
among five of the six wells (~1.8 h on average), whereas the
drift time in test well FW225 was notably short (~0.5 h;
Tab le 2). The percent mass recovery of bromide ranged from
a low of 41% in test well FW225 to a high of 71% in test well
FW221 (data not shown). In general, the experimental design,
aquifer properties (Table 1), and results of the push-pull tests
(Table 2) for this study were more similar to those from Istok
(2013)thanfromHalletal.(1991). However, it should be
noted that the drift times (t
d
) for this study were substantially
less than Istok (2013).
The effective porosity (n
e
) for each test well was calculated
by inputting the parameters from Tables 1and 2into the ex-
panded and truncated equations, Eqs. (18)and(20), respec-
tively. The effective porosity (n
e1
), per Eq. (18), ranged from a
low of 0.6% in test well FW220 to a high of 5.0% in test well
FW221 (Table 3). It should be noted that the negative value of
n
e1
(0.1%) in test well FW225 indicated that one or more
input parameters for Eq. (18) were not valid; this issue is
discussed in section Discussion: effective porosity. The ef-
fective porosity (n
e2
), per Eq. (20), ranged from a low of 0.1%
in test wells FW220 and FW225 to a high of 1.3% in test well
FW221 (Table 3). The effective porosity, per Eq. (18), which
accounts for the transport of tracer during the injection phase,
was substantially larger than that of Eq. (20), which does not
account for the transport of tracer during the injection phase
(Table 3). The range of effective porosity, per Eq. (18), was
representative of the lower end of those calculated from field-
scale tracer-based studies conducted in granular porous media,
whereas the range per Eq. (20) was representative of those
conducted in fractured porous media (Gelhar et al. 1992).
The effective porosity from Hall et al. (1991), per Eqs. (18)
and (20), were almost identical (6.2 versus 6.1%, respective-
ly), whereas from Istok (2013) they were notably different,
i.e., the expanded equation (n
e1
) yielded substantially higher
effective porosity than the truncated equation (n
e2
;37versus
13%; Table 3).
Uncertainty analysis results
The percent standard errors of the hydraulic gradient (dh/dr),
hydraulic conductivity (K) and drift time (t
d
)weretypically
less than ±2% (Table 4). The percent standard errors of the
remaining parameters, e.g., saturated aquifer thickness (b)and
the times (τ
i
,τ
e
) and volumes (Vi,Ve) at which the center of
mass of bromide was released and recovered, were typically
greater than ±2% but less than ±5% (Table 4). The error-
propagated uncertainty in effective porosity (n
e1
) was less than
±0.5% (Fig. 5). It should be noted that an uncertainly analysis
of effective porosity for the studies by Hall et al. (1991)and
Istok (2013) was not possible due to the lack of available data
on the uncertainty of pumping rates, volumes injected/extract-
ed, etc.
Discussion
Discussion: hydraulic gradient
The range of the near-well hydraulic gradient (0.020 to
0.085 m/m) in the test wells was relatively small (within a
single order of magnitude) and representative of the site-wide
average (0.045 m/m). The spatial variability of the hydraulic
gradient was expected due to the high level of aquifer
Tabl e 1 Hydraulic gradient (dh/dr) and hydraulic conductivity (K)for
tests in this study (FW220FW225) and for tests from Hall et al. (1991)
and Istok (2013)
Test well/study dh/dr
(m/m)
K
(m/s)
FW220 0.036 4.1 × 10
6
FW221 0.085 5.0 × 10
6
FW222 0.033 6.9 × 10
6
FW223 0.028 7.0 × 10
6
FW224 0.020 1.6 × 10
5
FW225 0.063 2.1 × 10
6
Hall et al. (1991)0.005 1.4 × 10
4
Istok (2013)0.015 2.8 × 10
5
Hydrogeol J
heterogeneity within Area 2 (Moon et al. 2006; Watson et al.
2004). However, it must be noted that the near-well hydraulic
gradient was not measured directly, i.e., graphically, rather it
was estimated based on a digital elevation model as discussed
in section Hydraulic gradient. Therefore, there is a level of
uncertainty in the near-well hydraulic gradient that must be
recognized; nevertheless, the model-generated values of the
near-well hydraulic gradient are likely much more representa-
tive of the near-well conditions than the graphically deter-
mined values at the site-wide scale.
Discussion: hydraulic conductivity
The steady-state discharge and drawdown conditions among
the test wells were consistent with the methodology of
Robbins et al. (2009) and Aragon-Jose and Robbins (2011).
It should be noted that the Robbins et al. (2009) study was
conducted in a confined aquifer comprised of fine sands,
whereas this study was conducted in an unconfined aquifer
comprised of silty and clayey fill. However, Aragon-Jose and
Robbins (2011) demonstrated the validity of the Robbins et al.
Fig. 4 Push-pull test data for all
six test wells (FW220FW225)
showing concentration of
bromide (y-axis) versus time
elapsed (x-axis) during the pull
phase of the test. Error bars
represent the analytical
uncertainty (±4%)
Tabl e 2 Results from single-well push-pull tests for this study (FW220FW225) and from Hall et al. (1991)andIstok(2013)
Test well/study b
(m)
τ
i
(s)
Vi
(m
3
)
t
d
(s)
τ
e
(s)
Ve
(m
3
)
FW220 2.34 1,800 0.010 6,600 3,948 0.014
FW221 2.60 1,740 0.010 7,320 3,984 0.015
FW222 2.31 1,890 0.010 7,200 4,087 0.012
FW223 2.33 1,950 0.010 4,980 3,077 0.011
FW224 2.24 1,410 0.010 6,600 3,349 0.014
FW225 2.42 810 0.010 1,740 3,496 0.006
Hall et al. (1991) 15.24 1,200 0.30 225,600 5,460 20.67
Istok (2013) 2.93 3,000 0.10 108,000 5,220 0.16
Hydrogeol J
(2009) method in an unconfined aquifer comprised of sandy
till and within test wells whose screens crossed the water table;
these hydrogeologic and test well conditions were very similar
to those in this study. Aragon-Jose and Robbins (2011)rec-
ommended that a valid application of the Robbins et al. (2009)
method in unconfined aquifers required minimal drawdown
with respect to the static saturated well screen length. The
drawdown in this study was typically less than 10% of the
static saturated screen length and was within the general range
of the percent drawdown reported by Aragon-Jose and
Robbins (2011;~812%).
There is a level of uncertainty in the measured drawdown
within the test wells that must be recognized. The total draw-
down within a well during pumping may due to a number of
components, including: (1) aquifer loss, (2) skin layer loss, (3)
gravel pack loss, (4) well screen loss, (5) up-flow loss in well
interior, (6) partial penetration of well screen, and (7) seepage
face (Houben 2015a,b). As previously discussed in section
Study site, the well screens fully penetrate the unconfined aqui-
fer and were installed without a gravel pack, i.e., the well screens
are in direct contact with the fill materials. The wells were also
routinely developed by mechanical means, i.e., surge and purge,
to limit skin layer loss. The pump intake was set at mid-screen,
i.e., 50% of the screen length, to limit up-flow loss in the well
interior (Houben and Hauschild 2011); therefore, it is likely that
the drawdown during pumping, in order of importance, was
attributed to: (1) the aquifer and (2) a seepage face. A seepage
face would lead to overestimating drawdown during pumping
and underestimating hydraulic conductivity. In turn,
underestimating hydraulic conductivity would lead to
underestimating effective porosity. Nevertheless, the presence
and extent of any seepage face during pumping was not known;
however, by limiting the drawdown to approximately less than
10% of the static saturated screen length, the effects of a seepage
face were likely mitigated.
The range of hydraulic conductivity (2.1 × 10
6
1.6 × 10
5
m/s) in the test wells was relatively small (within
a single order of magnitude) and within the lower and upper
method detection limits (~10
8
10
4
m/s; Robbins et al.
2009); the range of hydraulic conductivity was also within
that representative of silts and fine sands (Domenico and
Schwartz 1998). However, Watson et al. (2013)reportedthat
the hydraulic conductivity of the fill material, in Area 2 test
wells immediately east of the study site, was approximately
Tabl e 3 Effective porosity calculated from the truncated and expanded
solutions, (20)and(18), respectively, for tests in this study (FW220
FW225) and for tests from Hall et al. (1991)andIstok(2013), n
e1
from
Eq. (18), n
e2
from Eq. (20)
Test well/study n
e1
(%)
n
e2
(%)
FW220 0.6 0.1
FW221 5.0 1.3
FW222 3.3 0.4
FW223 2.8 0.2
FW224 2.3 0.5
FW225 0.1 0.1
Hall et al. (1991) 6.2 6.1
Istok (2013)3713
Tabl e 4 Percent standard errors (± %) for input parameters for Eq. (18) for tests in this study (FW220FW224). Test well FW225 is omitted due to
invalid results
Tes t
well
dh/dr
(± %)
K
(± %)
b
(± %)
τ
i
(± %)
Vi
(± %)
t
d
(± %)
τ
e
(± %)
Ve
(± %)
FW220 1.2 1.6 5.0 2.5 2.5 1.1 3.0 3.9
FW221 1.0 0.7 5.0 2.5 2.5 0.4 1.1 2.1
FW222 1.7 1.7 5.0 2.5 2.5 0.4 1.1 5.4
FW223 1.1 0.6 5.0 2.5 2.5 0.5 1.4 3.6
FW224 0.6 0.8 5.0 2.5 2.5 0.9 2.8 2.8
Fig. 5 Effective porosity (n
e1
)perEq.(18) for tests in this study
(FW220FW224). Test well FW225 is omitted due to invalid results
(see section Discussion: effective porosity). Error bars represent the
uncertainty
Hydrogeol J
3.8 × 10
4
m/s. Therefore, the range of hydraulic conductivity
reported in this study was notably less (up to two orders of
magnitude) than to the value previously reported. It is impor-
tant to note that Watson et al. (2013), and Phillips et al. (2008),
also reported that the fill material was gravelly, whereas no
gravel component is known to exist within the area of this
study site. Therefore, the lack of a gravel component in the
fill material within the study site may explain the lower values
of hydraulic conductivity. In summary, the single-well
pumping test data and analysis suggested that the variability
in the hydraulic conductivity of the fill material was relatively
low and within that representative of silts and fine sands.
Discussion: effective porosity
The breakthrough curve for a non-reactive tracer released
from an instantaneous point source, as it passes a fixed point
of observation, should resemble a bell-shaped curve when its
transport is governed by advection and dispersion during
steady-state groundwater flow in a homogeneous and an iso-
tropic granular porous medium (Baetsle 1969). The break-
through curves for bromide, observed during the pull phase
of the tests, resembled bell-shaped curves that were truncated
at the leading edges (early time) and possibly skewed towards
the following edges (late time). The truncation at the leading
edge indicated that the full spatial extent of the injectate did
not move beyond the test wells during the drift phase. Ideally,
the entire injectate should drift beyond the test wells under
natural-gradient (non-pumping) conditions and then the entire
injectate should be pumped back to the test wells under
forced-gradient (extraction pumping) conditions (Leap and
Kaplan 1988). However, if the injectate drifts too far from
the test wells, it may only partially return during the pull phase
and lead to a low mass recovery of the tracer. Although it may
be tempting to suggest that the drift times in this study were
too short, it must be noted that the average percent mass re-
covery of the tracer (bromide) was far less than 100%
(60 ± 10%, data not shown). Therefore, an increase in the drift
time would have likely resulted in a lower mass recovery of
bromide, and thus a weaker signal for analysis. In addition to
advective mass transport, diffusive mass transport of bromide
from mobile to immobile pore water may partially explain the
low mass recovery of bromide; mobile to immobile diffusive
mass transport is well documented and described at the OR-
IFRC site and at the nearby west Beak Creek Valley site (Luo
et al. 2005; Mayes et al. 2003; McKay et al. 2000; Reedy et al.
1996). The extent of sorption or degradation of bromide
was likely negligible based on previous batch and column
studies which demonstrated that mass recoveries of bro-
mide from OR-IFRC soils and sediments are nearly 100%
under acidic to neutral pH (4.57; Hu and Moran 2005;
McCarthy et al. 2000); the pH at the study site ranges from
approximately 6.58(Paradisetal.2016).
With regard to the possible skewness of the breakthrough
curves towards the following edge, this suggested that mass
transport mechanisms in addition to advection and dispersion
and/or anisotropy and heterogeneity of the porous media were
present. The likelihood that the fill materials were packed in
the vertical direction suggests that permeable media at the site
were anisotropic. The variability in the magnitude of the hy-
draulic conductivity among the test wells (2.1 × 10
6
1.6 × 10
5
m/s) also indicates a certain amount of heterogene-
ity. Although a thorough investigation of advection, disper-
sion, and other mass transport mechanisms was not an objec-
tive of this study, the skewness of the breakthrough curves
towards the following edge may be attributed to numerous
small-scale heterogeneities in aquifer hydraulic properties dur-
ing radially convergent flow to a well (Pedretti et al. 2013). In
summary, the breakthrough curves suggested that the injectate
drifted some distance beyond the test wells under natural-
gradient conditions and that an adequate amount of tracer
(bromide) was recovered during the pull phase to accurately
calculate effective porosity using Eqs. (18)and(20).
The effective porosity values from the expanded equation
(0.65.0%) were substantially larger than those from the trun-
cated equation (0.11.3%) which indicated that the transport of
the tracer during the injection phase was not truly negligible.
From Hall et al. (1991), the effective porosity values were al-
most identical (6.2 versus 6.1%) which indicated that the trans-
port of the tracer during the injection phase was truly negligible.
From Istok (2013), the effective porosity values were notably
different (37 versus 13%), as in the tests presented here, which
indicated that the transport of the tracer during the injection
phase was not truly negligible. Therefore, the agreement, or
lack thereof, of effective porosity from the expanded versus
the truncated equation can clearly identify and quantify the
relative importance of accounting for the transport of tracer
during the injection phase, as shown in the tests presented here
and in those from the literature (Hall et al. 1991;Istok2013).
The negative value of effective porosity (0.1%), using the
expanded equation for test well FW225, suggested that the
volume of water extracted until the center of mass of the tracer
was recovered (Ve) was less than the volume of water injected
until the center of mass of the tracer was released (Vi); this is
impossible due to the law of conservation of mass. An inspec-
tion of the breakthrough curve of bromide for test well FW225
shows that pumping stopped despite bromide concentrations
greater than 20 mg/L, whereas pumping stopped in the re-
maining five test wells at bromide concentrations less than
10 mg/L. Therefore, it is likely that the total pump-back time
in test well FW225 was too short to return an adequate volume
of water representative of the true center of mass of bromide.
As expected, this error in the application and data analysis of
the push-pull test goes unrecognized when using the truncated
equation, as shown by a positive value of effective porosity
(0.1%) for test well FW225.
Hydrogeol J
This is the first measurement of effective porosity in a fine-
grained fill material that the authors are aware of; hence, there
is no Bexpected^range of values for effective porosity in this
type of material. The effective porosity values from the ex-
panded equation (0.65.0%) were more similar to those pre-
viously calculated from field-scale tracer-based studies con-
ducted in unconsolidated, heterogeneous, and fine-grained
granular porous media, whereas those from the truncated
equation (0.11.3%) were more similar to those from frac-
tured porous media (Gelhar et al. 1992;Halletal.1991;
Stephens et al. 1998). Based on the hydrogeology of the study
site, i.e., silty and clayeyfill, the effective porosity values from
the expanded equation are likely more accurate than those
from the truncated equation. Moreover, the push-pull tests
by Istok (2013) were conducted in a gravel and sand aquifer,
which also suggests that the effective porosity of 37% from
the expanded equation is likely more accurate than the 13%
from the truncated equation. However, it must be emphasized
that values of effective porosity are dependent on the type of
tracer and the nature of the porous mediafor example, in
column experiments by van der Kamp et al. (1996), values of
effective porosity were equal to or far less than the total po-
rosity, depending on the type of solute tracer. van der Kamp
et al. (1996) attributed these findings to phenomena such as:
(1) ion exclusion, (2) enclosed pores, and (3) bound water. At
the nearby west Bear Creek Valley site, McKay et al. (2000)
conducted a multi-well natural-gradient tracer study and dem-
onstrated that the mean arrival times of colloidal tracers were
up to 500 times faster than those reported for solute tracers
from previous tests at the site conducted by Lee et al. (1992).
McKay et al. (2000) attributed these findings to transport of
the colloids through fractures, whereas the solute tracers ex-
perienced substantial diffusion into the immobile pore water
in the fine-grained matrix between fractures. This demon-
strates that different types of tracers can experience different
effective porosities in the same material and implies that even
the same solute tracer may encounter different pore regions
(mobile and immobile pore water) over the duration of a tracer
experiment. Therefore, the magnitude of the effective porosi-
ties calculated in this study may not be truly representative of
the void spaces through which water can flow.
Lastly, and perhaps most importantly, it must be recognized
that both the expanded and truncated equations were theoret-
ically developed for confined aquifers as opposed to uncon-
fined aquifers. However, the only in situ study to experimen-
tally test the validity of the truncated equation was by Hall
et al. (1991). Hall et al. (1991) arrived at similar values of
effective porosity (~6%) from both single-well push-pull and
dual-well natural-gradient tests which were conducted in an
unconfined, heterogeneous, and sandy aquifer. Therefore,
there is clearly a need to: (1) experimentally test the expanded
solution for the confined case, and (2) theoretically develop an
expanded solution for the unconfined case.
Discussion: uncertainty analysis
The error-propagated uncertainty in the calculated values of
effective porosity was relatively small (< ± 0.5%), due in part,
to the careful consideration for the precise determination of
the aquifer properties, e.g., hydraulic gradient, hydraulic con-
ductivity, and saturated aquifer thickness, and the push-pull
test parameters, e.g., the times and volumes at which the cen-
ter of mass of bromide was released and recovered. However,
the uncertainty analysis failed to capture the effects of: (1) the
presence and extent of seepage face during extraction
pumping, and (2) applying an analytical solution developed
for a confined aquifer to an unconfined aquifer. The presence
and extent of a seepage face could have been determined using
a down-well device with video capability during extraction
pumping. However, this was not possible due to the small
diameter (1.9 cm) of the wells and the presence of down-
well tubing (0.64 cm diameter) which limited the physical
space to deploy such a device. The effects of applying an
analytical solution developed for a confined aquifer to the
unconfined aquifer in this study was not known; however, as
previously discussed in section Discussion: effective porosi-
ty, Hall et al. (1991) demonstrated the validity of the truncat-
ed analytical solution, developed for a confined aquifer, as
applied to an unconfined, heterogeneous, and sandy aquifer.
Conclusions
The conclusions of this study are as follows: (1) the analytical
solution to describe the displacement of the center of mass of a
tracer during a push-pull test can be expanded to account for
displacement during the injection phase, (2) the transport of a
tracer during the injection phase of a push-pull test may not be
truly negligible, (3) the failure to account for displacement during
the injection phase may lead to a substantial underestimation of
the magnitude of effective porosity, (4) single-well push-pull tests
can be readily applied to multiple wells within a study site to
assess the spatial variability of effective porosity, and (5) the
error-propagated uncertainty in the value of effective porosity
can be mitigated to a reasonable level by careful consideration
for the precise determination of the aquifer properties and the
push-pull test parameters. Finally, it must be recognized that there
is a need to theoretically develop and experimentally test the
expanded solution presented here for the case of an unconfined
aquiferandfordifferenttypesofaquifermaterials.
Acknowledgements This material by ENIGMA Ecosystems and
Networks Integrated with Genes and Molecular Assemblies (http://
enigma.lbl.gov), a Scientific Focus Area Program at Lawrence Berkeley
National Laboratory is based upon work supported by the U.S.
Department of Energy, Office of Science, Office of Biological &
Environmental Research, under contract number DE-AC02-
05CH11231. The authors would like to thank Tonia Mehlhorn from the
Hydrogeol J
Oak Ridge National Laboratory and Julian Fortney from the University of
Tennessee Knoxville for their assistance and helpful suggestions during
the field-based portion of this study. The authors would also like to thank
Eriko Gordon and Emma Dixon from the University of Tennessee
Knoxville for their assistance with the final production of the manuscript.
Finally, the authors would like to thank the two anonymous reviewers for
their insightful comments and helpful suggestions which greatly im-
proved the quality of the manuscript.
Open Access This article is distributed under the terms of the Creative
Commons Attribution 4.0 International License (http://
creativecommons.org/licenses/by/4.0/), which permits unrestricted use,
distribution, and reproduction in any medium, provided you give
appropriate credit to the original author(s) and the source, provide a link
to the Creative Commons license, and indicate if changes were made.
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Hydrogeol J
... To link processes and factors from the gene scale to the ecosystem scale, ENIGMA has multiple studies at the field scale (Step 2a), mesocosm scale (Step 2b), and molecular/species level (Step 2c). To facilitate these studies, ENIGMA has major research thrusts aimed at field surveys (Smith et al., 2015;Paradis et al., 2018;Zelaya et al., 2019;Moon et al., 2020); laboratory and bioreactor studies of isolates (Vaccaro et al., 2016;Price et al., 2018;Carlson et al., 2019;Thorgersen et al., 2019); syncoms, enrichments, and improved isolation methods (Wu et al., , 2019; genetic tool development Price et al., 2018;Mutalik et al., 2019); and bioinformatics analyses and tools Lui et al., 2020;Price et al., 2020). ...
... At the field scale, ENIGMA has conducted surveys (Step 2a.1) to characterize the biotic and abiotic components of the subsurface using 16S amplicon and shotgun metagenomics sequencing to characterize the microbial communities (Smith et al., 2015;Zelaya et al., 2019;Tian et al., 2020) and biogeochemical measurements for the abiotic factors (Smith et al., 2015;Ge et al., 2020;Moon et al., 2020;Wu et al., 2020). Hydrology and topology studies of ORR indicate that there are significant groundwater flow rates influenced by frequent rain events (Watson et al., 2005), and preliminary tracer measurements with push-pull tests determined dispersal rates of chemicals like nitrate and their transfer between compartments (Paradis et al., 2018) (Step 2a.2). Sampling of sediment and groundwater from pristine and contaminated areas (Zhang et al., 2017) across time scales (Zelaya et al., 2019) confirmed geochemistry influencing highly variable communities (Smith et al., 2015;Hemme et al., 2016;Thompson et al., 2017a;He et al., 2018;Carlson et al., 2019;Thorgersen et al., 2019;Tian et al., 2019) (Step 2a.3). ...
... Step 2a.2, determining fluctuations of intensity and periodicity involves using the same approach as Step 2a.1, but in time-series studies to gather information on how the composition and abundance of microbial communities and chemicals change over time (both short and long term) (Hwang et al., 2009;Hug et al., 2015). Finally, for Step 2a.3, deciphering connections answers how, where, and the rate chemicals and microorganisms are being transferred and transported between compartments and around the location as a whole, encompassing terms like residence time, drift, and dispersion as exemplified in push-pull tests of a uranium-contaminated karst site (Paradis et al., 2018). ...
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Over the last century, leaps in technology for imaging, sampling, detection, high-throughput sequencing, and -omics analyses have revolutionized microbial ecology to enable rapid acquisition of extensive datasets for microbial communities across the ever-increasing temporal and spatial scales. The present challenge is capitalizing on our enhanced abilities of observation and integrating diverse data types from different scales, resolutions, and disciplines to reach a causal and mechanistic understanding of how microbial communities transform and respond to perturbations in the environment. This type of causal and mechanistic understanding will make predictions of microbial community behavior more robust and actionable in addressing microbially mediated global problems. To discern drivers of microbial community assembly and function, we recognize the need for a conceptual, quantitative framework that connects measurements of genomic potential, the environment, and ecological and physical forces to rates of microbial growth at specific locations. We describe the Framework for Integrated, Conceptual, and Systematic Microbial Ecology (FICSME), an experimental design framework for conducting process-focused microbial ecology studies that incorporates biological, chemical, and physical drivers of a microbial system into a conceptual model. Through iterative cycles that advance our understanding of the coupling across scales and processes, we can reliably predict how perturbations to microbial systems impact ecosystem-scale processes or vice versa. We describe an approach and potential applications for using the FICSME to elucidate the mechanisms of globally important ecological and physical processes, toward attaining the goal of predicting the structure and function of microbial communities in chemically complex natural environments.
... The study site is in Area 2 of the Y-12 S-3 pond field site which is a part of the Oak Ridge Reservation (ORR) and in Oak Ridge, Tennessee, USA ( Figure 1). The hydrogeology of the study site has been previously described (Watson et al. 2004;Paradis et al. 2016;Paradis et al. 2018). The subsurface consists of approximately 6 m of unconsolidated and heterogeneous materials comprised of silty and clayey fill underlain by undisturbed and clay-rich weathered bedrock. ...
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Microbial‐mediated nitrate removal from groundwater is widely recognized as the predominant mechanism for nitrate attenuation in contaminated aquifers and is largely dependent on the presence of a carbon‐bearing electron donor. The repeated exposure of a natural microbial community to an electron donor can result in the sustained ability of the community to remove nitrate; this phenomenon has been clearly demonstrated at the laboratory scale. However, in situ demonstrations of this ability are lacking. For this study, ethanol (electron donor) was repeatedly injected into a groundwater well (treatment) for six consecutive weeks to establish the sustained ability of a microbial community to remove nitrate. A second well (control) located up‐gradient was not injected with ethanol during this time. The treatment well demonstrated strong evidence of sustained ability as evident by ethanol, nitrate, and subsequent sulfate removal up to 21, 64, and 68%, respectively, as compared to the conservative tracer (bromide) upon consecutive exposures. Both wells were then monitored for six additional weeks under natural (no injection) conditions. During the final week, ethanol was injected into both treatment and control wells. The treatment well demonstrated sustained ability as evident by ethanol and nitrate removal up to 20 and 21%, respectively, as compared to bromide, whereas the control did not show strong evidence of nitrate removal (5% removal). Surprisingly, the treatment well did not indicate a sustained and selective enrichment of a microbial community. These results suggested that the predominant mechanism(s) of sustained ability likely exist at the enzymatic‐ and/or genetic‐levels. The results of this study demonstrated the in situ ability of a microbial community to remove nitrate can be sustained in the prolonged absence of an electron donor.
... One additional simplification of Hall et al. (1991) is that the time of the tracer transport during the injection phase is very short so it can be ignored. The work of Hall et al. (1991) has been improved by Paradis et al. (2018) and Paradis et al. (2019) by considering a finite tracer transport time during the injection phase. ...
... The schematic diagram of the mass center movement in the SWPP test with the regional flow field (Revised fromParadis et al. 2018). ...
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Simplified analytical models of the single-well push-pull (SWPP) test have been widely used to estimate the regional flow velocity and the aquifer porosity, where the simplifications refer to that the dispersion effect is negligible, and the flow is steady state during the entire SWPP test. However, the errors caused by such assumptions have not been investigated thoroughly. In this study, numerical modeling of the SWPP test without above-mentioned simplifications and the field experimental data will be employed to test the applicability of the simplified analytical models. The numerical simulation is based on a mathematical model composed of a two-dimensional transient flow and transport model, which will be solved by the finite-element method. The results indicate that errors increase with the increasing dispersivity when using the simplified analytical models to estimate both regional flow velocity and porosity. The errors refer to the relative difference between the input parameters of the numerical modeling and the estimated parameters by the simplified models. Such errors also depend on the input values of regional groundwater velocity, drift time of the SWPP test, and aquifer porosity. Specifically, the errors caused by the simplified models of estimating regional groundwater velocity decrease with increasing input regional groundwater velocity, increasing input drift time, and decreasing input porosity. The errors produced by the simplified models of estimating porosity decrease with increasing input regional groundwater velocity, increasing input drift time, and decreasing input porosity. Field in-situ experiments show that the fitness of the observed breakthrough curves (BTCs) by the numerical modeling is far better than the simplified analytical models. The estimated regional flow velocity by the numerical modeling of this study is closer to the estimated values by previous other studies.
... The study site is in Area 2 of the Y-12 S-3 pond field site which is a part of the Oak Ridge Reservation (ORR) and in Oak Ridge, Tennessee, USA ( Figure 1). The hydrogeology of the study site has been previously described (Watson et al. 2004;Paradis et al. 2016;Paradis et al. 2018). The subsurface consists of approximately 6 m of unconsolidated and heterogeneous materials comprised of silty and clayey fill underlain by undisturbed and clay-rich weathered bedrock. ...
... The groundwater pH is circumneutral (pH ≈ 6.5 to 8.0) and dissolved oxygen (DO) is relatively low (DO ≈ 1-2 mg/L). Nitrate and sulfate concentrations are persistent due to the lack of a suitable electron donor and range from approximately 5 to 75 and 10 to 200 mg/L, respectively; the groundwater geochemistry has been previously described (Watson et al. 2004;Paradis et al. 2016;Paradis et al. 2018). The test wells (FW222 [treatment well] and FW224 [control well]) are separated by approximately 6 m of horizontal distance and are oriented up-and downgradient with respect to each other ( Figure 1). ...
Preprint
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Microbial-mediated nitrate removal from groundwater is widely recognized as the predominant mechanism for nitrate attenuation in contaminated aquifers and is largely dependent on the presence of a carbon-bearing electron donor. The repeated exposure of a natural microbial community to an electron donor can result in the sustained ability of the community to remove nitrate; this phenomenon has been clearly demonstrated at the laboratory scale. However, in situ demonstrations of this ability are lacking. For this study, ethanol (electron donor) was repeatedly injected into a groundwater well (treatment) for six consecutive weeks to establish the sustained ability of a microbial community to remove nitrate. A second well (control) located up-gradient was not injected with ethanol during this time. The treatment well demonstrated strong evidence of sustained ability as evident by concomitant ethanol and nitrate removal and subsequent sulfate removal upon consecutive exposures. Both wells were then monitored for six additional weeks under natural (no injection) conditions. During the final week, ethanol was injected into both treatment and control wells. The treatment well demonstrated sustained ability as evident by concomitant ethanol and nitrate removal whereas the control did not. Surprisingly, the treatment well did not indicate a sustained and selective enrichment of a microbial community. These results suggested that the predominant mechanism(s) of sustained ability likely exist at the enzymatic- and/or genetic-levels. The results of this study demonstrated that the in situ ability of a microbial community to remove nitrate can be sustained in the prolonged absence of an electron donor. Moreover, these results implied that the electron-donor exposure history of nitrate-contaminated groundwater can play an important role nitrate attenuation. Article Impact Statement Groundwater microbes sustain ability to remove nitrate in absence of carbon and energy source.
... Despite the numerous studies of DFT considering the effects of skin and AGF, the solute (reactive) transport in VCW-induced flow field affected by skin and AGF has rarely been investigated. Extensive theoretical studies highlighted the effects of the skin and AGF on pumping and tracer tests using a single wellbore with a single well screen (Chen and Chang 2003;Chang and Yeh 2011;Paradis et al. 2018;Li et al. 2019aLi et al. , 2019bLi et al. , 2020, acting as either source or sink in a purely or approximately radial flow field. As a special kind of well with simultaneous pumping and injection, the VCW has a strong convergentdivergent flow field, in which the characterization of solute transport should account for advection-dispersion in both radial and vertical directions. ...
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As a special single-well test with dual-screened configuration, dipole flow test with a tracer (DFTT) has been an efficient tool for aquifer parameter interpretation. The tool is excellent for characterizing the vertical distribution of hydraulic conductivity, dispersivity and in situ reaction rate in aquifers. It is noteworthy that the effects of skin and ambient groundwater flow (AGF) on the solute transport, which have been widely investigated in terms of conventional tracer tests, have not been comprehensively studied with respect to DFTT. Meanwhile, it is important to elucidate the potentials of DFTT in identifying the primary skin properties as well as the methods to avoid the AGF effects on DFTT. Consequently, we developed a mathematical model for DFTT accounting for skin and AGF. The results show that a negative skin acts as a preferential pathway for tracer transport and the AGF effects on breakthrough curves (BTCs) can be easily mistaken for reaction. Through extensive mathematical model-based experiments, the BTCs calculated from the DFTT models with skin effects were categorized into four types, each of which is able to imply a specific kind of skin. Additionally, a new dimensionless parameter ξ' , composed of injection/extraction rate, hydraulic conductivity, hydraulic gradient of AGF and screen parameters, was defined to quantitatively indicate the AGF effects on the overestimation degree of the in situ first-order reaction, implying that one can adjust the field parameters of DFTT to keep ξ' less than 3.7% to achieve an overestimation error of reaction rate below 50%. This article is protected by copyright. All rights reserved.
... Minimum effective porosity of 0.20 was observed in FA at density index 90%, and maximum effective porosity of 0.38 was reported in GM at density index of 10%. An important boundary condition of permeability coefficient is soil porosity (Figure 2), in the form of total porosity [33], but much more important in this case is effective porosity [34,35]. The value of effective porosity is closely related to specific surface area which reflects the roughness of the particle surface and determines the soil capability to retain bound waters [36,37]. ...
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The aim of the article is to compare two classifications systems of engineering-geological environment sustainability in terms of its permeability evaluated on the basis of permeability coefficient. The first evaluated classification assumes a permeable environment to be a positive characteristic in the engineering-geological assessment, while the other considers an impermeable environment as favourable. The four fine-grained soil materials were selected, as they had very similar, almost identical grains-size distribution, but different microstructure characterized by grains sphericity, angularity, and roughness. At the same time, the influence of changes in the density of soil materials (density index 10%, 30%, 60%, 90%) was analysed. Permeability coefficient was determined using six methods (empirical formulae, laboratory and microscopic analysis). The laboratory method falling head test (FHT) was taken as a reference test that reflected the actual water flow through the soil. It was found that with an increase in grain angularity and roughness (and a decrease in sphericity), the permeability coefficient was decreasing and this trend culminated along with gradual compaction. Moreover, the research shows that unsuitable methods may classify soil materials into wrong engineering-geological permeability classes, which may have negative consequences during engineering-geological or geotechnical assessment and cause subsequent problems in foundation engineering.
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This paper was envisaged to provide deeper insights of the hydraulic jump value in pumping well in the loess aquifer. Herein, we discussed the research status and problems of the value, compared the differences between the analytical solution method and the empirical formula method. Subsequently, we proposed a fitting method with improvement and the tangent method to estimate the hydraulic jump value, and quantitatively analyzed the linear variation rule of the water level curve around the well. The results show that the value calculated by the traditional empirical formula was about one tenth of the theoretical value in constant flow and the water level around the well was found to be logarithmic in the range of N 1 ∼N 3 . When the range was extended, the water level curve changed to a parabolic nature and power function in turn. The hydraulic jump value obtained by h - r extension of the modified water level curve fitting equation was improved greatly, and the average error was found to be less than 1 m. The stability of the hydraulic jump value using the tangent method was poor, and the estimated horizontal distance was larger than 3 m. The results show that the reliability of the improved curve fitting method was better, while the empirical formula method and the tangent method exhibited a larger error and poor stability. When the error correction was performed, the improved curve fitting method could be used to estimate the hydraulic jump value under the same conditions, and can replace the theoretical calculation value.
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Methods for interpreting tracer tests often rely on equations assuming a natural regional flow which is straight and uniform. The main purpose of this project was to develop more realistic equations for the advective part of contaminant transport, by including the flow lines distortion occurring in the vicinity of the injection well. The complex potential of the flow during a tracer test was calculated by superimposing the complex potential of a natural, straight and uniform flow distorted by the presence of a passive well, and the complex potential of a radial flow corresponding to an isotropic injection alone. The equations were developed for a horizontal plan and the calculated complex potential yielded a groundwater velocity field, and after that a formula connecting the position of the advancing front of the tracer plume to the injection duration. These new equations were then tested with numerical simulations. A two-dimensional aquifer plan was modeled and set in order to numerically solve particle tracking and travel time computation of the moving front within a reasonable calculation time. This model provided a comparison of times needed to fully recover the tracer plume previously injected, the one calculated with the new equations and the one calculated with former equations neglecting the impact of the well presence on the groundwater flow field. The results showed that the new equations are significantly more precise, in particular when the injection rate is sufficiently low compared to the natural regional flow rate, with a relatively large well diameter and in the vicinity of the injection well. Three different plume shapes could be visualized numerically, and those shapes depend on the value of a parameter △ which compares the velocity component caused by the injection in the well and the component caused by the natural regional flow.
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An estimation method for evaluating groundwater velocity by means of the Single-Well Push-Pull (SWPP) test by Leap and Kaplan (1988) was applied to a confined aquifer at 100 m depth with a very slow groundwater movement. The SWPP test consists of a push phase, a drift phase, and a pull phase, and the groundwater velocity is evaluated based on the Breakthrough Curves obtained from the SWPP test. In this study, the accuracy of the SWPP test system was evaluated by performing a SWPP test without drift time four times in total. Also, four types of SWPP tests with different drift times from 10 to 1802 days were conducted to obtain an estimate of the regional groundwater velocity for a maximum of approximately five years. Furthermore, the stable isotope of water (δ¹⁸O and δD) and uranine, which are known as conservative tracers, were used as tracers in the SWPP tests so as to evaluate their availabilities. The SWPP test results showed a higher reproducibility of the SWPP test using δ¹⁸O and δD than that using uranine. The sorption of uranine in the aquifer was suggested based on the SWPP test results, indicating that the hydrological properties can be obtained by comparing the SWPP test results using δ¹⁸O, δD and uranine as tracers. The SWPP test yielded an actual groundwater velocity of 0.37 m/year, which is similar to approximately 0.1 m/year order of the estimated groundwater velocity based on the results of past studies. Moreover, setting the appropriate correction and drift time in the SWPP test played an important role in investigating the very slow groundwater flow in the aquifer. When a long-term drift time was set, the recovery rate of the tracer and the chaser of δ¹⁸O and δD was decreased by diffusion in the aquifer’s silt and clay layer.
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Reoxidation and mobilization of previously reduced and immobilized uranium by dissolved-phase oxidants poses a significant challenge for remediating uranium-contaminated groundwater. Preferential oxidation of reduced sulfur-bearing species, as opposed to reduced uranium-bearing species, has been demonstrated to limit the mobility of uranium at the laboratory scale yet field-scale investigations are lacking. In this study, the mobility of uranium in the presence of nitrate oxidant was investigated in a shallow groundwater system after establishing conditions conducive to uranium reduction and the formation of reduced sulfur-bearing species. A series of three injections of groundwater (200 L) containing U(VI) (5 μM) and amended with ethanol (40 mM) and sulfate (20 mM) were conducted in ten test wells in order to stimulate microbial-mediated reduction of uranium and the formation of reduced sulfur-bearing species. Simultaneous push-pull tests were then conducted in triplicate well clusters to investigate the mobility of U(VI) under three conditions: 1) high nitrate (120 mM), 2) high nitrate (120 mM) with ethanol (30 mM), and 3) low nitrate (2 mM) with ethanol (30 mM). Dilution-adjusted breakthrough curves of ethanol, nitrate, nitrite, sulfate, and U(VI) suggested that nitrate reduction was predominantly coupled to the oxidation of reduced-sulfur bearing species, as opposed to the reoxidation of U(IV), under all three conditions for the duration of the 36-day tests. The amount of sulfate, but not U(VI), recovered during the push-pull tests was substantially more than injected, relative to bromide tracer, under all three conditions and further suggested that reduced sulfur-bearing species were preferentially oxidized under nitrate-reducing conditions. However, some reoxidation of U(IV) was observed under nitrate-reducing conditions and in the absence of detectable nitrate and/or nitrite which suggested that reduced sulfur-bearing species may not be fully effective at limiting the mobility of uranium in the presence of dissolved and/or solid-phase oxidants. The results of this field study confirmed those of previous laboratory studies which suggested that reoxidation of uranium under nitrate-reducing conditions can be substantially limited by preferential oxidation of reduced sulfur-bearing species.
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Water wells are an indispensable tool for groundwater extraction. The analytical and empirical approaches available to describe the flow of groundwater towards a well are summarized. Such flow involves a strong velocity increase, especially close to the well. The linear laminar Darcy approach is, therefore, not fully applicable in well hydraulics, as inertial and turbulent flow components occur close to and inside the well, respectively. For common well set-ups and hydraulic parameters, flow in the aquifer is linear laminar, non-linear laminar in the gravel pack, and turbulent in the screen and the well interior. The most commonly used parameter of well design is the entrance velocity. There is, however, considerable debate about which value from the literature should be used. The easiest way to control entrance velocity involves the well geometry. The influence of the diameter of the screen and borehole is smaller than that of the screen length. Minimizing partial penetration can help to curb head losses.
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The push-pull test is a powerful site characterization technique that has been applied to a wide range of problems in contaminant hydrogeology. The theoretical and practical aspects of push-pull testing were initially developed to characterize groundwater aquifers but the method has now been extended to saturated and unsaturated soils and sediments and to surface water bodies. Dr. Istok and his collaborators have been instrumental in the development of these techniques and he is widely recognized as the world’s leading expert in push-pull testing, This is the only reference book available on this powerful method.
Book
This textbook provides an introduction to the study of hydrogeology, and maintains the process oriented approach of the earlier edition. The introduction is followed by chapters on: the origin of porosity and permeability; groundwater movement; equations of flow, boundary conditions and flow nets; groundwater in the basin hydrologic cycle; hydraulic testing; groundwater resources; stress, strain and pore fluids; heat transport in groundwater flow; solute transport; aqueous geochemistry; chemical reactions; colloids and microorganisms; mass transport equations; mass transport in natural groundwater systems and groundwater flow; contaminant hydrology; modelling of dissolved contaminant transport; multiphase fluid systems; remediation; and in situ destruction and risk assesment.
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Knowledge about the hydraulics of water wells is important to optimize their energy efficiency. By minimizing head losses around the well, energy consumption and ageing processes can be limited, thereby prolonging the well’s service life. The contribution of the individual components to total head loss (drawdown) in the well is analyzed in detail. The single most important contributor to drawdown is commonly the aquifer. Its hydraulic conductivity can only be improved slightly through development. The second most important contributor is the formation of a wellbore skin layer. This occurs if no proper well development was performed after drilling; the layer contains remnants of drilling-fluid additives or mobilized fine aquifer particles. The head loss caused by groundwater flow in the gravel pack, through the screen slots and inside the well, was found to be small. Thus, well development is the most important measure to influence well performance and energy efficiency. For longer operation times and pumped volumes, the energy gains outperform the cost for the development.
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Mathematical models of varying complexity have been developed since the 1960s to interpret environmental tracer concentrations in groundwater flow systems. This review examines published studies of model-based environmental tracer interpretation, the progress of different modelling approaches, and also considers the value of modelling tracer concentrations directly rather than estimations of groundwater age. Based on citation metrics generated using the Web of Science and Google Scholar reference databases, the most highly utilised interpretation approaches are lumped parameter models (421 citations), followed closely by direct age models (220 citations). A third approach is the use of mixing cell models (99 citations). Although lumped parameter models are conceptually simple and require limited data, they are unsuitable for characterising the internal dynamics of a hydrogeological system and/or under conditions where large scale anthropogenic stresses occur within a groundwater basin. Groundwater age modelling, and in particular , the simulation of environmental tracer transport that explicitly accounts for the accumulation and decay of tracer mass, has proven to be highly beneficial in constraining numerical models. Recent improvements in computing power have made numerical simulation of tracer transport feasible. We argue that, unlike directly simulated ages, the results of tracer mass transport simulation can be compared directly to observations, without needing to correct for apparent age bias or other confounding factors.
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[1] Anomalous transport in advection-dominated convergent flow tracer tests can occurs due to small-scale heterogeneities in aquifer hydraulic properties. These result in fluctuations of the groundwater velocity field and complex connectivity patterns between injection and extraction wells. While detailed characterization of heterogeneity is often not possible in practice, a proper understanding of what fundamental physical mechanisms can give rise to macroscopic behaviors that are measurable is essential for proper upscaling of solute transport processes. We analyze here how heavy-tailed breakthrough curves can arise in radially convergent flow to a well. The permeability fields are three-dimensional multi-Gaussian fields with varying statistical geometry and degrees of heterogeneity. We consider transport of conservative tracers from multiple injection locations by varying distance and angle from the extraction well. Anomalous power law tailing in breakthrough curves is attributed to a variety of features including the initial vertical stratification of the solute that arises due to a flux-weighted injection, the injection distance to the well relative to the depth of the aquifer, and the statistics of the heterogeneity field as defined by the correlation length and variance of the permeability. When certain conditions cooccur for a given injection, such as strong connectivity contrasts between aquifer layers, injection distances comparable to the horizontal heterogeneity integral scales, and large global variances, breakthrough curves tend to scale as a PL with unit slope at late time. These findings offer new insights to understand what physical processes must be understood to develop and choose appropriate upscaling approaches that might reproduce such anomalous transport in heterogeneous advection-dominated systems.