GEOPHYSICAL RESEARCH LETTERS, VOL. 40, 1098–1103, doi:10.1002/grl.50282, 2013
Resolving centimeter-scale flows in aquifers and their
hydrostratigraphic controls
G. Liu, S. Knobbe, and J.J. Butler Jr.
Received 3 January 2013; revised 18 February 2013; accepted 21 February 2013; published 27 March 2013.
[1] The rate of groundwater flow has long been recognized as
a critical control on solute transport in the subsurface.
However, information about groundwater flux and its
variability in space is rarely available, especially at the
resolution required for investigations at sites of groundwater
contamination. Recently, high-resolution information about
vertical variations in groundwater flux was obtained using
fiber-optic distributed temperature sensing technology to
monitor the temperature response to active heating in a well.
A series of vertical thermal profiles were acquired at a
1.4 cm resolution in a sand and gravel aquifer. These highresolution profiles, which display many of the same general
features as hydraulic conductivity (K) profiles obtained
using multiple techniques at the same well, provide new
insights into site hydrostratigraphy. In particular, the nearcontinuous profiles reveal the existence of thin zones of
relatively high or low velocity that would be difficult to
detect using other methods. These profiles also demonstrate
that vertical variations in K may not be an accurate indicator
of vertical variability in groundwater flux in highly
heterogeneous aquifers. Citation: Liu, G., S. Knobbe, and J. J.
Butler Jr. (2013), Resolving centimeter-scale flows in aquifers and
their hydrostratigraphic controls, Geophys. Res. Lett., 40, 1098–1103,
doi:10.1002/grl.50282.
1. Introduction
[2] The rate of groundwater flow is a critical control on solute
transport in the subsurface [e.g., Dagan, 1989]. Information
about groundwater flux and its spatial variability is essential at
sites of groundwater contamination for reliable risk assessments
and design of effective remediation systems. In recent years,
contaminant mass discharge, the product of groundwater
flux and contaminant concentration, has received increasing
attention as a metric for site characterization and remediation
activities [e.g., Suthersan et al., 2010]. Although this metric is
highly appealing, the characterization of groundwater flux has
proven to be a significant challenge.
[3] Many different approaches have been used to estimate
groundwater flux. The most common method is based on
Darcy’s law, q = K i, where q is the Darcy velocity, K is the
hydraulic conductivity, and i is the hydraulic gradient. Water
levels in a minimum of three wells are used to estimate i, and
All Supporting Information may be found in the online version of this
article.
1
Kansas Geological Survey, University of Kansas, Lawrence,
Kansas, USA.
Corresponding author: G. Liu, Kansas Geological Survey, University of
Kansas, 1930 Constant Ave., Lawrence, KS 66047, USA. ([email protected])
©2013. American Geophysical Union. All Rights Reserved.
0094-8276/13/10.1002/grl.50282
hydraulic tests are used to estimate K. The flux estimate
typically represents an average value over a relatively large
volume and thus rarely provides information at the resolution
needed for site characterization and remediation.
[4] There are a number of other approaches for estimating
groundwater flux (e.g., Ballard [1996], Hatfield et al. [2004],
and Devlin et al. [2009]; see summary in Bayless et al.
[2011]). Most of these are based on introducing a tracer
(e.g., heat or solute) into the subsurface and monitoring the
subsequent response. The underlying assumption is that
groundwater flow is the primary mechanism for tracer movement. A major disadvantage of most of these approaches is that
only a limited number of measurements, whether at a few points
or averaged over a discrete interval, can be acquired at a single
time. The result is that selection of measurement locations
becomes a critical issue; thin layers that act as preferential flow
pathways or barriers may often go undetected. Clearly, an
approach that provides more continuous information on the flux
distribution is needed. Such an approach and the insights that it
can provide are described here.
[5] In this paper, we present a new method for the nearcontinuous, high-resolution characterization of relative
variations in horizontal groundwater flux. This method couples
the proven concept of using a heat tracer to track groundwater
movement with distributed temperature sensing (DTS) technology. DTS technology, which is based on analyzing the Raman
backscatter after a laser light pulse is transmitted down a fiberoptic (FO) cable, yields high-resolution temporal (subminute)
and spatial (meter-scale) temperature measurements along the
FO cable [Selker et al., 2006; Tyler et al., 2009]. It has been
increasingly utilized for measuring and monitoring various
hydrologic processes [e.g., Lowry et al., 2007; Moffett et al.,
2008; Henderson et al., 2009; Leaf et al., 2012; Striegl
and Loheide, 2012]. As shown here, the high resolution
possible with DTS enables us to glean new insights into
hydrostratigraphic controls of groundwater flow.
2. Methodology
[6] The method developed for groundwater flux characterization (henceforth, GFC) is based on the temperature increase
produced by heating in the presence of flowing groundwater
(Figure 1a). While the spatial resolution of DTS temperature
measurements obtained with a FO cable is typically on the order
of a meter, previous work for other applications has shown that
cable wrapping can greatly increase the resolution of DTS
measurements [Vogt et al., 2010; Briggs et al., 2012]. In this
work, a 1.4 cm vertical resolution is obtained by wrapping the
cable around an 8.9 cm outer diameter (OD) PVC (polyvinyl
chloride) pipe (Figure 1b; see Figure S1 in the Supporting Information for a photo of the prototype tool). The FO cable used in
this study (AFL LSZH (low smoke zero halogen) FD-3690,
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LIU ET AL.: RESOLVING CENTIMETER-SCALE AQUIFER FLOW
Heat
Off
Heat
On
increase is sufficiently large to be above the noise level but
not large enough to initiate density-driven flow in the small
annular space (~0.2 cm) between the tool and the ID of the
well. After the heat is turned off, the tool can be moved to
another interval within the screen and the process repeated.
[8] Under a horizontal gradient, groundwater flows from
the aquifer through the filter pack (materials in the borehole
annulus) and well screen and then into the well where it
moves around the GFC tool. The heat is transported away
from the tool primarily through advection of water and
thermal conduction. Although the velocity of the annular
flow is different from that of the flow in the aquifer due to
the distortion of the flow field produced by the well and tool,
the two velocities are directly correlated with each other.
Thus, when vertical variations in the rate of thermal conduction can be neglected, vertical variations in the horizontal
groundwater flux in the aquifer can be characterized by the
average temperature increase during heating,
Temperature
Low Flux
T(t)
High Flux
T0
t0
Time
t1
(a)
Wrapped
Heating
Cable
Wrapped
FO Cable
8.9-cm PVC
Well Screen
Water
Heating Cable
FO Cable
ΔTave ¼
Support PVC
Air
Aquifer
(b)
(c)
Figure 1. (a) Heat-induced temperature increase at different
groundwater flux rates (assuming a constant rate of thermal
conduction), (b) schematic of the groundwater flux characterization (GFC) tool, and (c) planar schematic view of the GFC
tool in a well.
0.4 cm diameter) has two fibers encased in a hydrophobic-gelfilled tube that are spliced together at the bottom of the tool.
A resistance heating cable (0.1 cm diameter) is wrapped tightly
along the outside grooves of the FO cable, giving the tool a
9.8 cm OD. The wrapped PVC pipe is 3.05 m long (total length
of the wrapped FO cable is 219 m) and sealed at both ends. In
this configuration, the amount of thermal mass inside the
10.2 cm inner diameter (ID) test well (including the well, water,
heating and FO cables, and air-filled PVC pipe; see Figure 1c) is
kept small, thus enhancing the sensitivity to groundwater flux in
the aquifer. The temperature along the FO cable was measured
with a Sensornet Oryx DTS unit. The power for the heating cable was controlled by a variable-output transformer.
[7] For flux profiling, the GFC tool is moved to a measurement interval, and temperature is monitored for at least
30 min. Once the background temperature indicates that the
thermal disturbance from tool deployment has dissipated,
the heating period (5 h) begins. The power output for heating
is preset to a constant level (22 W) at which the temperature
1
t1 t0
Z
t1
½T ðt Þ T0 dt;
(1)
t0
where T0 is the background temperature before heating starts at
time t0 and t1 is the time when heating ceases. Equation (1) was
chosen over other metrics because of its integrated (cumulative
photon count) form [Sayde et al., 2010]. To facilitate comparisons, the duration of heating (t1 t0) is kept constant for all
profiles within a well. ΔTave is used here as a relative indicator
of groundwater flux variations; further work would be needed
to establish a quantitative relationship between ΔTave and
groundwater flux.
[9] Two key assumptions are invoked when using ΔTave to
characterize relative variations in horizontal groundwater flux.
First, the vertical component of groundwater flow is assumed
negligible, as vertical flow can move heat between depths and
distort the temperature responses produced by horizontal flow.
Vertical flow is driven by thermally induced density differences
and by background head differences. Density-driven flow can
be kept small through tool design (minimal annular space)
and control of the power output. Head differences, however,
will invariably produce some amount of vertical flow. In the
work described here, test results indicate that vertical flow is
insignificant, most likely as a result of the large distances to
the closest pumping wells and recharge/discharge areas.
Although vertical flow may impact temperature responses at
other sites, a zoned heating system can be readily incorporated
into the tool to allow discrete sections of the tool to be
heated while the temperature along the probe is monitored
for vertical movement.
[10] The second key assumption is that vertical variations in
the thermal conductivity (k) of materials in the vicinity of the
well are negligible, so that differences in ΔTave are primarily a
result of horizontal groundwater flow. Numerical simulations
(Figure S4 in the Supporting Information) show that ΔTave for
a 5 h heating period is primarily sensitive to the k within 7 cm
of the well screen, i.e., materials within the filter pack. This
assumption thus appears reasonable for wells with filter packs
because the filter pack is typically composed of a relatively
homogeneous mixture of sands and gravels. Artificial filter
packs (emplaced from the surface during well installation) have
this characteristic by design, while this condition is often
created in natural filter packs through formation collapse and
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LIU ET AL.: RESOLVING CENTIMETER-SCALE AQUIFER FLOW
systematic development (removal of near-well fine materials) of
discrete intervals along the well screen.
[11] The current GFC tool obtains a temperature measurement every minute for each 1.43 cm vertical interval along
the tool. In contrast to previous studies [e.g., Vogt et al.,
2010; Briggs et al., 2012] where a similar resolution was
obtained with FO cable wrapping, active heating is incorporated here so that relative variations in groundwater flux can
be characterized at a high resolution by tracking temperature
responses. When groundwater flux is not present, heatingincorporated DTS (no high-resolution cable wrapping)
has been used to estimate soil moisture [Sayde et al.,
2010] and k of wellbore materials [Freifeld et al., 2008].
[12] In this work, the measured temperature is an average
over the entire circumference of the probe, so information on
flow direction cannot be obtained. Although the current tool
is designed for a 10 cm well, a similar tool could be used
in smaller-diameter wells (a FO cable with a smaller bend
radius may be required).
highly uncertain. Three primary factors are contributing to
the large uncertainty in velocity estimates. First, there is
significant spatial variability in K at this site; K in the
sand and gravel interval ranges from ~1 104 to over
6 103 m/s with a vertically averaged value of
~1.4 103 m/s. Second, the hydraulic gradient is very
small and difficult to measure accurately (regional gradient
~4.5 104 [Devlin and McElwee, 2007]). Third, the flow
field is continuously changing with time in response to
localized recharge, stage changes in the Kansas River and
its tributaries, and two intermittently operating (typically
7–10 h/day) water supply wells that are 310 m and 530 m
from the test well. Although these conditions are far
from ideal, they are reflective of those commonly faced in
field settings.
[15] The 10.2 cm ID PVC well used for flux characterization
(Gems4S), which is screened over most of the sand and gravel
ΔTave(°C)
3. Field Application
1.4
1.2
1.1
1.0
0.9
0.8
300
360
10
[13] The GFC tool was applied at the Geohydrologic
Experimental and Monitoring Site (GEMS) in northeast
Kansas, United States (Figure S2 in the Supporting Information). Over the last two decades, GEMS has been the site of
extensive research on flow and transport in heterogeneous
formations [Butler, 2005]. The shallow subsurface consists
of ~10.7 m of alluvial sand and gravel (the focus of this
work) overlain and hydraulically confined by ~11.5 m of silt
and clay and underlain by low-K bedrock.
[14] Despite the great amount of previous work at GEMS,
information on groundwater velocity remains sparse and
Δ
11
12
Depth Below Land Surface (m)
13
1.6
1.4
1.2
ΔT (ºC)
1.3
1.0
0.8
0.6
14
15
16
17
0.4
18
0.2
0.0
11.8
12.3
12.8
13.3
13.8
14.3
14.8
19
Depth Below Land Surface (m)
12:19 AM
12:39 AM
01:09 AM
02:09 AM
03:09 AM
04:09 AM
05:09 AM
Average
Flowmeter K
MLST K
20
Figure 2. Heating-induced temperature change versus depth
for selected measurement times for the GFC tool located
between depths 11.8 and 14.9 m (interval labeled A on
Figure 3). Temperature data are the average of DTS signals
from both downward and upward fiber segments. Heating
was turned on and off at 12:09 A.M. and 5:09 A.M., respectively, on 4 January 2012. The dashed thick line represents
the average temperature increase during heating calculated with
(1). Intervals at both ends of the tool (0.20 m top and 0.34 m
bottom; see shaded areas) are affected by probe construction
and therefore excluded from all the profiles presented in Figures 3 and 4. A longer interval was excluded from the bottom
end due to the proximity to the cable splice; intervals for data
exclusion were the same for all profiles.
Dipole K
0
60
120
180
240
Hydraulic Conductivity (m/d)
Figure 3. Average temperature increase during heating
(ΔTave) at well Gems4S compared to K values obtained using
multiple techniques (borehole flowmeter, multilevel slug tests
(MLST), and dipole flow tests). The thin dashed lines are ΔTave
profiles for 27 heating tests conducted between 12 December
2011 and 22 February 2012, with the thick solid line
representing the average. The double-arrow lines on the right
show the five overlapping depth intervals (after removal of
the shaded intervals in Figure 2) that span the screened
interval; note the consistency in the overlapping areas between
adjacent profiles.
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LIU ET AL.: RESOLVING CENTIMETER-SCALE AQUIFER FLOW
interval (bottom 1.7 m not screened), was installed with a 28 cm
OD hollow-stem auger. The formation collapsed back virtually
instantaneously (natural filter pack) with the withdrawal of the
auger flights. The well was then intensively developed using
a straddle packer tool (pumping the interval between the
packers) that was moved in 0.3 m increments. The collapse
and subsequent development are assumed to have produced
a relatively homogeneous mixture of sands and gravels in
the immediate vicinity of the screen. Five test intervals were
used to span the screened interval, with adjacent profiles
overlapping by 0.5–1.0 m for quality control. All heating
tests were conducted during the overnight hours when the
nearby wells were typically not pumped. To reduce in-well
vertical water movement produced by pumping of these
wells, an inflatable packer was placed above the top of the
screen. This was necessary because pumping-induced head
changes in the confined aquifer are relatively large and water
can flow from and to the cased portion of the well during the
pumping and recovery periods, respectively. An ice bath
was used to calibrate DTS temperature measurements at
the surface (supplemented with measurements from two
downhole temperature sensors for some profiles); the
temperature calculation was based on a double-ended
calibration procedure [van de Giesen et al., 2012].
4. Results and Discussion
[16] Figure 2 displays example GFC temperature data
during heating. The high-frequency fluctuations on the
temperature traces are primarily caused by measurement
noise. This noise is greatly reduced by the averaging in
equation (1). The rate of temperature increase varies with
depth during a GFC heating test. For instance, the average
temperature increase during the 5 h of heating is 1.18 C at
depth 14.1 m, as compared to 1.05 C at 13.5 m and 1.03 C
at 14.5 m; the higher temperature increase at depth 14.1 m
can be explained by a relatively smaller rate of groundwater
flux. The Peclet number (ratio of thermal advection to
conduction) is about 0.1 (K 1.4 103 m/s, gradient
4.5 104, k 2 W/m C, and characteristic length (test well
ID) 0.1 m), indicating the relatively large role of conduction
in the overall heat transport. However, as emphasized
earlier, the k in the immediate vicinity of the well screen
(within the filter pack) should vary little, so differences
in ΔTave between depths can be primarily attributed to
variability in groundwater flux. Additional numerical
simulations (Figures S5–S10 in the Supporting Information)
show that when the k of the filter pack is 2 W/(m C) (a typical value for saturated sands), a horizontal Darcy flux of
4 106 m/s can reduce ΔTave by ~0.2 C as compared to
no flow (close to the maximum temperature difference
observed in our field tests).
[17] Figure 3 presents the average temperature increase
ΔTave, along with K estimates obtained using multiple
hydraulic test approaches (borehole flowmeter, multilevel
slug tests, and dipole flow tests [Butler, 2005]) at the same
well. The thin dashed lines are ΔTave profiles from 27
heating tests conducted between 12 December 2011 and
22 February 2012, with the thick solid line representing the
average. The spread of the individual ΔTave profiles around
the average is likely a result of the variability of the ambient
flow field and, to a lesser degree, unresolved DTS
calibration drifts and power input variations. Despite the
spread, all profiles across a given depth interval show
essentially identical hydrostratigraphic features (for the
aquifer at this site, smaller velocities!silts and finer
16.5
10.0
(a)
Depth Below Land Surface (m)
10.5
(b)
17.0
11.0
17.5
11.5
18.0
12.0
18.5
01102012
12.5
01112012
19.0
12122011
01122012
12132011
13.0
02082012
19.5
02202012
02092012
02212012
02132012
20.0
13.5
0.8
1.0
1.2
1.4
ΔTave (°C)
0.8
1.0
1.2
1.4
ΔTave (°C)
Figure 4. GFC profiles from well Gems4S obtained on different dates for (a) depths 10.55 to 13.05 m and (b) depths 17.05
to 19.6 m. The date format is month, day, year; a constant shift has been applied to each profile. In Figure 4a, all the profiles
closely match after applying a constant shift (0.02 C for profile 12122011, 0.03 C for 12132011, 0.03 C for 02202012,
and 0.02 C for 2212012). In Figure 4b, there is still a noticeable discrepancy between individual profiles after applying a
constant shift (0.05 C, 0.04 C, 0.05 C, 0.05 C, 0.05 C, and 0.03 C for profiles 01102012, 01112012, 01122012,
02082012, 02092012, and 02132012, respectively). The K for the depth range in Figure 4b is much higher than those of
other depths, and the temperature responses appear to be more affected by changes in the ambient flow field.
1101
LIU ET AL.: RESOLVING CENTIMETER-SCALE AQUIFER FLOW
sands—and; higher velocities!coarser sands and gravels).
The thermal profiles for the same depth range can be made
to nearly coincide by applying a constant temperature shift
(Figure 4; see Figures S3a–S3c in the Supporting Information for additional examples).
[18] The average of the thermal profiles from the heating
tests displays many of the general features seen in K profiles
from the same well (Figure 3). Most importantly, due to the unprecedented level of detail obtained with the GFC tool, valuable
new insights can be gleaned into the fundamental controls on
subsurface flow. For example, between 13.5 and 14.5 m, the
hydraulic test profiles indicate the presence of a low-K zone that
is generally consistent with grain size data (indicating a zone of
fine sediments); however, further information about that zone is
not available due to the relatively coarse resolution of those
profiles [Butler, 2005]. In contrast, the thermal profiles provide
a clear picture of the low-velocity zone, indicating a thin layer at
14.1 m that has a velocity much lower than that of the rest of the
zone. In addition, there is a zone of relatively higher velocity
(possibly the top of a coarsening upward sequence between
14.5 and 16 m) immediately below 14.5 m that was not detected
by hydraulic tests. Between 16.5 and 18.0 m, the hydraulic test
profiles show a decline of K. Based on the high-resolution
thermal profiles, however, the decline in K in this depth range
is primarily a result of another thin low-velocity layer at
17.3 m; between 16.5 and 17.3 m, the rate of groundwater flux
appears to be increasing, and there is a thin zone of relatively
high velocity immediately below the low-velocity layer. Obviously, for risk assessment and remediation activities, identification of such features will enable a more efficient allocation of
resources. The detection of these thin zones of relatively high
or low velocity, some of which are generally consistent with
the K profiles, can also be considered strong evidence that
vertical flow is of little significance at this site.
[19] The vertical distribution of K is commonly used as
a convenient surrogate for the vertical distribution in
horizontal groundwater flux. However, our results demonstrate that caution must be used when employing the vertical
distribution in K for this purpose. For example, GFC profiles
indicate that groundwater velocity at ~16 m depth is lower
than that at ~12 m depth (Figure 3), despite the K estimate
being considerably higher at ~16 m depth. This is likely
due to variability in the local hydraulic gradient produced
by hydrostratigraphic discontinuities. Although the vertical
distribution in K can be a valid surrogate for the flux
distribution in an aquifer with laterally continuous
stratification, our results indicate that it may be far from that
in more discontinuous systems.
[20] The current GFC tool has two major limitations. First,
it only provides a qualitative indication of groundwater
flux; further work is needed to establish the quantitative
relationship between the average temperature increase and
groundwater flux. This can be achieved through numerical
modeling of the heating tests and lab experiments under
controlled settings. Second, the current tool does not provide
information about vertical flow; as discussed earlier, zoned
heating can be used to address this limitation.
5. Conclusion
[21] We obtained near-continuous, high-resolution information about relative variations in horizontal groundwater
flux using the novel coupling of the proven concept of a
heat tracer for tracking groundwater movement with fiberoptic distributed temperature sensing (DTS) technology
(high-resolution wrapped cable configuration). The thermal
profiles display many of the same general features as
hydraulic conductivity (K) profiles from the same well.
The high resolution possible with DTS enables us to gain
important insights into groundwater flow under commonly
faced field conditions. Thin layers of relatively high or low
velocity, which have been poorly characterized by other
methods, are clearly identified from the thermal profiles.
Identification of such features will improve our understanding
of subsurface transport and lead to more efficient allocation
of resources for site characterization and remediation.
Finally, our results demonstrate that the vertical distribution
in K may not be an accurate indicator of vertical variability
in horizontal groundwater flux in highly heterogeneous
settings.
[22] Acknowledgments. The authors thank Scott Tyler, Christine
Hatch, and John Selker for generously sharing their DTS experience. Assistance on data processing from the Center for Transformative Environmental
Monitoring Programs is appreciated. We also thank three anonymous
reviewers and the Editor for their helpful comments.
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