The document describes several experiments analyzing heat transport through saturated sediments. A sandbox model was used to study heat flow, showing a cold front moving through the saturated zone over 3-5 hours. These results were modeled using TOUGH2 software. A flume experiment monitored temperature changes over 8 hours as the stream and groundwater reached equilibrium. Distributed temperature sensing (DTS) was then applied, measuring temperature variations in the flume induced by upstream heating. The high precision DTS data validated other measurements and provided spatial and temporal data on heat transport through the saturated sediments.

1. Spatial and Temporal Analysis of Heat Transport through Saturated Sediments
in Sandbox and Flume Models
Mitchell Schutte, John Teppler, and Cassandra Wolf
Department of Geosciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin
Geosciences Undergraduate
Research
Abstract
Spatial and temporal behavior of heat transport through fully saturated sediment was studied using a
variety of experimental models. Knowledge of heat transport was obtained by implementation of a
sandbox model. Point-based transducers were used to collect temperature and pressure readings
from input and output tanks. Once the model was fully saturated with warm water and steady state
flow was obtained, warm water was removed from the input tank and replaced to a constant cold ice
water flow. The transducer data allowed for interpretation of the dynamics of cold fronts through the
saturated zone and help generate a computer model showing heat changes through the sediment,
through time. Increasing the scale, transducers allowed study of flow through the saturated sand of
the flume. The transducers, through time, were able to read a gradual decrease in temperature in the
flow of the saturated sediment and an increase in stream temperature. After calibration times were
monitored, constants of fluid properties between the saturated zone and the stream flow of the flume
were established. With this background, distributed temperature sensing (DTS) through fiber optic
cables buried in the flume sediment were implemented with the capabilities to measure temperature
changes of 0.01 °C. Heat was induced upstream from the DTS to measure temperature variations
along the stream bed surface. The DTS refined prior conclusions of the relationships of saturated
flow rate to heat transport. This research advanced understanding of the use, application, and
capabilities of the DTS technology. Moving forward continued DTS research will be used to monitor
seasonal and diurnal changes in the hyporheic zone of streambeds of the Fox River.
Objectives
Evaluate small scale heat flow through saturated sediment in sandbox model
Understand fluid dynamics of flume environment
Apply Distributed Temperature Sensing calibration and implementation in large scale laboratory
setting
Understand how to properly implement long term DTS field study
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Conclusion
In Figure 9, the vertical black line indicates 240 minutes representing the time the heat was
introduced. The double black horizontal line represents the temperature the stream and ground
water reached. The goal was to obtain equal temperature through the stream and ground. The
equilibrium was not perfectly met, but the data shows an approximate 0.5 °C difference. After the 4
hours, all transducers both in sediment and stream, located 0.13 and 1.74 meters from heat source,
showed immediate increase in temperature response. The DTS wrapped cylinder laid within the
transducers boundary, coincided with immediate temperature response. Figure 10 combines 480
individual files creating a plot of time vs. length as a function of temperature. The top half of the
graph validates sediment transducer data of the initial 4 hour decrease of temperature. After the heat
was introduced at the black line, the slow warming color gradient shows the most dramatic increase
of temperature at the first 20 meters of wrapped cable. After the 4 hours of heat, the entire length of
wrapped cable shows a detectable raise in temperature. Figure 8 is a complete temperature vs.
length plot showing the full potential of how much cable can be deployed. The red circle highlights
the last 180 meters of cable applied in this experiment. It is important to note there is a considerable
amount of unused cable. Field settings would provide better use of the full cable length and deliver
more meaningful data. Future work for this project involves the installation of the full 1000 meter
cable in the Fox River.
Sandbox
The sandbox model was performed to demonstrate heat flow through saturated, well-sorted sand.
The dimensions of the sandbox are 1.175 meters by 0.500 meters. Head decreases to the right, from
the input tank, to the output tank. One transducer was placed in the input tank and two were
staggered top to bottom in the output tank. To start the experiment, hot water (42 °C) was injected
into the model for 2 hours until the output transducers showed an adequate temperature elevation
(23-30 °C). The hot water was drained from the input tank, filled with ice, and constant cold water (4
°C) filled the input tank and proceeded to progress through the model. Figure 2 shows the output
transducers interact with the cold front 3 hours into the experiment. From 3 to 5 hours the cold front
continued to decline the output transducers temperature until the input and output become equal.
Modeling Temperature Flow with TOUGH2
The TOUGH2 petrasim model is a 2-D representation of the sandbox system, with the same
dimensions, to simulate a similar system. A pressure gradient was assigned based on the head
gradient. Instead of an injection well on the right, a one grid block wide column was defined as an
extremely high density rock with a temperature of 4 °C to stimulate heat flow. This computer model
starts at hour 2 of the experiment, so the rest of the rock was given and initial temperature of 27 °C,
an average of the top and bottom output transducers. There was also no output tank in the model,
only a no flow boundary.
Distributed Temperature Sensing
Distributed Temperature Sensing (DTS) is a new technology that recently has been fine tuned for
geologic use. The applications range from surface and near surface hydrologic processes, ground to
surface water interaction, bore-hole circulation, and sensing temperatures of water, air, and various
other media. The DTS machine has optical connectors for multiple lengths and varieties of fiber optic
cables. Light is sent from a laser starting at DTS machine output, through the entire length of cable
and back. The temperature is measured from the ratio of backscattered photons: Stokes (lower
frequency) and Anti-Stokes (higher frequency). As temperature increases, the light photons vibrate at
a higher frequency, changing the ratio, resulting in the systems calculation of temperature along the
cable.
After flume dynamics were observed (Figure 5), appropriate background knowledge allows
implementation of DTS unit. After test ran for 4 hours, the stream to groundwater temperature has
converged steadily, the DTS then starts to capture induced heat flux through space and time, while
the stream and sediment transducers validate recorded DTS data. This 8 hour experiment consisted
of calibrating the temperature offset of the fiber optic cable and setting measurement time intervals.
This system allows for temperature measurement every 1 meter with 0.01 °C precision.
Acknowledgments: Dr. Weon Shik Han, Jack P. Graham
Flume
The Flume is a laboratory controlled model of stream sediment and flow. It is an elongated artificial
stream bed that recirculates water at variable flow velocities. The flume dimensions are 10.36m x
1.23m x 1.23m. This controlled environment provides a replicable setting for each consecutive
experiment. These experiments progress knowledge of the natural stream and sediment
interactions, and how the relationship of the two react to induced temperature.
The first experiment, seen in Figure 5, shows the interaction of stream and ground water
temperature over time with constant flow. This step is necessary to understand the natural system
properties over extended time periods. One can view this as a form of calibration. The stream flow
was initiated at a constant rate of 0.28 m/s for 5.5 hours.
Utilizing 5 buried point-based transducers, in 2 meter interval spacing (1m, 3m, 5m, 7m, and 9m),
the groundwater temperature was recorded throughout the length of the sediment. The stream
temperature was captured separately by 2 floating transducers placed near the upstream, input of
flow, and downstream, recirculating output tank.
Initially, groundwater data showed warmer temperatures ranging from 14.5-16.2 °C whereas stream
temperatures varied from 6.5-7.5 °C. Over the 5.5 hours, the temperature differences between the
two decreased, heading towards a steady state equilibrium temperature. Final experimental data
shows groundwater temperatures at 11.5-12.8 °C and stream temperatures reaching 9.8-10.5 °C.*
Figure 5 allows for interpolation of the ground and stream water reaching calibrated equilibrium in 8
hours at 11.8 °C.
Figure 4
Figure 1
Figure 3a
3d
Using Sensornet ORYX DTS unit accompanied by 1000 meter Brugg fiber optic cable, the calibration
was set to store data points formatted as separate distributed temperature files every 1 minute, while
the transducers collect data through one measurement per minute forming one continuous file.
Separate drainage from input and output tanks create an uneven desaturation of sediment, causing
sediment at 5 meters (center) to retain the most water. The cable was tightly wrapped around a
hollow cylindrical tube of 1.034 meters in length with a circumference of 0.7037 meters. The cable
circled the tube approximately 270 times validating the last 180 meters of measurements. The
wrapped cable was then buried in the sediment aligning the center of the tubing to the 5 meter
center of the flume. 1000 Watt titanium submersible heating device was placed 0.4 meters upstream
from DTS burial site. Two sediment and stream transducers were placed upstream and downstream,
4.35 and 5.96 meters respectfully, from the input tank.
Compared to the experiment, the simulated model shows the first cold front reaching the other side
of the tank at 1 hour, seen in Figure 3b. The same time the output transducers start to show a
decrease in temperature. The cold front continues to decrease the temperature as it travels to the
right and runs for 9 hours; since there is no output tank in the simulation, an accumulation of slightly
warmer temperatures linger on the right side.
Though the sandbox data ends at 3 hours after the cold water introduction, the simulated data
continues to show heat flow for 9 hours. This discrepancy could be due, in part, to the transducer
data recording only two output points whereas the simulation gathered data at every grid block, at
every time step. The discrepancy in the experimental data comes from the output tank allowing
warm water to leave the system whereas the simulation necessitates an equilibrium to be reached
with no removal of water.
Figure 6a 6b 6c
Figure 7 Figure 8
Figure 9a 9b
Figure 10
3b
3c
Output TankInput Tank
1.175 Meters
1 Hour
9 Hours4 Hours
Head Gradient
10 m 5 m 1 m
Figure 5
1.034
Meters
Figure 2