Intermediate-scale Lx=Ly=10? Lz=15?v

1
A THREE-DIMENSIONAL PHYSICAL MODEL TESTS TO
EVALUATE TRANSPORT PARAMETERS IN HETEROGENEOUS
AQUIFERS Daniel F. Garcia1, Tissa H.
Illangasekare 1, Hari Rajaram2  1 Environmental
Science and Engineering Division, Colorado School
of Mines, Golden, Colorado. 2 Department of
Civil, Environmental and Architectural
Engineering, University of Colorado, Boulder.
Large-scale LxLy80? Lz80?v
Intermediate-scale LxLy10? Lz15?v
ABSTRACT Obtaining accurate estimates of
transport parameters is crucial for the
prediction of contaminant migration in aquifers.
Frequently, tracer tests are used to obtain
transport parameters such as the dispersivity
coefficient. However, analysis and interpretation
of data from such tests have been found to be
difficult as the dispersivity is not only a
function of tracer plume displacement but also
depends on the type of test. In a previous
two-dimensional study, it was shown that
dispersivity estimated using a limited number of
convergent radial tracer tests was not adequate
to simulate plume migration under natural
gradient conditions. The discrepancy between
dispersivity estimates obtained from radial flow
(involving small sources) and uniform flow
(involving large sources) tracer experiments in
our two-dimensional study appear to be
attributable largely to non-ergodic effects. It
may be expected that effects are not so dramatic
in a realistic field setting where the small
vertical correlation scale permits a tracer
source that is several meters deep to sample the
medium heterogeneity effectively, even if its
horizontal dimensions are small as in typical
forced gradient tests. To further evaluate this,
experimental and modeling investigations were
conducted in a three-dimensional setting.
Experiments were conducted in a three-dimensional
sand tank packed with heterogeneous media, in a
configuration similar to well-studied field
sites. The heterogeneous medium is formed by five
different types of silica sands distributed in
the tank in such a way that the resulting
log-transmissivity field follows a second-order
stationary random function characterized by a
small vertical anisotropy ratio. Several
experiments were conducted by placing continuous
tracer injection points at different distances
from the pumping well and also by changing the
screen length of the injection well. An
accompanying computational study conducted using
a three-dimensional transport model that was
validated using the experimental data focused on
simulations of flow and transport in media larger
than the test domain. This investigation
provided accurate laboratory and numerical data
to evaluate stochastic theories of subsurface
transport under non-uniform flow that are used to
interpret tracer data.
Methodology
Figure 2 shows heterogeneous random field
generated to represent a field system. A portion
of this field system extracted from the center
was reproduced in the laboratory in an
intermediate-scale three-dimensional test tank
(Figure 1). Experimental and computational
investigations first focused on this portion of
the aquifer. Validation of the flow and transport
model using the experimental data generated at
this smaller scale permits us to further
investigate the flow and transport at much larger
field scale.
Figure 1
Figure 2

Intermediate-scale experimental setup
Preliminary Experimental Results
Instrumentation and Methods
Radial tracer tests were performed in a
three-dimensional tank 243.84 cm long, 121.92 cm
wide and 63.5 cm high. The tank frame structure
consists of plywood panels and aluminum beams.
Thin PVC sheets lined the inner part of the tank
and provided an excellent seal. The heterogeneous
packing depicted in Figure 1 is placed in the
middle of the tank using rigid screens. The
portion of the tank between the packing and the
tank walls was used as supply tanks to create
constant head boundary condition needed for
radial flow tests (Figure 3). A constant head
spill reservoir connected to the supply tank
ensures the constant head.
A total of 14 tracer injection devices were
placed in the tank at different radial distances
away from a centrally located pumping well
(Figure 3). These devices (point as well as line
sources) were used to inject tracers
continuously at different distances from the
well. During the test 3-ml. water samples were
collected from the pumping well. Tracer
concentrations in the collected aqueous samples
were measured with the HPLC.
A total of 24 pressure ports were placed
throughout the test domain as shown on Figure 4.
These ports were made of thin stainless steel
tubing that could be moved vertically to measure
the pressure at any depth in the tank. All
pressure ports were connected to a precision
pressure transducer through of a scanning fluid
switch. A solenoid controller was used to rotate
the scanning valve that connects the pressure
transducer to each port sequentially. The
heterogeneous packing was created using a metal
grid made of tin sheets that forms a rectangular
mesh of 20?20 cells. The grid had sufficient
depth to allow for the packing of three layers
before it was moved to the next elevation using a
pulley system.
Comparison between point and line source


Layout of injection and pressure ports
Figure 5
Summary of Experiments
Figure 4
Table 1
2
A THREE-DIMENSIONAL PHYSICAL MODEL TESTS TO
EVALUATE TRANSPORT PARAMETERS IN HETEROGENEOUS
AQUIFERS Daniel F. Garcia1, Tissa H.
Illangasekare 1, Hari Rajaram2  1 Environmental
Science and Engineering Division, Colorado School
of Mines, Golden, Colorado. 2 Department of
Civil, Environmental and Architectural
Engineering, University of Colorado, Boulder.
3-D View of the Evolution of the Plume
Transport Simulations
Validation of Flow Model
SUMMARY We conducted a series of
intermediate-scale flow and tracer experiments in
a three-dimensional test tank to generate a
comprehensive data set to validate upscaling
theories and modeling tools. Preliminary results
indicate that the flow and transport simulators
correctly represent the physical phenomena. It is
shown from experimental and numerical radial
tracer tests as well as from snapshots of the
solute plume associated with injections at the
same distance from the pumping well that a
three-dimensional aquifer may inherit large
degree of variability in transport parameter
estimates. It is postulated a less dramatic
effect compare to the previous two-dimensional
studies. Further, we illustrate the effect that
the use of different screen length of the
injection well may cause on the transport
estimate.
The Random Walk technique was found very
convenient in this case where radial mixing
induced by pumping from a full penetrating well
had to be simulated. The transport code provides
different velocity interpolation algorithms and
is designed to simulate radial flow tracer tests
with pulse and step inputs. The pulse response
function was generated using the numerical
model. The response to continuous tracer
injection was computed through discrete
convolution of the pulse response. This scheme
was computationally efficient as it did not
require the use of the numerical model to
simulate continuous injection of particles into
the system. The velocity field is obtained from a
seven-point finite difference groundwater model,
MODFLOW96. In Figure 7 we present the simulation
of experiment 2. Figure 7a shows snapshots of
the evolution of the solute plume whereas Figure
7b illustrates the model match to the
experimental breakthrough curve. We see that the
mathematical model can greatly reproduce the
physical behavior.
Head values simulated using the experimentally
determined hydraulic conductivities of the sand
matched well with the observed heads. The most
reliable measurements result in simulated pumping
rates with less than 5 of relative error.

Figure 7b

• FUTURE RESEARCH TASKS
• Validate numerical modeling tools (flow and
  transport simulators and inverse models) that
  will be used in data analysis.
• Quantify the scale dependence of dispersivities
  estimated from radial tracer tests using
  curve-fitting techniques as well as the
  variability of these estimates in
  three-dimensional aquifers.
• Use the understanding gained from laboratory and
  computational investigations to develop a
  systematic approach for characterizing field
  sites based on radial flow tests. Determine how
  many tracer tests and over what scale will lead
  to reliable estimates of transport parameters.
• Compare intermediate-scale and large-scale
  experimental and simulation results with existing
  theories. Specifically, study of the
• Scale dependence of effective hydraulic
  conductivity in radial flow.
• Experimentally and computationally quantify
  discrepancy between dispersivities estimated from
  uniform and forced-gradient tracer tests in a
  realistic three-dimensional aquifer.
• Quantify effect of the source type in
  three-dimensional aquifers.

Figure 7a
Figure 6
Top View of Snapshot of the Plumes
Side View of Snapshot of the Plumes
Figure 8a
Figure 9a
Table 2


Preliminary Computational Investigations
In Figure 8 and 9 we show some preliminary
intermediate-scale computational results in
dispersive radial flow in three-dimensional
aquifers to illustrate the effects that
variations in hydraulic conductivity may
originate in the behavior of solute migration.
Specifically, figures 8a and 9a show snapshots of
the evolution of the solute plume associated to
injections located at the same distance from the
pumping well. Figures 8b and 9b present the
breakthrough curves obtained at the pumping well
resulting from these injections. As previously
shown in two-dimensions Chao et al, 2000, it is
observed large variations in the arrival time of
peak concentrations as well as in the spread of
the breakthrough curve. This may lead to large
uncertainty in transport parameters estimates
obtained from single tracer tests. Quantification
of this effect in a three dimensional setting
will be done in future work. Within this context,
the third dimension is expected to lead to a less
dramatic effect compares to the previous
two-dimensional studies.
Injection points
REFERENCES
Chao, H.,-C., Rajaram, H., Illangasekare, T.,
2000. Intermediate-scale experiments and
numerical simulations of transport under radial
flow in a two-dimensional heterogeneous porous
medium. Water Res. Res., Vol. 36 (10), 2869-2884.
Figure 8b
Figure 9b