Introduction and Objective
Studying the transport of contaminants through the subsurface is
important in ensuring clean drinking water supplies and for developing
cost-effective strategies for cleanup of contaminated sites. Hydraulic
conductivity is the most critical parameter controlling
groundwater flow and contaminant transport, and is extremely variable. It is important to
represent small-scale heterogeneities in the hydraulic conductivity distribution when modeling
contaminant transport, as contaminants tend to move along pathways of higher conductivity and
avoid areas of low conductivity (Zheng and Bennet, 1995). Recent studies have suggested that
fractals have the innate ability to represent heterogeneities at a wide range of scales. Fractals are
essentially scaling laws that can be used to generate non-smooth hydraulic conductivity
distributions. Typically, smoothing techniques such as kriging are widely used, even though real
hydraulic conductivity distributions are not smooth (Molz and Bozman, 1993).
The MADE (macrodispersion experiment) and NATS (natural attenuation
study) site at
the Columbus Air Force Base (AFB) in Mississippi will serve as the study site for this
project. The aquifer at the site is at least an order of magnitude more heterogeneous than
those at other sites. Zheng and Jiao (1998) simulated tracer tests at this site using a
standard advection-dispersion model, and found that the simulated plume is highly sensitive to
the interpretation of the hydraulic conductivity field. In the study, a detailed hydraulic
conductivity data set was available, yet the simulated plume failed to accurately represent fast
spreading observed in the field. This spreading is believed due to transport along certain
preferential flow pathways resulting from a highly heterogeneous hydraulic conductivity
distribution. It is evident that the advection-dispersion model with smooth hydraulic
conductivity distributions cannot accurately characterize transport along preferential flow
The method of hydraulic conductivity interpretation based on fractal
allow for improved representation of spreading of the tracer at diluted concentrations, as it is
capable of characterizing the fine structures of the flow paths (on microscopic scales) which
induce dispersive effects at the macroscopic scale (Impey and Grindrod, 1991).
The primary objective of this project is to evaluate the solute
transport behavior in fractal-
based hydraulic conductivity fields by simulating tracer tests conducted at the MADE/NATS site.
The simulation results for the tracer tests will be compared with observations and other
simulation results based on standard interpolation techniques such as kriging. This will provide
an excellent opportunity to test the hypothesis that fractal-based hydraulic conductivity
distributions allow for more accurate modeling of solute transport in highly heterogeneous
Alluvial terrace deposits make up the shallow unconfined aquifer underlying the
MADE/NATS site. It averages a thickness of 11 m. The aquifer consists of unconsolidated
poorly sorted to well sorted sandy gravel and gravely sand with minor amounts of silt and clay.
An aquitard of the Eutaw Formation is beneath these sediments, consisting of clay, silts, and
fine-grained sands. The general direction of groundwater movement is northward, although
local differences in the magnitude and the direction of hydraulic gradient are evident (Zheng and
Jiao, 1998). In the MADE-2 test conducted between 1991 and 1993 (Boggs et al., 1993), a
tritium tracer was injected into the aquifer for two days (3.3 L/min) and extensive snapshots of
the tracer plume were taken at 27, 132, 224, 328, and 440 days. Hydraulic conductivity values
throughout the site were determined from over 2000 borehole flowmeter measurements.
Hydraulic head values were collected by a network of 48 piezometers at different elevations,
and sixteen of these piezometers were equipped with continuous groundwater level recorders
(Boggs et. al., 1993). In the more recent NATS test (T. B. Stauffer, unpublished data), a known
amount of the bromide tracer mixed with soils was introduced into the aquifer through
excavation. Distributions of the plume have been monitored at regular time intervals since
December 1995. Additional hydraulic conductivity and hydraulic head data have also been
Methods and Approach
Hydraulic conductivity distributions will be generated directly from the
measured borehole flowmeter data using fractal-based techniques.
The fractal-based hydraulic conductivity fields will be used in a
three-dimensional flow and transport model of the
MADE/NATS site. The flow and transport model will be run for each new
hydraulic conductivity field generated. Simulated plumes based on
fractal generated hydraulic conductivity distributions will be compared
with those based on kriging interpolated hydraulic conductivity distributions
and with those from a previous model of the site (Zheng and Jiao, 1998).
From the comparisons it can be determined if models based on fractal-based
generated hydraulic conductivity distributions can reproduce the wide
spreading of tracers at diluted concentrations as observed in the field.
Moment analysis will be used to calculate the zeroth, first and second
moments of observed and calculated tracer plumes for comparison purposes.
If fractal-based techniques for interpreting hydraulic conductivity
the vast amount of available data results in significant improvement in
modeling the anomalous tracer spreading,further continuation of the study
will examine if a sparse hydraulic conductivity data set can be
interpolated through fractal-based techniques while retaining
heterogeneities. It will be imperative to note how many data points are
needed to define the fractal scaling law as well as how much the data can
be scaled up. The ability of transport simulations with fractal-based
hydraulic conductivity distributions to reproduce plume-scale features
observed in tracer tests will then be documented.
Significance and Anticipated Results
By testing the hypothesis that transport models based on fractal generated
hydraulic conductivity fields are more likely to reproduce anomalous
spreading of contaminant plumes at the highly heterogeneous MADE/NATS site,
this research project will improve our understanding of solute transport
processes in heterogeneous aquifers. It will also contribute to
the development of more effective methods for accommodating small-scale
heterogeneities in contaminant transport models, an issue of enormous
practical implications, as more accurate characterization of
heterogeneities will lead to more cost-effective strategies for cleaning
up contaminated aquifers.
Boggs, J.M., L.M. Beard, S.E. Long, M.P. McGee, W.G. MacIntyre, C.P.
Antworth, and T.B.
Stauffer, 1993, Database for the Second Macrodispersion Experiment
(MADE-2), Tech. Rep.
TR-102072, Elec. Power Res. Inst., Palo Alto, CA.
Impey, M.D. and P. Grindrod. Fractal Field Simulations of tracer migration within the WIPP
Culebra dolomite. Draft for approval IM2856-1 version 1. Intera Information Technologies,
Molz, F. J. and G. K. Bozman, A fractal-based stochastic interpolation scheme in subsurface
hydrology, Water Resources Research, 29, 3769-3774,1993.
Wheatcraft, S. W. and S. W.Tyler. An explanation of scale-dependent dispersivity in
heterogeneous aquifers using concepts of fractal geometry. Water Resources Research,
24(4), 566-578, 1988.
Zheng, C. and G. D. Bennet, Applied Contaminant Transport Modeling: Theory and Practice,
Van Nostrand Reinhold, New York, 1995, 440pp.
Zheng, C. and J.J. Jiao, Numerical simulation of tracer tests in a heterogeneous aquifer, Journal
of Environmental Engineering, to appear in June 1998 issue.
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