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 pathways. The method of hydraulic conductivity interpretation based on fractal scaling may 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 aquifers.

Site Description

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 collected.

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 using 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, Dec. 1991.

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.

Return to my page.

Return to the Hydrogeology Group at University of Alabama