Dec. 21, 1998 Water flows in mysterious ways. Lawrence Berkeley National Laboratory hydrogeologist Boris Faybishenko has discovered that the mystery of water flowing through the earth can be explained using chaos theory. Using this theory, he and his colleagues may be better able to model how water - and therefore waterborne contaminants - seeps from the earth's surface to the water table below.
Current modeling methods can predict water movements through the ground fairly well, if limited to homogenous soils such as sand. Many sites with radioactive or organic contaminants, however, such as the Department of Energy's Hanford and Savannah River sites and the Idaho National Engineering and Environmental Laboratory, sit on heterogeneous soils or fractured rock. "Heterogeneous soils are the rule rather than the exception," said Faybishenko.
In these mixed soil or fractured rock environments between the earth's surface and the water table, said Faybishenko, water flow processes are non-linear and chaotic - that is, small differences in the system's initial conditions can lead to large differences later on in the system. Furthermore, different equations and models are needed to describe the water flow depending on the scale one chooses to examine. In a presentation to the fall 1998 American Geophysical Union meeting in San Francisco on December 10, Faybishenko proposed a hierarchic set of models - some traditional and some chaotic -- to describe water flow through fractured rock.
Faybishenko and his colleagues, funded by the Department of Energy's Environmental Management Science Program, have investigated water movements at a range of scales. At the smallest scale, they studied water seeping between two glass plates. At the other end of the spectrum, a 1994 infiltration study led by project manager Tom Wood and a team of hydrologists from the INEEL tested water and short-lived radioactive tracer transport from a 6.5-acre pool through the underlying 600 feet of rock and soil to the aquifer below. Faybishenko and Wood first began to suspect that water flow through fractured rock might be a chaotic process when analyzing data from this large-scale test.
For about 15 years, Faybishenko had been keeping up with the scientific literature about chaos theory as a hobby. He expected to find applications of the theory in hydrogeology, and when he began working on field experiments in Idaho, his interest and knowledge reached a "critical mass," he said. Since then, he has returned to past data sets and found more evidence of chaotic behavior.
Faybishenko's collaborators at the INEEL have performed extensive field studies of water flow through fractures in basalt at small (less than one meter) and intermediate (ten-meter) scales. "The 100-meter scale is much easier to understand and model because of averaging properties in fractured rock," said department manager for ground water restoration Tom Stoops of the INEEL. "But the 10-meter or smaller scale," he said, "is crucial for environmental restoration." Gasoline stations, waste burial pits, and many spills are governed by the small-scale properties that the group is learning to characterize using chaos theory. "Clean-up takes place at the meter scale, one barrel at a time," said Stoops.
In order to uncover the chaotic equations that describe water flow at this scale, 5,000 or more data points must be collected, said environmental engineer Rob Podgorney of the INEEL. To generate all this data, the team spent last summer tracking water dripping through several fractures at Hell's Half Acre, a lava field outside of Idaho Falls. Because their approach combined the precision of a laboratory experiment with the real-world conditions of a field study, the INEEL researchers had to make or adapt many of the instruments they used for the tests. Water seeped from an artificial pond (whose level was maintained by a converted motorcycle carburetor) through a fracture in an overhang. Below, 20 sensors (using the same pressure sensor technology that makes kids' tennis shoes light up with each step) recorded the time and location of drips leaving the fracture. The innards from a laboratory balance measured the outflow of water along different portions of the fractures.
Strangely, subsequent experimental trials gave different results although the starting conditions were seemingly identical. The researchers kept track of temperature, humidity, flow rate, soil water pressure, and other variables - but nothing they measured could account for the wide variation of final results. "All of my training and experience suggested that if you do the exact same thing, again and again, the results should be fairly consistent," said Wood. "But they weren't."
This pattern of apparent unpredictability is a hallmark of chaotic systems. However, once the right equations are found - a process which may require a lot of ingenuity and computer time - they can predict the range of possible outcomes given a set of starting conditions. Faybishenko has already uncovered equations that describe the pattern of fractures in basalt and the trajectory of flow paths in the basalt. These non-linear equations also describe chaotic systems that have been discovered in biology, chemistry, and atmospheric sciences. "It's all the same nature," said Faybishenko.
When Faybishenko and his colleagues find the best equations to describe water flow at the appropriate scales, their hierarchical model may help guide waste remediation efforts and environmental monitoring. With the best models in hand, environmental restoration stands the best chance of stopping contamination before it steals into the water table.
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