Where It Goes, Nobody Knows

by Laura Helmuth
Idaho National E & E Laboratory

In the more typical mixed soil or fractured rock environments between the earth's surface and the water table, said hydrogeologist Boris 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.

Faybishenko's collaborators at the Idaho National E & E Laboratory (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. 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.