A Novel Approach for Determining Transverse Dispersion

WRHSRC researchers have created two novel devices to measure pore-scale transverse dispersivity, an aquifer property that facilitates dilution and mixing of contaminants in groundwater. Their experiments with helical and cochlear devices suggest that the rates of pore-scale transverse dispersivity may be greater than the values often assumed in aquifer modeling and cleanup simulations.

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Figure 1 helps illustrate the concept of pore-scale dispersion. As solute moves through the pores of an aquifer it travels along multiple flow paths. Differences in pathway lengths, widths, and orientation, as well as local velocity variations, cause the solute to spread and mix with the surrounding groundwater. Rates of dispersion are controlled by average flow velocity, molecular diffusion, and by the dispersivity of the aquifer media, a property that describes the interconnectedness, size, and shape of aquifer pore-spaces.

Longitudinal dispersivity is parallel to the flow direction and can be measured in laboratory column experiments. When a tracer is introduced continuously at one end of the column, all of the tracer does not simultaneously arrive at the other end of the column. Instead, the tracer “breakthrough curve” shows spreading – with concentration gradually increasing (Figure 2). The width of the breakthrough curve is proportional to the longitudinal dispersivity. Unfortunately, a simple concentration breakthrough curve obtained at the outlet of a column experiment does not permit measurement of dispersivity perpendicular, or transverse, to the flow direction.

But what if the column was curved? In 2000, Stanford University professor Peter Kitanidis and his post-graduate researcher Olaf Cirpka, proposed measuring transverse dispersivity in a helix-shaped device (Cirpka and Kitanidis, 2001). The device makes use of the radial velocity differences created by shear flow in the helix. A solute will move more quickly along the inside of the curve than along the outside. When a tracer is introduced, this velocity gradient will enhance spreading of the breakthrough curve. Since transverse dispersion acts perpendicular to the flow direction, it will cause mixing in the helix transverse to the main flow direction and reduce the spreading of the breakthrough curve. The relationship between these two quantities is exact and allows transverse dispersivity to be calculated from the amount of spreading of the breakthrough curve. In fact, because the relationship is inverse, very small transverse dispersivities can be measured accurately -- the smaller the transverse dispersivity, the larger the spreading of the breakthrough curve.

Stanford graduate student Ioannis Benekos made dispersion experiments with the helix and a different spiraling device, a cochlea, the focus of his dissertation (Figure 3). Benekos ran multiple trials with the cochlea and helix and varied the types of tracers, glass-bead media, and flow rates. For each, he compared the experimentally determined breakthrough curve with a numerically predicted breakthrough curve and used an optimization process to adjust the numerical parameters until the curves matched. This process allowed him to estimate transverse dispersivity for each trial.

The helix and cochlea experiments were successful. The dispersivities that Benekos estimated with the helix matched those that he estimated with the cochlea and the confidence intervals within each set of experiments overlapped. Importantly, he found that his estimates for transverse dispersivity agreed with the high end of estimates reported in the literature for similar sized glass beads. He also found that the ratio of transverse dispersivity to longitudinal dispersivity was usually 1/2 to 1/3 – instead of the ratio of 1/10 that is assumed.

The team's findings have implications for the prediction of reaction rates, solute transport, and plume remediation times. For example, suppose that a groundwater model is used to predict the timeframe for natural attenuation of a contaminant plume. Use of a higher dispersivity ratio in the model would lead to a prediction of more mixing and faster dilution of the plume. This in turn, might decrease the remediation time predicted for the site.

The helix and cochlea methods are appealing for their simplicity. They allow accurate measurement of the illusive property of transverse dispersion with a procedure similar to a classic column experiment.