Summary of the Problem
Contaminants in groundwater tend to disperse –
that is they tend to spread and create a diffuse plume
rather than move as a front with a constant concentration.
Dispersion perpendicular to the aquifer flow direction
is called transverse dispersion and plays an important
role in the remediation of contaminants. It helps
to dilute their concentration and to mix the contaminants
with reactive compounds and microbes in the surrounding
Despite its importance, dispersion
is difficult to measure and is poorly understood.
This research brief describes work by WRHSRC researcher
Kitanidis and his research team at Stanford University
to develop novel devices that can accurately measure
pore-scale transverse dispersion.
A Novel Approach for Determining
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.
Click on highlighted words for illustrations and links.
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.
Peter Kitanidis, or refer to the following:
Benekos, I. D., O. A. Cirpka, and P. K. Kitanidis (2006) Experimental determination of transverse dispersivity in a helix and a cochlea. Water Resources Research, 42, W07406, 10.1029/2005WR004712.
Benekos, Ioannis D. (2005) On the Determination
of Transverse Dispersivity: Experiments and simulations
in a helix and a cochlea. PhD dissertation, Department of
Civil and Environmental Engineering, Stanford University,
Benekos, I., and P.K. Kitanidis (2004) Experimental
Determination of Transverse Dispersivity in a Cochlear Device,
Western Pacific Geophysics Meeting, August 15-21, Honolulu,
Benekos, I., and P.K. Kitanidis (2004) An
Optimization Approach Using Tracer Concentration Breakthrough
Curves for Determining the Transverse Dispersivity in a
Cochlear Device” EPA-HSRC Workshop on Risk Assessment
and Monitoring Research, November 4-5, Las Vegas, NV.
Benekos, I., P.K. Kitanidis, M.A. Rahman, and O.A. Cirpka
(2001) Experimental and Mathematical Studies of Pore-Scale
Transverse Dispersion in a Helical Soil Column, AGU Fall
Meeting, December 10-14, San Francisco, CA.
Cirpka, O.A. Kitanidis, P.K. (2001) Theoretical basis for
the measurement of local transverse dispersion in isotropic
porous media. Water Resources Research 37(2):243-252. Link