Tracer tests are used to "trace" the path of flowing water. Tracer tests are conducted in pipelines, lakes, rivers and groundwater. The tracer chemical must be dissolved in water at concentrations that do not significantly change the aqueous density. Tracer chemicals must behave conservatively --> meaning no mass is lost through reaction or partitioning into differing phases (vapor, solids). Thus, the only solute transport processes affecting a conservative tracer are advection and dispersion. Advection is the movement of the solute (dissolved tracer) due to groundwater flowing and moving. The mean pore-water velocity (calculated from Darcy's Law) is used to predict advection. As the pore-water velocities within the groundwater are not uniform (variability around the mean velocity), some solute will move slower than the mean velocity and other solute will move faster than the mean velocity. The resulting dispersion of the solute causes a broadening of the solute plume and a decrease in the concentration. The ambient or background level of tracer chemical in the receiving waters must be low.

 

The most common tracers used in groundwater studies are:

• fluorescent dyes such as fluorescein and rhodamine-WT
• halides such as chloride, bromide and iodide

At the SDSU Well Field Site, groundwaters are fairly high in chloride. The high background chloride levels prohibit the use of chloride as a tracer. Bromide and iodide can be used as tracers but can be expensive. We will be using fluorescein dye, a greenish-yellow fluorescent dye, for our tracer test. Fluorescein can be degraded photochemically by sunlight. Limiting the exposure to sunlight at the surface will eliminate the concern of photochemical degradation. Rhodamine-WT can be used as a tracer but has been found to sorb onto the aquifer solids to some extent at this field site.

 

Fluorescein levels will be measured in water samples and standards by a Turner fluorometer. Standards will be prepared from a concentrated stock solution of fluorescein and used to create a calibration curve. Water samples with an unknown concentration will have their fluorescent levels for fluorescein measured with the fluorometer and its calibration curve.

The tracer must be introduced into the flowing water at an injection point. You must have some prior knowledge of the direction of water flow to be able to identify monitoring points downstream or downgradient.

In groundwater systems, the simplest flow field is a uniform regional hydraulic gradient which produces a uniform pore-water velocity in one direction.

In this case:

Darcy's Law: velocity = K x hydraulic gradient/porosity

For review of groundwater flow and contours see http://www.geology.sdsu.edu/classes/geol351/gwtutorial.htm

Measurement of the hydraulic gradient allows you to identify the direction downgradient of your injection point. With estimates of hydraulic conductivity, K, and porosity, you can estimate the length of time for the tracer to travel from the injection to the monitoring point.

Tracer transport time = (distance between injection and monitoring point) / velocity

 

In our tracer test, a radial flow system will be set up by the pumping well.

Note from the flow lines shown, that many flow lines are captured by the pumping well which will contain no tracer. This will cause dilution within the pumping well and the measured tracer concentration in a pumping well will be much lower than the injected tracer concentration. This process is independent of dispersion.

The cross-sectional area of flow toward the pumping well has the shape of the walls of a cylinder (sides of a can). The area is the perimeter of the circle of the cylinder (2 pi r) multiplied by the height of the cylinder (b):

 

The flow according to Darcy's Law is Q = K A i = K (2 pi r b) i. Where, r = distance from the pumping well. Looking at this equation, we know that Q and K are constants for a homogeneous isotropic aquifer and constant pumping. What must happen to the hydraulic gradient (i) with decreasing r from the pumping well?

Pore-water velocity is v = Q/(A theta) where theta = effective porosity of the aquifer. Substituting in our cross-sectional area for radial flow, we can calculate the mean pore-water velocity within the radial flow system (see equation below). Note that it is not constant and is dependent on the radial distance from the well.

Assuming neglible contributions from the regional flow field and from the tracer injection point, the pore-water velocity produced by a pumping well varies with radial distance from the well:

v(r) = Qe / (2 pi r b theta) = dr/dt

where, v(r) = pore-water velocity as a function of r

Qe = pumping rate [L cubed/T]

r = radial distance from pumping well [L]

b = aquifer or permeable zone thickness [L]

theta = porosity

dr = differential change in radial distance

dt = differential change in time

 

Integration of the above equation provides an equation for the travel time from radial distance, r2, to radial distance, r1. Note that in radial coordinates, the pumping well is at r=0 and water and tracer moves from larger radial distances to smaller radial distances (towards the well).

Travel time = [pi b theta/Qe] [(r2)^2 - (r1)^2]