Exercise Set 3

If you have not already downloaded the spreadsheets for the exercises and their solutions that are presented in this book, you can do so at the gw-project.org website on the Groundwater Velocity book page by downloading the interactive Microsoft-Excel spreadsheets titled “GWP_Velocity_Exercises.xlsm” and “KeyFile_GWP_Velocity_Exercises.xlsm”.

Open the spreadsheet “GWP_Velocity_Exercises.xlsm”. You may receive a message about enabling content, updating content, or circular references. Proceed by clicking enable content, not updating content, and clicking OK for circular references. Then click on the Exercise 3 tab and look over the interwell tracer test model domain (area in green) as shown in Figure Exercise 3-1. The dispersivities are set to 0.1 m in the flow direction and 0.01 m in the transverse direction.

Above the model domain, the area shaded blue contains three input variables

1) the seepage velocity in m/d

2) the tracer pulse dimension (centered on the injection well) in the flow direction

3) the tracer pulse dimension (centered on the injection well) transverse to flow

This plume is calculated on a two-dimensional plane assuming a unit thickness in the third dimension (into the page) with uniform conditions throughout the model in that direction.

Three control buttons are provided:

1) ‘Reset the time’ button that resets the model to initial conditions, at time = 0 days immediately after the tracer is injected.

2) ‘Start the test’ button to start the clock (and flow) in the test.

3) ‘Stop Execution’ button suspends the simulation. Once this button is depressed, the test cannot be resumed. A new test must be started by once again pressing the reset button and then the start button.

Beneath the domain is a clock, with bold writing and an orange background. The clock reports the time in days since injection.

To the right of the model domain are two graphs. The upper one shows the concentration of tracer along a line that runs left to right through the middle of the plume at each instant in time. This is a ‘profile of the pulse’ as shown in Figure Exercise 3-1a. The red dashed line in Figure Exercise 3-1a shows the location of the well on the centerline of the plume. The other graph shows the history of tracer in each of two wells located 10 m from the injection well. One well is on the centerline and the other is off to the side. These graphs of concentration versus time are known as ‘breakthrough curves’ as shown in Figure Exercise 3-1b.

Starting an interwell tracer test:

The first time the sheet is accessed, the entry for velocity in the input (blue) area will be blank. This is the correct condition to start a test in which the user must determine a velocity chosen by the sheet. At the end of the test, after the user has pushed the ‘stop execution’ button, the user’s estimate of v can be typed into cell O29 and the sheet will report either “Success!” or “Please try again”.

1. If the user wishes to see a test with a particular velocity, then the user-entered value can be typed into cell C5 and the model will run with that velocity.

To start a test, press “Reset the Time” followed by “Start the test”. The tracer will begin its journey from the injection well to the monitoring wells.

Enter a velocity of 1 m/d into C5 and run a simulation. How many days pass before the peak of the tracer pulse reaches the monitor on the centerline?

*The solution for Exercise 3-1 extends from row 169 to row 186 of the Solutions Tab of KeyFile_GWP_Velocity_Exercises.xlsm*

2. Delete the entry in C5 so the velocity input appears to be blank. Reset the time and start the test again.

This time note the time required for the tracer pulse peak to reach the monitor 10 m away and calculate the groundwater velocity. Enter this value in O29 and determine whether or not your answer is correct.

*The solution for Exercise 3-2 extends from row 187 to row 205 of the Solutions Tab of KeyFile_GWP_Velocity_Exercises.xlsm*

3. In Exercise 3-2, the velocity was estimated from the arrival time of the peak. Is this the best part of the curve to use?

Run tests with input shown in Figure Exercise 3–3 and repeat tests for x_o = 2, 4, and 6 m, effectively changing the source size. Note the arrival time of C = 0.1, C= 0.5 (relative to the maximum concentration that crosses the monitor on the centerline), and the peak and calculate the apparent velocity from each. Which one is closest to the correct value of 1? Explain what is happening here.

*The solution for Exercise 3-3 extends from row 206 to row 226 of the Solutions Tab of KeyFile_GWP_Velocity_Exercises.xlsm*

4. If you ran an interwell tracer test with your monitor well not on the centerline, would the velocity estimate be accurate?

Answer this using the breakthrough curve graphs. Run several tests with the input y_o varying between 1 m and 8 m and record the velocity determined from each monitor. Type a velocity of 1 m into the v input cell (cell C5) and leave x_o at 2 m. Run all simulations with this velocity value fixed. Under what conditions are the estimates in best agreement? Worst?

*The solution for Exercise 3-4 extends from row 230 to row 248 of the Solutions Tab of KeyFile_GWP_Velocity_Exercises.xlsm*