Exercise Set 4

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 4 tab and look over the interface. There are two areas where the user can input parameter values. In the range B4 to C9 is a table where the user can input the x and y coordinates for 5 wells (Figure Exercise 4-1a). These wells will be sampled for water levels – taken from the flow model automatically – and subjected to point velocity determinations, also automatically done by the sheet when prompted by the user.

The second place for user input is in the range R3 to R11. Here the user specifies aspects of the flow model (Figure Exercise 4-1b).

Areas of the “GWP_Velocity_Exercises.xlsm” spreadsheet where the user can vary parameter values of the model.
Figure Exercise 4-1 – Areas of the “GWP_Velocity_Exercises.xlsm” spreadsheet where the user can vary parameter values of the model. a) Well location coordinates. b) Dispersivities, effective porosity, hydraulic conductivities, and time.


dx = the space between nodes (spreadsheet cells) in the model going left to right

dy = the space between nodes (spreadsheet cells) in the model going up to down

ne = the effective porosity

Khigh = the hydraulic conductivity of the most permeable sediments

Kmid and Klow = available to advanced users, but not active in the default settings

Kgeom = the geometric mean of the hydraulic conductivity in the model domain

time = the time interval used to calculate the velocity vector lengths (for graphics purposes)

Figure Exercise 4-1b lists the default values of these input parameters to be used for the exercises below.

The calculations performed automatically on this sheet are initiated by clicking on the buttons shown in Figure Exercise 4-1a. The Porous Medium 1 and Porous Medium 2 buttons enter two pre-set hydraulic conductivity distributions into the model. These two media are used in the exercises that follow. Users can enter any custom K distribution by simply typing over the K entries in the range R32 to AF46.

The flow system analysis consists of 2 parts: 1) an analysis based on water levels in the 5 wells (Figure Exercise 4-1a) and Darcy’s Law; and, 2) point velocity analysis. Both analyses begin by clicking on the Points Update button (Figure Exercise 4-1a).

A user form appears (Figure Exercise 4-2a) when Points Update (Figure Exercise 4-1a) is clicked allowing users to enter well location coordinates manually or automatically. The Autofill option prompts the sheet to randomly select five locations for the wells and enter them into the input table. Calculations begin with the selection of the Calc. Points button (Figure Exercise 4-2a). If the Autofill option is selected, this entails the generation of the random 5 well locations, and the sampling of the flow model for the point velocities, otherwise the manually entered values appear in the Well Input (Figure Exercise 4-1a). The output from this sampling are presented in a table (range B52 to F56, Figure Exercise 4-2b) and a graph (Figure Exercise 4-2c). The graph shows the well locations as orange circles and the direction of flow as blue lines. The lengths of the lines reflect the speed of the water (seepage velocity magnitude). The graph also shows the outcome of the Darcy analysis. This velocity speed and direction is indicated by a large pink circle and rose-colored arrow in the center of the graph.

Well locations, velocity magnitude and direction at each well
Figure Exercise 4-2 – a) Input well locations. b) Velocity magnitude and direction at each well. c) Location of wells with velocity arrows and overall velocity.

If the user changes the input to the values shown in Figure Exercise 4-1b, the Points Update button must be clicked again, followed by a click of the Calc. Points button to update the results.

A summary of the Darcy and point velocity analyses is presented in the range B29 to D42 (Figure Exercise 4-3a). Selected model inputs are reviewed in the pink area. The results of the matrix analysis (calculated in columns J through O) and Darcy calculations are given in the green area and the point velocity analysis is summarized in the yellow area.

Darcy and point velocity analyses
Figure Exercise 4-3 – Summary of a) the Darcy and point velocity analyses given b) the listed x-y locations of the wells.

1. Input the x, y coordinates shown in Figure Exercise 4-3b into cells B5 to C9 of the Exercise 4 sheet. Make certain the default flow model parameters shown in Figure Exercise 4-1b are correctly entered in range R4 to R11. Click on the Porous Medium 1 button to load that aquifer. Click the Points Update button again, then click the Calc. Points button to update the results.

Compare the Darcy estimate of seepage velocity to the average velocity determined from the point measurements. Compare both the magnitude and direction of average water movement.
Next, comment on the range of water speeds and directions identified by the point measurements. Is this variability a concern? Explain why or why not.

*The solution for Exercise 4-1 extends from row 253 to row 282 of the Solutions Tab of KeyFile_GWP_Velocity_Exercises.xlsm*

2. Load Porous Medium 2.

Repeat (1) and extend your answer by contrasting the importance of the velocity variability in the two scenarios and the implications for contaminant transport in these two aquifers.

*The solution for Exercise 4-2 extends from row 284 to row 302 of the Solutions Tab of KeyFile_GWP_Velocity_Exercises.xlsm*

3. For both Porous Medium 1 and Porous Medium 2, Autofill the well location table and fill in the ‘Run 1’ row in the tables provided in the spreadsheet (cells B71 to H71) based the output in range B29 to D42 in the Exercise 4 sheet (recall Figure Exercise 4-3a). A table is provided from C64 to H68 where you can copy the calculated values for the appropriate run and use paste-special to paste as values into the table below on the appropriate run line. Repeat the Autofill process five times, generating 5 different well location scenarios to fully complete the table for each porous medium.

Investigators often do not know the details of subsurface structures before locating wells. Some well placements may provide representative information that permits reasonable risk assessments. Other well placements may not. Comment on the success or failure of the five well placements summarized in the uncompleted table to the right in the ‘Questions’ sheet and the box and whisker plots provided immediately below (as completed in the ‘Solutions‘ sheet X305 to AX356 for the data used there).

*The solution for Exercise 4-3 extends from row 305 to row 356 of the Solutions Tab of KeyFile_GWP_Velocity_Exercises.xlsm*

4. Comment on the role point velocity measurements might have in contaminant hydrogeological site investigations, based on the results of the simulations above.

*The solution for Exercise 4-3 extends from row 358 to row 365 of the Solutions Tab of KeyFile_GWP_Velocity_Exercises.xlsm*


Groundwater Velocity Copyright © 2020 by J.F. Devlin. All Rights Reserved.