Exercise Set 1

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”.

1. 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 tab for ‘Exercise 1’. Consider the simplified porous medium shown. Just as aquifers composed of sediment grains are imperfectly packed, this cartoon displays empty spaces between the grains (blue in Figure Exercise 1-1a). In the spreadsheet, drag the individual grains from the ‘real’ porous medium to the empty vessel illustrated in Figure Exercise 1-1. Stack the grains with no space between them (that is, finish the process started in Figure Exercise 1-1c). Assume that the area of each grain is 4 square units.

What is the fraction of open space to total space, i.e., the total porosity, in the porous medium?

Figure showing imperfectly packed grains
Figure Exercise 1-1 – a) Imperfectly packed grains of an aquifer sample are to be moved into panel b) the total space of the sample so that in c) they are stacked in a closely packed arrangement.

*The solution for Exercise 1-1 begins on row 6 of the Solutions Tab of KeyFile_GWP_Velocity_Exercises.xlsm*

2. Now, scroll down in the spreadsheet to look at the porous medium with ovate grains on row 24. Each of these grains has the same area as the square grains in question 1 of Exercise Set 1.

What is the total porosity for this medium? Justify your answer on a purely qualitative argument (no calculations).

Ovate grains can isolate pockets of the ‘aquifer’ space – i.e., pores. Count the number of isolated pores. For the purposes of this exercise, allow single isolated pores or pairs of pores in isolation to constitute ‘dead end’ pores. Three or more connected pores do not represent dead ends. It might help the process to color the dead-end pores as shown in Figure Exercise 1-2).

Assuming each pore has an area of 1 square unit, subtract the area of deadend pores from the total open space area and recalculate the porosity.

Example of coloring in a closed pore
Figure Exercise 1-2 – Example of coloring in a closed pore.

This recalculated porosity is called the effective porosity since it represents the porosity capable to transmitting water.

*The solution for Exercise 1-2 begins on row 27 of the Solutions Tab of KeyFile_GWP_Velocity_Exercises.xlsm*

3. Scroll further down the spreadsheet and consider the porous medium with two sizes of ovate grains. Drag all of the small grains (1 square unit each) and place them in the spaces between the large grains (4 square units each) in the neighboring ‘aquifer’. This is analogous to making the medium less well sorted.

Recalculate the total and effective porosities with the small grains added to the porous medium. Compare both with the answers obtained in (1) and (2) and explain the reasons for any differences.

Figure showing the filling of pore space between larger grains by smaller grains
Figure Exercise 1-3 – Drag the small grains into the sample to fill in pores between the larger grains and color in pores that are disconnected from the other pores.

*The solution for Exercise 1-3 begins on row 48 of the Solutions Tab of KeyFile_GWP_Velocity_Exercises.xlsm*


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