# 7 Exercises

# Exercise 1

Singha (2008) provides an active learning exercise for introducing the concept of groundwater extraction from confined aquifers. This exercise uses a juice container as a simple analog for a confined pore space, and demonstrates how a decrease in fluid pressure from pumping causes an increase in effective stress assuming a constant total stress.

In brief, a bag of juice is used to represent a pore in a confined aquifer. The experimenter is asked to apply a downward force on the top of the juice container to represent the weight of the overburden material and maintain this constant force as they proceed. This force represents the total stress. The experimenter thinks about: 1) why the container does not collapse in response to the force; and 2) what will happen with a straw is inserted in the container. Then the experimenter inserts a straw (equivalent to drilling the confined aquifer). Next, while maintaining the force, they “pump” the aquifer by sipping juice from the straw. The experimenter will notice that the volume of the juice container decreases and is asked to consider what is happening in the “aquifer.” The experimenter will see that the container does not collapse prior to pumping when the overburden force is applied because the effective stress of the aquifer (the container), and the fluid pressure in the pore (the juice) push against weight of the overburden (their hand). Depending on the magnitude of the overburden force and the length of the straw, it may be that juice squirts out when the straw is inserted which is analogous to a flowing artesian well. If the force is not as large, the juice will rise in the straw above the container, but will not flow out of the straw. Singha (2008) provides more details.

# Exercise 2

The goal of this experiment is to measure the specific storage *S*_{s} of a balloon, which simulates aquifer elasticity. The experiment is designed to provide observational meaning to the variable, increment of fluid content, and the influence of the state of stress on the specific storage.

In short, a balloon is stretched over the end of a burette clamped to a meter stick and attached to a tall ring stand. The balloon and burette are filled with a known volume of water to an arbitrary height on the meter stick such that the volume in the balloon can be determined. Then a measured volume of water is added and, assuming the compressibility of water and the burette are small, the volume of water must go into either the balloon or the burette. The volume entering the balloon can be determined by knowing the volume that went into the burette as determined from the water level in the burette. The three-dimensional storage properties of the balloon are then determined by adding water and noting the head change in the burette. This can be repeated a number of times to determine if the storage value is constant. Water can be removed and the process repeated to determine if the balloon is elastic. Finally, the experiment can be repeated with the balloon laterally confined in a plexiglass tube to obtain the one-dimensional specific storage (S_{s}) of the balloon which can be compared with the measurement in the case of three-dimensional expansion of the balloon.

The details of the exercise (including diagrams) as well, as information about using the exercise to teach the concept, are available on the Science Education Resource Center at Carleton College website. A pdf of the laboratory exercise titled “Aquifer Elasticity and Specific Storage” is available here. The underlying theory is discussed in this book as well as in a textbook chapter by Herb F. Wang that is available on the same website (textbook chapter).