Ground Water Hydrology

Earth Science Extras

by Russ Colson

Turquoise Lake in Mystery Cave, Minnesota.

 

Porosity

Contrary to popular mythology, most underground liquids--either water or oil--do not occur in giant underground caverns. Rather, most underground liquids exist in the pore spaces between sediment grains within the rock.

 

Different rocks can have different amounts of pore space, a property of rock called porosity.

Porosity = volume void space/total volume x 100%

We can define two types of porosity:

1) Primary porosity, which is porosity that is related to the original deposition of the sediment and the arrangement of particles in it. For example, square or angular particles might have less pore space than spherical particles. Poorly sorted sediment in which tiny partilces fill in the spaces between larger particles might have less pore space than well-sorted sediment. How the particles fit together (packing) also affects sorting--imagine spheres that either nest together or sit on top of each other.

and

2) Secondar porosity, which is porosity arising from things that happened to the rock after its formation, such as fracturing, shrinkage cracks (as fine-grained sediment dries out), or formation of cavities due to solution (like caves).

 

Porosity varies widely between different kinds of rocks and also between different samples of the same kind of rock, depending on the arrangement of particles, how much cement has filled in the spaces between grains during lithification processes,and what has happened to the rock since it formed.

Value: 3

Choose each of the following in which the first of the listed pair is likely to have greater porosity. You may need to look up any terms you are not familiar with.

[mark all correct answers]

 
 
 
 

Often porosity in clastic rocks (those made out of deposited sediment particles) ranges from 3 to 30%; porosity in limestone and dolostone often ranges from 1 to 30%; porosity in crystalline intrusive igneous rocks often ranges from 2 to 5%; and porosity in vesicular volcanic rocks can range up to 87%. Weathering can produce secondary porosity of 30 to 60%. The easy-solubility of echinoderm fossils in limestone can result in calcium carbonate dissolving and re-precipitating in pore spaces, decreasing the pore space--a consideration in availability of oiil in some oil fields.

Value: 3

Suppose that you want to experimentally measure the porosity of two different sediments, one with larger particles and one with smaller particles. You decide to do this by seeing how much water will soak into each of the different sediments. Match up the following experimental variables with the role which that variable plays in your experimental design.

The task is to match the lettered items with the correct numbered items. Appearing below is a list of lettered items. Following that is a list of numbered items. Each numbered item is followed by a drop-down. Select the letter in the drop down that best matches the numbered item with the lettered alternatives.

a. A variable which you might measure, but is not required for the experiment

b. The dependent variable, the one you measure

c. A constant in the experiment, something that you control to keep constant

d. Independent variable, the one you change

 

Value: 2

Which of the following expressions would correctly calculate the porosity of a sediment from the experiment implied in the previous question?

 
 
 
 
 

 

Porosity affects how much liquid--water or petroleum for example--can fit into rock. However, it is another property of rock--permeability--that determines how easily that liquid can move through the rock.

 

Permeability

Abundant pore space does not necessarily mean that liquids can move through a rock easily. When we drill a well for water, not only does there have to be water available at the depth that we dirll to, but that water has to move through the rock easily enough to be replenished as we pump water out. To get oil out of the ground, the liquid petroleum has to be able to move through the rock to where we are pumping it from ("tight" oil is oil in very impermeable rock that cannot be easily pumped out).

Permeabilty is the ease with which a liquid can move through rock or sediment, such that higher permeability means that liquid can move through rock more quickly and easily.

Permeability and porosity don't necessarily correlate to each other. Consider the reasoning puzzle below.

Value: 2

You observe pumice, a volcanic rock, floating in sea water. Pumice from explosive volcanic eruptions has been known to float for months in shipping lanes before eventually sinking. The floating pumice tells us that

 
 
 
 

 

As with porosity, there can be both primary and secondary permeability. A rock that is otherwise quite impermeable, such as shale, can become more permeable if it is fractured either naturally by tectonic processes or by people. Creating secondary porosity to aid in extraction is the purpose of "fracking" for tight oil--an impermeable shale is fractured by high pressure fluid, and then sand is pumped into the fractures to provide permeably conduits.

Another example of secondary permeability is when a dense, impermeable limestone is made more permeable by formation of solution joiints.

Factors that affect permeability include sediment sorting, the amount of cement present, the particle size, the amount of fracturing, and the fraction of solution cavities.

Value: 2

List the following in order of increasing permeability, Look up any terms you are not familiar with online.

Below is a sequence of events. Place them in the order they should occur, number 1 being the first item. Select the step number from the drop down next to each item.
Items to order:

1. aquifer


2. aquiclude


3. aquifuge


4. aquitard


 

An exercise in mathematical thinking

Mathematical thinking as applied in science (and science education) involves more than simply plugging numbers into an equation someone else gives you. It involves inferring mathematical relationships and figuring out how those relationships relate to the natural world. We are going to figure out the key elements of Darcy's Law--the mathematical expression for discharge of ground water.

As in surface water hydrology, discharge is an important consideration in understanding of the movement of water underground. The key expression for discharge of ground water is analogous to the equation for discharge of water in surface streams (Discharge = cross-sectional area times velocity), but has somewhat different terms, reflecting different forces and constraints on ground water flow. Darcy's original experiments were done in the 1800s to address an engineering problem--how various filter configurations might influence movement of water through a water filtration system. To do that, he studied the movement of water through various layers of sediment, with application to the flow of water through filtration pipes.

Value: 2

We can consider several variables that will affect the discharge of water through a filtration pipe (such as one filled with filtration sand--Darcy's original material of interest). Key variables include the diameter of the pipe, the length of the pipe, the different in pressure (hydraulic head) from one end of the pipe to the other, and the intrinsic permeability of the filtration material.

Which of the following mathematical expressions best relates these variables to the discharge of water through the pipe. Darcy did extensive research to confirm these relationships, however, you can choose the best of the following set of possibilities simply through your observatonal experience in the world and by using a bit of logical reasoning.

In these equations, Q = discharge, P= permeability, A = cross sectional area of the pipe (or sedimentary layer), L=length of pipe (or length of sedimentary layer), and f= difference in force per unit area (pressure) that is moving the liquid through the pipe (or sediment).

 
 
 
 
 
 
 

Value: 2

To extend Darcy's Law to other fluids, such as different varieties of petroleum, we need to also consider the viscosity of the fluid. We will let the term µ equal viscosity. High viscosity would be a fluid like cold corn syrup, whereas low viscosity would be a fluid like water.

We are also going to introduce a new term "I" = the pressure gradient. This is equal to the difference in pressure (which we called 'f' before) divided by the distance over which the pressure change occurs (which we called 'L').

Which of the following will give us the modified version of Darcy's Law?

 
 
 
 

 

Value: 2

Suppose that you set up an experiment like that shown below to measure the permeability of different sediments. Remembering the equation for discharge

Q = PIA, where Q = discharge (= volume of water per unit time), P = permeability, I = pressure gradient, A = cross sectional area

Which one of the following variables will be the dependent (response) variable that you need to measure, that will change when you put different sediments into the tube?

 
 
 
 

 

Value: 2

Which one of the following changes to the experiment discussed above would provide a test of the prediction of Darcy's Law that discharge should remain constant if the hydraulic gradient stays constant, even if the length of the tube changes.

Q = (P * f * A) / L

f/L = hydraulic gradient, L = length of tube

 
 
 
 

Considerations of ground water, water table, and pressure gradient

Ground water can be one of three different types: Connate, juvenile, and meteoric. Do some checking online to find the differences among these and some of their typical attributes.

When you've done this excercise, check to see that you've got at least the basic idea with the question below.

Value: 2

After doing some work online to learn about the characteristics of different types of ground water--connate, juvenile, and meteoric--check that you at least have the basic differences among them.

The task is to match the lettered items with the correct numbered items. Appearing below is a list of lettered items. Following that is a list of numbered items. Each numbered item is followed by a drop-down. Select the letter in the drop down that best matches the numbered item with the lettered alternatives.

a. Juvenile

b. Meteoric

c. Connate

d. Uh, none of these

 

 

Water table is the boundary between the regions where the pores in the rock or sediment are completely saturated with water (below the water table) and where the pores are not saturated (above the water table).

The vadose zone (zone of saturation) is the region below the water table.

The phreatic zone (zone of aeration) is the region above the water table.

 

Pressure gradients in rock or sediment are created because of higher and lower areas of the water table. Water moves from areas of higher water elevation (higher hydraulic head) to areas of lower water elevation (lower hydraulic head). Differences in elevation of the water table are maintained in a dynamic balance because the water trying to level out due to movement of water toward areas of lower elevation is balanced by new rainwater seeping into areas of high elevation.

 

Recharge areas are areas where water from rain or snow are entering the groundwater aquifer.

Discharge areas are areas where ground water is leaving the aquifer and entering the surface water system.

A spring is an area where ground water flows out onto the surface of its own accord. It requires that the underground water have a hydraulic head at least equal to the elevation of the landscape.

 

Value: 2

Which of the following is the most correct statement of the direction of groundwater flow?

 
 
 
 

 

An artesian well is a well where water rises of its own accord, without having to be pumped. It requires that the underground water have a hydraulic head that is higher than the elevation of the landscape. This can occur where an impermeable layer prevents water from rising to the surface even though the potentiometric surface (the trace of the hydraulic head elevation) is above ground level. The recharge area must be at higher elevation than the artesian well. There were many artesian wells drilled into the Dakota Sandstone in the early 1900s. The Dakota Sandstone is an important regional aquifer across North and South Dakota overlain by 10s to 100s of feet of impermeable shale or clay. The hydraulic head in many of these wells was higher than any local landscapes, suggesting the recharge area may have been near the Rocky Mountains. One particularly spectacular well drilled in the Red River Valley north of Fargo-Moorhead shot tens of feet into the air for days before the underground overpressure was relaxed. In Minnesota, artesian wells can form where permeable rock is overlain by impermeable glacial till and where lakebed clay overlies sandy deposits such as along the east shore of former Glacial Lake Agassiz.

Value: 2

Which one of the following cross sectional illustrations, showing topography and underlying rock layers, indicates the location of a well that might be artesian (well locations shown with a vertical line).

 
 
 
 

 

When people pump water out of a well, it depresses the elevation of the water table in the vicinity of the well. This area of water table depression is called a cone of depression. This will change the local hyraulic gradient and cause water to flow toward the well. The lower the permeability of the rock, the longer it takes water to flow through the rock and the deeper the cone of depression can be. In marine coastal areas, pumping fresh water from the ground can depress the water table and sometimes reverse flow direction such that marine water invades the subsurface along the coastline, causing fresh water wells to turn salty.

 

It's possible to have more than one water table. A perched water table is one that sits on a layer or lens of impermeable rock that lies above the wider, regional water table.

Although not shown in the picture below, it is also possible to have more than one aquifer, with the aquifers divided from each other by impermeable layers (aquifuge, aquiclude). The pollutant characteristics, or other characteristics, of the two aquifers can be different.

 

Value: 2

Suppose that the municipal wells for a small city lie near a plume of hydrocarbon-rich pollutants leaking into the groundwater from a corroded underground diesel storage tank. Fortunately, the pollutant stream bypasses the municipal wells. Suppose that in response to urban growth the town doubles the pump rate from those same wells. This is likely to

 
 
 
 

 

For the survivalists among you.

Value: 2

Suppose that you find yourself lost in the desert in a bad adventure movie and desparately need to find water. You are of course prepared with your sheet of plastic, weight, and small water container, so you can set up a small still to extract water from moist earth. But where are you most likely to find moist earth (even if you can't find a full-out spring?)

 
 
 
 

 

Karst Terrane of SE Minnesota

Value: 2

The karst terrane of south east Minnesota is an area where water trickling through underlying limestone has widened joints and fracture by dissolution of the calcite in the limestone, creating large secondary porosity and permeability. Often sinkholes form where groundwater swirls into the underground aquifer systems. Comparing to a situation in which aquifers are mainly due to primary porosity (such as in sandstone), a pollutant on the surface in SE Minnesota is likely to

 
 
 
 

 

 

last updated 4/12//2020.   Text and pictures are the property of Russ Colson.

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