math in the news: 6/27/11
DESCRIPTION
In this issue of Math in the News we look at the math behind the technology of oil fracking.TRANSCRIPT
6/27/11
Drilling for Oil and Gas
• Fracking is a process whereby a hole is drilled horizontally to reach the oil and gas. Click on this video link for an overview of fracking.
• http://youtu.be/O0kmskvJFt0
Drilling for Oil and Gas
• The process of drilling for oil involves removing a cylinder-shaped amount of earth to dig a hole.
• In this illustration you can see the vertical bore hole and its cylindrical shape.
Drilling for Oil and Gas
• The volume of a cylinder is shown in the formula on the right.
• In the context of oil drilling, r is half the width of the bore hole and h is the depth of the hole.
Drilling for Oil and Gas
• Suppose the first part of a fracking drilling operation involves drilling a hole 10,000 feet deep and 4 feet wide.
• How could you use the formula for the volume of a cylinder to calculate how much earth was removed?
Drilling for Oil and Gas
• For this scenario– h = 10,000– r = 2
• The total volume is shown on the right. And it is a sizable amount of earth. Although the bore hole is quite narrow, the depth of the hole accounts for the large volume of earth extracted.
Drilling for Oil and Gas
• The mass of this earth can be calculated indirectly.
• Can you think of a way of measuring the mass without actually weighing all the dirt that was dug up?
Drilling for Oil and Gas
• Density is the mass divided by the volume. To calculate the mass, simply multiply the volume (which we already calculated) by the the density of the Earth’s crust.
• In this case, let’s use metric units.
Drilling for Oil and Gas
• Finally, how much energy is required to move this mass of earth?
Drilling for Oil and Gas
• The amount of work involved in moving the earth is the product of the mass, the acceleration due to gravity, and the distance traveled.
Drilling for Oil and Gas
• For simplicity, we look at the center of mass, as opposed to the entire cylinder. So the distance moved is h/2.
• The amount of work is shown in the formula on the right. The metric unit of energy is a Joule.
• The number of Joules needed is equivalent to 27 tons of dynamite!
Drilling for Oil and Gas
• Because of the amount of energy needed to drill a well, there is a great deal of expense required for drilling.
• For this reason, any techniques that allow for the reuse of vertical wells will save money. This is one reason that horizontal drilling is popular.
• One technique, called fracking, is used to drill for natural gas.
Drilling for Oil and Gas
• The horizontal part of the hole is placed near a shale deposit that includes natural gas.
• Small explosions are used to fracture the rock around the shale.
Drilling for Oil and Gas
• Liquid is pumped into the fractures to further increase the amount of fracturing in the rocks. This aids in releasing the trapped natural gas.
Drilling for Oil and Gas
• Once the fracking fluid is removed, natural gas can flow through the pipes.
Drilling for Oil and Gas
• One of the largest deposits of shale containing natural gas is the Marcellus Shale, shown on the map. This deposit of shale covers a number of states (including New York, Pennsylvania, and West Virginia)SOURCE: USGS.GOV.
Drilling for Oil and Gas
• Estimates are that 5 • 1012 cubic feet of natural gas are in the Marcellus Shale.
Drilling for Oil and Gas
• As with all processes that affect the environment, the process of fracking is not without critics.
• Read the following document from USGS to get a better understanding of these concerns. http://md.water.usgs.gov/publications/fs-200
9-3032/fs-2009-3032.pdf
Drilling for Oil and Gas
• Work as a group to list the pros and cons of the technology of fracking. Make each item a brief point about the technology.
• Avoid:– Generalities. Each pro or con should be
a specific item.– Opinions masking as facts. Make sure
each item is factual and backed up by evidence.
Pros Cons
Drilling for Oil and Gas
• Suppose you are chairing a panel made up of oil and gas executives, environmentalists, politicians, and concerned citizens. Make a series of concrete recommendations about fracking technology in the Marcellus Shale region and that addresses:– Environmental concerns– The impact on America’s energy
needs– The Impact on the local and national
economy
Recommendations