math in the news: 6/27/11

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6/27/11

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In this issue of Math in the News we look at the math behind the technology of oil fracking.

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Page 1: Math in the News: 6/27/11

6/27/11

Page 2: Math in the News: 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

Page 3: Math in the News: 6/27/11

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.

Page 4: Math in the News: 6/27/11

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.

Page 5: Math in the News: 6/27/11

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?

Page 6: Math in the News: 6/27/11

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.

Page 7: Math in the News: 6/27/11

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?

Page 8: Math in the News: 6/27/11

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.

Page 9: Math in the News: 6/27/11

Drilling for Oil and Gas

• Finally, how much energy is required to move this mass of earth?

Page 10: Math in the News: 6/27/11

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.

Page 11: Math in the News: 6/27/11

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!

Page 12: Math in the News: 6/27/11

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.

Page 13: Math in the News: 6/27/11

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.

Page 14: Math in the News: 6/27/11

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.

Page 15: Math in the News: 6/27/11

Drilling for Oil and Gas

• Once the fracking fluid is removed, natural gas can flow through the pipes.

Page 16: Math in the News: 6/27/11

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.

Page 17: Math in the News: 6/27/11

Drilling for Oil and Gas

• Estimates are that 5 • 1012 cubic feet of natural gas are in the Marcellus Shale.

Page 18: Math in the News: 6/27/11

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

Page 19: Math in the News: 6/27/11

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

Page 20: Math in the News: 6/27/11

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

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