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

  1. 1. 6/27/11<br />
  2. 2. Drilling for Oil and Gas<br />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.<br /><br />
  3. 3. Drilling for Oil and Gas<br />The process of drilling for oil involves removing a cylinder-shaped amount of earth to dig a hole. <br />In this illustration you can see the vertical bore hole and its cylindrical shape.<br />
  4. 4. Drilling for Oil and Gas<br />The volume of a cylinder is shown in the formula on the right.<br />In the context of oil drilling, r is half the width of the bore hole and h is the depth of the hole.<br />
  5. 5. Drilling for Oil and Gas<br />Suppose the first part of a fracking drilling operation involves drilling a hole 10,000 feet deep and 4 feet wide.<br />How could you use the formula for the volume of a cylinder to calculate how much earth was removed?<br />
  6. 6. Drilling for Oil and Gas<br />For this scenario<br />h = 10,000<br />r = 2<br />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.<br />
  7. 7. Drilling for Oil and Gas<br />The mass of this earth can be calculated indirectly. <br />Can you think of a way of measuring the mass without actually weighing all the dirt that was dug up?<br />
  8. 8. Drilling for Oil and Gas<br />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.<br />In this case, let’s use metric units.<br />
  9. 9. Drilling for Oil and Gas<br />Finally, how much energy is required to move this mass of earth?<br />
  10. 10. Drilling for Oil and Gas<br />The amount of work involved in moving the earth is the product of the mass, the acceleration due to gravity, and the distance traveled.<br />
  11. 11. Drilling for Oil and Gas<br />For simplicity, we look at the center of mass, as opposed to the entire cylinder. So the distance moved is h/2. <br />The amount of work is shown in the formula on the right. The metric unit of energy is a Joule.<br />The number of Joules needed is equivalent to 27 tons of dynamite!<br />
  12. 12. Drilling for Oil and Gas<br />Because of the amount of energy needed to drill a well, there is a great deal of expense required for drilling.<br />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. <br />One technique, called fracking, is used to drill for natural gas.<br />
  13. 13. Drilling for Oil and Gas<br />The horizontal part of the hole is placed near a shale deposit that includes natural gas.<br />Small explosions are used to fracture the rock around the shale.<br />
  14. 14. Drilling for Oil and Gas<br />Liquid is pumped into the fractures to further increase the amount of fracturing in the rocks. This aids in releasing the trapped natural gas.<br />
  15. 15. Drilling for Oil and Gas<br />Once the fracking fluid is removed, natural gas can flow through the pipes.<br />
  16. 16. Drilling for Oil and Gas<br />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)<br />SOURCE: USGS.GOV.<br />
  17. 17. Drilling for Oil and Gas<br />Estimates are that 5 • 1012 cubic feet of natural gas are in the Marcellus Shale.<br />
  18. 18. Drilling for Oil and Gas<br />As with all processes that affect the environment, the process of fracking is not without critics.<br />Read the following document from USGS to get a better understanding of these concerns.<br /><br />
  19. 19. Drilling for Oil and Gas<br />Work as a group to list the pros and cons of the technology of fracking. Make each item a brief point about the technology. <br />Avoid:<br />Generalities. Each pro or con should be a specific item.<br />Opinions masking as facts. Make sure each item is factual and backed up by evidence.<br />
  20. 20. Drilling for Oil and Gas<br />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:<br />Environmental concerns<br />The impact on America’s energy needs<br />The Impact on the local and national economy<br />