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

1. 6/27/11

2. 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

3. 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.

4. 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.

5. 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?

6. 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.

7. 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?

8. 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.

9. Drilling for Oil and Gas Finally, how much energy is required to move this mass of earth?

10. 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.

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!

12. 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.

13. 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.

14. 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.

15. Drilling for Oil and Gas Once the fracking fluid is removed, natural gas can flow through the pipes.

16. 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.

17. Drilling for Oil and Gas Estimates are that 5 • 1012 cubic feet of natural gas are in the Marcellus Shale.

18. 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-2009-3032/fs-2009-3032.pdf

19. 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.

20. 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