# How Much Oil Leaked from Deepwater Horizon?

## Summary

This is a homework assignment given to students in an introductory course, Fundamentals of Sustainability, at the University of Arkansas. Students develop an estimate of the total quantity of petroleum discharged from the Deepwater Horizon from 20 April to 15 July 2010 using only two known facts, the diameter of the riser and the flow rate of the oil/gas mixture emanating from the riser.

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## Learning Goals

The exercise is intended to help students develop problem solving and mathematical reasoning skills including:
1) estimation skills
2) skills for unit conversion
3) interpretation of data

## Context for Use

This is an exercise aimed at first and second year college students in an introductory course, Fundamentals of Sustainability, at the University of Arkansas. The exercise is assigned as homework during the first week of the course. Total time to complete the assignment is 1 - 2 hours. The exercise is intended to aid development of estimation skills in students as well as provide practice in unit conversions. Using only two pertinent facts about the fractured drill stem and riser from the BP Deepwater Horizon (diameter of the riser and flow rate of the oil/gas mixture), students are guided through a series of calculations to arrive at a final estimate of the total quantity of petroleum discharged from the site that is remarkably close to values derived from rigorous analysis by a government appointed task force. The outcome of this exercise serves to illustrate the value of estimation in describing various processes appropriate scaling, and extrapolation from meager initial data.

## Description and Teaching Materials

The 'Tragedy of the Commons' played out for all to see between 20 April and 15 July 2010. On 20 April 2010 (ironically, Earth Day), the Deepwater Horizon drilling vessel in the Gulf of Mexico suffered a catastrophic blow-out and explosion resulting in the loss of 11 men and ultimately the loss of the \$540 million dollar vessel. Loss of control of the oil well permitted oil to flow freely into the Gulf of Mexico for 86 days. It stands today one of the largest oil spills in history. The root causes of the calamity were technical incompetence and human error. For those with an interest in the details of this spill, the reports of the National Commission on the BP Deepwater Horizon Oil Spill and Offshore Drilling are freely available: https://www.govinfo.gov/content/pkg/GPO-OILCOMMISSION/pdf/GPO-OILCOMMISSION.pdf

The exercise begins with the instructor showing a brief video clip of oil emanating from the ruptured riser of the Deep Water Horizon on the floor of the Gulf of Mexico. These video clips are publicly available online from YouTube (http://www.youtube.com/watch?v=kZoOJga5wbc&feature=related).

Students are informed that the diameter of the riser pipe is 21 inches (they will convert to metric units later). They are also informed that the oil/gas mixture streams from the riser at ca. 21 inches per second. From these two bits of information, they are asked to estimate the total quantity of oil released from the site from 20 April to 15 July 2010 by completing a series of sequential calculations on a worksheet (attached). They are to assume the flow rate did not change during this time.

At the end of the worksheet, they derive an estimate that is remarkably close to the final quantity reported by the National Commission on the BP Deepwater Horizon Oil Spill and Offshore Drilling. How Much Oil Leaked From Deep Water Horizon? (Microsoft Word 32kB Jun20 12)

## Teaching Notes and Tips

This is a remarkably simple activity producing a remarkably accurate estimate. Students should be reminded of the formula for the area of a circle (area of the riser pipe opening). In addition, the estimate of the flow rate of the oil/gas mixture from the pipe was derived from analysis of the video. Video commonly runs at 30 frames per second. Using video editing software, one can step through the video frame-by-frame and estimate the flow rate as approximately 21 inches per second. Multiplying this linear rate by the area of the pipe yields the discharge in cubic inches per second. All subsequent calculations derive from this initial estimate. A common error students make is in the conversion of cubic inches to cubic feet. Many students will mistakenly multiply cubic inches by 12 to arrive at an incorrect conversion to cubic feet. Of course, the appropriate conversion is 12 x 12 x 12 = 1728 cubic inches = 1 cubic foot. Instructors may wish to share the information that Google.com can accomplish unit conversions very easily. If one enters "X cubic inches to cubic feet" in the Google search box, Google will return the proper conversion in the specified units.

## Assessment

The assessment is straight forward as all students should derive the same values from their calculations.

## References and Resources

The authoritative source of information on the Deep Water Horizon calamity is the website of the National Commission on the BP Deepwater Horizon Oil Spill and Offshore Drilling. The full report and multimedia summaries of the report are freely available online at: https://www.govinfo.gov/content/pkg/GPO-OILCOMMISSION/pdf/GPO-OILCOMMISSION.pdf

A video clip of the leaking Deep Water Horizon riser is available online at: