Focus Problem- Math

Question

For 87 days in the spring and summer of 2010, British Petroleum's Deepwater Horizon spilled millions of gallons of crude oil into the Gulf of Mexico, resulting in one of the largest oil spills in the history of the United States and one of the largest unintentional oil spills in history.

In addition to the cost of cleaning up the spill and compensation to those affected, BP was also responsible for penalties under the Clean Water Act, which calls for fines of $1,100 per barrel, for simple negligence, up to $3,000 per barrel, for gross negligence. The federal prosecutors argued that the fines should go as high as $4,300 under the Environmental Protection Agency rules.

An important part of determining the appropriate fine was estimating the size of the spill. Experts offered differing opinions on the flow rate of the oil from the undersea well. Initially, an expert from BP insisted that the oil was flowing at a rate of only 5,000 barrels per day. It turned out that this was a gross underestimate of the flow rate, and the BP expert was eventually prosecuted for misleading the investigation. An expert in fluid dynamics studied the flow rate on video and computed a rate of approximately 70,000 barrels per day (+/−20%).

During the third phase of the trial, a judge was left to weigh the differing opinions and decide on a penalty for BP. A final settlement amount of $18.7 billion was eventually agreed upon. The trial took two years and was one of the most complicated civil cases in the history of the U.S. courts.

Use the fluid dynamics expert's range on the number of barrels per day, along with the allowed penalty range under the Clean Water Act and EPA guidelines, to calculate a minimum and maximum penalty for BP.

What percent of this maximum was the final settlement? Is the final amount closer to the minimum, the maximum, or the midrange (mean of the two)? Do you think the penalty imposed by the judge in the third phase of the trial was fair? Explain your response and include some information you learned from researching the topic in news reports. What was the value of the oil BP lost in the spill at the time of the spill? What would the oil be worth now? Convert the number of barrels of oil spilled to gallons. Convert this amount to something practical to make sense of the size of the spill.

Some estimates of the size of the oil spill relied on analyzing the flow rate from the pipe as seen on video footage. If the circular opening of the pipe has a diameter of 21 inches and the oil was estimated to be flowing at 30 inches/second, how many cubic feet of oil were leaving the pipe each second? Each day? How does this estimate compare to the other estimates mentioned for gallons per day? Discuss some possible reasons for the discrepancy.

Compare the size of this oil spill to others in history to put it into perspective.

Answer 1

This question is missing some information we'd need to answer it entirely, it looks as if it was copied directly off a HW assignment. . . ("Explain your response and include some information you learned from researching the topic in news reports"). I digress.

When approaching this question as if it were on an exam we ought to strategize so that it takes the least amount of time possible. For this we need to not get caught up in the irrelevant information. My suggestion would be to read this type of question once through, circling/highlighting/underlining (whatever method works best for you) all the numerical values in the text as you come across them. This will give you quick visual references when you have to break apart what the problem is actually asking you to do.

Make sure you answer all parts of a question like this--the first value we're instructed to give is the "minimum and maximum penalty for BP".

We can write ourselves a little outline of all the parts of the question we need to address before we make any calculations:

I. Calculate min. and max. penalty for BP

i. absolute max penalty is going to be (70,000 barrels + 70,000(.20) barrels) multiplied by 4300 dollars per barrel multiplied by 87 days

(70,000 + 14,000) x 4300 =

84,000 x 4300 =

361.2 million x 87 days = 31,424,400,000

ii. absolute minimum penalty is going to be (70,000 barrels - 70,000(.20) barrels) multiplied by 1100 dollars per barrel multiplied by 87 days

(70,000 - 14,000) x 1100 =

56,000 x 1100 =

61.6 million x 87 days = 5,359,200,000

A. Final settlement = what % of max.?

18,700,000,000 over 31,424,400,000 = .59507

convert decimal to get 59.51% of max

B. Final settlement closest to min. max. or midrange?

i. calculate mean of min and max. (the midrange)

31,424,400,000 - 5,359,200,000 = 26,065,200,000

26,065,200,000 / 2 = 13,032,600,000

ii. determine the difference between final settlement and min, max, and midrange (roughly)

approx. 9 billion between min and final

approx. 18 billion between max and final

approx. 5 billion between midrange and final

closest to midrange

C. Was 3rd phase fair?

This is fairly open ended, and we're not given a lot of details. With the limited information I would make the point that the final settlement was less than the average between the max and min possible penalty, so it was quite lenient compared to the fullest penalty of the regulations. In this sense it's fair.

D. What was the value of the oil at the time? What is its value now?

70,000 barrels per day x 87 days = 60,900,000 barrels

1 barrel = 42 gallons of oil

42 x 60,900,000 = 2,557,800,000 gallons

multiply this estimate by crude oil price at each time and you're done

E. "Practical" understanding of quantity

A bathtub conveniently also holds approx. 42 gallons, so using our calculations we can see that the spill is around the same size as 60,900,000 bathtubs full of oil!

II. Flow rate calculations

i. this problem most likely wants to think of the flowing pipe as a perfect cylinder of oil is exiting the pipe constantly in time. it's height is 30 inches and it's radius is 21 inches / 2 = 10.5 inches. 30 inches are 2.5 ft. 10.5 inches is 0.875 ft.

Volume_cylinder = (pi)(r²)(h)

V_c = (pi)(0.875²)(2.5)

= 6.0132 ft³

ii. per second = 6.0132 ft³ / s

iii. per day = (6.0132 ft³ / s ) multiplied by (43200 seconds / day)

= 259,770.24 ft³ / day

iv. how does this compare to the gallon estimate?

1 ft³ = 7.48052 US liquid gallons

= 259,770.24 multiplied by 7.48052

= 1,943,216.4757 gallons per day

we must compare this to the 70,000 barrels per day approximation (2,940,000 gallons per day). there might be a discrepancy due to a different, more complex formula used to calculate the flow rate, they may have used the highest possible estimate.

III. Comparison to other oil spills

I'll leave this up to the reader because it requires information we are not given.