Math Analysis: BP Oil Spill For 87 Days In Spring And Summer

Math Analysis BP Oil For 87 days in the spring and summer of 2010 Brit

BP Oil spill in 2010 involved estimating the flow rate of crude oil from the Deepwater Horizon spill, which occurred over 87 days. Two primary estimates of this flow rate are given: an initial estimate by BP of 5,000 barrels per day, which was significantly underestimated, and a fluid dynamics expert’s estimate of approximately 70,000 barrels per day with a margin of error of plus or minus 20%. The spill led to substantial legal penalties based on the estimated flow rate, with fines ranging from $1,100 to $4,300 per barrel under various regulations. A final settlement of $18.7 billion was agreed upon after extensive litigation over the appropriate penalties amid differing expert opinions. This calculation focuses on assessing the range of flow rates, potential penalties, and evaluating the fairness of the final penalty.

Paper For Above instruction

1. Calculating the minimum and maximum flow rate per day

The fluid dynamics expert estimated the spill rate at approximately 70,000 barrels per day with a margin of error of ±20%. To determine the minimum and maximum flow rates per day, we apply this range to the estimate.

The minimum flow rate is calculated by subtracting 20% from 70,000:

70,000 - (20/100 × 70,000) = 70,000 - 14,000 = 56,000 barrels per day.

Similarly, the maximum flow rate is calculated by adding 20%:

70,000 + (20/100 × 70,000) = 70,000 + 14,000 = 84,000 barrels per day.

Thus, the estimated range of flow rate per day is between 56,000 and 84,000 barrels.

2. Calculating the minimum and maximum penalties and percentage of the final settlement beyond maximum

Using the range of barrels per day, and considering the penalty rates under the Clean Water Act and EPA guidelines, we can compute the potential penalties.

- At the minimum flow rate of 56,000 barrels per day:

- Minimum total barrels over 87 days: 56,000 × 87 = 4,872,000 barrels.

- Penalties:

- At the minimum rate ($1,100 per barrel): 4,872,000 × $1,100 = $5,359,200,000.

- At the maximum rate ($4,300 per barrel): 4,872,000 × $4,300 = $20,973,600,000.

- At the maximum flow rate of 84,000 barrels per day:

- Total barrels over 87 days: 84,000 × 87 = 7,308,000 barrels.

- Penalties:

- At the minimum rate: 7,308,000 × $1,100 = $8,038,800,000.

- At the maximum rate: 7,308,000 × $4,300 = $31,424,400,000.

The actual settlement amount was $18.7 billion. To understand how it compares with these potential penalties:

- The settlement is approximately 87.6% of the maximum potential penalty based on the maximum flow rate and highest fine:

- ($18.7 billion / $20.97 billion) × 100 ≈ 89.2%.

- It is roughly 59.3% of the maximum potential penalty based on the maximum flow rate with the highest fine:

- ($18.7 billion / $31.42 billion) × 100 ≈ 59.5%.

This indicates the settlement falls within the higher range of potential penalties, skewing closer to the upper estimate but still below the maximum possible.

3. Is the penalty imposed by the judge fair?

The fairness of the penalty imposed on BP depends on the context provided by the flow rate estimates and the regulatory guidelines. Given that the expert’s fluid dynamics estimate suggested a flow rate of about 70,000 barrels per day with a ±20% margin, the resulting potential fines ranged broadly up to over $31 billion if maximum fines per barrel applied. The final settlement of $18.7 billion sits well within this broad spectrum, indicating a compromise that reflects the severity of the spill but also considers the uncertainties inherent in estimating the flow rate. Considering BP's initial gross underestimate and the legal debates, the settlement appears to be a fair resolution, balancing accountability with the uncertainties surrounding the actual spill size. While some critics might argue that the penalty should match the maximum possible fines for gross negligence, the settlement appropriately reflects the complexities and the extensive legal process involved. Overall, the imposed penalty aligns with the scale of the disaster and regulatory standards, making it a reasonable conclusion in this context.

References

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