Mathematical Calculation and Analysis Completed by Dr. Shane Rollans, Assistant Professor, Department of Mathematics and Statistics, Thompson Rivers University, Kamloops, British Columbia, Canada, at the Request of Mr. Kelly Marsh, Independent Researcher, Kitimat, British Columbia, Canada, July 2012
What are the chances of a hydrocarbon spill at some point during the life of an oil transportation system? The standard practice of reporting the estimated average spill return periods (the average time between spills) is somewhat hard to interpret. It is easier to understand what the spill return periods mean when they are translated into probabilities. With the proposed Enbridge Northern Gateway Project and its projected operational lifetime of 50 years presently in the news, it is of interest to calculate the probability of at least one spill during the 50 year operational life of this pipeline. Enbridge has estimated the spill return periods for the different sections of the pipeline and reported these in its application to the National Energy Board. I will use these rates with the Poisson distribution to model the number of leaks during the 50 year period. The Poisson distribution is commonly used to model the number of occurrences of an event during a time period. When combining regions or types of leaks, I assume that the spills are independent. The assumptions of independence and the Poisson model are the same assumptions used by Enbridge, for example in Table 8-4 on page 132 of Marine Shipping Quantitative Risk Analysis, Enbridge Northern Gateway Project, Det Norske Veritas, Oslo Norway 2010
Probabilities of a Medium Spill in a 50 Year Period.
Medium spills are defined to be no more than one million litres except for maritime travel where they are defined as no more than 20 million litres. The probabilities are for one or more medium spills in a 50 year period.
Table 1: Estimated probabilities of at least one medium spill in a 50 year period.
1 Volume 7B: Risk Assessment and Management of Spills-Pipelines (May 2010), Table 3-2, Page 3-2.
http://www.northerngateway.ca/assets/pdf/application/MASTER_Vol%207B_Final_14May10.pdf
2 Volume 7C: Risk Assessment and Management of Spills-Kitimat Terminal (May 2010) Table 3-1 Page 3-2 http://www.northerngateway.ca/assets/pdf/application/MASTER_Vol%207C_Final_14May10.pdf
3 Volume 8C: Risk Assessment and Management of Spills-Marine Transportation (May 2010) Page 3-2
http://www.northerngateway.ca/assets/pdf/application/Master_Vol%208C_Final_14May10.pdf
4 The total combined risk is derived by summing the rates for the 8 regions: 1/287+1/136+1/1082+1/462+1/118+1/454+1/294+1/550 which is approximately 1 per 33.53 years or 0.02982 per year or 1.49 per 50 years.
This makes the estimated probability of at least one medium spill in 50 years:
or 77.5%.
5 The rate per year for a return period of 287 years is 1/287 or about .00348 per year or .174 per 50 years. The probability of no spills in the 50 year period is then or about 84%. This means that the probability of at least one medium spill is 16%. The other probabilities are calculated similarly.
Probabilities of a Large Hydrocarbon Spill in a 50 Year Period
The Enbridge application includes spill return periods for large spills (defined as greater than 1,000,000 litres) in the six sections of the pipeline. The probabilities in this table are for at least one large spill during the 50 year life of the project.
Table 2: Estimated probabilities of one or more large spills over the 50 years.
There is a 41% probability of at least one or more large spills from the pipeline over the 50 years.
Enbridge asserts that the largest credible Kitimat Terminal spill is 250,000 litres (Volume 7C: Risk Assessment and Management of Spills-Kitimat Terminal (May 2010) Page 3-2) so there is no return period for a large spill at the Kitimat Terminal.
The spill return period for a spill of greater than 20 million litres for maritime transit is approximately 2800 years (Volume 8C: Risk Assessment and Management of Spills-Marine Transportation (May 2010) Page 3-2) giving a 1.8% probability of at least one large maritime spill during the 50 year life of the project.
Probabilities of a Medium or Large Hydrocarbon Spill in a 50 Year Period
Table 3: Estimated probabilities of at least one spill (medium or large) in a 50 year period.
There is an 82.8% chance of at least one medium or large leak in the pipeline during the 50 year life of the project.
The overall return period for maritime transit is about 460 years giving about a 10% chance of at least one medium or large maritime spill during the life of the project.
Combining the results for medium or large spills from the Kitimat Terminal, the pipeline and maritime transit, the spill return period is about 24.5 years and the probability of at least one medium or large spill over the 50 years is about 87%.
There is a 60% chance of at least two, a 33% chance of at least three and a 15% chance of at least four such spills during that time period.
The probabilities given here are contingent on the numbers and assumptions used by Enbridge being correct. It should also be noted that the environmental impact of a spill is heavily dependent upon the location of the spill.