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The Canadian Joint Review Panel for the proposed Enbridge Northern Gateway Project recommended that the federal government approve the project, subject to 209 required conditions.
According to Northern Gateway risk assessments, the probability of a tanker spill of any size would be about 0.4 per cent in any given year. The company estimated the return period (average interval between events) would be 250 years for a marine spill.
National Energy Board & Canadian Environmental Assessment Agency (2013-12-19) Joint Review PanelNorthern Gateway said the probability of a full-bore rupture on the oil pipeline would be 0.2 per cent in a given year, based on an estimated return period of 464 years.
One curiosity of their report is the risk numbers. Let us crunch their numbers for fun! This may be of interest as they should perhaps change their calculations in future. They calculated the expected time until the first spill, however the median time, for example, until a spill may be more informative.
Northern Gateway estimates the probability of a major spill on the pipeline is 0.2%
That is, if $p$ is the probability of a spill each year, the expected time to the first spill, $\text{E}[s]$, is:
$$\text{E}[s] = \frac{1}{p}$$The probability of the first spill being in year $n+1$ is the probability there is no spill in the first $n$ years, $(1-p)^n$, times the probability, $p$, that there is a spill in year $n+1$. This makes the expected year in which the first spill occurs:
$$\text{E}[s] = \sum_{n=0}^\infty (n+1)(1-p)^np$$This fortunately is a well-known infinite sum. To obtain a closed form for it we need to make some observations. First note that, when $q<1$:
$$1 = \sum_{n=0}^\infty q^n - q( \sum_{n=0}^\infty q^n)$$so that
$$\frac{1}{(1-q)} = \sum_{n=0}^\infty q^n$$differentiating this with respect to $q$ gives:
$$\frac{1}{(1-q)^2} = \sum_{n=1}^\infty nq^{n-1} = \sum_{n=0}^\infty (n+1)q^n$$so that
$$\text{E}[s] = \frac{1}{(1-(1-p))^2}p = \frac{1}{p}$$Thus, the Joint Review Panel got their math correct, although they could revisit significant digits.
Interestingly, you can reverse this calculation! That is, if one has a pipeline with a first spill (assuming this has happened roughly at the expected value) one can calculate $p$. Consider the Kalamazoo oil spill in 2010, the largest on-land oil spill, and one of the costliest spills, in U.S. history. Of course, as it was maintained by the same company who is now proposing to build the Northern Gateway, it cannot be viewed as being completely irrelevant. This pipeline was described by the company as an aging pipeline. It was, in fact, built in the sixties so it was roughly 50 years old when it ruptured. Using this as baseline, this fixes the risk of a spill at 2% per year.
$$p = \frac{1}{\text{E}[s]} = \frac{1}{50} = 0.02$$This suggests:
In fact, surely the panel should be thinking about the probability that there is no spill over the lifetime of the pipeline. Suppose the pipeline is to be decommissioned in 30 years, let us calculate the probability that there will be no spill in that time:
In order to gain insight into the potential risk of an oil spill, you can play with the parameters below! You can drag the blue highlighted numbers to adjust the interactive graph.
Let's say the probability of a spill is
When the probability of a spill is
Figure 1: Probability of no spill when the failure rate is
Table 1: Northern Gateway's summary of representative parameters for oil spill probabilities. Click a row to change the graph above.
Spill Type | Return Period | Annual Probability | Page Reference |
Oil Pipeline, Other Spills | 4 years | page 67 (html) | |
Marine Terminal Spill | 61 years | page 67 (html) | |
Oil Pipeline, Full-bore Rupture | 240 years | page 67 (html) | |
Tanker Spill (any size) | 250 years | page 60 (html) | |
Full-Bore Rupture, Oil Pipeline | 464 years | page 60 (html) |