*everywhere*, it seemed like a good idea to be concerned about this problem and try to figure out how to at least minimize the damage should this disaster scenario come sometime soon.

Today I'm marginally wiser than I was then, so I like to verify myself if these types of things I hear through the media are true or not. I decided to look up some of the details about this whole peak oil thing and wonder, "when would this whole thing start going down?"

I looked on Natural Resources Canada's web page to see some information about oil production. I found this tidbit which says, "Canada's oil reserves are sufficient to meet demand for the next 200 years at current rates of production." Nice! I suppose that means I don't have to care, and let the future generations figure out how they are going to deal with this problem.

Right?

Well, maybe not. The first thing we want to do is verify that this number is actually correct. After all, while we know that the government would

*never*lie to us, it's always a smart idea to figure things out for yourself in case somebody over there made a mistake.

To figure out our rate of extraction, this FAQ tells us that Canada currently produces about 2.5 million barrels of crude oil per day (consistent with some data that is mentioned below). To figure out how much oil Canada has proved to have, a 2010 report by the US Energy Information Association tells us that Canada currently has about 178 billion barrels of proven oil reserves that can be extracted, including the oil sands. If you take this number and divide it by the amount of oil we produce each day, we get approximately 195 years of producing oil; the number given by the government website is more or less correct.

Does this mean all is well for the next 200 years? Well, not really. See, the bit that breaks this whole analysis is right in the quote taken from the government's FAQ: "at current rates of production." The 200 year figure assumes that Canadian production of oil will not grow at all over the next 200 years. Intuitively that doesn't seem right, but let's be scientific about this. Maybe it is in fact true that oil production is constant.

Doing a bit of a search with my trusty sidekicks Google and Wikipedia, I found some data here on the website of the Canadian Association of Petroleum Producers that shows the yearly oil production in Canada from 1971 to 2010. Rather than describe it to you, here's a picture:

If the government's assumption were true, this graph would be a flat line at 2.5. As you can see it is definitely not, in fact it seems to be increasing at a fairly quick rate!

What happens to our numbers if we start increasing oil production each year? Let's find out.

With a linear model, we get that it is increasing by about 0.0336 Mbbl, or 33 000 barrels of oil per year. If this trend continues, it means that the reserves will run out in...194 years. So one year less than if we assumed it would be flat.

Of course, typically in economics it is assumed that economies grow

*exponentially*, not linearly. Since both population and productivity due to technology seem to increase at exponential rates, it a fairly safe assumption to make that production of anything increases at an exponential rate provided nothing stops it.

When we use an exponential model, we can calculate that the oil production is growing at about 1.68% per year. If we extrapolate this out, it turns out our oil supply will run out after...87 years. That's a bit shorter than the last time frame! Even scarier for the people living in that time, we will use up the first half of our current amount in about 60 years, with the second half being used up in a short 27 year time frame! So in short, if production keeps up as it has been, then our grandchildren (assuming you're my age, I'm 25) will see the day when the known oil deposits of Canada will run dry.

In fact, there's another problem with this analysis. The data set we're using includes the 1970's with a massive oil boom followed by a collapse in the mid-70's that lasted until about 1980. If we re-run the exponential model after dropping the 1970's (so we are left with 30 years of data) the rate of increase goes up to 2.56% with an R

^{2}of 0.98 (meaning a near perfect fit). With that rate of increase, our oil will run out in 70 years. This is a lot closer than the 200 years given by NR Canada.

I tried to leave out any speculation from this post and just use numbers and math based on what has been happening and from those numbers, make a simple extrapolation to see what would happen should the existing trends continue. The growth rate of 2.56% per year may change in the future (up or down), which obviously would change the results of this simple analysis.

To add my own little bit of speculation, from what I've seen in the news I think that this rate of production will actually increase over time given the attitudes of the current Canadian government - as more projects such as the Keystone pipeline get completed it will be even cheaper to transport oil into the United States and other countries from Canada. An economics 101 class will tell you that as the efficiency of supply increases, the amount of production will increase: as Canadians get better at shipping the oil to other places, more oil will be produced to ship.

As always with my statistics-oriented posts, you can see the code here. In the code you can see I did a linear model with the 1970's excluded but didn't talk about it here, it's because the exponential model fits both better with the data and better with economic theory.

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