At this point in time, we (humans) really like oil. What's not to like? From oil we get gasoline. Gasoline is cheaper than milk with a higher energy density than batteries. You can put it in your car and drive 400 miles and then refuel in less than 5 minutes. Gasoline is like magic juice and humans love it.

Of course, there are problems too. The burning of oil based products produces carbon dioxide and other stuff that's not so nice. Also, there is only so much oil in the ground. Sure, the Earth keeps making more through a very slow process. But we are using it up way faster than it is being created by natural means.

So, the question is: how much oil can we find? How long will it last? Let's get started.

## How Much Oil Is There?

There are several methods for estimating the amount of oil. Let me use a model that predicts the cumulative oil found based on oil found in the past. I will use the data from this very interesting and thorough publication - Giant Oil Fields - The Highway to Oil: Giant Oil Fields and their Importance for Future Oil Production (Fredrik Robelius).

In this publication, there is a plot of the volume of oil discovered as a function of year. Here is a replot of that data.

With that data, I can just add up the amount of oil discovered each year for a cumulative total. Here is a plot of "how much oil have we found so far?"

As you can see, there is a model to fit to this data with the following form:

Yes. That is a "sideways" parabola. Why would anyone pick that function to fit this data? Even though it clearly doesn't fit data before 1955, from 1956-2005 it seems to fit fairly well. Of course this function also says that as time (*t*) goes to infinity so does the cumulative amount of oil. According to this fit there is INFINITE OIL. But really, no one thinks there is really an infinite amount of oil in the Earth even if we act like we will never run out. If you wanted to get more sophisticated, you could model this data with a function that "levels out" over time - but let's stick with the infinite oil model for now.

## How Long Will Our Infinite Oil Last?

Here is the real question. Would infinite oil last forever? Of course the answer depends on how fast we consume the oil. This data (available on Wikipedia) shows that the world continues to use more oil each year.

I fit a linear function to the data from 1960 and later. Since then it seems that our use of oil increases linearly with time. Of course that makes sense. Every year there are more people on the Earth and more countries are becoming industrialized with higher demands for oil. Will this oil demand keep increasing forever? Probably not, but let's just model the oil use as a linear function. Ok, so now we have two things. First, the amount total amount of oil found is increasing (each year we find more). Second, the demand for oil is also increasing. In order to make a comparison between oil production and oil consumption, we need to first get a model for total oil used (not instantaneous oil). Since I fit a linear function to the instantaneous oil consumed, I can call this slope the rate of oil consumed. What happens when you have some function that has a constantly increasing slope (think about kinematics with a constant acceleration)? Yes, this means that the total volume of oil consumed vs. time would be a parabolic function. If I assume that in the year 1930 there was no oil consumed (just an assumption), then I get the following function. Now I can plot the both the cumulative oil produced and the cumulative oil consumed.