Ok, so I am taking Quantitative Reasoning and I want to do my class project on PO. I'd like to do an HL analysis on world production, but first I have to show that the method is valid. No problem, I'll just plot an HL for the the United States. I can show the method works by matching the linear projection with what we now know to be true. Problem, they aren't matching!

I plot the data easy enough and it seems to settle into a linear pattern at about 1942, so I plot a linear projection from 1942-1970 and I get an estimated URR of a little more than 160Gb. Of course, I have the data from 1970-2005 plotted too and it clearly points to an estimated URR that is well past 200Gb, which of course is much more inline with reality.

One possible problem is that I have no data for before 1920, but they are such small amounts before 1920 would they make that much difference? I could plot the trendline using later data, but the whole point is to show that the method is an accurate predictor before the event so using data after 1970 would defeat the purpose. Any help would be appreicated.

Here is my spreadsheet:
http://www.mylinuxisp.com/~blawrence/oi ... ctions.xls

I grabbed data from the EIA for 1920-2005 from here:
http://tonto.eia.doe.gov/dnav/pet/hist/mcrfpus1M.htm

[Edit: I found my problem and fixed it, see below]

I've only looked at Hubbert's model fairly briefly, but isn't production supposed to follow a gaussian curve? And in that case, I don't think you get a line here.

I remember reading Defeyes' book that he said Hubbert used a logistical curve when the data actually fit better a gaussian. Maybe this is what you're finding here.

I think you have the cart before the horse here. I hadn't gotten that far yet. Before you can plot the logistic (or gaussian) curve, you have to at least work out the values for the Hubbert linearization. The HL is useful in its own right for projecting what will be the ultimately recoverable amount. The URR is determined by where the linear projection meets the X axis. Where the linear projection meets the Y axis is also important as this is a key input into Hubbert's logistic curve (as is the URR).


Chapter 3 of Deffeyes book covers both the Hubbert linearization and logistic curve.

Good news, I corrected my linearization and went on to do the logistic curve. I was just grabbing to far back and the data hadn't stabilized yet. I'm now using 1955-1970 to plot the line. The first graph shows my corrected HL which projects a URR of 230Gb for the United States. The second graph shows my logistic curve and as you can see it fits well with what we now know to be true about U.S. production.

Now to do the same for the whole world...

good work Geko45. Mind if I use your charts for dog&pony shows at City Hall? They're purty charts

I'd be honored! If you've already downloaded the spreadhseet then download it again, because I just posted the full one at the link above. Its got all the charts I've posted here on PO and a few I haven't (yet). Check back regularly too since there are a few more charts that I plan to do but haven't gotten too yet.

Thanks Geko

Ok, I finished my world Hubbert linearization and logistic charts. My projections put peak oil on March 14, 2007, a nice sunny Wednesday. I'm not sure what grande cosmic significance there is to the date falling on a "hump day", but there you have it. My linearization chart yielded a world URR of about 2.23 trillion barrels. Here are the graphs.

PS. Many thanks to Stuart Staniford who provided world production data for the years 1930-1964 (the BP Statitical Review of World Energy only goes back as far as 1965).

Geko45,
I suppose you learned something about plotting and fitting curves, but remember that this Hubbert Linearization is purely an empirical approach. All parameters to the model are based on heuristics that have no physical meaning (or they have an absurd physical meaning that does not even obey dimensional analysis or a Gedunken experiment).

No one has yet shown how you can derive the curve from first principles.

Now that would have been a really inventive class project.

Methinks that you are being to philosophically minded to be of any metaphysical good.

If you think it's a gaussian, it derives pretty much from the Central Limit Theorem. A big enough collection of curves under certain conditions that production curves will fulfill will aggregate to a gaussian curve.

For the most important question of our time, we find a failure to commit. The fear of not succeeding strikes again.

But no one thinks it is a Gaussian. Consider that this makes absolutely no sense from first principles. Gaussians extend symmetrically to the left and right of the peak. However, since oil was only discovered in the USA in 1859 and a few years before that worldwide, no way can you even begin to fit it to a Gaussian. That is, you can't fit to the tails before 1859, which is what the Gaussian expects.

A better, but not by much, approximation is to use a Log-Normal distribution, which forces a positive value (i.e. time) to go negative by taking the logarithm of the number.

But in general, the Central Limit Theorem rarely works for a stochastic time series, which is what the oil discovery profile is.

We'll gee, I bet you're a load of fun at parties. Cut me some slack here, this is my first attempt at doing modeling of any significant complexity. I understand your point, but I'm not there yet and if no one else has done it then I'd guess that you're not there yet either. To be perfectly honest, I am exceeeding the expectations of my current undergrad class with this project. I've also managed to get the other members of my project team thinking along these lines where they were completely oblivious to this problem before. I also have a chance to present this to the remainder of my class and I may make a few of them aware too. I consider that a significant (albeit humble) contribution to awareness.

So in summary.