This is a guest post by Apparent Peak. He started his career as an aeronautical engineer and is currently retired. Now he has more time to study peak oil and write posts for TOD. He has selected "Apparent Peak" for his handle which will become obvious once you have read the post.

1) Background

I have followed the subject of peak oil since the seminal article by Campbell and Laherrère appeared in the March 1998 edition of Scientific American. Approximately one year ago, I began to casually follow some of the discussion threads at TOD. The posts, the ensuing discussions and in particular, discussions on HL, logistic functions and Khebab's The Loglet Analysis caught my interest. I decided to investigate these topics since I did not know what HL was, let alone logistic functions. A quick trip to Wikipedia explained the Logistic function. As it turns out, it is a fancy exponential function that has characteristics similar to the Gaussian distribution.

Having read Khebab’s paper a few more times I realized that I did not have the patience to understand “successive Fischer-Pry decompositions”. However, one sentence in his paper was very insightful: “The Loglet decomposition is an elegant mathematical framework which consists in fitting a sum of logistic curves”. The idea of fitting a sum of logistic functions to model oil production made the process sound much simpler than successive Fischer-Pry decompositions.

More recently there has been much discussion regarding estimating a country’s URR using HL, Hubbert’s linearization, and especially the URR of the Kingdom of Saudi Arabia (KSA) and its potential oil production decline due to the depletion of the Ghawar oilfield (Ghawar reserves update and revisions by Euan Mearns and Depletion Levels in Ghawar by Stuart Staniford). To get a better understanding of the logistic function and its role in peak oil analysis, I decided to combine the concept of least squares with fitting the sum of multiple logistic functions to the oil production history of KSA as suggested by Khebab.

The least squares approach would provide a best fit to the country’s oil production and would address my curiosity to assess the quality of the results this method of analysis would produce. One of my objectives was to find another methodology that would complement HL and at the same time provide further insight into those situations that are difficult for HL.

As I recently re-read some articles on the debate about global oil reserves, a thought struck about how one could arrive at a rough estimate for such a number.

The search for that magic number of total oil in place and hence an estimate of how much can be realistically recovered has been a bone of contention across the Peak Oil divide. In fact, the absence or unreliability of data provides a sufficient haze for one group to point in one direction whilst another points in a completely opposite path. Hence we will find that estimates varying from 2 trillion barrels of URR up to 3 trillion barrels are the typical of the debate. Now a difference of one trillion barrels is important. At a current global consumption rate of 85 mbpd (original was 30 bbpd, that isn't right...PG) we get another 33 years of time to get things sorted out in terms of alternate energy sources and so on (though increasing demand would pull that number back to 20-25 years).

So I was considering the oil life of the United States of America...