An Oil Production Model from Roger Bentley

Aug 7, 2008 (2 days ago) europe

This is a guest article by Dudley Stark, Reader in Mathematics and Probability in the School of Mathematical Sciences, Queen Mary, University of London. Bentley introduced the following model of oil production on page 204 of Global oil & gas depletion:an overview , and it is dicussed in the book The Last Oil Shock by David Strahan. This posting is meant to explain his model and some results I obtained for it. Consider the following oil production curve: It rises quickly to it's peak at time t=1 and decreases slowly until no oil is produced at time t=6. The idea is that the natural pressure of the oil field causes rapid production initially, after which decline is more gradual. Before and after the peak the curve is linear, so it looks like a triangle. [break] Suppose the next oil field looks the same as the first one, but oil production begins one unit of time later and the total amount of oil produced is only 75% of the oil in the first field. It looks like this: Adding the production of the two oil fields together gives this production curve: If you do this eight times, each time shifting the start of production by one time unit from the previous oil field and also making the amount of oil produced 75% of the previous oil field, you get a curve like this: It is starting to look like a plausible oil production curve. Note, however, that it is not too realistic because, for one thing, the curve is linear in between integers.