The logistic curve, and its derivative the hubbert's curve, has been widely used to model population growth. And it has been applied to model oil production by M. King Hubbert. The model comes from the following differential equation:
where Q(t) is a function of time (measured in years) and it is defined as the cumulative production of a region until the end of year t. The parameter URR is the "Ultimately Recoverable Resources" or the maximum cumulative production that can be reached. K is the Malthusian parameter or the maximum cumulative production growth.
The value dQ/dt for a specific year s, can be approximated by
The data from 1857 till 1958 is from "API Facts and Figures Centennial edition 1959" (thanks to Laherrere and Stuart Staniford). For 1959-1964 it is from "Twentieth Century Petroleum Statistics2004" of DeGolyer & MacNaughton. And for 1965-2005 it is from BP Statistical Review of World Energy.
First I will put links to all the images of regions ordered by continents:
- Algeria, Angola, Cameroon, Chad, Egypt, Equatorial_Guinea, Gabon, Libya, Nigeria, Rep_of_Congo, Sudan, Tunisia, other_Africa.
- Australia, Brunei, China, India, Indonesia, Malaysia, Taylandia, Vientnam, other_Asia.
- Denmark, FSU, Italy, Norway, Rumania, UK, other_Europe.
- MIDDLE EAST:
- Iran, Iraq, Kuwait, Oman, Qatar, Saudi_Arabia, Syria, UAE, Yemen, Other_ME.
- NORTH AMERICA:
- Canada, Mexico, US.
- SOUTH AND CENTRAL AMERICA:
- Argentina, Brazil, Colombia, Ecuador, Peru, Trinidad, Venezuela, Other_S_and_Cent_America.
After a quick inspection of the plots we can divide countries in three groups:
COUNTRIES THAT BEHAVE WELL:
Egypt Gabon Rep_of_Congo Brunei India Indonesia Vientnam Denmark FSU Italy Norway Rumania other_Europe Oman Syria Mexico US Argentina Peru Trinidad
TOO EARLY TO SAY COUNTRIES:
Angola Chad Equatorial_Guinea Sudan Taylandia other_Asia Qatar Brazil Colombia
- COUNTRIES THAT DO NOT BEHAVE WELL:
Algeria Cameroon Libya Nigeria Tunisia other_Africa Australia China Malaysia UK Iran Iraq Kuwait Other_ME Saudi_Arabia UAE Yemen Canada Ecuador Other_S_and_Cent_America Venezuela
Probably they haven't reach peak production yet. These group includes 9 countries.
Countries for which the points of the second plot just keep increasing between the two lines. Normally they increase in a very strait line. These group has 21 countries.