In 1838 Verhulst published a mathematical expression (now known as the logistic equation) for population growth proportional to the environment’s unoccupied carrying capacity. M. King Hubbert in 1982 explained that the logistic equation would apply if the success in finding oil were proportional to the remaining undiscovered oil. Population biologists, and Hubbert, used a graph that converted the logistic curve to a straight line. The abscissa is the cumulative production and the ordinate is the annual production as a percentage of the cumulative.

In his earlier papers, Hubbert used two measures of success. One was the actual production and the other, which he called “discoveries”, was the cumulative production up to a given year plus the known reserves as of that year. These two measures can be plotted using two different symbols on the same graph. A single straight line drawn through the points gives a probable outlook for the short-term future. In contrast, a computerized evaluation of the same data involves a nonlinear, four-parameter fit.

Of course, the biggest single question is the year when world oil production reaches a Hubbert peak and then declines forever. Both the graphical and the computer fits identify 2004 as the probable year. The largest single uncertainty is the enormous reserves in Saudi Arabia. An alternative way of estimating the peak year became possible when the Saudi government recently announced a production capacity of 10.5 million barrels per day, compared to their current production of 8 million. The newly focused question is: how soon will the production decline in the rest of the world require the 2.5 million barrel remaining Saudi capacity? The most optimistic straight line on the non-Saudi world graph suggests that the surplus capacity will be used up in the year 2004. The least optimistic plausible line puts the world Hubbert peak in 2002.