The parabolic technique for the projection of the production of conventional world oil resources over time was developed to model the period near the expected peak. It will not model the later time in the cycle well because the parabola falls to a definite point on the abscissa. A slow decline is more likely past a certain point with this final section best modelled by a logistic curve that approaches the abscissa asymptotically. Although the quantity of oil produced declines as time passes and becomes steadily less important in an energy supply sense, this predicted output in the later period is of importance when carbon dioxide emissions must be estimated.
In this note a simple method is presented for deriving compound decline curves which link parabolic and logistic sections. The technique is applied to a range of peaks in world conventional oil production extending at five-year intervals from 2010 to 2025. The time of the transition point at which the decline curves switch from the parabolic to the logistic mode is chosen to meet the criterion that the oil remaining to be produced is ten times the production in the transition year (R/P = 10). The details of the mathematical procedure employed appear in an appendix.