『Abstract
　In recent years, the economic and political aspects of energy problems have prompted many researchers and analysts to focus their attention on the Hubbert Peak Theory with the aim of forecasting future trends in world oil production.
　In this paper, a model that attempts to contribute in this regard is presented; it is based on a variant of the well-known Hubbert curve. In addition, the sum of multiple-Hubbert curves (two cycles) is used to provide a better fit for the historical data on oil production (crude and natural gas liquid (NGL)).
　Taking into consideration three possible scenarios for oil reserves, this approach allowed us to forecast when peak oil production, referring to crude oil and NGL, should occur.
　In particular, by assuming a range of 2250-3000 gigabarrels (Gb) for ultimately recoverable conventional oil, our predictions foresee a peak between 2009 and 2021 at 29.3-32.1 Gb/year.

Keywords: Oil production; Hubbert theory; Oil peak forecasts』

1. Introduction
2. World oil production data
3. Hubbert peak oil
　3.1. A variant of the Hubbert curve
　3.2. The multiple-Hubbert approach
　3.3. Choice of the oil production reference curve and the Ultimate range
4. Results and comments
5. Impacts of the peaking of world oil production
6. Conclusion
Appendix A. Calculation of peak value and area for variant of the Hubbert curve
Appendix B. Calculation of the integral (A2)
References

Fig. 1. World oil production historical data from different sources. Fig. 5. Comparisons of world oil production (crude+NGL) calculated for a global Ultimate between 2250 and 3000 Gb. Fig. 6. World oil production (crude+NGL) peak value and peak year calculated as a function of the global Ultimate. Maggio and Cacciola(2009)による『A variant of the Hubbert curve for world oil production forecasts』から