theoretical modeling

The depletion of the world oil resource based upon the logistic function has been updated and fitted to the recent history of oil production. The analysis uses data through the year 2009 and further introduces the asymmetric Gompertz function in order to account for additional oil resources. Results of these calculations depict a range of production rates under different resource limits. The characteristic curvature coefficients and the peak years of production are fitted to United States Geological Survey estimates of ultimately recoverable resource (URR) limits between 2.5 and 4.5 terabarrels (TB). The logistic fittings yield peak productions from 30.4 to 38.6 gigabarrels per year (GB/yr) for URRs from 2.5 to 3.0 TB in years 2008 through 2016. The lower probability of occurrence URRs (from 4.0 to 4.5 TB) inclusive of forms of oils yet to be introduced yield peak productions from 30.9 to 33.5 GB/yr during the years 2018 through 2023. The Gompertz function is used as the model for the lower probability URR production.

Published in: Energy Sources, Part B: Economics, Planning, and Policy, Volume 6, Issue 2, Pages 178–186
Available from: Informaworld

In 1956, M. King Hubbert, chief consultant for the Shell Development Company's exploration and production research division, forecasted that U.S. oil production would peak in the early 1970s. He subsequently updated this prediction using newer data, but the predicted timing of peaking did not change significantly (see Hubbert [1982] for a review and references to earlier papers). In 1971, U.S. annual production of crude oil peaked at slightly more than three billion barrels (bbl). Yet, Hubbert's model continues to be challenged by some. For instance, according to economist Michael Lynch, president of Strategic Energy and Economic Research, Inc., Winchester, Mass., it was only after Hubbert published his predictions “that the Hubbert curve came to be seen as explanatory in and of itself, that is, geology requires that production should follow such a curve” [Lynch, 2003].

Published in: EOS (Transactions American Geophysical Union), Volume 87, Issue 20, May 2006, Pages 199-219
Available from: American Geophysical Union

The year 2008 has witnessed unprecedented fluctuations in the oil prices. During the first three-quarters, the oil price abruptly increased to $140/bbl, a level that has never been reached before; then because of the global economic crisis, the price dramatically plunged to less than $50/bbl by the end of the year losing more than 64% of the maximum price in less than three months period. The supply of crude oil to the international market oscillated to follow suite according to the law of supply and demand. This behavior affected oil production in all exporting countries. Nonetheless, the demand for crude oil in some developing countries, such as China and India, has increased in the past few years because of the rapid growth in the transportation sector in addition to the absence of viable economic alternatives for fossil fuel. The rapid growth in fuel demand has forced the policy makers worldwide to include uninterrupted crude oil supply as a vital priority in their economic and strategic planning.

Even though forecasting should be handled with extreme caution, it is always desirable to look ahead as far as possible to make an intellectual judgment on the future supplies of crude oil. Over the years, accurate prediction of oil production was confronted by fluctuating ecological, economical, and political factors, which imposed many restrictions on its exploration, transportation, and supply and demand. The objective of this study is to develop a forecasting model to predict world crude oil supply with better accuracy than the existing models. Even though our approach originates from Hubbert model, it overcomes the limitations and restrictions associated with the original Hubbert model. As opposed to Hubbert single-cycle model, our model has more than one cycle depending on the historical oil production trend and known oil reserves. The presented method is a viable tool to predict the peak oil production rate and time. The model is simple, accurate, and totally data driven, which allows a continuous updating once new data are available. The analysis of 47 major oil producing countries estimates the world’s ultimate crude oil reserve by 2140 BSTB and the remaining recoverable oil by 1161 BSTB. The world production is estimated to peak in 2014 at a rate of 79 MMSTB/D. OPEC has remaining reserve of 909 BSTB, which is about 78% of the world reserves. OPEC production is expected to peak in 2026 at a rate of 53 MMSTB/D. On the basis of 2005 world crude oil production and current recovery techniques, the world oil reserves are being depleted at an annual rate of 2.1%.

Published in: Energy & Fuels, Volume 24, Issue 3, February 2010, Pages 1788–1800
Available from: ACS publications

"Peak oil" refers to the future decline in world Production of crude oil and to the accompanying potentially calamitous effects. The majority of the literature on peak oil is non-economic and ignores price effects even when analyzing policies. Unfortunately, most economic models of depletable resources do not generate production peaks. I present four models which generate production peaks in equilibrium. Production increases in the models are driven by: demand increases, cost reductions through advancing technology, cost reductions through reserve additions, and production capacity increases through site development. Production decreases are driven by scarcity. The models do not rely on market failures and indicate that a peak in production may arise from efficient intertemporal optimization. The models show that prices are a better indicator of impending scarcity than peaking is and that peak production can occur when any percentage from 0-100% of the original deposit remains.

Published in: Energy Journal, Volume 29, Issue 2, 2008, Pages 61-79
Available from: The Energy Journal

According to the long term scenarios of the International Energy Agency (IEA) and the U.S. Energy Information Administration (EIA), conventional oil production is expected to grow until at least 2030. EIA has published results from a resource constrained production model which ostensibly supports such a scenario. The model is here described and analyzed in detail. However, it is shown that the model, although sound in principle, has been misapplied due to a confusion of resource categories. A correction of this methodological error reveals that EIA’s scenario requires rather extreme and implausible assumptions regarding future global decline rates. This result puts into question the basis for the conclusion that global “peak oil” would not occur before 2030.

Published in: Energy Policy, article in press
Available from: ScienceDirect or Global Energy Systems

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.

Published in: Energy Policy, article in press
Available from: ScienceDirect

The logistic function has been used to describe the discovery and production of oil and natural gas at the national level. This type of functional representation provides a direct approach for estimating the available supply of the resource and the time at which that supply will be essentially depleted. The mathematical characteristics of the function imply restrictions, which are not necessarily applicable to natural resource-production patterns. We examine these restrictions in the context of crude-oil production at a regional level. We attempt to show that statistical estimates of the functional parameters based on actual crude-oil production could satisfy the mathematical restrictions inherent in the logistic function.

Published in: Energy, Volume 9, Issue 7, July 1984, Pages 565-570
Available from: ScienceDirect

Hubbert predicted the time of U.S. peak production and the ultimate recovery of crude oil
by analysing smoothed growth curves derived from discovery and production data. Early work’
depended on independent recovery quantity estimates and predicted the production peak to be
about 1965-1970. Later, growth curves were used to predict both the year (1967) of the peak
more precisely and the quantity (170 billion bbl). A recent survey of growth curves describes their use as a well-established tool. However, the effect on ultimate oil production quantity due to social, political, economic, and technological effects has not been well addressed. Energy growth curves generally assume that future production will reflect previous production, which limits the recovery efficiency, for example, to an average of past values.

The amount of ultimately recoverable crude oil is found to be 181.1 billion bbl for the conterminous U.S. (including offshore). Inclusion of Alaska raises the total to 217.2 billion bbl.

Published in: Energy, Volume 19, Issue 7, July 1994, Pages 813-815
Available from: ScienceDirect

Oil is the black blood that runs through the veins of the modern global energy system. While being the dominant source of energy, oil has also brought wealth and power to the western world. Future supply for oil is unsure or even expected to decrease due to limitations imposed by peak oil. Energy is fundamental to all parts of society. The enormous growth and development of society in the last two-hundred years has been driven by rapid increase in the extraction of fossil fuels. In the foresee-able future, the majority of energy will still come from fossil fuels. Consequently, reliable methods for forecasting their production, especially crude oil, are crucial. Forecasting crude oil production can be done in many different ways, but in order to provide realistic outlooks, one must be mindful of the physical laws that affect extraction of hydrocarbons from a reser-voir. Decline curve analysis is a long established tool for developing future outlooks for oil production from an individual well or an entire oilfield. Depletion has a fundamental role in the extraction of finite resources and is one of the driving mechanisms for oil flows within a reservoir. Depletion rate also can be connected to decline curves. Consequently, depletion analysis is a useful tool for analysis and forecasting crude oil production. Based on comprehensive databases with reserve and production data for hundreds of oil fields, it has been possible to identify typical behaviours and properties. Using a combination of depletion and decline rate analysis gives a better tool for describing future oil production on a field-by-field level. Reliable and reasonable forecasts are essential for planning and necessary in order to understand likely future world oil production.

Published in: Uppsala University, Licentiate thesis
Available from: Global Energy Systems

In this paper we consider the parameter estimation (PE) problem for the logistic function-model in case when it is not possible to measure its values. We show that the PE problem for the logistic function can be reduced to the PE problem for its derivative known as the Hubbert function. Our proposed method is based on finite differences and the total least squares method.
Given the data (pi, ti, yi), i = 1, …, m, m > 3, we give necessary and sufficient conditions which guarantee the existence of the total least squares estimate of parameters for the Hubbert function, suggest a choice of a good initial approximation and give some numerical examples.

Published in: Proceedings of the Conference on Applied Mathematics and Scientific Computing 2005, Part II, Pages 217-234
Available from: SpringerLink