theoretical modeling

"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

Oil shocks are generally acknowledged to have important effects on both economic activity and macroeconomic policy. The aim of this paper is to investigate how oil price shocks affect the growth rate of output of a subset of developed countries by comparing alternative regime switching models. Different Markov–Switching (MS) regime autoregressive models are, therefore, specified and estimated. In a successive step, univariate MS models are extended in order to verify if the inclusion of asymmetric oil shocks as an exogenous variable improves the ability of each specification to identify the different phases of the business cycle for each country under scrutiny. Following the wide literature on this topic, seven different definitions of oil shocks which are able to describe oil price changes, asymmetric transformations of oil price changes, oil price volatility, and oil supply conditions are considered.

Our findings can be summarized as follows. While the introduction of different oil shock specifications is never rejected, positive oil price changes, net oil price increases and oil price volatility are the oil shock definitions which contribute to a better description of the impact of oil on output growth. In addition, models with exogenous oil variables generally outperform the corresponding univariate specifications which exclude oil from the analysis. However, a stability analysis of the coefficients across different subsamples shows that the role of oil shocks in explaining recessionary episodes has changed over time. Improvements in energy efficiency, together with a better systematic approach to external supply and demand shocks by monetary and fiscal authorities are argued to be responsible for the changing macroeconomic effects of oil shocks. Finally, the impact of G-7 countries aggregate growth on oil market conditions is considered and assessed empirically. The null hypothesis of the absence of a reverse relationship from real GDP growth to oil prices is rejected by the data.

Published in: Economic Modelling, Volume 26, Issue 1, January 2009, Pages 1-29
Available from: ScienceDirect

An analogy between thermodynamic and economic theories and processes is developed further, following a previous paper published by the author in 1982. Economic equivalents are set out concerning the ideal gas equation, the gas constant, pressure, temperature, entropy, work done, specific heat and the 1st and 2nd Laws of Thermodynamics. The law of diminishing marginal utility was derived from thermodynamic first principles. Conditions are set out concerning the relationship of economic processes to entropic gain. A link between the Le Chatelier principle and economic processes is developed, culminating in a derivation of an equation similar in format to that of Cobb Douglas production function, but with an equilibrium constant and a disequilibrium function added to it. A trade cycle is constructed, utilising thermodynamic processes, and equations are derived for cycle efficiency, growth and entropy gain. A thermodynamic model of a money system is set out, and an attempt is made to relate interest rates, the rate of return, money demand and the velocity of circulation to entropy gain. Aspects concerning the measurement of economic value in thermodynamic terms are discussed.

Published in: International Journal of Exergy, Volume 4, Issue 3, Pages 302-337
Available from: Inderscience Publishers
also available from: Vocat International Ltd

When assessing the oil reserves of a given region, often the statistic S = R/P is used, where R denotes the amount of proven reserves in the region and P is the current rate of production. This statistic can be misleading because the rate of production typically varies over time.
We investigate a general framework for oil discovery and production and find the limit of S as time tends to infinity for several selected models.

Published in: International Journal of Pure and Applied Mathematical Sciences, accepted for print
Available from: Queen Mary, University of London