A New Model for the Lifetime of Fossil Fuel Resources


A critical examination of Hubbert’s model proves that it does not account for several factors that have significantly influenced the production of petroleum and other fossil fuels. The effect of these factors comes into the price of the fossil fuels, and the latter has a significant influence on the demand and rate of production of energy resources as well as on the long-term rate of production growth at both the regional and global levels. Based on several observations of historical production data, a simple mathematical model is constructed and presented in this paper for the lifetime of a fossil fuel resource. The recent data of global petroleum and natural gas production show that a very important period in the life of energy resources is a period when the demand of these resources increases almost linearly. The linear part of the production curve makes the entire lifetime production of the resource asymmetric. Information on the total available quantity of a resource at any time and of the average slope during this linear period yields an estimate of the timescale, T 2, when peak production is reached and depletion follows. The total available quantity of the energy resource is laden with significant uncertainty, which propagates in the estimates of the timescale of the peak production in any resource model. The time asymmetry of the current model leads to a delay of the timescale, when the onset of the resource production commences (e.g., peak oil). However, the rate of the resource production decline is significantly higher than that predicted by other models that use a symmetrical curve-fitting method.

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  1. 1.

    1 bbl is equal to 0.1590 m3. This quantity is equal to 270.3 × 109 m3.

  2. 2.

    In the literature, there are several definitions for the ultimate recoverable reserves (URR), which include slightly different classes of recoverable resources. Because the numerical values of the URR per the different definitions are very similar, the numerical results generated for the oil peak do not vary significantly. In this paper, the estimates used are based on the definition given by the USGS.

  3. 3.

    The original, non-optimized Hubbert curve peaked in 1973 at 3 billion bbl/yr (0.48 billion m3/yr) (Hubbert 1956).

  4. 4.

    1 m3 is equal to 35.315 scf. Hence, 1.96 trillion scf is equivalent to 55.5 m3.

  5. 5.

    The decreasing trend of the prices of alternative energy sources makes this substitution effect more likely in the near future. However, even if alternative energy sources remain expensive, the demand for energy is inelastic and those with means will buy needed energy at very high prices even in an era of diminishing fossil fuel resources.


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This research was supported in part by the W.A. “Tex” Moncrief Chair of Engineering at TCU. The author is also indebted to two anonymous reviewers for several meaningful comments and suggestions.

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Correspondence to Efstathios E. Michaelides.

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Michaelides, E.E. A New Model for the Lifetime of Fossil Fuel Resources. Nat Resour Res 26, 161–175 (2017). https://doi.org/10.1007/s11053-016-9307-2

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  • Peak oil
  • Hubbert’s curve
  • Petroleum
  • Natural gas
  • Fossil fuels
  • Depletion of resources