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Power laws in oil and natural gas production

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Abstract

Power-law distributions can be generated by a variety of theoretical processes and have been found in many areas of economics and finance. This paper demonstrates that the distribution of cumulative oil and gas recovery in Texas is best described by a power-law distribution, with exponent approximately equal to 1.1 for oil production and 1.6 for gas production. Estimation is carried out using lease and well-level data from a cross section of over 600,000 observations gathered by DrillingInfo. The goodness of fit of the hypothesized power law is verified with regression-based and likelihood ratio tests, as well as nested and composite hypotheses. Results are significant because they show that production data are heavy tailed, that empirical variance estimates do not converge, and that 1 % of oil leases are responsible for 70 % of cumulative recovery. The distribution has consequences for efficient management and implications about peak oil because wells close to the mean account for so little of the cumulative distribution of recovery.

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Notes

  1. The literature reports both the exponent for the probability distribution function, \(\alpha \), and the exponent for the counter-cumulative distribution function, \(\gamma \). For clarity, if the the counter-cumulative distribution is \(P(\mathrm{Recovery}>x)=kx^{-\gamma }\), then the associated PDF is \(p(x)=k\gamma x^{-(\gamma +1)}\). With \(\gamma +1 \equiv \alpha \), the pdf can be written more succinctly as \(p(x)=cx^{-\alpha } \).

  2. Gabaix (2009) provides a primer on power laws.

  3. The issue of censored production is more salient in the estimation of the lognormal distribution. As more time passes, the mode of the distribution would progressively decrease as the less productive fields come into production (Barton and Scholz 1995).

  4. Indeed, they are the only family of distributions where the parameters do not depend on the units of measurement; hence, they are also known as scale-free or scaling distributions (Farmer and Geanakoplos 2008).

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  1. 8317 Freret Street, New Orleans, LA, 70118, USA

    Andrew Balthrop

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Balthrop, A. Power laws in oil and natural gas production. Empir Econ 51, 1521–1539 (2016). https://doi.org/10.1007/s00181-015-1054-4

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