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OIL PRODUCTION MODELS WITH NORMAL RATE CURVES

Published online by Cambridge University Press:  31 March 2011

Dudley Stark
Dudley Stark
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, United Kingdom E-mail: D.S.Stark@maths.qmul.ac.uk
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Abstract

The normal curve has been used to fit the rate of both world and US oil production. In this article we give the first theoretical basis for these curve fittings. It is well known that oil field sizes can be modeled by independent samples from a lognormal distribution. We show that when field sizes are lognormally distributed, the starting time of the production of a field is approximately a linear function of the logarithm of its size, and production of a field occurs within a small enough time interval, then the resulting total rate of production is close to being a normal curve.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 2 , April 2011 , pp. 205 - 217
Copyright
Copyright © Cambridge University Press 2011

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References

1.Barton, C.C. & Scholz, C.H. (1995). The fractal size and spatial distribution of hydrocarbon accumulations: Implications for resource assessment and exploration strategy. In Barton, C.C. & La Pointe, P.R. (eds.), Fractals in petroleum geology and earth processes. New York: Plenum Press, pp. 13–34.CrossRefGoogle Scholar
2.Bentley, R.W. (2002). Global oil and gas depletion: an overview. Energy Policy 30: 189–205.CrossRefGoogle Scholar
3.Brandt, A.R. (2007). Testing Hubbert. Energy Policy 35: 3074–3088.CrossRefGoogle Scholar
4.Deffeyes, K.A. (2001). Hubbert's peak. Princeton, NJ: Princeton University Press.Google Scholar
5.Durrett, R. (1991). Probability: Theory and examples. New York: Wadsworth & Brooks/Cole.Google Scholar
6.Goldberg, G. (1967). The Pareto law and the pyramid distribution. Publication 505. Houston, TX: Shell Development.Google Scholar
7.Hubbert, M.K. (1956). Nuclear energy and the fossil fuels. In American Petroleum Institute Drilling and Production Practise, Proceedings of Spring Meeting, San Antonio, TX.Google Scholar
8.Laherrere, J. (2005). Forecasting production from discovery. Talk delivered at the Association for the Study of Peak Oil & Gas (ASPO) Conference, Lisbon, Portugal. Available from www.cge.uevora.pt/aspo2005/abscom/ASPO2005/Laherrere.pdf.Google Scholar
9.Mandelbrot, B.B. (1962). The statistics of natural resources and the law of Pareto. In Barton, C.C. & La Pointe, P.R. (eds.), Fractals in petroleum geology and earth processes. New York: Plenum Press, pp. 1–12.Google Scholar
10.Michel, B. (2010). Oil production: A probabilistic model of the Hubbert curve. doi:10.1002/asmb.851.CrossRefGoogle Scholar
11.Stark, D. (2008). Peak production in an oil depletion model with triangular field profiles. Journal of Interdisciplinary Mathematics 11: 695–706.CrossRefGoogle Scholar