Hostname: page-component-669899f699-8p65j Total loading time: 0 Render date: 2025-04-25T08:16:13.764Z Has data issue: false hasContentIssue false
  • English
  • Français

A mathematical model of an oil and gas field development process

Published online by Cambridge University Press:  08 March 2010

C. ATKINSON  and
R. ISANGULOV
C. ATKINSON
Affiliation:
Department of Mathematics, Imperial College of Science, London, UK
R. ISANGULOV
Affiliation:
Schlumberger Cambridge Research, Cambridge, UK email: rustam.isangulov@slb.com
Get access Rights & Permissions [Opens in a new window]

Abstract

A mathematical model of the development of an oil and gas field is presented. The field development process is treated as sequential in nature. Completion of a well and its production are considered to be random processes. The model uses results from renewal theory where the completion of a well and failure to produce economical amount of oil or gas are analogous to the failure of a component. In principle, the theory described can give the complete probability distribution associated with a field development. Explicit expressions are given for the expected value and variance of the number of completed wells.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 21 , Issue 3 , June 2010 , pp. 205 - 227
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Adams, A. J., Gibson, C. & Smith, R. (2009) Probabilistic well time estimation revisited. In: SPE 119287, SPE/IADC Drilling Conference and Exhibition, Amsterdam.Google Scholar
[2]Aldred, W., Belaskie, J., Isangulov, R., Crockett, B., Edmondson, B., Florence, F. & Srinivasan, S. (2005) Changing the way we drill. Oilfield Rev. 17 (1), 42–49.Google Scholar
[3]Alhanai, W. T. (2002) Management and control of the inventory of problematic wells: A stochastic process. In: SPE 78554, 10th Abu Dhabi International Petroleum Exhibition and Conference, 13–16 October, 2002, Abu Dhabi, UAE.Google Scholar
[4]Brett, J. F. & Millheim, K. K. (1986) The drilling performance curve: A yardstick for judging drilling performance. In: SPE 15362, 61st Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, 5–8 October, 1986, New Orleans, USA.Google Scholar
[5]Cox, D. R. & Smith, W. L. (1961) Queues, Chapman & Hall/CRC, CRC Press LLC, 2000 N.W. Corporate Blod, Boca Raton, Florida 33431, USA.Google Scholar
[6]Walter, L. S. (1958) Renewal theory and its ramifications. J. R. Stat. Soc. 20 (2), 243–302.Google Scholar
[7]Hormann, W., Leydold, L. & Derflinger, G. (2004) Automatic Nonuniform Random Variate Generation, Springer, New York.CrossRefGoogle Scholar