Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-22T08:20:31.669Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximising output from oil reservoirs without water breakthrough

Published online by Cambridge University Press:  17 February 2009

S. K. Lucas
S. K. Lucas
Affiliation:
School of Mathematics and Statistics, University of South Australia, Mawson Lakes, SA 5095, Australia; e-mail: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Often in oil reservoirs a layer of water lies under the layer of oil. The suction pressure due to a distribution of oil wells will cause the oil-water interface to rise up towards the wells. Given a particular distribution of oil wells, we are interested in finding the flow rates of each well that maximise the total flow rate without the interface breaking through to the wells. A method for finding optimal flow rates is developed using the Muskat model to approximate the interface height, and a version of the Nelder-Mead simplex method for optimisation. A variety of results are presented, including the perhaps nonintuitive result that it is better to turn off some oil wells when they are sufficiently close to one another.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 3 , January 2004 , pp. 401 - 422
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Bear, J., Dynamics of fluids in porous media (McGraw-Hill, New York, 1972).Google Scholar
[2]Blake, J. R. and Kucera, A., “Coning in oil reservoirs”, Math. Scientist 13 (1988) 36–47.Google Scholar
[3]Gunning, J., Paterson, L. and Poliak, B., “Coning in dual completed systems”, J. Pet. Sci. Eng. 23 (1999) 27–39.CrossRefGoogle Scholar
[4]Lucas, S. K., Blake, J. R. and Kucera, A., “A boundary-integral method applied to water coning in oil reservoirs”, J. Austral. Math. Soc. Ser. B 32 (1991)261–283.Google Scholar
[5]Lucas, S. K. and Kucera, A., “A 3D boundary integral method applied to the water coning problem”, Physics of Fluids 8 (1996) 3008–3022.Google Scholar
[6]Math Works Inc., Matlab, the language of technical computing, 1994–2001, http://www.mathworks.com/.Google Scholar
[7]McKinnon, K. I. M., “Convergence of the Nelder-Mead simplex method to a nonstationary point”, SIAM J. Optim. 9 (1998) 148–158.Google Scholar
[8]Muskat, M., Physical principles of oil production (McGraw-Hill, New York, 1949).Google Scholar
[9]Muskat, M. and Wyckoff, R. D., “An approximate theory of water coning in oil production”, Trans. AIME 114 (1935) 144–159.Google Scholar
[10]Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P., Numerical recipes in Fortran 77, 2nd ed. (Cambridge University Press, Cambridge, 1992).Google Scholar
[11]Price, C. J., Coope, I. D. and Byatt, D., “A convergent variant of the Nelder-Mead algorithm”, J. Optim. Theory Appl. 113 (2002) 5–19.Google Scholar
[12]Zhang, H., Barry, D. A. and Hocking, G. C., “Analysis of continuous and pulsed pumping of a phreatic aquifer”, Adv. Wat. Res. 22 (1999)623–632.CrossRefGoogle Scholar
[13]Zhang, H. and Hocking, G. C., “Axisymmetric flow in an oil reservoir of finite depth caused by a point sink above an oil-water interface”, J. Engrg. Math. 32 (1997) 365–376.Google Scholar