Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-20T06:20:27.534Z Has data issue: false hasContentIssue false

Gas and water cresting towards horizontal wells

Published online by Cambridge University Press:  17 February 2009

J. F. McCarthy
Affiliation:
BHP Research - Melbourne Laboratories, P.O. Box 264, Clayton, Vic. 3168, Australia.
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.

The hodograph method for flow in porous media is used to study the problem of simultaneous gas and water cresting towards a horizontal well in a thin oil column reservoir. Shapes of the free interfaces are found and an expression for the optimal placement of the well with respect to the interfaces is given. In addition, a numerical technique is used to find the shape of the free interface and values of critical heights for the case of water cresting towards a horizontal well beneath an impermeable plane.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Bear, J., Dynamics of fluids in porous media (American Elsevier, New York, 1972).Google Scholar
[2]Bear, J. and Dagan, G., “Some exact solutions of interface problems by means of the hodograph method”, J. Geophys. Res. 69 (1964) 15631572.CrossRefGoogle Scholar
[3]Blake, J. R. and Kucera, A., “Coning in oil reservoirs”, Math. Scientist 13 (1988) 3647.Google Scholar
[4]Blake, J. R., Lucas, S. K. and Kucera, A., “A boundary-integral method applied to water coning in oil reservoirs”, J. Aust. Math., Soc. Ser. B 32 (1991) 261283.Google Scholar
[5]Collings, I. L., “Two infinite froude number cusped free surface flows due to a submerged line source or sink”, J. Aust. Math. Soc. Ser. B 28 (1986) 260270.CrossRefGoogle Scholar
[6]Dupuit, J., Etudes théoriques et pratiques sur le mouvement des eaux, 2nd ed. (Dumont, Paris, 1863).Google Scholar
[7]Ekrann, S., “Production from thin oil zones”, in Report no. SPT T-6/87, SPOR, Norway, 1987).Google Scholar
[8]Giger, F. M., “Analytic 2-D models of water cresting before breakthrough for horizontal wells”, SPE Res. Eng. (November 1989) 409416.Google Scholar
[9]Hocking, G. C., “Cusp-like free-surface flows due to a submerged source or sink in the presence of a flat or sloping bottom”, J. Aust. Math. Soc. Ser. B 26 (1985) 470486.CrossRefGoogle Scholar
[10]Meyer, H. I. and Garder, A. O., “Mechanics of two immiscible fluids in porous media”, J. Appl. Phys. 25 (1954) 14001406.Google Scholar
[11]Muskat, M. and Wyckoff, R. B., “An approximate theory of water coning in oil production”, Trans. AIME 114 (1935) 144163.Google Scholar
[12]Polubarinova-Kochina, P. Y., Theory of groundwater movement, English transl. by De Wiest, R. J. M., Princeton University Press, Princeton, N.J., 1962 (Gostek-hizdat, Moscow, 1952).Google Scholar
[13]Tuck, E. O. and Broeck, J. M. Vanden, “A cusp-like free-surface flow due to a submerged source or sink”, J. Aust. Math. Soc. Ser. B 25 (1984) 443450.Google Scholar
[14]Broeck, J. M. Vanden and Keller, J. B., “Free surface flow due to a sink”, J. Fluid Mech. 175 (1987) 207224.Google Scholar