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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.
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Abstract

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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