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A boundary-integral method applied to water coning in oil reservoirs

Published online by Cambridge University Press:  17 February 2009

S. K. Lucas ,
J. R. Blake  and
A. Kucera
S. K. Lucas
Affiliation:
Department of Mechanical Engineering, University of Sydney, Sydney, N.S.W. 2006.
J. R. Blake
Affiliation:
School of Mathematics and Statistics, University of Birmingham, Birmingham B15 2TT, U.K.
A. Kucera
Affiliation:
Department of Mathematics, Australian Defence Force Academy, Campbell, A.C.T. 2600.
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Abstract

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In oil reservoirs, the less-dense oil often lies over a layer of water. When pumping begins, the oil-water interface rises near the well, due to the suction pressures associated with the well. A boundary-integral formulation is used to predict the steady interface shape, when the oil well is approximated by a series of sources and sinks or a line sink, to simulate the actual geometry of the oil well. It is found that there is a critical pumping rate, above which the water enters the oil well. The critical interface shape is a cusp. Efforts to suppress the cone by using source/sink combinations are presented.

Type
Research Article
Information
The ANZIAM Journal , Volume 32 , Issue 3 , January 1991 , pp. 261 - 283
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Abramowitz, M. and Stegun, I. A., (1972). Handbook of mathematical functions, (Dover, N. Y. 1965).Google Scholar
[2]Bear, J., (1972). Dynamics of Fluids in Porous Media, (McGraw-Hill, N. Y. 1972).Google Scholar
[3]Bear, J. and Dagan, G., “Some exact solutions of interface problems by means of the hodograph method”, J. Geophys. Res. 69 (1964) 1563–1572.CrossRefGoogle Scholar
[4]Blake, J. R. and Kucera, A., “Coning in oil reservoirs”, Math. Scientist 13 (1988) 36–47.Google Scholar
[5]Blake, J. R., Taib, B. and Doherty, G., “Transient Cavities near Boundaries Part 1. Rigid Boundary”, J Fluid Mech. 170 (1986) 479–497.CrossRefGoogle Scholar
[6]Collings, I. L., “Two infinite-Froude number cusped free-surface flows due to a sub-merged line source or sink” J. Austral. Math. Soc. B28 (1987) 260–270.CrossRefGoogle Scholar
[7]Craya, A., “Theoretical research on the flow of a non-homogeneous fluids” Homille Blanche 4 (1949) 44–55.CrossRefGoogle Scholar
[8]Ewing, R. E., The Mathematics of Reservoir Simulation (SIAM, Philadelphia, 1983).Google Scholar
[9]Hinch, E.J., “The recovery of oil from underground reservoirs”, PCH 6 (1985) 601–622.Google Scholar
[10]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. Austral. Math. Soc. B26 (1984) 470–486.Google Scholar
[11]Hocking, G. C., “Infinite Fronde number solutions to the problem of a submerged source or sink” J. Austral. Math. Soc. B29 (1988) 401–409.CrossRefGoogle Scholar
[12]Lucas, S. K., “Water coning in oil reservoirs”, (Univ. of Wollongong, Dep. Math., Honours Thesis 1988).Google Scholar
[13]MacDonald, R. C., “Methods for numerical simulation of water and gas coning”, Trans. Soc. Pet. Eng. 249 (1970) 423–434.Google Scholar
[14]Muskat, M., Physical principles of oil production, (McGraw-Hill, N. Y. 1949).Google Scholar
[15]Piessens, R., De Doncker-Kapenga, E., Uberhuber, C. W. and Kahauer, D. K., QUAD-PACK, A subroutine package for automatic integration, (Springer-Verlag, Berlin, 1983).Google Scholar
[16]Tuck, E. O. and Vanden-Broeck, J., “A cusp-like free-surface flow due to a submerged source or sink” J. Austral. Math. Soc. B25 (1984) 443–450.CrossRefGoogle Scholar