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A NOTE ON AXISYMMETRIC SUPERCRITICAL CONING IN A POROUS MEDIUM

Published online by Cambridge University Press:  07 August 2014

G. C. HOCKING  and
H. ZHANG
G. C. HOCKING*
Affiliation:
Mathematics & Statistics, Murdoch University, Perth, Australia email [email protected]
H. ZHANG
Affiliation:
Griffith School of Engineering, Griffith University, Gold Coast Campus, QLD 4222, Australia email [email protected]
*
✉[email protected]
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Abstract

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The steady response of a fluid with two layers of different density in a porous medium is considered during extraction through a point sink. Supercritical withdrawal in which both layers are being withdrawn is investigated using a spectral method. We show that for each withdrawal rate, there is a single entry angle of the interface into the point sink. As the flow rate decreases the angle of entry steepens until it becomes almost vertical, at which point the method fails. This limit is shown to correspond to the upper bound on sub-critical (single-layer) flow.

Keywords

porous mediapoint sinkaxisymmetric flowconing
Type
Research Article
Information
The ANZIAM Journal , Volume 55 , Issue 4 , April 2014 , pp. 327 - 335
Copyright
Copyright © 2014 Australian Mathematical Society 

References

Bear, J., Dynamics of fluids in porous media (McGraw-Hill, New York, 1972).Google Scholar
Bear, J. and Dagan, G., “Some exact solutions of interface problems by means of the hodograph method”, J. Geophys. Res. 69 (1964) 1563–1572; doi:10.1029/JZ069i008p01563.Google Scholar
Blake, J. R. and Kucera, A., “Coning in oil reservoirs”, Math. Sci. 13 (1988) 36–47.Google Scholar
Forbes, L. K. and Hocking, G. C., “Withdrawal from a two-layer inviscid fluid in a duct”, J. Fluid Mech. 361 (1998) 275–296; doi:10.1017/S0022112098008805.Google Scholar
Forbes, L. K. and Hocking, G. C., “On the computation of steady axi-symmetric withdrawal from a two-layer fluid”, Comput. Fluids 32 (2003) 385–401; doi:10.1016/S0045-7930(01)00085-8.Google Scholar
Giger, F. M., “Analytic 2-D models of water cresting before breakthrough for horizontal wells”, SPE Res. Engnrg. (1989) 409–416.Google Scholar
Henderson, N., Flores, E., Sampaio, M., Freitas, L. and Platt, G. M., “Supercritical fluid flow in porous media: modeling and simulation”, Chem. Eng. Sci. 60 (2005) 1797–1808; doi:10.1016/j.ces.2004.11.012.CrossRefGoogle Scholar
Hinch, E. J., “The recovery of oil from underground reservoirs”, J. Physico-Chemical Hydrodynamics 6 (1985) 601–622.Google Scholar
Hocking, G. C., “Supercritical withdrawal from a two-layer fluid through a line sink”, J. Fluid Mech. 297 (1995) 37–47; doi:10.1017/S0022112095002990.Google Scholar
Hocking, G. C. and Forbes, L. K., “Supercritical withdrawal from a two-layer fluid through a line sink if the lower layer is of finite depth”, J. Fluid Mech. 428 (2001) 333–348; doi:10.1017/S0022112000002780.CrossRefGoogle Scholar
Hocking, G. C. and Zhang, H., “A note on withdrawal from a two-layer fluid through a line sink in a porous medium”, ANZIAM J. 50 (2008) 101–110; doi:10.1017/S144618110800028X.CrossRefGoogle Scholar
Hocking, G. C. and Zhang, H., “Coning during withdrawal from two fluids of different density in a porous medium”, J. Eng. Math. 65 (2009) 101–109; doi:10.1007/s10665-009-9267-1.Google Scholar
Lukas, S. K., Blake, J. R. and Kucera, A., “A boundary-integral method applied to water coning in oil reservoirs”, J. Aust. Math. Soc. Ser. B 32 (1991) 261–283; doi:10.1017/S0334270000006858.Google Scholar
McCarthy, J. F., “Gas and water cresting towards horizontal wells”, J. Aust. Math. Soc. Ser. B 35 (1993) 174–197; doi:10.1017/S0334270000009115.Google Scholar
Muskat, M. and Wyckoff, R. D., “An approximate theory of water coning in oil production”, Trans. AIME (Petroleum Development Technologies) 114 (1935) 144–163.CrossRefGoogle Scholar
Yu, D., Jackson, K. and Harmon, T. C., “Dispersion and diffusion in porous media under supercritical conditions”, Chem. Eng. Sci. 54 (1999) 357–367; doi:10.1016/S0009-2509(98)00271-1.Google Scholar
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. Eng. Math. 32 (1997) 365–376; doi:10.1017/S0334270000008845.Google Scholar
Zhang, H., Hocking, G. C. and Barry, D. A., “An analytical solution for critical withdrawal of layered fluid through a line sink in a porous medium”, J. Aust. Math. Soc. Ser. B 39 (1997) 271–279; doi:10.1017/S0334270000008845.Google Scholar
Zhang, H., Hocking, G. C. and Seymour, B., “Critical and supercritical withdrawal from a two-layer fluid through a line sink in a partially bounded aquifer”, Adv. Water Resour. 32 (2009) 1703–1710; doi:10.1016/j.advwatres.2009.09.002.Google Scholar