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A spectral modelling approach for fluid flow into a line sink in a confined aquifer

Published online by Cambridge University Press:  01 November 2021

S. AL-ALI
Affiliation:
Mathematics and Statistics, Murdoch University, Perth, Australia emails: suhaibrahim3@tu.edu.iq, g.hocking@murdoch.edu.au Mathematics Department, Computer Science and Mathematics College, Tikrit University, Salah al Din 34001, Iraq
G. C. HOCKING
Affiliation:
Mathematics and Statistics, Murdoch University, Perth, Australia emails: suhaibrahim3@tu.edu.iq, g.hocking@murdoch.edu.au
D. E. FARROW
Affiliation:
School of Physics, Mathematics & Computing, University of Western Australia, Perth, Australia email: Duncan.Farrow@uwa.edu.au
H. ZHANG
Affiliation:
School of Engineering and Built Environment, Griffith University, Gold Coast, Australia email: Hong.Zhang@griffith.edu.au

Abstract

A spectral method is developed to study the steady and unsteady flow of fluid into a line sink from a horizontally confined aquifer, and the results are compared to solutions obtained implementing the finite element package COMSOLTM. The aquifer or drain is considered to be confined below so that the solutions are fundamentally unsteady. Comparison is made between the two methods in determining the drawdown of the surface.

Type
Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Al-Ali, S., Hocking, G. C. & Farrow, D. E. (2019) Critical surface coning due to a line sink in a vertical drain containing a porous medium. ANZIAM J. 61, 249269. doi: 10.1017/S1446181119000099.Google Scholar
Bear, J. (1972) Dynamics of Fluids in Porous Media, Elsevier, New York.Google Scholar
Blake, J. R. & Kucera, A. (1988) Coning in oil reservoirs. Maths Sci. 13, 3647.Google Scholar
Childs, E. C. (1969) An Introduction to the Physical Basis of Soil Water Phenomena, Wiley, London.Google Scholar
Darcy, H. P. G. (1856) Les Fontaines publiques de la ville de Dijon. Exposition et application des principes à suivre et des formules à employer dans les questions de distribution d’eau, Dalmont, Paris.Google Scholar
Giger, F. M. (1989) Analytic 2-d models of water cresting before breakthrough for horizontal wells. SPE Res. Eng. 4, 409416. doi: 10.2118/15378-PA.Google Scholar
Hinch, E. J. (1985) The recovery of oil from underground reservoirs. Theor. Appl. Mech., Ed: Niordson, F. I. & Olhoff, N., Elsevier, 135161. doi: 10.1016/B978-0-444-87707-9.50017-8.CrossRefGoogle Scholar
Hocking, G. C. (1995) Supercritical withdrawal from a two-layer fluid through a line sink. J. Fluid Mech. 297, 3747. doi: 10.1017/S0022112095002990.CrossRefGoogle Scholar
Kacimov, A. R. & Obnosov, Y. V. (2021) Infiltration-induced phreatic surface flow to periodic drains: Vedernikov-Engelund-Vasil‘ev’s legacy revisited, Appl. Math. Model. 91, 9891003.CrossRefGoogle Scholar
Letchford, N. A., Forbes, L. K. & Hocking, G. C. (2012) Inviscid and viscous models of axisymmetric fluid jets or plumes. ANZIAM J. 53, 228250. doi: 10.1017/S1446181112000156.Google Scholar
Lucas, S. K., Blake, J. R. & Kucera, A. (1991) A boundary-integral method applied to water coning in oil reservoirs. J. Austral. Math. Soc. Ser. B. 32, 261283. doi: 10.1017/S0334270000006858.CrossRefGoogle Scholar
McCarthy, J. F. (1993) Gas and water cresting towards horizontal wells, J. Austral. Math. Soc. Ser. B (now ANZIAM J.) 35, 174197. doi: 10.1017/S0334270000009115.CrossRefGoogle Scholar
Mi, L., Jiang, H., Li, J., Li, T. & Tian, Y. (2014) The investigation of fracture aperture effect on shale gas transport using discrete fracture model. J. Natural Gas Sci. Eng. 21, 631635. doi: 10.1016/j.jngse.2014.09.029.CrossRefGoogle Scholar
Mozafari, B., Fahs, M., Ataie-Ashtiani, B., Simmons, C. T. & Younes, R. (2018) On the use of COMSOLTM Multiphysics for seawater intrusion in fractured coastal aquifers. In: E3S Web of Conferences, Vol. 54. EDP Sciences, p. 00020. doi: 10.1051/e3sconf/20185400020.CrossRefGoogle Scholar
Muskat, M. & Wyckoff, R. D. (1935) An approximate theory of water coning in oil production. Trans. AIME. 114, 144163. doi: 10.2118/935144-G.CrossRefGoogle Scholar
Russell, P. S., Forbes, L. K. & Hocking, G. C. (2017) The initiation of a planar fluid plume beneath a rigid lid. J. Eng. Math. 106, 107121. doi: 10.1007/s10665-016-9895-1.CrossRefGoogle Scholar
Van Deemter, C. C. (1951) Results of mathematical approach to some flow problems connected with drainage and irrigation. Appl. Sci. Res. 2(1), 3353.CrossRefGoogle Scholar
Youngs, E. G. (1970) Hodograph solution of the drainage problem with very small drain diameter. Water Resour. Res. 6(2), 594600.CrossRefGoogle Scholar
Zhang, H., Barry, D. A. & Hocking, G. C. (1999) Analysis of continuous and pulsed pumping of a phreatic aquifer. Adv. Water Resour. 22, 623632. doi: 10.1016/S0309-1708(98)00038-4.CrossRefGoogle Scholar
Zhang, H., Hocking, G. C. & Barry, D. A. (1997) An analytical solution for critical withdrawal of layered fluid through a line sink in a porous medium. ANZIAM J. 39, 271279. doi: 10.1017/S0334270000008845.Google Scholar

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